idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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49,001 | Doubt regarding mixed modeling format | But, I'm wondering if I can also add information about the food and weather, which are not part of my fixed effects into my model( without including interactions)
Yes, you can. By not including them as fixed effects, but including them as random slopes, you are saying that the overall mean slope is zero, but each indi... | Doubt regarding mixed modeling format | But, I'm wondering if I can also add information about the food and weather, which are not part of my fixed effects into my model( without including interactions)
Yes, you can. By not including them | Doubt regarding mixed modeling format
But, I'm wondering if I can also add information about the food and weather, which are not part of my fixed effects into my model( without including interactions)
Yes, you can. By not including them as fixed effects, but including them as random slopes, you are saying that the ove... | Doubt regarding mixed modeling format
But, I'm wondering if I can also add information about the food and weather, which are not part of my fixed effects into my model( without including interactions)
Yes, you can. By not including them |
49,002 | What are some non-toy applications of autoencoders? | One statistical application of denoising autoencoders is multiple imputation: the autoencoder tries to compress the data to a low-dimensional signal (that isn't missing) plus noise (that's sometimes missing). Compared to either Bayesian data augmentation or the popular 'mice' algorithms, the autoencoders seem to scale ... | What are some non-toy applications of autoencoders? | One statistical application of denoising autoencoders is multiple imputation: the autoencoder tries to compress the data to a low-dimensional signal (that isn't missing) plus noise (that's sometimes m | What are some non-toy applications of autoencoders?
One statistical application of denoising autoencoders is multiple imputation: the autoencoder tries to compress the data to a low-dimensional signal (that isn't missing) plus noise (that's sometimes missing). Compared to either Bayesian data augmentation or the popula... | What are some non-toy applications of autoencoders?
One statistical application of denoising autoencoders is multiple imputation: the autoencoder tries to compress the data to a low-dimensional signal (that isn't missing) plus noise (that's sometimes m |
49,003 | What are some non-toy applications of autoencoders? | From the Autoencoder Wikipedia article:
One milestone paper on the subject was that of Geoffrey Hinton with his publication in Science Magazine in 2006 [Reducing the Dimensionality of Data with Neural Networks by G. E. Hinton and et al.]: in that study, he pretrained a multi-layer autoencoder with a stack of RBMs ... | What are some non-toy applications of autoencoders? | From the Autoencoder Wikipedia article:
One milestone paper on the subject was that of Geoffrey Hinton with his publication in Science Magazine in 2006 [Reducing the Dimensionality of Data with Neura | What are some non-toy applications of autoencoders?
From the Autoencoder Wikipedia article:
One milestone paper on the subject was that of Geoffrey Hinton with his publication in Science Magazine in 2006 [Reducing the Dimensionality of Data with Neural Networks by G. E. Hinton and et al.]: in that study, he pretra... | What are some non-toy applications of autoencoders?
From the Autoencoder Wikipedia article:
One milestone paper on the subject was that of Geoffrey Hinton with his publication in Science Magazine in 2006 [Reducing the Dimensionality of Data with Neura |
49,004 | What are some non-toy applications of autoencoders? | One increasingly popular biological area of application for autoenconders is single cell transcriptomics, which typically generates large sparse data matrixes. Here autoencoders have been applied for both de-noising purposes and rapid dimensionality reduction. | What are some non-toy applications of autoencoders? | One increasingly popular biological area of application for autoenconders is single cell transcriptomics, which typically generates large sparse data matrixes. Here autoencoders have been applied for | What are some non-toy applications of autoencoders?
One increasingly popular biological area of application for autoenconders is single cell transcriptomics, which typically generates large sparse data matrixes. Here autoencoders have been applied for both de-noising purposes and rapid dimensionality reduction. | What are some non-toy applications of autoencoders?
One increasingly popular biological area of application for autoenconders is single cell transcriptomics, which typically generates large sparse data matrixes. Here autoencoders have been applied for |
49,005 | What are some non-toy applications of autoencoders? | One of the application of auto-encoder that i am exploring is for building content-based image search engine.
Training auto-encoder network on product catalogue data ( images )
Extract encoder layer from the trained model and encode images [ based on latent dimensions ]
Index the encoded features of images
During quer... | What are some non-toy applications of autoencoders? | One of the application of auto-encoder that i am exploring is for building content-based image search engine.
Training auto-encoder network on product catalogue data ( images )
Extract encoder layer | What are some non-toy applications of autoencoders?
One of the application of auto-encoder that i am exploring is for building content-based image search engine.
Training auto-encoder network on product catalogue data ( images )
Extract encoder layer from the trained model and encode images [ based on latent dimension... | What are some non-toy applications of autoencoders?
One of the application of auto-encoder that i am exploring is for building content-based image search engine.
Training auto-encoder network on product catalogue data ( images )
Extract encoder layer |
49,006 | When computing parameters, why is dimensions of hidden-output state of an LSTM-cell assumed same as the number of LSTM-cell? | I came across this link https://stackoverflow.com/questions/38080035/how-to-calculate-the-number-of-parameters-of-an-lstm-network, and it seems to suggest that hidden output state dimension = number of lstm cells in the layer. Why is that?
Each cell's hidden state is 1 float. As an example, the reason you'd have outpu... | When computing parameters, why is dimensions of hidden-output state of an LSTM-cell assumed same as | I came across this link https://stackoverflow.com/questions/38080035/how-to-calculate-the-number-of-parameters-of-an-lstm-network, and it seems to suggest that hidden output state dimension = number o | When computing parameters, why is dimensions of hidden-output state of an LSTM-cell assumed same as the number of LSTM-cell?
I came across this link https://stackoverflow.com/questions/38080035/how-to-calculate-the-number-of-parameters-of-an-lstm-network, and it seems to suggest that hidden output state dimension = num... | When computing parameters, why is dimensions of hidden-output state of an LSTM-cell assumed same as
I came across this link https://stackoverflow.com/questions/38080035/how-to-calculate-the-number-of-parameters-of-an-lstm-network, and it seems to suggest that hidden output state dimension = number o |
49,007 | When computing parameters, why is dimensions of hidden-output state of an LSTM-cell assumed same as the number of LSTM-cell? | Regarding the question: "why the dimension of the hidden state is related to the number of cells in a LSTM layer"?, what I understand, a layer of 4 cells would be represented as the picture I attached.
It is clear with the picture that the state H has dimension 4, which is directly related to the number of cells (hidde... | When computing parameters, why is dimensions of hidden-output state of an LSTM-cell assumed same as | Regarding the question: "why the dimension of the hidden state is related to the number of cells in a LSTM layer"?, what I understand, a layer of 4 cells would be represented as the picture I attached | When computing parameters, why is dimensions of hidden-output state of an LSTM-cell assumed same as the number of LSTM-cell?
Regarding the question: "why the dimension of the hidden state is related to the number of cells in a LSTM layer"?, what I understand, a layer of 4 cells would be represented as the picture I att... | When computing parameters, why is dimensions of hidden-output state of an LSTM-cell assumed same as
Regarding the question: "why the dimension of the hidden state is related to the number of cells in a LSTM layer"?, what I understand, a layer of 4 cells would be represented as the picture I attached |
49,008 | Expected Value of Maximum of Uniform Random Variables | The issue is that you aren't considering the full support of cdf of $Y=\text{max}\{X_1,X_2,X_3\}$. The full support is $(0, \infty)$. Taking a look here: https://en.wikipedia.org/wiki/Uniform_distribution_(continuous) at the definition of $F(x)$. Then consider that you'll have 1 minus this value, so for your problem yo... | Expected Value of Maximum of Uniform Random Variables | The issue is that you aren't considering the full support of cdf of $Y=\text{max}\{X_1,X_2,X_3\}$. The full support is $(0, \infty)$. Taking a look here: https://en.wikipedia.org/wiki/Uniform_distribu | Expected Value of Maximum of Uniform Random Variables
The issue is that you aren't considering the full support of cdf of $Y=\text{max}\{X_1,X_2,X_3\}$. The full support is $(0, \infty)$. Taking a look here: https://en.wikipedia.org/wiki/Uniform_distribution_(continuous) at the definition of $F(x)$. Then consider that ... | Expected Value of Maximum of Uniform Random Variables
The issue is that you aren't considering the full support of cdf of $Y=\text{max}\{X_1,X_2,X_3\}$. The full support is $(0, \infty)$. Taking a look here: https://en.wikipedia.org/wiki/Uniform_distribu |
49,009 | Expected Value of Maximum of Uniform Random Variables | I think
if $\ x \sim Uniform(a=200,b=600)$ ,$\ n={3}$
then
$\ E{[max(X1,X2,X3)=m]}=\int_a^b m.p(m).dm=
\\(n/(n+1)).(b-a)+a=(3/4).(400)+200=500$
where
$\ p(m)=P(max(X1,X2,X3))=
\\P(X1)⋅P(X2≤X1)⋅P(X3≤X1)+P(X2)⋅P(X1≤X2)⋅P(X3≤X2)+P(X3)⋅P(X1≤X3)⋅P(X2≤X3)=$
\begin{equation}
\\ \sum^{n=3}_{i=1} [1/(b-a)].[(m-a)/(b-a)]^{n-1}=[... | Expected Value of Maximum of Uniform Random Variables | I think
if $\ x \sim Uniform(a=200,b=600)$ ,$\ n={3}$
then
$\ E{[max(X1,X2,X3)=m]}=\int_a^b m.p(m).dm=
\\(n/(n+1)).(b-a)+a=(3/4).(400)+200=500$
where
$\ p(m)=P(max(X1,X2,X3))=
\\P(X1)⋅P(X2≤X1)⋅P(X3≤X1 | Expected Value of Maximum of Uniform Random Variables
I think
if $\ x \sim Uniform(a=200,b=600)$ ,$\ n={3}$
then
$\ E{[max(X1,X2,X3)=m]}=\int_a^b m.p(m).dm=
\\(n/(n+1)).(b-a)+a=(3/4).(400)+200=500$
where
$\ p(m)=P(max(X1,X2,X3))=
\\P(X1)⋅P(X2≤X1)⋅P(X3≤X1)+P(X2)⋅P(X1≤X2)⋅P(X3≤X2)+P(X3)⋅P(X1≤X3)⋅P(X2≤X3)=$
\begin{equatio... | Expected Value of Maximum of Uniform Random Variables
I think
if $\ x \sim Uniform(a=200,b=600)$ ,$\ n={3}$
then
$\ E{[max(X1,X2,X3)=m]}=\int_a^b m.p(m).dm=
\\(n/(n+1)).(b-a)+a=(3/4).(400)+200=500$
where
$\ p(m)=P(max(X1,X2,X3))=
\\P(X1)⋅P(X2≤X1)⋅P(X3≤X1 |
49,010 | Three-Way Anova: What does a significant three way interaction tell you, conceptually? | Your techinical interpretation is quite correct.
So, let's say that Gatorade was associated with faster mile times than water, and this association was larger in males than in females.
The three-way interaction with age group may then tell you, for example, that this association disappeared entirely in the older age gr... | Three-Way Anova: What does a significant three way interaction tell you, conceptually? | Your techinical interpretation is quite correct.
So, let's say that Gatorade was associated with faster mile times than water, and this association was larger in males than in females.
The three-way i | Three-Way Anova: What does a significant three way interaction tell you, conceptually?
Your techinical interpretation is quite correct.
So, let's say that Gatorade was associated with faster mile times than water, and this association was larger in males than in females.
The three-way interaction with age group may the... | Three-Way Anova: What does a significant three way interaction tell you, conceptually?
Your techinical interpretation is quite correct.
So, let's say that Gatorade was associated with faster mile times than water, and this association was larger in males than in females.
The three-way i |
49,011 | Kernel Mean Embedding relationship to regular kernel functions | To simplify matters, I'll assume the kernel $k$ is bounded. Otherwise for technical reasons (basically to guarantee the expectation in the definition of the kernel mean map exists), we need to restrict attention to only probability distributions satisfying
$$\mathbb{E}_{X\sim P} \sqrt{k(X,X)} <\infty$$
Let $\mathrm{Pr... | Kernel Mean Embedding relationship to regular kernel functions | To simplify matters, I'll assume the kernel $k$ is bounded. Otherwise for technical reasons (basically to guarantee the expectation in the definition of the kernel mean map exists), we need to restri | Kernel Mean Embedding relationship to regular kernel functions
To simplify matters, I'll assume the kernel $k$ is bounded. Otherwise for technical reasons (basically to guarantee the expectation in the definition of the kernel mean map exists), we need to restrict attention to only probability distributions satisfying... | Kernel Mean Embedding relationship to regular kernel functions
To simplify matters, I'll assume the kernel $k$ is bounded. Otherwise for technical reasons (basically to guarantee the expectation in the definition of the kernel mean map exists), we need to restri |
49,012 | Are two coin flips conditionally independent if we know that the coin is biased towards heads? | The quoted section is implicitly assuming that the event $C = \{ \theta > 0.5 \}$ is sufficient to fully describe the parameter, and so it attains conditional independence of the observable coin flips (e.g., there may be an assumption that there is only one allowable value of $\theta$ in the biased range). Contrarily... | Are two coin flips conditionally independent if we know that the coin is biased towards heads? | The quoted section is implicitly assuming that the event $C = \{ \theta > 0.5 \}$ is sufficient to fully describe the parameter, and so it attains conditional independence of the observable coin flip | Are two coin flips conditionally independent if we know that the coin is biased towards heads?
The quoted section is implicitly assuming that the event $C = \{ \theta > 0.5 \}$ is sufficient to fully describe the parameter, and so it attains conditional independence of the observable coin flips (e.g., there may be an ... | Are two coin flips conditionally independent if we know that the coin is biased towards heads?
The quoted section is implicitly assuming that the event $C = \{ \theta > 0.5 \}$ is sufficient to fully describe the parameter, and so it attains conditional independence of the observable coin flip |
49,013 | Distribution of gradients across dimensions for neural networks | The exact answer is going to depend greatly on the type of network, the inputs, how it's trained....
For a simple way to see this:
If we're at a (local) optimum, the full gradient (across the entire training dataset) will be zero. In the interpolating regime common to modern neural networks, the individual gradient fo... | Distribution of gradients across dimensions for neural networks | The exact answer is going to depend greatly on the type of network, the inputs, how it's trained....
For a simple way to see this:
If we're at a (local) optimum, the full gradient (across the entire | Distribution of gradients across dimensions for neural networks
The exact answer is going to depend greatly on the type of network, the inputs, how it's trained....
For a simple way to see this:
If we're at a (local) optimum, the full gradient (across the entire training dataset) will be zero. In the interpolating reg... | Distribution of gradients across dimensions for neural networks
The exact answer is going to depend greatly on the type of network, the inputs, how it's trained....
For a simple way to see this:
If we're at a (local) optimum, the full gradient (across the entire |
49,014 | Why do my (coefficients, standard errors & CIs, p-values & significance) change when I add a term to my regression model? | Coefficient change
Let some there be some data distributed according to a quadratic curve:
$$y \sim \mathcal{N}(\mu = a+bx+cx^2, \sigma^2 = 10^{-3})$$
For instance with $x \sim \mathcal{U}(0,1)$ and $a=0.2$, $b=0$ and $c=1$. Then a linear curve and a polynomial curve will have very different coefficients for the linear... | Why do my (coefficients, standard errors & CIs, p-values & significance) change when I add a term to | Coefficient change
Let some there be some data distributed according to a quadratic curve:
$$y \sim \mathcal{N}(\mu = a+bx+cx^2, \sigma^2 = 10^{-3})$$
For instance with $x \sim \mathcal{U}(0,1)$ and $ | Why do my (coefficients, standard errors & CIs, p-values & significance) change when I add a term to my regression model?
Coefficient change
Let some there be some data distributed according to a quadratic curve:
$$y \sim \mathcal{N}(\mu = a+bx+cx^2, \sigma^2 = 10^{-3})$$
For instance with $x \sim \mathcal{U}(0,1)$ and... | Why do my (coefficients, standard errors & CIs, p-values & significance) change when I add a term to
Coefficient change
Let some there be some data distributed according to a quadratic curve:
$$y \sim \mathcal{N}(\mu = a+bx+cx^2, \sigma^2 = 10^{-3})$$
For instance with $x \sim \mathcal{U}(0,1)$ and $ |
49,015 | Why do my (coefficients, standard errors & CIs, p-values & significance) change when I add a term to my regression model? | The ordinary least squares solution is simply given by:
$$\beta = (X'X)^{-1}X'y$$
Let's imagine we augment $X_{n\times p}$ with one or more variables $\tilde X_{n\times \tilde p}$, appending its corresponding values as columns, and call the resulting matrix ${X^*}_{n\times p^*}$, $p^* = p + \tilde p$.
Now, given enough... | Why do my (coefficients, standard errors & CIs, p-values & significance) change when I add a term to | The ordinary least squares solution is simply given by:
$$\beta = (X'X)^{-1}X'y$$
Let's imagine we augment $X_{n\times p}$ with one or more variables $\tilde X_{n\times \tilde p}$, appending its corre | Why do my (coefficients, standard errors & CIs, p-values & significance) change when I add a term to my regression model?
The ordinary least squares solution is simply given by:
$$\beta = (X'X)^{-1}X'y$$
Let's imagine we augment $X_{n\times p}$ with one or more variables $\tilde X_{n\times \tilde p}$, appending its cor... | Why do my (coefficients, standard errors & CIs, p-values & significance) change when I add a term to
The ordinary least squares solution is simply given by:
$$\beta = (X'X)^{-1}X'y$$
Let's imagine we augment $X_{n\times p}$ with one or more variables $\tilde X_{n\times \tilde p}$, appending its corre |
49,016 | Where is the measure theoretic probability theory actually applied? | Two examples:
All of functional analysis, which I guess you will know underlies a lot of machine learning, relies on measure theory. There is no "undergraduate" probability measure that describes a distribution over function spaces, as far as I'm aware.
Statistical analysis of nonlinear dynamical systems - there is gen... | Where is the measure theoretic probability theory actually applied? | Two examples:
All of functional analysis, which I guess you will know underlies a lot of machine learning, relies on measure theory. There is no "undergraduate" probability measure that describes a di | Where is the measure theoretic probability theory actually applied?
Two examples:
All of functional analysis, which I guess you will know underlies a lot of machine learning, relies on measure theory. There is no "undergraduate" probability measure that describes a distribution over function spaces, as far as I'm aware... | Where is the measure theoretic probability theory actually applied?
Two examples:
All of functional analysis, which I guess you will know underlies a lot of machine learning, relies on measure theory. There is no "undergraduate" probability measure that describes a di |
49,017 | Relationship between completeness and sufficiency | A complete sufficient statistic is a minimal sufficient statistic whenever a minimal sufficient statistic exists.
Suppose for a family of distributions parameterized by $\theta$, there exists a minimal sufficient statistic $S(X)$ and a complete sufficient statistic $T(X)$ based on the data $X$. We show that $T$ is als... | Relationship between completeness and sufficiency | A complete sufficient statistic is a minimal sufficient statistic whenever a minimal sufficient statistic exists.
Suppose for a family of distributions parameterized by $\theta$, there exists a minim | Relationship between completeness and sufficiency
A complete sufficient statistic is a minimal sufficient statistic whenever a minimal sufficient statistic exists.
Suppose for a family of distributions parameterized by $\theta$, there exists a minimal sufficient statistic $S(X)$ and a complete sufficient statistic $T(... | Relationship between completeness and sufficiency
A complete sufficient statistic is a minimal sufficient statistic whenever a minimal sufficient statistic exists.
Suppose for a family of distributions parameterized by $\theta$, there exists a minim |
49,018 | Number of Causal Assumptions in an Overview by Pearl | None of the below causal arrows appear in Fig. 2(a). I am assuming time flows from top left to bottom right (i.e. so that $Y \to X$ cannot be a causal assumption because causes must precede effects.).
$U_{Z} \to U_{X}$
$U_{Z} \to U_{Y}$
$U_{Z} \to X$
$U_{Z} \to Y$
$U_{X} \to U_{Y}$
$U_{X} \to Y$
$Z \to Y$
This means ... | Number of Causal Assumptions in an Overview by Pearl | None of the below causal arrows appear in Fig. 2(a). I am assuming time flows from top left to bottom right (i.e. so that $Y \to X$ cannot be a causal assumption because causes must precede effects.). | Number of Causal Assumptions in an Overview by Pearl
None of the below causal arrows appear in Fig. 2(a). I am assuming time flows from top left to bottom right (i.e. so that $Y \to X$ cannot be a causal assumption because causes must precede effects.).
$U_{Z} \to U_{X}$
$U_{Z} \to U_{Y}$
$U_{Z} \to X$
$U_{Z} \to Y$
$... | Number of Causal Assumptions in an Overview by Pearl
None of the below causal arrows appear in Fig. 2(a). I am assuming time flows from top left to bottom right (i.e. so that $Y \to X$ cannot be a causal assumption because causes must precede effects.). |
49,019 | Number of Causal Assumptions in an Overview by Pearl | An exchange of comments with @Alexis (and their correspondence with Pearl himself) cleared things up for me. I can summarize as follows:
For the exogenous variables $U_X, U_Y, U_Z$ we only allow/count double arrows (just... because?). For these variables we have three missing (double) arrows, which are $U_X \leftright... | Number of Causal Assumptions in an Overview by Pearl | An exchange of comments with @Alexis (and their correspondence with Pearl himself) cleared things up for me. I can summarize as follows:
For the exogenous variables $U_X, U_Y, U_Z$ we only allow/coun | Number of Causal Assumptions in an Overview by Pearl
An exchange of comments with @Alexis (and their correspondence with Pearl himself) cleared things up for me. I can summarize as follows:
For the exogenous variables $U_X, U_Y, U_Z$ we only allow/count double arrows (just... because?). For these variables we have thr... | Number of Causal Assumptions in an Overview by Pearl
An exchange of comments with @Alexis (and their correspondence with Pearl himself) cleared things up for me. I can summarize as follows:
For the exogenous variables $U_X, U_Y, U_Z$ we only allow/coun |
49,020 | What proportion of missing data can be considered acceptable for inference with a mixed-effects model | Does this level of missingness catastrophically reduce the value of the inferences you would make from a longitudinal mixed effects model?
Not necessarily. A great deal depends on the reasons for dropout. If the data are missing at random (MAR), then a suitable multiple imputation approach can result in unbiased, or a... | What proportion of missing data can be considered acceptable for inference with a mixed-effects mode | Does this level of missingness catastrophically reduce the value of the inferences you would make from a longitudinal mixed effects model?
Not necessarily. A great deal depends on the reasons for dro | What proportion of missing data can be considered acceptable for inference with a mixed-effects model
Does this level of missingness catastrophically reduce the value of the inferences you would make from a longitudinal mixed effects model?
Not necessarily. A great deal depends on the reasons for dropout. If the data ... | What proportion of missing data can be considered acceptable for inference with a mixed-effects mode
Does this level of missingness catastrophically reduce the value of the inferences you would make from a longitudinal mixed effects model?
Not necessarily. A great deal depends on the reasons for dro |
49,021 | Why do output coefficients not resemble true coefficients in a linear model? | The day three
The elders of the statistics guild have discovered a problem in the divine parameters. There is no single solution possible because the system is over-determined. We can scale the different values of the groups and the results will remain true.
For instance when we divide the 'constant' coefficient by tw... | Why do output coefficients not resemble true coefficients in a linear model? | The day three
The elders of the statistics guild have discovered a problem in the divine parameters. There is no single solution possible because the system is over-determined. We can scale the differ | Why do output coefficients not resemble true coefficients in a linear model?
The day three
The elders of the statistics guild have discovered a problem in the divine parameters. There is no single solution possible because the system is over-determined. We can scale the different values of the groups and the results wi... | Why do output coefficients not resemble true coefficients in a linear model?
The day three
The elders of the statistics guild have discovered a problem in the divine parameters. There is no single solution possible because the system is over-determined. We can scale the differ |
49,022 | Bootstrap confidence interval on heavy tailed distribution | a) Distributions with heavy tails may have infinite variance, or mean (Ex: Cauchy distribution)
True.
b) Heavy tailed means that there are a few outliers that are very different from the most of the samples. And these outliers have non-negligible impact on the future statistic procedures.
Partly true. This might be ... | Bootstrap confidence interval on heavy tailed distribution | a) Distributions with heavy tails may have infinite variance, or mean (Ex: Cauchy distribution)
True.
b) Heavy tailed means that there are a few outliers that are very different from the most of the | Bootstrap confidence interval on heavy tailed distribution
a) Distributions with heavy tails may have infinite variance, or mean (Ex: Cauchy distribution)
True.
b) Heavy tailed means that there are a few outliers that are very different from the most of the samples. And these outliers have non-negligible impact on th... | Bootstrap confidence interval on heavy tailed distribution
a) Distributions with heavy tails may have infinite variance, or mean (Ex: Cauchy distribution)
True.
b) Heavy tailed means that there are a few outliers that are very different from the most of the |
49,023 | Bootstrap confidence interval on heavy tailed distribution | Here's what I understand:
a) Distributions with heavy tails may have infinite variance, or mean (Ex: cauchy distribution)
b) Heavy tailed means that there are a few outliers that are very different from the most of the samples. And these outliers have non-negligible impact on the future statistic procedures.
c) L... | Bootstrap confidence interval on heavy tailed distribution | Here's what I understand:
a) Distributions with heavy tails may have infinite variance, or mean (Ex: cauchy distribution)
b) Heavy tailed means that there are a few outliers that are very differen | Bootstrap confidence interval on heavy tailed distribution
Here's what I understand:
a) Distributions with heavy tails may have infinite variance, or mean (Ex: cauchy distribution)
b) Heavy tailed means that there are a few outliers that are very different from the most of the samples. And these outliers have non-n... | Bootstrap confidence interval on heavy tailed distribution
Here's what I understand:
a) Distributions with heavy tails may have infinite variance, or mean (Ex: cauchy distribution)
b) Heavy tailed means that there are a few outliers that are very differen |
49,024 | Bootstrap confidence interval on heavy tailed distribution | Bootstrapping the sampling distribution of a sample mean will work (in the sense of being consistent as n diverges) only if a Central Limit Theorem applies, thus existence of the variance is practically required. See Mammen, 'When Will Bootstrap Work, Springer 1992. The intuition is indeed that otherwise observations r... | Bootstrap confidence interval on heavy tailed distribution | Bootstrapping the sampling distribution of a sample mean will work (in the sense of being consistent as n diverges) only if a Central Limit Theorem applies, thus existence of the variance is practical | Bootstrap confidence interval on heavy tailed distribution
Bootstrapping the sampling distribution of a sample mean will work (in the sense of being consistent as n diverges) only if a Central Limit Theorem applies, thus existence of the variance is practically required. See Mammen, 'When Will Bootstrap Work, Springer ... | Bootstrap confidence interval on heavy tailed distribution
Bootstrapping the sampling distribution of a sample mean will work (in the sense of being consistent as n diverges) only if a Central Limit Theorem applies, thus existence of the variance is practical |
49,025 | Confusion on how skip gram implementation is formulated | 1 - The architecture in the CS224n course lecture notes is correct. The likelihood is given by the product of the probabilities $ \Pi_{w\in \rm{Text}} \Pi_{c \in C(w)} P(c | w)$ (where $C(w)$ is the context of the target word). Note that I have added the product over all the words in the corpus (see details https://a... | Confusion on how skip gram implementation is formulated | 1 - The architecture in the CS224n course lecture notes is correct. The likelihood is given by the product of the probabilities $ \Pi_{w\in \rm{Text}} \Pi_{c \in C(w)} P(c | w)$ (where $C(w)$ is the | Confusion on how skip gram implementation is formulated
1 - The architecture in the CS224n course lecture notes is correct. The likelihood is given by the product of the probabilities $ \Pi_{w\in \rm{Text}} \Pi_{c \in C(w)} P(c | w)$ (where $C(w)$ is the context of the target word). Note that I have added the product... | Confusion on how skip gram implementation is formulated
1 - The architecture in the CS224n course lecture notes is correct. The likelihood is given by the product of the probabilities $ \Pi_{w\in \rm{Text}} \Pi_{c \in C(w)} P(c | w)$ (where $C(w)$ is the |
49,026 | Confusion on how skip gram implementation is formulated | I also had similar confusion in the past so I made a skip-gram model demo in this GitHub repo in javascript. Hopefully, it can help people to understand how the skip-gram model works by visualizing it. | Confusion on how skip gram implementation is formulated | I also had similar confusion in the past so I made a skip-gram model demo in this GitHub repo in javascript. Hopefully, it can help people to understand how the skip-gram model works by visualizing it | Confusion on how skip gram implementation is formulated
I also had similar confusion in the past so I made a skip-gram model demo in this GitHub repo in javascript. Hopefully, it can help people to understand how the skip-gram model works by visualizing it. | Confusion on how skip gram implementation is formulated
I also had similar confusion in the past so I made a skip-gram model demo in this GitHub repo in javascript. Hopefully, it can help people to understand how the skip-gram model works by visualizing it |
49,027 | How does Fisher calculate his $p$-value? | Fisher's approach, in a fully parametric framework, was to reduce the data $X$ to a (one-dimensional) statistic sufficient, or conditionally sufficient, for the parameter of interest $\theta$, & to base inference on its distribution under the null hypothesis $\theta=\theta_0$. Typically he used the (or a) maximum-likel... | How does Fisher calculate his $p$-value? | Fisher's approach, in a fully parametric framework, was to reduce the data $X$ to a (one-dimensional) statistic sufficient, or conditionally sufficient, for the parameter of interest $\theta$, & to ba | How does Fisher calculate his $p$-value?
Fisher's approach, in a fully parametric framework, was to reduce the data $X$ to a (one-dimensional) statistic sufficient, or conditionally sufficient, for the parameter of interest $\theta$, & to base inference on its distribution under the null hypothesis $\theta=\theta_0$. T... | How does Fisher calculate his $p$-value?
Fisher's approach, in a fully parametric framework, was to reduce the data $X$ to a (one-dimensional) statistic sufficient, or conditionally sufficient, for the parameter of interest $\theta$, & to ba |
49,028 | Can anyone suggest a distribution for this histogram | I collected $2^{20}$ values from a unit normal process, did the FFT and binned the magnitudes. Then overplotted with a Rayleigh distribution:
I did no scaling on anything, because I was working fast, but I will go back and do it. | Can anyone suggest a distribution for this histogram | I collected $2^{20}$ values from a unit normal process, did the FFT and binned the magnitudes. Then overplotted with a Rayleigh distribution:
I did no scaling on anything, because I was working fast, | Can anyone suggest a distribution for this histogram
I collected $2^{20}$ values from a unit normal process, did the FFT and binned the magnitudes. Then overplotted with a Rayleigh distribution:
I did no scaling on anything, because I was working fast, but I will go back and do it. | Can anyone suggest a distribution for this histogram
I collected $2^{20}$ values from a unit normal process, did the FFT and binned the magnitudes. Then overplotted with a Rayleigh distribution:
I did no scaling on anything, because I was working fast, |
49,029 | Can anyone suggest a distribution for this histogram | So I have understood my problem. This is basically a consequence of taking the FFT of time transient data and taking the absolute value of it. The FFT spectrum analyser device actually spits out the absolute value -- so the phase and sign information of the original transient is LOST.
You can prove this simply by gene... | Can anyone suggest a distribution for this histogram | So I have understood my problem. This is basically a consequence of taking the FFT of time transient data and taking the absolute value of it. The FFT spectrum analyser device actually spits out the a | Can anyone suggest a distribution for this histogram
So I have understood my problem. This is basically a consequence of taking the FFT of time transient data and taking the absolute value of it. The FFT spectrum analyser device actually spits out the absolute value -- so the phase and sign information of the original ... | Can anyone suggest a distribution for this histogram
So I have understood my problem. This is basically a consequence of taking the FFT of time transient data and taking the absolute value of it. The FFT spectrum analyser device actually spits out the a |
49,030 | Coefficient of determination relationship? | $$R^2 = 1-\frac{SSRES}{SSTOT}$$
When there there is no residual variation ($SSRES=0$) then the regression line fits the data perfectly and $R^2$ is 1, whereas when there is there is large residual variation, $\frac{SSRES}{SSTOT}$ approaches 1 and so $R^2$ approaches 0.
what do we say the relationship between X and Y i... | Coefficient of determination relationship? | $$R^2 = 1-\frac{SSRES}{SSTOT}$$
When there there is no residual variation ($SSRES=0$) then the regression line fits the data perfectly and $R^2$ is 1, whereas when there is there is large residual var | Coefficient of determination relationship?
$$R^2 = 1-\frac{SSRES}{SSTOT}$$
When there there is no residual variation ($SSRES=0$) then the regression line fits the data perfectly and $R^2$ is 1, whereas when there is there is large residual variation, $\frac{SSRES}{SSTOT}$ approaches 1 and so $R^2$ approaches 0.
what d... | Coefficient of determination relationship?
$$R^2 = 1-\frac{SSRES}{SSTOT}$$
When there there is no residual variation ($SSRES=0$) then the regression line fits the data perfectly and $R^2$ is 1, whereas when there is there is large residual var |
49,031 | Coefficient of determination relationship? | I think it's important to consider what regression is doing. Then the coefficient of determination makes sense.
Let's say that we collect some data on the heights of people. From our data, we find a mean of 5'2" with a middle range (Q1 to Q3) of 4'2" to 6'2". Given a new person, what height do you guess?
Depending on y... | Coefficient of determination relationship? | I think it's important to consider what regression is doing. Then the coefficient of determination makes sense.
Let's say that we collect some data on the heights of people. From our data, we find a m | Coefficient of determination relationship?
I think it's important to consider what regression is doing. Then the coefficient of determination makes sense.
Let's say that we collect some data on the heights of people. From our data, we find a mean of 5'2" with a middle range (Q1 to Q3) of 4'2" to 6'2". Given a new perso... | Coefficient of determination relationship?
I think it's important to consider what regression is doing. Then the coefficient of determination makes sense.
Let's say that we collect some data on the heights of people. From our data, we find a m |
49,032 | What is the relation between a surrogate function and an acquisition function? | I think of an acquisition function as describing the utility of the point to be evaluated next in the Bayesian optimization framework.
To give more details, let's think about the general concept of Bayesian Optimization and the setting in which it is usually applied. Consider a black-box function $f$ which is expensive... | What is the relation between a surrogate function and an acquisition function? | I think of an acquisition function as describing the utility of the point to be evaluated next in the Bayesian optimization framework.
To give more details, let's think about the general concept of Ba | What is the relation between a surrogate function and an acquisition function?
I think of an acquisition function as describing the utility of the point to be evaluated next in the Bayesian optimization framework.
To give more details, let's think about the general concept of Bayesian Optimization and the setting in wh... | What is the relation between a surrogate function and an acquisition function?
I think of an acquisition function as describing the utility of the point to be evaluated next in the Bayesian optimization framework.
To give more details, let's think about the general concept of Ba |
49,033 | One-to-one correspondence between penalty parameters of equivalent formulations of penalised regression methods | According to Karush–Kuhn–Tucker conditions and this post, the first problem is equivalent to the second problem, and $t = ||\hat\beta||^2$, $\hat\beta = (X^TX+\lambda I)^{-1}X^TY$, so $t=Y^TX(X^TX+\lambda I)^{-2}X^TY$. Then we only need to prove $t$ is an one-to-one function of $\lambda$.
Suppose $T_1=X^TX+\lambda_1 I$... | One-to-one correspondence between penalty parameters of equivalent formulations of penalised regress | According to Karush–Kuhn–Tucker conditions and this post, the first problem is equivalent to the second problem, and $t = ||\hat\beta||^2$, $\hat\beta = (X^TX+\lambda I)^{-1}X^TY$, so $t=Y^TX(X^TX+\la | One-to-one correspondence between penalty parameters of equivalent formulations of penalised regression methods
According to Karush–Kuhn–Tucker conditions and this post, the first problem is equivalent to the second problem, and $t = ||\hat\beta||^2$, $\hat\beta = (X^TX+\lambda I)^{-1}X^TY$, so $t=Y^TX(X^TX+\lambda I)^... | One-to-one correspondence between penalty parameters of equivalent formulations of penalised regress
According to Karush–Kuhn–Tucker conditions and this post, the first problem is equivalent to the second problem, and $t = ||\hat\beta||^2$, $\hat\beta = (X^TX+\lambda I)^{-1}X^TY$, so $t=Y^TX(X^TX+\la |
49,034 | One-to-one correspondence between penalty parameters of equivalent formulations of penalised regression methods | Assume that the solution of your problem $(1)$ is $\beta_\lambda^*$, where index $\lambda$ indicates dependence on a particular value of $\lambda$.
The second problem is solved using Langrange multipliers ($\mu$) and considering KKT conditions, one of which is that $\mu(\Vert \beta\Vert^2 -t) =0$.
Set $t$ in the KTT co... | One-to-one correspondence between penalty parameters of equivalent formulations of penalised regress | Assume that the solution of your problem $(1)$ is $\beta_\lambda^*$, where index $\lambda$ indicates dependence on a particular value of $\lambda$.
The second problem is solved using Langrange multipl | One-to-one correspondence between penalty parameters of equivalent formulations of penalised regression methods
Assume that the solution of your problem $(1)$ is $\beta_\lambda^*$, where index $\lambda$ indicates dependence on a particular value of $\lambda$.
The second problem is solved using Langrange multipliers ($\... | One-to-one correspondence between penalty parameters of equivalent formulations of penalised regress
Assume that the solution of your problem $(1)$ is $\beta_\lambda^*$, where index $\lambda$ indicates dependence on a particular value of $\lambda$.
The second problem is solved using Langrange multipl |
49,035 | Why is RMSEA typically reported with a 90% confidence interval, and not 95%? | Curran et al. (2003) write that:
It is common to report 90 percent confidence intervals for the RMSEA,
primarily because of the resulting direct link to hypothesis testing
based on the model test statistic.
Three hypothesis tests sometimes reported in the SEM literature are.
The test of exact fit, $H_{0}: \epsil... | Why is RMSEA typically reported with a 90% confidence interval, and not 95%? | Curran et al. (2003) write that:
It is common to report 90 percent confidence intervals for the RMSEA,
primarily because of the resulting direct link to hypothesis testing
based on the model tes | Why is RMSEA typically reported with a 90% confidence interval, and not 95%?
Curran et al. (2003) write that:
It is common to report 90 percent confidence intervals for the RMSEA,
primarily because of the resulting direct link to hypothesis testing
based on the model test statistic.
Three hypothesis tests someti... | Why is RMSEA typically reported with a 90% confidence interval, and not 95%?
Curran et al. (2003) write that:
It is common to report 90 percent confidence intervals for the RMSEA,
primarily because of the resulting direct link to hypothesis testing
based on the model tes |
49,036 | Thin Plate Regression Splines mgcv? | The motivation for performing an eigendecomposition of the design matrix is indeed, as you mentioned, to reduce the computational cost of the algorithm. Fitting splines, particularly in the case where $d > 1$, is a very computationally intensive task - in the paper you cite, Wood mentions that all of the algorithms fo... | Thin Plate Regression Splines mgcv? | The motivation for performing an eigendecomposition of the design matrix is indeed, as you mentioned, to reduce the computational cost of the algorithm. Fitting splines, particularly in the case wher | Thin Plate Regression Splines mgcv?
The motivation for performing an eigendecomposition of the design matrix is indeed, as you mentioned, to reduce the computational cost of the algorithm. Fitting splines, particularly in the case where $d > 1$, is a very computationally intensive task - in the paper you cite, Wood me... | Thin Plate Regression Splines mgcv?
The motivation for performing an eigendecomposition of the design matrix is indeed, as you mentioned, to reduce the computational cost of the algorithm. Fitting splines, particularly in the case wher |
49,037 | Model Deployment: export Scikit Learn Pipeline or Model only? | You have to export the model which includes the list of transformers defined by the pipeline and the final estimator.
To give a simple example:
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LinearRegression
from sklearn.datasets import load_boston
from sklearn.pipeline import Pipelin... | Model Deployment: export Scikit Learn Pipeline or Model only? | You have to export the model which includes the list of transformers defined by the pipeline and the final estimator.
To give a simple example:
from sklearn.preprocessing import StandardScaler
from sk | Model Deployment: export Scikit Learn Pipeline or Model only?
You have to export the model which includes the list of transformers defined by the pipeline and the final estimator.
To give a simple example:
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LinearRegression
from sklearn.da... | Model Deployment: export Scikit Learn Pipeline or Model only?
You have to export the model which includes the list of transformers defined by the pipeline and the final estimator.
To give a simple example:
from sklearn.preprocessing import StandardScaler
from sk |
49,038 | Stationary processes for AR, MA, ARMA | Short answers:
We restrict ourself to the stationary region as on the non-stationary one ARMA processes become explosive (that is, they go to infinity)
It is possible to fit a non-stationary model to time series but that won't be an ARMA model (but it may belong to the family of ARMA models)
Non-stationary time serie... | Stationary processes for AR, MA, ARMA | Short answers:
We restrict ourself to the stationary region as on the non-stationary one ARMA processes become explosive (that is, they go to infinity)
It is possible to fit a non-stationary model t | Stationary processes for AR, MA, ARMA
Short answers:
We restrict ourself to the stationary region as on the non-stationary one ARMA processes become explosive (that is, they go to infinity)
It is possible to fit a non-stationary model to time series but that won't be an ARMA model (but it may belong to the family of ... | Stationary processes for AR, MA, ARMA
Short answers:
We restrict ourself to the stationary region as on the non-stationary one ARMA processes become explosive (that is, they go to infinity)
It is possible to fit a non-stationary model t |
49,039 | Stationary processes for AR, MA, ARMA | Intuition
For AR it depends on what you're going to use the model for, see details below.
It doesn't make sense to estimate the MA part of the ARMA. Remember, if a series follows a unit root every shock persists, forever. Said another way, an error from today or a hundred years ago has the same impact on the series... | Stationary processes for AR, MA, ARMA | Intuition
For AR it depends on what you're going to use the model for, see details below.
It doesn't make sense to estimate the MA part of the ARMA. Remember, if a series follows a unit root every | Stationary processes for AR, MA, ARMA
Intuition
For AR it depends on what you're going to use the model for, see details below.
It doesn't make sense to estimate the MA part of the ARMA. Remember, if a series follows a unit root every shock persists, forever. Said another way, an error from today or a hundred years... | Stationary processes for AR, MA, ARMA
Intuition
For AR it depends on what you're going to use the model for, see details below.
It doesn't make sense to estimate the MA part of the ARMA. Remember, if a series follows a unit root every |
49,040 | Stationary processes for AR, MA, ARMA | I think it would be difficult to even estimate an ARIMA model with non-stationarity, because the tools such as PACF and ACF look different when non-stationarity exists. Knowing what was the right order, the AR and MA levels, would be difficult at least given the classical presentations used to identify these. | Stationary processes for AR, MA, ARMA | I think it would be difficult to even estimate an ARIMA model with non-stationarity, because the tools such as PACF and ACF look different when non-stationarity exists. Knowing what was the right orde | Stationary processes for AR, MA, ARMA
I think it would be difficult to even estimate an ARIMA model with non-stationarity, because the tools such as PACF and ACF look different when non-stationarity exists. Knowing what was the right order, the AR and MA levels, would be difficult at least given the classical presentat... | Stationary processes for AR, MA, ARMA
I think it would be difficult to even estimate an ARIMA model with non-stationarity, because the tools such as PACF and ACF look different when non-stationarity exists. Knowing what was the right orde |
49,041 | Incremental solution for matrix inverse using Shermann-Morrison in $O(n^2)$ | Within the context of linear regression, the estimated $\beta$ parameters are given $(X^TX)^{-1}X^Ty$. The main computational burden in this formula is the inversion the matrix $A = X^TX$. In the use-case of batch learning, we have already estimate for $A$ as well as for $A^{-1} = (X^TX)^{-1}$ from our previous iterati... | Incremental solution for matrix inverse using Shermann-Morrison in $O(n^2)$ | Within the context of linear regression, the estimated $\beta$ parameters are given $(X^TX)^{-1}X^Ty$. The main computational burden in this formula is the inversion the matrix $A = X^TX$. In the use- | Incremental solution for matrix inverse using Shermann-Morrison in $O(n^2)$
Within the context of linear regression, the estimated $\beta$ parameters are given $(X^TX)^{-1}X^Ty$. The main computational burden in this formula is the inversion the matrix $A = X^TX$. In the use-case of batch learning, we have already esti... | Incremental solution for matrix inverse using Shermann-Morrison in $O(n^2)$
Within the context of linear regression, the estimated $\beta$ parameters are given $(X^TX)^{-1}X^Ty$. The main computational burden in this formula is the inversion the matrix $A = X^TX$. In the use- |
49,042 | warning: Some predictor variables are on very different scales: consider rescaling | A reasonable approach is to do a "summary" of the dataset and look at the means and medians of the numerical variables, and also possibly their variances. If you see any that are orders of magnitude different from others, that will give you a clue.
You could just simply standardise all the numeric variables first and ... | warning: Some predictor variables are on very different scales: consider rescaling | A reasonable approach is to do a "summary" of the dataset and look at the means and medians of the numerical variables, and also possibly their variances. If you see any that are orders of magnitude d | warning: Some predictor variables are on very different scales: consider rescaling
A reasonable approach is to do a "summary" of the dataset and look at the means and medians of the numerical variables, and also possibly their variances. If you see any that are orders of magnitude different from others, that will give ... | warning: Some predictor variables are on very different scales: consider rescaling
A reasonable approach is to do a "summary" of the dataset and look at the means and medians of the numerical variables, and also possibly their variances. If you see any that are orders of magnitude d |
49,043 | Is MLE intrinsically connected to logs? | The answer to your main question can be yes or no, depending on one's perspective.
First, the maximum likelihood principle can be motivated without any logs. In contrast to your approach, one needs to start with the probability of a sample of size $n$ instead of the $n$ probabilities of $n$ samples. There is a reason ... | Is MLE intrinsically connected to logs? | The answer to your main question can be yes or no, depending on one's perspective.
First, the maximum likelihood principle can be motivated without any logs. In contrast to your approach, one needs t | Is MLE intrinsically connected to logs?
The answer to your main question can be yes or no, depending on one's perspective.
First, the maximum likelihood principle can be motivated without any logs. In contrast to your approach, one needs to start with the probability of a sample of size $n$ instead of the $n$ probabil... | Is MLE intrinsically connected to logs?
The answer to your main question can be yes or no, depending on one's perspective.
First, the maximum likelihood principle can be motivated without any logs. In contrast to your approach, one needs t |
49,044 | How to Fine Tune a pre-trained network | I would like to share my understanding here. Here is a thesis and in its related work author has explained Transfer learning and Fine-Tuning. Also, the survey on Transfer Learning is a good read to understand these concepts in detail.
Unsupervised pre-training is a good strategy to train deep neural
networks for sup... | How to Fine Tune a pre-trained network | I would like to share my understanding here. Here is a thesis and in its related work author has explained Transfer learning and Fine-Tuning. Also, the survey on Transfer Learning is a good read to un | How to Fine Tune a pre-trained network
I would like to share my understanding here. Here is a thesis and in its related work author has explained Transfer learning and Fine-Tuning. Also, the survey on Transfer Learning is a good read to understand these concepts in detail.
Unsupervised pre-training is a good strateg... | How to Fine Tune a pre-trained network
I would like to share my understanding here. Here is a thesis and in its related work author has explained Transfer learning and Fine-Tuning. Also, the survey on Transfer Learning is a good read to un |
49,045 | Predict when a user logins next | Without having seen the data, I don't think machine learning is the appropriate choice here because your data is not IID.
It is reasonable to believe that users may have different login habits, and we should allow for that in our model by modelling time between logins as a hierarchical model.
Posit that each user's tim... | Predict when a user logins next | Without having seen the data, I don't think machine learning is the appropriate choice here because your data is not IID.
It is reasonable to believe that users may have different login habits, and we | Predict when a user logins next
Without having seen the data, I don't think machine learning is the appropriate choice here because your data is not IID.
It is reasonable to believe that users may have different login habits, and we should allow for that in our model by modelling time between logins as a hierarchical m... | Predict when a user logins next
Without having seen the data, I don't think machine learning is the appropriate choice here because your data is not IID.
It is reasonable to believe that users may have different login habits, and we |
49,046 | Does every loss function correspond to MLE/MAP | 2 years later I'll give a partial answer, this encompasses the first three example (log loss, weighted log loss, L1 regression) and many more point wise losses.
Let $L : \mathcal{Y} \times \mathcal{Y}$ be a point-wise loss (i.e. scores a predicted $\hat y$ and $y$ by $L(\hat y,y)$). The essence would be to define the l... | Does every loss function correspond to MLE/MAP | 2 years later I'll give a partial answer, this encompasses the first three example (log loss, weighted log loss, L1 regression) and many more point wise losses.
Let $L : \mathcal{Y} \times \mathcal{Y} | Does every loss function correspond to MLE/MAP
2 years later I'll give a partial answer, this encompasses the first three example (log loss, weighted log loss, L1 regression) and many more point wise losses.
Let $L : \mathcal{Y} \times \mathcal{Y}$ be a point-wise loss (i.e. scores a predicted $\hat y$ and $y$ by $L(\h... | Does every loss function correspond to MLE/MAP
2 years later I'll give a partial answer, this encompasses the first three example (log loss, weighted log loss, L1 regression) and many more point wise losses.
Let $L : \mathcal{Y} \times \mathcal{Y} |
49,047 | Which estimation technique minimizes the MAPE? | If the probability density of your future distribution is positively skewed, then typically (though not always; von Hippel, 2005) the median will be lower than its mean. So a technique that aims at the median as a point forecast will be biased low. Since the MAPE usually prefers a low biased prediction, such a techniqu... | Which estimation technique minimizes the MAPE? | If the probability density of your future distribution is positively skewed, then typically (though not always; von Hippel, 2005) the median will be lower than its mean. So a technique that aims at th | Which estimation technique minimizes the MAPE?
If the probability density of your future distribution is positively skewed, then typically (though not always; von Hippel, 2005) the median will be lower than its mean. So a technique that aims at the median as a point forecast will be biased low. Since the MAPE usually p... | Which estimation technique minimizes the MAPE?
If the probability density of your future distribution is positively skewed, then typically (though not always; von Hippel, 2005) the median will be lower than its mean. So a technique that aims at th |
49,048 | Value iteration does not converge when using Q learning | Ok, so I've slightly modified the initial example and the code below gives me working policy
states_space_size = 16 # 4x4 size of the board
actions_space_size = len(DIRECTIONS)
QSA = np.zeros(shape=(states_space_size, actions_space_size))
max_iterations = 80
gamma = 1 # discount factor
alpha = 0.9 # learning rate
e... | Value iteration does not converge when using Q learning | Ok, so I've slightly modified the initial example and the code below gives me working policy
states_space_size = 16 # 4x4 size of the board
actions_space_size = len(DIRECTIONS)
QSA = np.zeros(shape= | Value iteration does not converge when using Q learning
Ok, so I've slightly modified the initial example and the code below gives me working policy
states_space_size = 16 # 4x4 size of the board
actions_space_size = len(DIRECTIONS)
QSA = np.zeros(shape=(states_space_size, actions_space_size))
max_iterations = 80
gam... | Value iteration does not converge when using Q learning
Ok, so I've slightly modified the initial example and the code below gives me working policy
states_space_size = 16 # 4x4 size of the board
actions_space_size = len(DIRECTIONS)
QSA = np.zeros(shape= |
49,049 | How to determine block size for a block bootstrap and it's variants? | Not sure if you still need this, but the classic texts are on subject are Hall and Horowitz "On Blocking Rules for the Bootstrap with Dependent Data", Lahiri "Theoretical Comparisons of Block Bootstrap Methods", in addition to the Lahiri book you mentioned. I found Hongyi Li and Maddala "Bootstrapping Time Series Model... | How to determine block size for a block bootstrap and it's variants? | Not sure if you still need this, but the classic texts are on subject are Hall and Horowitz "On Blocking Rules for the Bootstrap with Dependent Data", Lahiri "Theoretical Comparisons of Block Bootstra | How to determine block size for a block bootstrap and it's variants?
Not sure if you still need this, but the classic texts are on subject are Hall and Horowitz "On Blocking Rules for the Bootstrap with Dependent Data", Lahiri "Theoretical Comparisons of Block Bootstrap Methods", in addition to the Lahiri book you ment... | How to determine block size for a block bootstrap and it's variants?
Not sure if you still need this, but the classic texts are on subject are Hall and Horowitz "On Blocking Rules for the Bootstrap with Dependent Data", Lahiri "Theoretical Comparisons of Block Bootstra |
49,050 | Significance testing when the treatment group was only partially treated (an unknown set of individuals did not receive the treatment) | I disagree with the other answer by @mkt that no inference is possible, but yes, inference, like hypothesis testing, might be difficult. But there are some possibilities.
In the treatment group, where only about 60% of the subjects/items actually received treatment, we might model the distribution of the outcome as a ... | Significance testing when the treatment group was only partially treated (an unknown set of individu | I disagree with the other answer by @mkt that no inference is possible, but yes, inference, like hypothesis testing, might be difficult. But there are some possibilities.
In the treatment group, wher | Significance testing when the treatment group was only partially treated (an unknown set of individuals did not receive the treatment)
I disagree with the other answer by @mkt that no inference is possible, but yes, inference, like hypothesis testing, might be difficult. But there are some possibilities.
In the treatm... | Significance testing when the treatment group was only partially treated (an unknown set of individu
I disagree with the other answer by @mkt that no inference is possible, but yes, inference, like hypothesis testing, might be difficult. But there are some possibilities.
In the treatment group, wher |
49,051 | Significance testing when the treatment group was only partially treated (an unknown set of individuals did not receive the treatment) | EDIT: kjetil b halvorsen's new answer has persuaded me that my answer below is incorrect.
+1, this is an interesting question
To summarize: the goal is to try to compare people who did receive treatment ($X$) with those who were controls ($C$). However, $X$ is a subset of the population supposed to receive treatment ... | Significance testing when the treatment group was only partially treated (an unknown set of individu | EDIT: kjetil b halvorsen's new answer has persuaded me that my answer below is incorrect.
+1, this is an interesting question
To summarize: the goal is to try to compare people who did receive treat | Significance testing when the treatment group was only partially treated (an unknown set of individuals did not receive the treatment)
EDIT: kjetil b halvorsen's new answer has persuaded me that my answer below is incorrect.
+1, this is an interesting question
To summarize: the goal is to try to compare people who di... | Significance testing when the treatment group was only partially treated (an unknown set of individu
EDIT: kjetil b halvorsen's new answer has persuaded me that my answer below is incorrect.
+1, this is an interesting question
To summarize: the goal is to try to compare people who did receive treat |
49,052 | Why is it important that estimators are unbiased and consistent? | From a frequentist perspective,
Unbiasedness is important mainly with experimental data where the experiment can be repeated and we control the regressor matrix. Then we can actually obtain many estimates of the unknown parameters, and then, we do want their arithmetic average to be really close to the true value, wh... | Why is it important that estimators are unbiased and consistent? | From a frequentist perspective,
Unbiasedness is important mainly with experimental data where the experiment can be repeated and we control the regressor matrix. Then we can actually obtain many est | Why is it important that estimators are unbiased and consistent?
From a frequentist perspective,
Unbiasedness is important mainly with experimental data where the experiment can be repeated and we control the regressor matrix. Then we can actually obtain many estimates of the unknown parameters, and then, we do want ... | Why is it important that estimators are unbiased and consistent?
From a frequentist perspective,
Unbiasedness is important mainly with experimental data where the experiment can be repeated and we control the regressor matrix. Then we can actually obtain many est |
49,053 | Limits of integration of a density function | Both densities involve indicators$$f_X(x)=\mathbb{I}_{(a,b)}(x)\big/(b-a)\quad f_{Y|X}(y|x)=\mathbb{I}_{(a,x)}(y)\big/(x-a)$$and$$f_{X,Y}(x,y)=\mathbb{I}_{(a,b)}(x)\mathbb{I}_{(a,x)}(y)\big/b-y)(x-a)$$This implies
$$\mathbb{I}_{(a,b)}(x)\mathbb{I}_{(a,x)}(y)=\mathbb{I}_{(a,b)}(y)\mathbb{I}_{(y,b)}(x)$$hence
\begin{alig... | Limits of integration of a density function | Both densities involve indicators$$f_X(x)=\mathbb{I}_{(a,b)}(x)\big/(b-a)\quad f_{Y|X}(y|x)=\mathbb{I}_{(a,x)}(y)\big/(x-a)$$and$$f_{X,Y}(x,y)=\mathbb{I}_{(a,b)}(x)\mathbb{I}_{(a,x)}(y)\big/b-y)(x-a)$ | Limits of integration of a density function
Both densities involve indicators$$f_X(x)=\mathbb{I}_{(a,b)}(x)\big/(b-a)\quad f_{Y|X}(y|x)=\mathbb{I}_{(a,x)}(y)\big/(x-a)$$and$$f_{X,Y}(x,y)=\mathbb{I}_{(a,b)}(x)\mathbb{I}_{(a,x)}(y)\big/b-y)(x-a)$$This implies
$$\mathbb{I}_{(a,b)}(x)\mathbb{I}_{(a,x)}(y)=\mathbb{I}_{(a,b)... | Limits of integration of a density function
Both densities involve indicators$$f_X(x)=\mathbb{I}_{(a,b)}(x)\big/(b-a)\quad f_{Y|X}(y|x)=\mathbb{I}_{(a,x)}(y)\big/(x-a)$$and$$f_{X,Y}(x,y)=\mathbb{I}_{(a,b)}(x)\mathbb{I}_{(a,x)}(y)\big/b-y)(x-a)$ |
49,054 | Find the UMVUE of $\frac{\mu^2}{\sigma}$ where $X_i\sim\mathsf N(\mu,\sigma^2)$ | I have skipped some details in the following calculations and would ask you to verify them.
As usual, we have the statistics $$\overline X=\frac{1}{4}\sum_{i=1}^4 X_i\qquad,\qquad S^2=\frac{1}{3}\sum_{i=1}^4(X_i-\overline X)^2$$
Assuming both $\mu$ and $\sigma$ are unknown, we know that $(\overline X,S^2)$ is a complet... | Find the UMVUE of $\frac{\mu^2}{\sigma}$ where $X_i\sim\mathsf N(\mu,\sigma^2)$ | I have skipped some details in the following calculations and would ask you to verify them.
As usual, we have the statistics $$\overline X=\frac{1}{4}\sum_{i=1}^4 X_i\qquad,\qquad S^2=\frac{1}{3}\sum_ | Find the UMVUE of $\frac{\mu^2}{\sigma}$ where $X_i\sim\mathsf N(\mu,\sigma^2)$
I have skipped some details in the following calculations and would ask you to verify them.
As usual, we have the statistics $$\overline X=\frac{1}{4}\sum_{i=1}^4 X_i\qquad,\qquad S^2=\frac{1}{3}\sum_{i=1}^4(X_i-\overline X)^2$$
Assuming bo... | Find the UMVUE of $\frac{\mu^2}{\sigma}$ where $X_i\sim\mathsf N(\mu,\sigma^2)$
I have skipped some details in the following calculations and would ask you to verify them.
As usual, we have the statistics $$\overline X=\frac{1}{4}\sum_{i=1}^4 X_i\qquad,\qquad S^2=\frac{1}{3}\sum_ |
49,055 | Find the UMVUE of $\frac{\mu^2}{\sigma}$ where $X_i\sim\mathsf N(\mu,\sigma^2)$ | An R simulation to verify StubbornAtom's well-explained answer:
In the case of $\mu=3$ and $\sigma=7$ we have $$\frac{\mu^2}{\sigma}=\frac{9}{7}=1.285714$$
The simulation with $10^7$ trials gives $\widehat{\theta}=1.286482$
y=0
for(i in c(1:10^7))
{x<-rnorm(4,3,7)
y=y+sqrt(pi/6)*mean(x)^(2)/sd(x)-(1/8)*sqrt(3*pi/2)*sd(... | Find the UMVUE of $\frac{\mu^2}{\sigma}$ where $X_i\sim\mathsf N(\mu,\sigma^2)$ | An R simulation to verify StubbornAtom's well-explained answer:
In the case of $\mu=3$ and $\sigma=7$ we have $$\frac{\mu^2}{\sigma}=\frac{9}{7}=1.285714$$
The simulation with $10^7$ trials gives $\wi | Find the UMVUE of $\frac{\mu^2}{\sigma}$ where $X_i\sim\mathsf N(\mu,\sigma^2)$
An R simulation to verify StubbornAtom's well-explained answer:
In the case of $\mu=3$ and $\sigma=7$ we have $$\frac{\mu^2}{\sigma}=\frac{9}{7}=1.285714$$
The simulation with $10^7$ trials gives $\widehat{\theta}=1.286482$
y=0
for(i in c(1... | Find the UMVUE of $\frac{\mu^2}{\sigma}$ where $X_i\sim\mathsf N(\mu,\sigma^2)$
An R simulation to verify StubbornAtom's well-explained answer:
In the case of $\mu=3$ and $\sigma=7$ we have $$\frac{\mu^2}{\sigma}=\frac{9}{7}=1.285714$$
The simulation with $10^7$ trials gives $\wi |
49,056 | GAMM with Zero-Inflated Negative Binomial - Looking for a package in R | This model is possible with the brms R package which is an interface to R:
A slight modification of one of the examples from https://cran.r-project.org/web/packages/brms/vignettes/brms_distreg.html shows essentially what is involved in setting up and fitting the model
## load package
library('brms')
## load data
zinb <... | GAMM with Zero-Inflated Negative Binomial - Looking for a package in R | This model is possible with the brms R package which is an interface to R:
A slight modification of one of the examples from https://cran.r-project.org/web/packages/brms/vignettes/brms_distreg.html sh | GAMM with Zero-Inflated Negative Binomial - Looking for a package in R
This model is possible with the brms R package which is an interface to R:
A slight modification of one of the examples from https://cran.r-project.org/web/packages/brms/vignettes/brms_distreg.html shows essentially what is involved in setting up an... | GAMM with Zero-Inflated Negative Binomial - Looking for a package in R
This model is possible with the brms R package which is an interface to R:
A slight modification of one of the examples from https://cran.r-project.org/web/packages/brms/vignettes/brms_distreg.html sh |
49,057 | Multi-agent actor-critic MADDPG algorithm confusion | (1) how subsampling would resolve the non-stationarity problem
The idea about sampling a variety of sub-policies for other agents to execute during training is that this introduces more variety in the behaviour of competing agents, rather than always only training against the single most recent "version" of opponents ... | Multi-agent actor-critic MADDPG algorithm confusion | (1) how subsampling would resolve the non-stationarity problem
The idea about sampling a variety of sub-policies for other agents to execute during training is that this introduces more variety in th | Multi-agent actor-critic MADDPG algorithm confusion
(1) how subsampling would resolve the non-stationarity problem
The idea about sampling a variety of sub-policies for other agents to execute during training is that this introduces more variety in the behaviour of competing agents, rather than always only training ag... | Multi-agent actor-critic MADDPG algorithm confusion
(1) how subsampling would resolve the non-stationarity problem
The idea about sampling a variety of sub-policies for other agents to execute during training is that this introduces more variety in th |
49,058 | State-of-the-art algorithms for the training of neural networks with GRU or LSTM units | This article is a good place to start.
"Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network" by Alex Sherstinsky
Because of their effectiveness in broad practical applications, LSTM networks have received a wealth of coverage in scientific journals, technical blogs, and implementat... | State-of-the-art algorithms for the training of neural networks with GRU or LSTM units | This article is a good place to start.
"Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network" by Alex Sherstinsky
Because of their effectiveness in broad practical | State-of-the-art algorithms for the training of neural networks with GRU or LSTM units
This article is a good place to start.
"Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network" by Alex Sherstinsky
Because of their effectiveness in broad practical applications, LSTM networks have... | State-of-the-art algorithms for the training of neural networks with GRU or LSTM units
This article is a good place to start.
"Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network" by Alex Sherstinsky
Because of their effectiveness in broad practical |
49,059 | Difference between independence and stationarity tests in time series | As a preliminary matter, it is worth noting that "independence" is a very vague condition unless it comes with a clear specification of what is independent from what. Conceptually, independence is a much broader concept, whereas stationarity of a time-series is a particular condition on the series that can be framed a... | Difference between independence and stationarity tests in time series | As a preliminary matter, it is worth noting that "independence" is a very vague condition unless it comes with a clear specification of what is independent from what. Conceptually, independence is a | Difference between independence and stationarity tests in time series
As a preliminary matter, it is worth noting that "independence" is a very vague condition unless it comes with a clear specification of what is independent from what. Conceptually, independence is a much broader concept, whereas stationarity of a ti... | Difference between independence and stationarity tests in time series
As a preliminary matter, it is worth noting that "independence" is a very vague condition unless it comes with a clear specification of what is independent from what. Conceptually, independence is a |
49,060 | Difference between independence and stationarity tests in time series | To the best of my understanding, the concepts mean the following:
Testing for independence, would be useful to see whether there is any relationship between time and your variable of choice at all.
Looking a the definition of stationarity, it does not say anything about independence. The most important takeaway is tha... | Difference between independence and stationarity tests in time series | To the best of my understanding, the concepts mean the following:
Testing for independence, would be useful to see whether there is any relationship between time and your variable of choice at all.
L | Difference between independence and stationarity tests in time series
To the best of my understanding, the concepts mean the following:
Testing for independence, would be useful to see whether there is any relationship between time and your variable of choice at all.
Looking a the definition of stationarity, it does n... | Difference between independence and stationarity tests in time series
To the best of my understanding, the concepts mean the following:
Testing for independence, would be useful to see whether there is any relationship between time and your variable of choice at all.
L |
49,061 | Is there an alternative to categorical cross-entropy with a notion of "class distance"? | The earth mover's distance (EMD) provides a way to do this. When computed between probability distributions, the EMD is equivalent to the 1st Wasserstein distance. Intuitively, each distribution can be imagined as a pile of dirt, consisting of a certain amount of dirt at each location. A pile can be transformed by movi... | Is there an alternative to categorical cross-entropy with a notion of "class distance"? | The earth mover's distance (EMD) provides a way to do this. When computed between probability distributions, the EMD is equivalent to the 1st Wasserstein distance. Intuitively, each distribution can b | Is there an alternative to categorical cross-entropy with a notion of "class distance"?
The earth mover's distance (EMD) provides a way to do this. When computed between probability distributions, the EMD is equivalent to the 1st Wasserstein distance. Intuitively, each distribution can be imagined as a pile of dirt, co... | Is there an alternative to categorical cross-entropy with a notion of "class distance"?
The earth mover's distance (EMD) provides a way to do this. When computed between probability distributions, the EMD is equivalent to the 1st Wasserstein distance. Intuitively, each distribution can b |
49,062 | Geometric interpretation of mathematical expectation of a random variable | The mathematical expectation is the x-coordinate of the centre of gravity.
The picture above is borrowed from Wikipedia. | Geometric interpretation of mathematical expectation of a random variable | The mathematical expectation is the x-coordinate of the centre of gravity.
The picture above is borrowed from Wikipedia. | Geometric interpretation of mathematical expectation of a random variable
The mathematical expectation is the x-coordinate of the centre of gravity.
The picture above is borrowed from Wikipedia. | Geometric interpretation of mathematical expectation of a random variable
The mathematical expectation is the x-coordinate of the centre of gravity.
The picture above is borrowed from Wikipedia. |
49,063 | Does Intention-to-treat apply to the cases that should have been excluded but not able to do so during recruitment? | I guess yours is a randomized trial. If it is not, then the whole intention-to-treat (ITT) vs as-treated (AT) vs per-protocol (PP) Mexican standoff is meaningless (eg McCoy, 2017).
Accordingly, if they were not randomized, you could exclude them and still consider the corresponding analysis as an ITT one.
Otherwise, if... | Does Intention-to-treat apply to the cases that should have been excluded but not able to do so duri | I guess yours is a randomized trial. If it is not, then the whole intention-to-treat (ITT) vs as-treated (AT) vs per-protocol (PP) Mexican standoff is meaningless (eg McCoy, 2017).
Accordingly, if the | Does Intention-to-treat apply to the cases that should have been excluded but not able to do so during recruitment?
I guess yours is a randomized trial. If it is not, then the whole intention-to-treat (ITT) vs as-treated (AT) vs per-protocol (PP) Mexican standoff is meaningless (eg McCoy, 2017).
Accordingly, if they we... | Does Intention-to-treat apply to the cases that should have been excluded but not able to do so duri
I guess yours is a randomized trial. If it is not, then the whole intention-to-treat (ITT) vs as-treated (AT) vs per-protocol (PP) Mexican standoff is meaningless (eg McCoy, 2017).
Accordingly, if the |
49,064 | Does Intention-to-treat apply to the cases that should have been excluded but not able to do so during recruitment? | This is a very interesting question and is unlikely to have a single right answer. I would argue that if they should never have been included in the trial in the first place then they should be excluded even post-randomisation and this would not affect the intention to teat analysis. The point of the trial is to be abl... | Does Intention-to-treat apply to the cases that should have been excluded but not able to do so duri | This is a very interesting question and is unlikely to have a single right answer. I would argue that if they should never have been included in the trial in the first place then they should be exclud | Does Intention-to-treat apply to the cases that should have been excluded but not able to do so during recruitment?
This is a very interesting question and is unlikely to have a single right answer. I would argue that if they should never have been included in the trial in the first place then they should be excluded e... | Does Intention-to-treat apply to the cases that should have been excluded but not able to do so duri
This is a very interesting question and is unlikely to have a single right answer. I would argue that if they should never have been included in the trial in the first place then they should be exclud |
49,065 | Ridge regression to minimize RMSE instead of MSE | minimizing
$$ \left\| X \vec{c} - \vec{y} \right\|_2^2 + \left\| \Gamma \vec{c} \right\|_2^2 $$
and minimizing
$$ \sqrt{\left\| X \vec{c} - \vec{y} \right\|_2^2} + \left\| \Gamma \vec{c} \right\|_2^2 $$
do not directly relate to minimizing ${\left\| X \vec{c} - \vec{y} \right\|_2^2}$ or $\sqrt{\left\| X \vec{c} - \v... | Ridge regression to minimize RMSE instead of MSE | minimizing
$$ \left\| X \vec{c} - \vec{y} \right\|_2^2 + \left\| \Gamma \vec{c} \right\|_2^2 $$
and minimizing
$$ \sqrt{\left\| X \vec{c} - \vec{y} \right\|_2^2} + \left\| \Gamma \vec{c} \right\|_2 | Ridge regression to minimize RMSE instead of MSE
minimizing
$$ \left\| X \vec{c} - \vec{y} \right\|_2^2 + \left\| \Gamma \vec{c} \right\|_2^2 $$
and minimizing
$$ \sqrt{\left\| X \vec{c} - \vec{y} \right\|_2^2} + \left\| \Gamma \vec{c} \right\|_2^2 $$
do not directly relate to minimizing ${\left\| X \vec{c} - \vec{y... | Ridge regression to minimize RMSE instead of MSE
minimizing
$$ \left\| X \vec{c} - \vec{y} \right\|_2^2 + \left\| \Gamma \vec{c} \right\|_2^2 $$
and minimizing
$$ \sqrt{\left\| X \vec{c} - \vec{y} \right\|_2^2} + \left\| \Gamma \vec{c} \right\|_2 |
49,066 | Linear regression with $l_0$ regularization | First, note that NP-hardness is a property of a problem, rather than a specific algorithm--it puts bounds on the performance of any algorithm. The proof works by establishing relationships between problems to prove membership in complexity classes.
Background
A complexity class is a set of computational problems define... | Linear regression with $l_0$ regularization | First, note that NP-hardness is a property of a problem, rather than a specific algorithm--it puts bounds on the performance of any algorithm. The proof works by establishing relationships between pro | Linear regression with $l_0$ regularization
First, note that NP-hardness is a property of a problem, rather than a specific algorithm--it puts bounds on the performance of any algorithm. The proof works by establishing relationships between problems to prove membership in complexity classes.
Background
A complexity cla... | Linear regression with $l_0$ regularization
First, note that NP-hardness is a property of a problem, rather than a specific algorithm--it puts bounds on the performance of any algorithm. The proof works by establishing relationships between pro |
49,067 | Similarity LAD and quantile regression | Assume we have the following regression model:
$\mathbf{y} = f(\mathbf{x},\mathbf{\beta}) + \mathbf{\epsilon}$
The $\beta$ estimate of LAD regression is given by:
$ \hat{\beta}_{LAD} = \text{argmin}_{ b} \sum_{i=1}^n |y_i - f(\mathbf{b},x_i)|$
The $\beta$ estimate of Quantile regression is given by:
$ \hat{\beta}_{... | Similarity LAD and quantile regression | Assume we have the following regression model:
$\mathbf{y} = f(\mathbf{x},\mathbf{\beta}) + \mathbf{\epsilon}$
The $\beta$ estimate of LAD regression is given by:
$ \hat{\beta}_{LAD} = \text{argmin} | Similarity LAD and quantile regression
Assume we have the following regression model:
$\mathbf{y} = f(\mathbf{x},\mathbf{\beta}) + \mathbf{\epsilon}$
The $\beta$ estimate of LAD regression is given by:
$ \hat{\beta}_{LAD} = \text{argmin}_{ b} \sum_{i=1}^n |y_i - f(\mathbf{b},x_i)|$
The $\beta$ estimate of Quantile ... | Similarity LAD and quantile regression
Assume we have the following regression model:
$\mathbf{y} = f(\mathbf{x},\mathbf{\beta}) + \mathbf{\epsilon}$
The $\beta$ estimate of LAD regression is given by:
$ \hat{\beta}_{LAD} = \text{argmin} |
49,068 | What influences fluctuations in validation accuracy? | First of all, does your $x$ axis represent training steps or epochs?
My guess would be epochs (keras default), because of the stability in the training accuracy. If that is not the case, a low batch size would be the prime suspect in fluctuations, because the accuracy would depend on what examples the model sees at eac... | What influences fluctuations in validation accuracy? | First of all, does your $x$ axis represent training steps or epochs?
My guess would be epochs (keras default), because of the stability in the training accuracy. If that is not the case, a low batch s | What influences fluctuations in validation accuracy?
First of all, does your $x$ axis represent training steps or epochs?
My guess would be epochs (keras default), because of the stability in the training accuracy. If that is not the case, a low batch size would be the prime suspect in fluctuations, because the accurac... | What influences fluctuations in validation accuracy?
First of all, does your $x$ axis represent training steps or epochs?
My guess would be epochs (keras default), because of the stability in the training accuracy. If that is not the case, a low batch s |
49,069 | Special values in continuous numerical variables/features in Random Forest | My instinct is to split features for which this is the case into two new feature, one with the numerical values, and NA values where there was previously a special value, and another feature with NAs for the cases where the original value was numeric, and strings for the special values, coding this as a "factor" variab... | Special values in continuous numerical variables/features in Random Forest | My instinct is to split features for which this is the case into two new feature, one with the numerical values, and NA values where there was previously a special value, and another feature with NAs | Special values in continuous numerical variables/features in Random Forest
My instinct is to split features for which this is the case into two new feature, one with the numerical values, and NA values where there was previously a special value, and another feature with NAs for the cases where the original value was nu... | Special values in continuous numerical variables/features in Random Forest
My instinct is to split features for which this is the case into two new feature, one with the numerical values, and NA values where there was previously a special value, and another feature with NAs |
49,070 | Find $\lim_{n \downarrow 1} t_{n-1, \alpha/2} / \sqrt{n}$ and prove the limit | Noting that the division by $\sqrt{n}$ does not change the result (because it converges to $1$) and writing $\nu=n-1$ and $2\gamma = 1-\alpha,$ the problem is to analyze the behavior of the function $x_\gamma(\nu)$ defined implicitly by
$$\gamma = \frac{\Gamma(\nu/2+1/2)}{\Gamma(1/2)\Gamma(\nu/2)}\int_0^{x_\gamma(\nu)}... | Find $\lim_{n \downarrow 1} t_{n-1, \alpha/2} / \sqrt{n}$ and prove the limit | Noting that the division by $\sqrt{n}$ does not change the result (because it converges to $1$) and writing $\nu=n-1$ and $2\gamma = 1-\alpha,$ the problem is to analyze the behavior of the function $ | Find $\lim_{n \downarrow 1} t_{n-1, \alpha/2} / \sqrt{n}$ and prove the limit
Noting that the division by $\sqrt{n}$ does not change the result (because it converges to $1$) and writing $\nu=n-1$ and $2\gamma = 1-\alpha,$ the problem is to analyze the behavior of the function $x_\gamma(\nu)$ defined implicitly by
$$\ga... | Find $\lim_{n \downarrow 1} t_{n-1, \alpha/2} / \sqrt{n}$ and prove the limit
Noting that the division by $\sqrt{n}$ does not change the result (because it converges to $1$) and writing $\nu=n-1$ and $2\gamma = 1-\alpha,$ the problem is to analyze the behavior of the function $ |
49,071 | Can a GAN be used for tabular/vector data augmentation? | GANs are primarily used for data augmentation. If you have 1D signals you could use MLP or 1D convolutions. Hope those links will help: http://www.rricard.me/machine/learning/generative/adversarial/networks/keras/tensorflow/2017/04/05/gans-part2.html https://github.com/timzhang642/GAN-1D-Gaussian-Distribution | Can a GAN be used for tabular/vector data augmentation? | GANs are primarily used for data augmentation. If you have 1D signals you could use MLP or 1D convolutions. Hope those links will help: http://www.rricard.me/machine/learning/generative/adversarial/ne | Can a GAN be used for tabular/vector data augmentation?
GANs are primarily used for data augmentation. If you have 1D signals you could use MLP or 1D convolutions. Hope those links will help: http://www.rricard.me/machine/learning/generative/adversarial/networks/keras/tensorflow/2017/04/05/gans-part2.html https://githu... | Can a GAN be used for tabular/vector data augmentation?
GANs are primarily used for data augmentation. If you have 1D signals you could use MLP or 1D convolutions. Hope those links will help: http://www.rricard.me/machine/learning/generative/adversarial/ne |
49,072 | Can a GAN be used for tabular/vector data augmentation? | Of course, you can generate some new data as data augmentation, check out
Take look at review two recent papers https://towardsdatascience.com/review-of-gans-for-tabular-data-a30a2199342
With code https://github.com/Diyago/GAN-for-tabular-data | Can a GAN be used for tabular/vector data augmentation? | Of course, you can generate some new data as data augmentation, check out
Take look at review two recent papers https://towardsdatascience.com/review-of-gans-for-tabular-data-a30a2199342
With code ht | Can a GAN be used for tabular/vector data augmentation?
Of course, you can generate some new data as data augmentation, check out
Take look at review two recent papers https://towardsdatascience.com/review-of-gans-for-tabular-data-a30a2199342
With code https://github.com/Diyago/GAN-for-tabular-data | Can a GAN be used for tabular/vector data augmentation?
Of course, you can generate some new data as data augmentation, check out
Take look at review two recent papers https://towardsdatascience.com/review-of-gans-for-tabular-data-a30a2199342
With code ht |
49,073 | Sampling from characteristic/moment generating function | Some time ago I worked on something similar.
If you are still interested in an implementation of the Devoye (1981) method you can give a look here https://www.kent.ac.uk/smsas/personal/msr/webfiles/rlaptrans/rdevroye.r
This is the code by Martin Ridout.
Prof. Ridout also wrote a really interesting paper on the topic... | Sampling from characteristic/moment generating function | Some time ago I worked on something similar.
If you are still interested in an implementation of the Devoye (1981) method you can give a look here https://www.kent.ac.uk/smsas/personal/msr/webfiles/r | Sampling from characteristic/moment generating function
Some time ago I worked on something similar.
If you are still interested in an implementation of the Devoye (1981) method you can give a look here https://www.kent.ac.uk/smsas/personal/msr/webfiles/rlaptrans/rdevroye.r
This is the code by Martin Ridout.
Prof. R... | Sampling from characteristic/moment generating function
Some time ago I worked on something similar.
If you are still interested in an implementation of the Devoye (1981) method you can give a look here https://www.kent.ac.uk/smsas/personal/msr/webfiles/r |
49,074 | Survey: dismiss an answer based on quality of other answers? | The way you describe it, this participant gave not one, but multiple problematic answers. In addition, the one answer that is your focus here also needs interpretation as to which way it leans.
It is quite common to run survey questions past multiple independent scorers are exclude those that are judged to be unclear b... | Survey: dismiss an answer based on quality of other answers? | The way you describe it, this participant gave not one, but multiple problematic answers. In addition, the one answer that is your focus here also needs interpretation as to which way it leans.
It is | Survey: dismiss an answer based on quality of other answers?
The way you describe it, this participant gave not one, but multiple problematic answers. In addition, the one answer that is your focus here also needs interpretation as to which way it leans.
It is quite common to run survey questions past multiple independ... | Survey: dismiss an answer based on quality of other answers?
The way you describe it, this participant gave not one, but multiple problematic answers. In addition, the one answer that is your focus here also needs interpretation as to which way it leans.
It is |
49,075 | Normal Distribution With Many Zero Values | I think you might be better off treating this as a mixture of two distributions rather than trying to apply the standard normal-theory tools, so instead I'm going to outline a bit about the zero inflated Gamma distribution, including computing its first two moments, to give you a sense of how this goes. You could prett... | Normal Distribution With Many Zero Values | I think you might be better off treating this as a mixture of two distributions rather than trying to apply the standard normal-theory tools, so instead I'm going to outline a bit about the zero infla | Normal Distribution With Many Zero Values
I think you might be better off treating this as a mixture of two distributions rather than trying to apply the standard normal-theory tools, so instead I'm going to outline a bit about the zero inflated Gamma distribution, including computing its first two moments, to give you... | Normal Distribution With Many Zero Values
I think you might be better off treating this as a mixture of two distributions rather than trying to apply the standard normal-theory tools, so instead I'm going to outline a bit about the zero infla |
49,076 | $\mathbb{E}(\log(X_{max}/X_{min}) )$ of Weibull(alpha, 1) | Simplifying the problem: The Weibull distribution with unit shape is the exponential distribution, so your specified sampling mechanism is equivalent to $X_1, ..., X_n \sim \text{IID Exp}(\text{Scale} = \alpha)$. For all arguments $x \geqslant 0$ you have the density and distribution functions:
$$f_X(x) = \frac{1}{\al... | $\mathbb{E}(\log(X_{max}/X_{min}) )$ of Weibull(alpha, 1) | Simplifying the problem: The Weibull distribution with unit shape is the exponential distribution, so your specified sampling mechanism is equivalent to $X_1, ..., X_n \sim \text{IID Exp}(\text{Scale} | $\mathbb{E}(\log(X_{max}/X_{min}) )$ of Weibull(alpha, 1)
Simplifying the problem: The Weibull distribution with unit shape is the exponential distribution, so your specified sampling mechanism is equivalent to $X_1, ..., X_n \sim \text{IID Exp}(\text{Scale} = \alpha)$. For all arguments $x \geqslant 0$ you have the d... | $\mathbb{E}(\log(X_{max}/X_{min}) )$ of Weibull(alpha, 1)
Simplifying the problem: The Weibull distribution with unit shape is the exponential distribution, so your specified sampling mechanism is equivalent to $X_1, ..., X_n \sim \text{IID Exp}(\text{Scale} |
49,077 | Representation input and output nodes in neural network for $\textit{AlphaZero}$ chess? | A good place to look might be the Deep Mind paper on the topic, "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm" by David Silver et al.
The game of chess is the most widely-studied domain in the history of artificial intelligence. The strongest programs are based on a combinatio... | Representation input and output nodes in neural network for $\textit{AlphaZero}$ chess? | A good place to look might be the Deep Mind paper on the topic, "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm" by David Silver et al.
The game of chess is th | Representation input and output nodes in neural network for $\textit{AlphaZero}$ chess?
A good place to look might be the Deep Mind paper on the topic, "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm" by David Silver et al.
The game of chess is the most widely-studied domain in ... | Representation input and output nodes in neural network for $\textit{AlphaZero}$ chess?
A good place to look might be the Deep Mind paper on the topic, "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm" by David Silver et al.
The game of chess is th |
49,078 | How to efficiently calculate the PDF of a multivariate gaussian with linear algebra (python) | Least squares optimizer has an elegant solution using linear algebra. You are solving the system $A\hat x=\hat b$, where be is A is your matrix ( [[1,x0,z0],[1,x1,y2],...] ), $b$ is a column of [z0; z1; ;..] and $x$ is a vector containing the estimated parameters which your solving for. The vector $b$ is NOT in the col... | How to efficiently calculate the PDF of a multivariate gaussian with linear algebra (python) | Least squares optimizer has an elegant solution using linear algebra. You are solving the system $A\hat x=\hat b$, where be is A is your matrix ( [[1,x0,z0],[1,x1,y2],...] ), $b$ is a column of [z0; z | How to efficiently calculate the PDF of a multivariate gaussian with linear algebra (python)
Least squares optimizer has an elegant solution using linear algebra. You are solving the system $A\hat x=\hat b$, where be is A is your matrix ( [[1,x0,z0],[1,x1,y2],...] ), $b$ is a column of [z0; z1; ;..] and $x$ is a vector... | How to efficiently calculate the PDF of a multivariate gaussian with linear algebra (python)
Least squares optimizer has an elegant solution using linear algebra. You are solving the system $A\hat x=\hat b$, where be is A is your matrix ( [[1,x0,z0],[1,x1,y2],...] ), $b$ is a column of [z0; z |
49,079 | Does a quadratic log-likehood mean the MLE is (approximately) normally distributed? | If you are not working with the asymptotic case, that "around the best fit" is key; if functions are twice differentiable, they are "locally linear" and also "locally quadratic", which latter implies that the quadratic approximation is arbitrarily good as you shrink the region over which you are approximating towards a... | Does a quadratic log-likehood mean the MLE is (approximately) normally distributed? | If you are not working with the asymptotic case, that "around the best fit" is key; if functions are twice differentiable, they are "locally linear" and also "locally quadratic", which latter implies | Does a quadratic log-likehood mean the MLE is (approximately) normally distributed?
If you are not working with the asymptotic case, that "around the best fit" is key; if functions are twice differentiable, they are "locally linear" and also "locally quadratic", which latter implies that the quadratic approximation is ... | Does a quadratic log-likehood mean the MLE is (approximately) normally distributed?
If you are not working with the asymptotic case, that "around the best fit" is key; if functions are twice differentiable, they are "locally linear" and also "locally quadratic", which latter implies |
49,080 | LASSO: selection of penalty term: "one-standard-error" rule | I don't know of any rigorous justification for the "one-standard-error" rule. It seems to be a rule of thumb for situations where the analyst is more interested in parsimony than in predictive accuracy.
It's important to recognize the artificial model being evaluated in the section of ESL that brings up the "one-standa... | LASSO: selection of penalty term: "one-standard-error" rule | I don't know of any rigorous justification for the "one-standard-error" rule. It seems to be a rule of thumb for situations where the analyst is more interested in parsimony than in predictive accurac | LASSO: selection of penalty term: "one-standard-error" rule
I don't know of any rigorous justification for the "one-standard-error" rule. It seems to be a rule of thumb for situations where the analyst is more interested in parsimony than in predictive accuracy.
It's important to recognize the artificial model being ev... | LASSO: selection of penalty term: "one-standard-error" rule
I don't know of any rigorous justification for the "one-standard-error" rule. It seems to be a rule of thumb for situations where the analyst is more interested in parsimony than in predictive accurac |
49,081 | LASSO: selection of penalty term: "one-standard-error" rule | Regarding your first question:
The authors use this figure on p. 244 to illustrate what they mean with 'one-standard-error' rule.
Standard error bars are shown, which are the standard errors of the
individual misclassification error rates for each of the ten parts.
Both curves have minima at p = 10, although the C... | LASSO: selection of penalty term: "one-standard-error" rule | Regarding your first question:
The authors use this figure on p. 244 to illustrate what they mean with 'one-standard-error' rule.
Standard error bars are shown, which are the standard errors of the
| LASSO: selection of penalty term: "one-standard-error" rule
Regarding your first question:
The authors use this figure on p. 244 to illustrate what they mean with 'one-standard-error' rule.
Standard error bars are shown, which are the standard errors of the
individual misclassification error rates for each of the te... | LASSO: selection of penalty term: "one-standard-error" rule
Regarding your first question:
The authors use this figure on p. 244 to illustrate what they mean with 'one-standard-error' rule.
Standard error bars are shown, which are the standard errors of the
|
49,082 | LASSO: selection of penalty term: "one-standard-error" rule | To answer the second part of your question:
Robert Tibshirani (who introduced the Lasso) writes in "introduction to statistical learning" on the subject of tuning parameter selection:
Cross-validation provides a simple way to tackle this problem. We choose a grid of λ values, and compute the cross-validation error fo... | LASSO: selection of penalty term: "one-standard-error" rule | To answer the second part of your question:
Robert Tibshirani (who introduced the Lasso) writes in "introduction to statistical learning" on the subject of tuning parameter selection:
Cross-validati | LASSO: selection of penalty term: "one-standard-error" rule
To answer the second part of your question:
Robert Tibshirani (who introduced the Lasso) writes in "introduction to statistical learning" on the subject of tuning parameter selection:
Cross-validation provides a simple way to tackle this problem. We choose a... | LASSO: selection of penalty term: "one-standard-error" rule
To answer the second part of your question:
Robert Tibshirani (who introduced the Lasso) writes in "introduction to statistical learning" on the subject of tuning parameter selection:
Cross-validati |
49,083 | Why is bridge regression called "bridge"? | The word "bridge" does not occur in the particular reference. But in other references it does occur. For instance equation 33 in Friedman, Jerome H. "An overview of predictive learning and function approximation." From statistics to neural networks (1994).
Another approach is to approximate the discontinuous penalty (... | Why is bridge regression called "bridge"? | The word "bridge" does not occur in the particular reference. But in other references it does occur. For instance equation 33 in Friedman, Jerome H. "An overview of predictive learning and function ap | Why is bridge regression called "bridge"?
The word "bridge" does not occur in the particular reference. But in other references it does occur. For instance equation 33 in Friedman, Jerome H. "An overview of predictive learning and function approximation." From statistics to neural networks (1994).
Another approach is ... | Why is bridge regression called "bridge"?
The word "bridge" does not occur in the particular reference. But in other references it does occur. For instance equation 33 in Friedman, Jerome H. "An overview of predictive learning and function ap |
49,084 | Finding complete sufficient statistic | Recall:
Definition: A statistic $T$ is complete for $\theta$ if $$E(g(T)) = 0, \ \text{ for all $\theta$} \quad \Rightarrow \quad P(g(T) = 0) = 1, \ \text{ for all $\theta$}$$
The part about $P(g(T) = 0) = 1$ basically says that the function $g$ is trivially $0$ everywhere (except possibly on a set of measure 0).
So... | Finding complete sufficient statistic | Recall:
Definition: A statistic $T$ is complete for $\theta$ if $$E(g(T)) = 0, \ \text{ for all $\theta$} \quad \Rightarrow \quad P(g(T) = 0) = 1, \ \text{ for all $\theta$}$$
The part about $P(g(T | Finding complete sufficient statistic
Recall:
Definition: A statistic $T$ is complete for $\theta$ if $$E(g(T)) = 0, \ \text{ for all $\theta$} \quad \Rightarrow \quad P(g(T) = 0) = 1, \ \text{ for all $\theta$}$$
The part about $P(g(T) = 0) = 1$ basically says that the function $g$ is trivially $0$ everywhere (exce... | Finding complete sufficient statistic
Recall:
Definition: A statistic $T$ is complete for $\theta$ if $$E(g(T)) = 0, \ \text{ for all $\theta$} \quad \Rightarrow \quad P(g(T) = 0) = 1, \ \text{ for all $\theta$}$$
The part about $P(g(T |
49,085 | Finding complete sufficient statistic | Method 1
$(X_{(1)},X_{(n)})$ is not complete because we can find $g\neq0$ but $\mathbb{E}\left[g(X_{(1)},X_{(n)})\right]=0,\forall\theta$. $g$ is $(t_1,t_2)\rightarrow\frac{n+1}{n-1}t_2-\frac{n+1}{1-n}t_1$.
This is because $\mathbb{E}(X_{(n)})=\frac{n-1}{n+1}\theta$ and $\mathbb{E}(X_{(1)})=\frac{1-n}{n+1}\theta$. Thu... | Finding complete sufficient statistic | Method 1
$(X_{(1)},X_{(n)})$ is not complete because we can find $g\neq0$ but $\mathbb{E}\left[g(X_{(1)},X_{(n)})\right]=0,\forall\theta$. $g$ is $(t_1,t_2)\rightarrow\frac{n+1}{n-1}t_2-\frac{n+1}{1-n | Finding complete sufficient statistic
Method 1
$(X_{(1)},X_{(n)})$ is not complete because we can find $g\neq0$ but $\mathbb{E}\left[g(X_{(1)},X_{(n)})\right]=0,\forall\theta$. $g$ is $(t_1,t_2)\rightarrow\frac{n+1}{n-1}t_2-\frac{n+1}{1-n}t_1$.
This is because $\mathbb{E}(X_{(n)})=\frac{n-1}{n+1}\theta$ and $\mathbb{E... | Finding complete sufficient statistic
Method 1
$(X_{(1)},X_{(n)})$ is not complete because we can find $g\neq0$ but $\mathbb{E}\left[g(X_{(1)},X_{(n)})\right]=0,\forall\theta$. $g$ is $(t_1,t_2)\rightarrow\frac{n+1}{n-1}t_2-\frac{n+1}{1-n |
49,086 | How to compute joint entropy of high-dimensional data? | Generally, estimating the entropy in high-dimensions is going to be intractable. What you can do instead is estimate an upper bound on the entropy.
Note that entropy can be written as an expectation:
$$H(X_1, \ldots, X_n) = -\mathbb E_p \log p(x)$$
Here, $\mathbb E_p$ is an expectation over the distribution $p(x)$.
I... | How to compute joint entropy of high-dimensional data? | Generally, estimating the entropy in high-dimensions is going to be intractable. What you can do instead is estimate an upper bound on the entropy.
Note that entropy can be written as an expectation: | How to compute joint entropy of high-dimensional data?
Generally, estimating the entropy in high-dimensions is going to be intractable. What you can do instead is estimate an upper bound on the entropy.
Note that entropy can be written as an expectation:
$$H(X_1, \ldots, X_n) = -\mathbb E_p \log p(x)$$
Here, $\mathbb ... | How to compute joint entropy of high-dimensional data?
Generally, estimating the entropy in high-dimensions is going to be intractable. What you can do instead is estimate an upper bound on the entropy.
Note that entropy can be written as an expectation: |
49,087 | Derivation of the conditional median for linear regression in “The elements of statistical learning ” | First, I think you misspelled something in the question. In your case it should be
$$
EPE(f)=\mathbb{E}(\vert Y-f(X)\vert).
$$
What you want to show is that
$$
\text{argmin}_{f \text{ measurable}}EPE(f)=\left(X\mapsto\text{median}(Y\vert X)\right)
$$
This is in fact equivalent to showing that the median is the best con... | Derivation of the conditional median for linear regression in “The elements of statistical learning | First, I think you misspelled something in the question. In your case it should be
$$
EPE(f)=\mathbb{E}(\vert Y-f(X)\vert).
$$
What you want to show is that
$$
\text{argmin}_{f \text{ measurable}}EPE( | Derivation of the conditional median for linear regression in “The elements of statistical learning ”
First, I think you misspelled something in the question. In your case it should be
$$
EPE(f)=\mathbb{E}(\vert Y-f(X)\vert).
$$
What you want to show is that
$$
\text{argmin}_{f \text{ measurable}}EPE(f)=\left(X\mapsto\... | Derivation of the conditional median for linear regression in “The elements of statistical learning
First, I think you misspelled something in the question. In your case it should be
$$
EPE(f)=\mathbb{E}(\vert Y-f(X)\vert).
$$
What you want to show is that
$$
\text{argmin}_{f \text{ measurable}}EPE( |
49,088 | Derivation of the conditional median for linear regression in “The elements of statistical learning ” | INTUITION
This part is taken from this answer.
Assume that $S$ is a finite set, with say $k$ elements. Line them up in order, as $s_1<s_2<\cdots <s_k$.
If $k$ is even there are (depending on the exact definition of median) many medians. $|x-s_i|$ is the distance between $x$ and $s_i$, so we are trying to minimize the... | Derivation of the conditional median for linear regression in “The elements of statistical learning | INTUITION
This part is taken from this answer.
Assume that $S$ is a finite set, with say $k$ elements. Line them up in order, as $s_1<s_2<\cdots <s_k$.
If $k$ is even there are (depending on the exa | Derivation of the conditional median for linear regression in “The elements of statistical learning ”
INTUITION
This part is taken from this answer.
Assume that $S$ is a finite set, with say $k$ elements. Line them up in order, as $s_1<s_2<\cdots <s_k$.
If $k$ is even there are (depending on the exact definition of m... | Derivation of the conditional median for linear regression in “The elements of statistical learning
INTUITION
This part is taken from this answer.
Assume that $S$ is a finite set, with say $k$ elements. Line them up in order, as $s_1<s_2<\cdots <s_k$.
If $k$ is even there are (depending on the exa |
49,089 | Derivation of the conditional median for linear regression in “The elements of statistical learning ” | Let's call $(Y - f(X))^2 = g(Y)$. Then, we know that, for continuous cases (for example)
$$ E[g(Y)] = \int g(y) f_Y(y) dy $$
And we also know that $$ P(A, B) = P(A|B) P(B)$$ or,
$$ f_{y, x}(y, x) = f_{y | x}(y | x) f_{x}(x) $$
Then, to derive $E_X \Big [ E_{Y|X} [g(Y) | X ] \Big ]$, we can do:
$$E_x \Big [ E_{Y|X... | Derivation of the conditional median for linear regression in “The elements of statistical learning | Let's call $(Y - f(X))^2 = g(Y)$. Then, we know that, for continuous cases (for example)
$$ E[g(Y)] = \int g(y) f_Y(y) dy $$
And we also know that $$ P(A, B) = P(A|B) P(B)$$ or,
$$ f_{y, x}(y, x) | Derivation of the conditional median for linear regression in “The elements of statistical learning ”
Let's call $(Y - f(X))^2 = g(Y)$. Then, we know that, for continuous cases (for example)
$$ E[g(Y)] = \int g(y) f_Y(y) dy $$
And we also know that $$ P(A, B) = P(A|B) P(B)$$ or,
$$ f_{y, x}(y, x) = f_{y | x}(y | x)... | Derivation of the conditional median for linear regression in “The elements of statistical learning
Let's call $(Y - f(X))^2 = g(Y)$. Then, we know that, for continuous cases (for example)
$$ E[g(Y)] = \int g(y) f_Y(y) dy $$
And we also know that $$ P(A, B) = P(A|B) P(B)$$ or,
$$ f_{y, x}(y, x) |
49,090 | Data matrix, predictor matrix, observation matrix, model matrix, and design matrix. What do they mean? | I wouldn't get caught up in the terms. Just know they are referring to your data. Every discipline (engineering, CS, statistics) has different terms for the same thing.
However, to dive in to the detail, if your data is all numerical (no categorical data), then the model matrix = design matrix because there are no cate... | Data matrix, predictor matrix, observation matrix, model matrix, and design matrix. What do they mea | I wouldn't get caught up in the terms. Just know they are referring to your data. Every discipline (engineering, CS, statistics) has different terms for the same thing.
However, to dive in to the deta | Data matrix, predictor matrix, observation matrix, model matrix, and design matrix. What do they mean?
I wouldn't get caught up in the terms. Just know they are referring to your data. Every discipline (engineering, CS, statistics) has different terms for the same thing.
However, to dive in to the detail, if your data ... | Data matrix, predictor matrix, observation matrix, model matrix, and design matrix. What do they mea
I wouldn't get caught up in the terms. Just know they are referring to your data. Every discipline (engineering, CS, statistics) has different terms for the same thing.
However, to dive in to the deta |
49,091 | Data matrix, predictor matrix, observation matrix, model matrix, and design matrix. What do they mean? | The answer by @Jon states that these terms are just synonyms. I do not agree with that. Certainly there will be differences in use between disciplines and softwares, so you must always look out for the authors/programmers definitions.
But there are at least two different concepts here:
The raw data matrix just contai... | Data matrix, predictor matrix, observation matrix, model matrix, and design matrix. What do they mea | The answer by @Jon states that these terms are just synonyms. I do not agree with that. Certainly there will be differences in use between disciplines and softwares, so you must always look out for th | Data matrix, predictor matrix, observation matrix, model matrix, and design matrix. What do they mean?
The answer by @Jon states that these terms are just synonyms. I do not agree with that. Certainly there will be differences in use between disciplines and softwares, so you must always look out for the authors/program... | Data matrix, predictor matrix, observation matrix, model matrix, and design matrix. What do they mea
The answer by @Jon states that these terms are just synonyms. I do not agree with that. Certainly there will be differences in use between disciplines and softwares, so you must always look out for th |
49,092 | Proper way to use NDCG@k score for recommendations | In "plain" language
The Discounted Cumulative Gain for k shown recommendations ($DCG@k$) sums the relevance of the shown items for the current user (cumulative), meanwhile adding a penalty for relevant items placed on later positions (discounted).
The Normalized Cumulative Gain for k shown recommendations ($NDCG@k$) di... | Proper way to use NDCG@k score for recommendations | In "plain" language
The Discounted Cumulative Gain for k shown recommendations ($DCG@k$) sums the relevance of the shown items for the current user (cumulative), meanwhile adding a penalty for relevan | Proper way to use NDCG@k score for recommendations
In "plain" language
The Discounted Cumulative Gain for k shown recommendations ($DCG@k$) sums the relevance of the shown items for the current user (cumulative), meanwhile adding a penalty for relevant items placed on later positions (discounted).
The Normalized Cumula... | Proper way to use NDCG@k score for recommendations
In "plain" language
The Discounted Cumulative Gain for k shown recommendations ($DCG@k$) sums the relevance of the shown items for the current user (cumulative), meanwhile adding a penalty for relevan |
49,093 | Job interview on drawing a random number | The conclusion of the interviewer is silly, and it is an example of the Gambler's fallacy. Both classical and Bayesian methods lead to the conclusions that are broadly the opposite of his conclusion. Whenever you take draws at random from a distribution this leads you to a series of independent and identical distribu... | Job interview on drawing a random number | The conclusion of the interviewer is silly, and it is an example of the Gambler's fallacy. Both classical and Bayesian methods lead to the conclusions that are broadly the opposite of his conclusion. | Job interview on drawing a random number
The conclusion of the interviewer is silly, and it is an example of the Gambler's fallacy. Both classical and Bayesian methods lead to the conclusions that are broadly the opposite of his conclusion. Whenever you take draws at random from a distribution this leads you to a ser... | Job interview on drawing a random number
The conclusion of the interviewer is silly, and it is an example of the Gambler's fallacy. Both classical and Bayesian methods lead to the conclusions that are broadly the opposite of his conclusion. |
49,094 | Why don't we average Confidence Intervals? | The issue here is that the average of CIs are simply not “efficient” (not the appropriate use of this word from a statistical perspective, but reasonable in an informal sense for this context). If you take the average of the boundaries of the CIs, you will end up with a new interval that has about the same length as ... | Why don't we average Confidence Intervals? | The issue here is that the average of CIs are simply not “efficient” (not the appropriate use of this word from a statistical perspective, but reasonable in an informal sense for this context). If y | Why don't we average Confidence Intervals?
The issue here is that the average of CIs are simply not “efficient” (not the appropriate use of this word from a statistical perspective, but reasonable in an informal sense for this context). If you take the average of the boundaries of the CIs, you will end up with a new ... | Why don't we average Confidence Intervals?
The issue here is that the average of CIs are simply not “efficient” (not the appropriate use of this word from a statistical perspective, but reasonable in an informal sense for this context). If y |
49,095 | Random Forest Probability vs Logistic Regression Probability | In a nutshell, logistic regression aims to produce an estimation of the probability of belonging to a specific class. So there is only one "probability estimate" after a logistic regression. On the other hand, the probability obtained using random forest is more like a by product, taking advantage of having many trees ... | Random Forest Probability vs Logistic Regression Probability | In a nutshell, logistic regression aims to produce an estimation of the probability of belonging to a specific class. So there is only one "probability estimate" after a logistic regression. On the ot | Random Forest Probability vs Logistic Regression Probability
In a nutshell, logistic regression aims to produce an estimation of the probability of belonging to a specific class. So there is only one "probability estimate" after a logistic regression. On the other hand, the probability obtained using random forest is m... | Random Forest Probability vs Logistic Regression Probability
In a nutshell, logistic regression aims to produce an estimation of the probability of belonging to a specific class. So there is only one "probability estimate" after a logistic regression. On the ot |
49,096 | What's the meaning of "Corrected for chance"? | Look at the definition of ARI in terms of the Rand index RI.
Correction for chance means that the RI score is adjusted in a way that a random result ('result by chance') gets a score of 0.
On certain data sets, a random result can score an RI if 0.9 - on other data sets this would be a good results. The ARI is this mor... | What's the meaning of "Corrected for chance"? | Look at the definition of ARI in terms of the Rand index RI.
Correction for chance means that the RI score is adjusted in a way that a random result ('result by chance') gets a score of 0.
On certain | What's the meaning of "Corrected for chance"?
Look at the definition of ARI in terms of the Rand index RI.
Correction for chance means that the RI score is adjusted in a way that a random result ('result by chance') gets a score of 0.
On certain data sets, a random result can score an RI if 0.9 - on other data sets thi... | What's the meaning of "Corrected for chance"?
Look at the definition of ARI in terms of the Rand index RI.
Correction for chance means that the RI score is adjusted in a way that a random result ('result by chance') gets a score of 0.
On certain |
49,097 | Chi Square test in SPSS Exploratory Factor Analysis | This chi-square goodness-of-fit test which SPSS outputs under Maximum likelihood or Generalized least squares methods of factor extraction is one of the many methods to estimate the "best" number of factors to extract from the data. The test assumes that the data comes from multivariate normal population.
This chi-squa... | Chi Square test in SPSS Exploratory Factor Analysis | This chi-square goodness-of-fit test which SPSS outputs under Maximum likelihood or Generalized least squares methods of factor extraction is one of the many methods to estimate the "best" number of f | Chi Square test in SPSS Exploratory Factor Analysis
This chi-square goodness-of-fit test which SPSS outputs under Maximum likelihood or Generalized least squares methods of factor extraction is one of the many methods to estimate the "best" number of factors to extract from the data. The test assumes that the data come... | Chi Square test in SPSS Exploratory Factor Analysis
This chi-square goodness-of-fit test which SPSS outputs under Maximum likelihood or Generalized least squares methods of factor extraction is one of the many methods to estimate the "best" number of f |
49,098 | how is covariate shift associated with domain adaptation? | Covariate Shift: source domain and target domain have the same input space 𝑋, output space 𝑌. And they share the same conditional distributions of 𝑌, but different marginal distributions of 𝑋. Formally, $𝑃_S (y│𝑥)= 𝑃_T (y│𝑥)$, but $𝑃_S (x)≠ 𝑃_T (x)$.
Obviously, domain adaptation is a more general concept, it ... | how is covariate shift associated with domain adaptation? | Covariate Shift: source domain and target domain have the same input space 𝑋, output space 𝑌. And they share the same conditional distributions of 𝑌, but different marginal distributions of 𝑋. Formall | how is covariate shift associated with domain adaptation?
Covariate Shift: source domain and target domain have the same input space 𝑋, output space 𝑌. And they share the same conditional distributions of 𝑌, but different marginal distributions of 𝑋. Formally, $𝑃_S (y│𝑥)= 𝑃_T (y│𝑥)$, but $𝑃_S (x)≠ 𝑃_T (x)$.
O... | how is covariate shift associated with domain adaptation?
Covariate Shift: source domain and target domain have the same input space 𝑋, output space 𝑌. And they share the same conditional distributions of 𝑌, but different marginal distributions of 𝑋. Formall |
49,099 | Truncated Beta parameters - method of moments | Your data is drawn from a censored Beta distribution, with the censoring point unknown as well as how many observations were censored. The PDF of the distribution is:
$$p(x; a, b, c) = {x^{a-1}(1-x)^{b-1} \over \int_0^c t^{a-1}(1-t)^{b-1}\text{d}t}$$
The usual Beta functions cancel out between the numerator and the de... | Truncated Beta parameters - method of moments | Your data is drawn from a censored Beta distribution, with the censoring point unknown as well as how many observations were censored. The PDF of the distribution is:
$$p(x; a, b, c) = {x^{a-1}(1-x)^ | Truncated Beta parameters - method of moments
Your data is drawn from a censored Beta distribution, with the censoring point unknown as well as how many observations were censored. The PDF of the distribution is:
$$p(x; a, b, c) = {x^{a-1}(1-x)^{b-1} \over \int_0^c t^{a-1}(1-t)^{b-1}\text{d}t}$$
The usual Beta functio... | Truncated Beta parameters - method of moments
Your data is drawn from a censored Beta distribution, with the censoring point unknown as well as how many observations were censored. The PDF of the distribution is:
$$p(x; a, b, c) = {x^{a-1}(1-x)^ |
49,100 | Understanding svycontrast in R with simple random sampling | svycontrast computes "linear or nonlinear contrasts of estimates produced by survey functions (or any object with coef and vcov methods)."
That is, it takes the estimates that it is given and computes functions of them. It does not do anything with the individual data -- it does not even see the individual data (in ge... | Understanding svycontrast in R with simple random sampling | svycontrast computes "linear or nonlinear contrasts of estimates produced by survey functions (or any object with coef and vcov methods)."
That is, it takes the estimates that it is given and computes | Understanding svycontrast in R with simple random sampling
svycontrast computes "linear or nonlinear contrasts of estimates produced by survey functions (or any object with coef and vcov methods)."
That is, it takes the estimates that it is given and computes functions of them. It does not do anything with the individ... | Understanding svycontrast in R with simple random sampling
svycontrast computes "linear or nonlinear contrasts of estimates produced by survey functions (or any object with coef and vcov methods)."
That is, it takes the estimates that it is given and computes |
Subsets and Splits
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