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 |
|---|---|---|---|---|---|---|
13,001 | How to smooth data and force monotonicity | The recent scam package by Natalya Pya and based on the paper "Shape constrained additive models" by Pya & Wood (2015) can make part of the process mentioned in Gavin's excellent answer much easier.
library(scam)
con <- scam(y ~ s(x, k = k, bs = "mpd"), data = df)
plot(con)
There are a number of bs functions you can u... | How to smooth data and force monotonicity | The recent scam package by Natalya Pya and based on the paper "Shape constrained additive models" by Pya & Wood (2015) can make part of the process mentioned in Gavin's excellent answer much easier.
l | How to smooth data and force monotonicity
The recent scam package by Natalya Pya and based on the paper "Shape constrained additive models" by Pya & Wood (2015) can make part of the process mentioned in Gavin's excellent answer much easier.
library(scam)
con <- scam(y ~ s(x, k = k, bs = "mpd"), data = df)
plot(con)
Th... | How to smooth data and force monotonicity
The recent scam package by Natalya Pya and based on the paper "Shape constrained additive models" by Pya & Wood (2015) can make part of the process mentioned in Gavin's excellent answer much easier.
l |
13,002 | Weighted principal components analysis | It depends on what exactly your weights apply to.
Row weights
Let $\mathbf{X}$ be the data matrix with variables in columns and $n$ observations $\mathbf x_i$ in rows. If each observation has an associated weight $w_i$, then it is indeed straightforward to incorporate these weights into PCA.
First, one needs to compute... | Weighted principal components analysis | It depends on what exactly your weights apply to.
Row weights
Let $\mathbf{X}$ be the data matrix with variables in columns and $n$ observations $\mathbf x_i$ in rows. If each observation has an assoc | Weighted principal components analysis
It depends on what exactly your weights apply to.
Row weights
Let $\mathbf{X}$ be the data matrix with variables in columns and $n$ observations $\mathbf x_i$ in rows. If each observation has an associated weight $w_i$, then it is indeed straightforward to incorporate these weight... | Weighted principal components analysis
It depends on what exactly your weights apply to.
Row weights
Let $\mathbf{X}$ be the data matrix with variables in columns and $n$ observations $\mathbf x_i$ in rows. If each observation has an assoc |
13,003 | Weighted principal components analysis | Thank you very much amoeba for the insight regarding row weights. I know that this is not stackoverflow, but I had some difficulties to find an implementation of row-weighted PCA with explanation and, since this is one of the first results when googling for weighted PCA, I thought it would be good to attach my solution... | Weighted principal components analysis | Thank you very much amoeba for the insight regarding row weights. I know that this is not stackoverflow, but I had some difficulties to find an implementation of row-weighted PCA with explanation and, | Weighted principal components analysis
Thank you very much amoeba for the insight regarding row weights. I know that this is not stackoverflow, but I had some difficulties to find an implementation of row-weighted PCA with explanation and, since this is one of the first results when googling for weighted PCA, I thought... | Weighted principal components analysis
Thank you very much amoeba for the insight regarding row weights. I know that this is not stackoverflow, but I had some difficulties to find an implementation of row-weighted PCA with explanation and, |
13,004 | Auto.arima with daily data: how to capture seasonality/periodicity? | If there is weekly seasonality, set the seasonal period to 7.
salests <- ts(data,start=2010,frequency=7)
modArima <- auto.arima(salests)
Note that the selection of seasonal differencing was not very good in auto.arima() until very recently. If you are using v2.xx of the forecast package, set D=1 in the call to auto.a... | Auto.arima with daily data: how to capture seasonality/periodicity? | If there is weekly seasonality, set the seasonal period to 7.
salests <- ts(data,start=2010,frequency=7)
modArima <- auto.arima(salests)
Note that the selection of seasonal differencing was not very | Auto.arima with daily data: how to capture seasonality/periodicity?
If there is weekly seasonality, set the seasonal period to 7.
salests <- ts(data,start=2010,frequency=7)
modArima <- auto.arima(salests)
Note that the selection of seasonal differencing was not very good in auto.arima() until very recently. If you ar... | Auto.arima with daily data: how to capture seasonality/periodicity?
If there is weekly seasonality, set the seasonal period to 7.
salests <- ts(data,start=2010,frequency=7)
modArima <- auto.arima(salests)
Note that the selection of seasonal differencing was not very |
13,005 | Auto.arima with daily data: how to capture seasonality/periodicity? | The problem with fitting seasonal ARIMA to daily data is that the "seasonal component" may only operate on the weekends or maybe just the weekdays thus overall there is a non-significnat "seasonal component". Now what you have to do is to augment your data set with 6 dummies representing the days of the week and perhap... | Auto.arima with daily data: how to capture seasonality/periodicity? | The problem with fitting seasonal ARIMA to daily data is that the "seasonal component" may only operate on the weekends or maybe just the weekdays thus overall there is a non-significnat "seasonal com | Auto.arima with daily data: how to capture seasonality/periodicity?
The problem with fitting seasonal ARIMA to daily data is that the "seasonal component" may only operate on the weekends or maybe just the weekdays thus overall there is a non-significnat "seasonal component". Now what you have to do is to augment your ... | Auto.arima with daily data: how to capture seasonality/periodicity?
The problem with fitting seasonal ARIMA to daily data is that the "seasonal component" may only operate on the weekends or maybe just the weekdays thus overall there is a non-significnat "seasonal com |
13,006 | Can a posterior probability be >1? | The assumed conditions do not hold- it can never be true that $P(a)/P(x) < P(a|x)$ by the definition of conditional probability:
$P(a|x) = P(a\cap x) / P(x) \leq P(a) / P(x)$ | Can a posterior probability be >1? | The assumed conditions do not hold- it can never be true that $P(a)/P(x) < P(a|x)$ by the definition of conditional probability:
$P(a|x) = P(a\cap x) / P(x) \leq P(a) / P(x)$ | Can a posterior probability be >1?
The assumed conditions do not hold- it can never be true that $P(a)/P(x) < P(a|x)$ by the definition of conditional probability:
$P(a|x) = P(a\cap x) / P(x) \leq P(a) / P(x)$ | Can a posterior probability be >1?
The assumed conditions do not hold- it can never be true that $P(a)/P(x) < P(a|x)$ by the definition of conditional probability:
$P(a|x) = P(a\cap x) / P(x) \leq P(a) / P(x)$ |
13,007 | Can a posterior probability be >1? | No, it is not possible for the posterior probability to exceed one. That would be a breach of the norming axiom of probability theory. In your question you specify that $\mathbb{P}(a)/\mathbb{P}(x) < \mathbb{P}(a | x)$ as part of your example. However, using the rules of conditional probability, you must have:
$$\ma... | Can a posterior probability be >1? | No, it is not possible for the posterior probability to exceed one. That would be a breach of the norming axiom of probability theory. In your question you specify that $\mathbb{P}(a)/\mathbb{P}(x) | Can a posterior probability be >1?
No, it is not possible for the posterior probability to exceed one. That would be a breach of the norming axiom of probability theory. In your question you specify that $\mathbb{P}(a)/\mathbb{P}(x) < \mathbb{P}(a | x)$ as part of your example. However, using the rules of conditiona... | Can a posterior probability be >1?
No, it is not possible for the posterior probability to exceed one. That would be a breach of the norming axiom of probability theory. In your question you specify that $\mathbb{P}(a)/\mathbb{P}(x) |
13,008 | Can a posterior probability be >1? | The Bayes formula $\displaystyle P(B \mid A) = \frac{P(A\mid B)P(B)}{P(A)}$ cannot give values for $P(B\mid A)$ exceeding $1$. An intuitive way to see this is to express $P(A)$ via the law of total probability as
$$P(A) = P(A\mid B)P(B) + P(A\mid B^c)P(B^c)$$ giving that
$$P(B \mid A) = \frac{P(A\mid B)P(B)}{P(A)} = \f... | Can a posterior probability be >1? | The Bayes formula $\displaystyle P(B \mid A) = \frac{P(A\mid B)P(B)}{P(A)}$ cannot give values for $P(B\mid A)$ exceeding $1$. An intuitive way to see this is to express $P(A)$ via the law of total pr | Can a posterior probability be >1?
The Bayes formula $\displaystyle P(B \mid A) = \frac{P(A\mid B)P(B)}{P(A)}$ cannot give values for $P(B\mid A)$ exceeding $1$. An intuitive way to see this is to express $P(A)$ via the law of total probability as
$$P(A) = P(A\mid B)P(B) + P(A\mid B^c)P(B^c)$$ giving that
$$P(B \mid A)... | Can a posterior probability be >1?
The Bayes formula $\displaystyle P(B \mid A) = \frac{P(A\mid B)P(B)}{P(A)}$ cannot give values for $P(B\mid A)$ exceeding $1$. An intuitive way to see this is to express $P(A)$ via the law of total pr |
13,009 | $P[X=x]=0$ when $X$ is a continuous variable | Probabilities are models for the relative frequencies of observations.
If an event $A$ is observed to have occurred $N_A$ times on $N$ trials, then its
relative frequency is
$$\text{relative frequency of }(A) = \frac{N_A}{N}$$
and it is generally believed that the numerical value of the above ratio
is a close approxim... | $P[X=x]=0$ when $X$ is a continuous variable | Probabilities are models for the relative frequencies of observations.
If an event $A$ is observed to have occurred $N_A$ times on $N$ trials, then its
relative frequency is
$$\text{relative frequenc | $P[X=x]=0$ when $X$ is a continuous variable
Probabilities are models for the relative frequencies of observations.
If an event $A$ is observed to have occurred $N_A$ times on $N$ trials, then its
relative frequency is
$$\text{relative frequency of }(A) = \frac{N_A}{N}$$
and it is generally believed that the numerical... | $P[X=x]=0$ when $X$ is a continuous variable
Probabilities are models for the relative frequencies of observations.
If an event $A$ is observed to have occurred $N_A$ times on $N$ trials, then its
relative frequency is
$$\text{relative frequenc |
13,010 | $P[X=x]=0$ when $X$ is a continuous variable | Let $(\Omega,\mathscr{F},P)$ be the underlying probability space. We say that a measurable function $X:\Omega\to\mathbb{R}$ is an absolutely continuous random variable if the probability measure $\mu_X$ over $(\mathbb{R},\mathscr{B})$ defined by $\mu_X(B)=P\{X\in B\}$, known as the distribution of $X$, is dominated by ... | $P[X=x]=0$ when $X$ is a continuous variable | Let $(\Omega,\mathscr{F},P)$ be the underlying probability space. We say that a measurable function $X:\Omega\to\mathbb{R}$ is an absolutely continuous random variable if the probability measure $\mu_ | $P[X=x]=0$ when $X$ is a continuous variable
Let $(\Omega,\mathscr{F},P)$ be the underlying probability space. We say that a measurable function $X:\Omega\to\mathbb{R}$ is an absolutely continuous random variable if the probability measure $\mu_X$ over $(\mathbb{R},\mathscr{B})$ defined by $\mu_X(B)=P\{X\in B\}$, known... | $P[X=x]=0$ when $X$ is a continuous variable
Let $(\Omega,\mathscr{F},P)$ be the underlying probability space. We say that a measurable function $X:\Omega\to\mathbb{R}$ is an absolutely continuous random variable if the probability measure $\mu_ |
13,011 | $P[X=x]=0$ when $X$ is a continuous variable | $X$ is a continuous random variable means its distribution function $F$ is continuous. This is the only condition we have but from which we can derive that $P(X = x) = 0$.
In fact, by continuity of $F$, we have $F(x) = F(x-)$ for every $x \in \mathbb{R}^1$, therefore:
$$P(X = x) = P(X \leq x) - P(X < x) = F(x) - F(x-)... | $P[X=x]=0$ when $X$ is a continuous variable | $X$ is a continuous random variable means its distribution function $F$ is continuous. This is the only condition we have but from which we can derive that $P(X = x) = 0$.
In fact, by continuity of $ | $P[X=x]=0$ when $X$ is a continuous variable
$X$ is a continuous random variable means its distribution function $F$ is continuous. This is the only condition we have but from which we can derive that $P(X = x) = 0$.
In fact, by continuity of $F$, we have $F(x) = F(x-)$ for every $x \in \mathbb{R}^1$, therefore:
$$P(X... | $P[X=x]=0$ when $X$ is a continuous variable
$X$ is a continuous random variable means its distribution function $F$ is continuous. This is the only condition we have but from which we can derive that $P(X = x) = 0$.
In fact, by continuity of $ |
13,012 | $P[X=x]=0$ when $X$ is a continuous variable | This is really a question about probabilities.
It could be rephrased something like
Suppose there are an infinite number of disjoint events. Why must their probabilities eventually become arbitrarily small?
Well, if they didn't become small, there would be a positive number $\epsilon$ smaller than all those probabili... | $P[X=x]=0$ when $X$ is a continuous variable | This is really a question about probabilities.
It could be rephrased something like
Suppose there are an infinite number of disjoint events. Why must their probabilities eventually become arbitrarily | $P[X=x]=0$ when $X$ is a continuous variable
This is really a question about probabilities.
It could be rephrased something like
Suppose there are an infinite number of disjoint events. Why must their probabilities eventually become arbitrarily small?
Well, if they didn't become small, there would be a positive numbe... | $P[X=x]=0$ when $X$ is a continuous variable
This is really a question about probabilities.
It could be rephrased something like
Suppose there are an infinite number of disjoint events. Why must their probabilities eventually become arbitrarily |
13,013 | $P[X=x]=0$ when $X$ is a continuous variable | There are many answers here which address the technical reasons for why infinitesimally small slices of a continuous probability distribution, $Pr(X=x)$, are 0. The key idea here is that this probability is uncountable.
Instead of adding to the mathematically driven answers here, I would like to connect this phenomenon... | $P[X=x]=0$ when $X$ is a continuous variable | There are many answers here which address the technical reasons for why infinitesimally small slices of a continuous probability distribution, $Pr(X=x)$, are 0. The key idea here is that this probabil | $P[X=x]=0$ when $X$ is a continuous variable
There are many answers here which address the technical reasons for why infinitesimally small slices of a continuous probability distribution, $Pr(X=x)$, are 0. The key idea here is that this probability is uncountable.
Instead of adding to the mathematically driven answers ... | $P[X=x]=0$ when $X$ is a continuous variable
There are many answers here which address the technical reasons for why infinitesimally small slices of a continuous probability distribution, $Pr(X=x)$, are 0. The key idea here is that this probabil |
13,014 | $P[X=x]=0$ when $X$ is a continuous variable | This question is very simple. PDF is the density, then to get the probability you need to multiply it by the width of the region. So, when you get a smaller region around the point of interest $x$ the height of the density doesn't change, hence the probability is smaller and smaller while you squeeze the area around yo... | $P[X=x]=0$ when $X$ is a continuous variable | This question is very simple. PDF is the density, then to get the probability you need to multiply it by the width of the region. So, when you get a smaller region around the point of interest $x$ the | $P[X=x]=0$ when $X$ is a continuous variable
This question is very simple. PDF is the density, then to get the probability you need to multiply it by the width of the region. So, when you get a smaller region around the point of interest $x$ the height of the density doesn't change, hence the probability is smaller and... | $P[X=x]=0$ when $X$ is a continuous variable
This question is very simple. PDF is the density, then to get the probability you need to multiply it by the width of the region. So, when you get a smaller region around the point of interest $x$ the |
13,015 | Fitting t-distribution in R: scaling parameter | fitdistr uses maximum-likelihood and optimization techniques to find parameters of a given distribution. Sometimes, especially for t-distribution, as @user12719 noticed, the optimization in the form:
fitdistr(x, "t")
fails with an error.
In this case you should give optimizer a hand by providing starting point and low... | Fitting t-distribution in R: scaling parameter | fitdistr uses maximum-likelihood and optimization techniques to find parameters of a given distribution. Sometimes, especially for t-distribution, as @user12719 noticed, the optimization in the form:
| Fitting t-distribution in R: scaling parameter
fitdistr uses maximum-likelihood and optimization techniques to find parameters of a given distribution. Sometimes, especially for t-distribution, as @user12719 noticed, the optimization in the form:
fitdistr(x, "t")
fails with an error.
In this case you should give optim... | Fitting t-distribution in R: scaling parameter
fitdistr uses maximum-likelihood and optimization techniques to find parameters of a given distribution. Sometimes, especially for t-distribution, as @user12719 noticed, the optimization in the form:
|
13,016 | Fitting t-distribution in R: scaling parameter | MASS, the book (4th edition, page 110) advises against trying to estimate $\nu$, the degrees of freedom parameter in the $t$-distribution with maximum likelihood (with some literature references: Lange et al. (1989), "Robust statistical modeling Using the t distribution", JASA, 84, 408, and
Fernandez & Steel (1999), "M... | Fitting t-distribution in R: scaling parameter | MASS, the book (4th edition, page 110) advises against trying to estimate $\nu$, the degrees of freedom parameter in the $t$-distribution with maximum likelihood (with some literature references: Lang | Fitting t-distribution in R: scaling parameter
MASS, the book (4th edition, page 110) advises against trying to estimate $\nu$, the degrees of freedom parameter in the $t$-distribution with maximum likelihood (with some literature references: Lange et al. (1989), "Robust statistical modeling Using the t distribution", ... | Fitting t-distribution in R: scaling parameter
MASS, the book (4th edition, page 110) advises against trying to estimate $\nu$, the degrees of freedom parameter in the $t$-distribution with maximum likelihood (with some literature references: Lang |
13,017 | Fitting t-distribution in R: scaling parameter | In the help for fitdistr is this example:
fitdistr(x2, "t", df = 9)
indicating that you just need a value for df. But that assumes standardization.
For more control, they also show
mydt <- function(x, m, s, df) dt((x-m)/s, df)/s
fitdistr(x2, mydt, list(m = 0, s = 1), df = 9, lower = c(-Inf, 0))
where the parameters w... | Fitting t-distribution in R: scaling parameter | In the help for fitdistr is this example:
fitdistr(x2, "t", df = 9)
indicating that you just need a value for df. But that assumes standardization.
For more control, they also show
mydt <- function(x | Fitting t-distribution in R: scaling parameter
In the help for fitdistr is this example:
fitdistr(x2, "t", df = 9)
indicating that you just need a value for df. But that assumes standardization.
For more control, they also show
mydt <- function(x, m, s, df) dt((x-m)/s, df)/s
fitdistr(x2, mydt, list(m = 0, s = 1), df =... | Fitting t-distribution in R: scaling parameter
In the help for fitdistr is this example:
fitdistr(x2, "t", df = 9)
indicating that you just need a value for df. But that assumes standardization.
For more control, they also show
mydt <- function(x |
13,018 | Fitting t-distribution in R: scaling parameter | You can use fitdistrplus library after extending the location and scaling parameters for the student t in base R according to this article on wikipedia. Below is sample code
library(fitdistrplus)
x<-rt(100,23)
dt_ls <- function(x, df=1, mu=0, sigma=1) 1/sigma * dt((x - mu)/sigma, df)
pt_ls <- function(q, df=1, mu=0, si... | Fitting t-distribution in R: scaling parameter | You can use fitdistrplus library after extending the location and scaling parameters for the student t in base R according to this article on wikipedia. Below is sample code
library(fitdistrplus)
x<-r | Fitting t-distribution in R: scaling parameter
You can use fitdistrplus library after extending the location and scaling parameters for the student t in base R according to this article on wikipedia. Below is sample code
library(fitdistrplus)
x<-rt(100,23)
dt_ls <- function(x, df=1, mu=0, sigma=1) 1/sigma * dt((x - mu)... | Fitting t-distribution in R: scaling parameter
You can use fitdistrplus library after extending the location and scaling parameters for the student t in base R according to this article on wikipedia. Below is sample code
library(fitdistrplus)
x<-r |
13,019 | Fitting t-distribution in R: scaling parameter | The parameters of the t-distribution are referred to as the location, scale, and degrees of freedom $\nu$. The location can be estimated by the mean of the samples if $\nu > 1$; otherwise the mean is not defined. By not defined, this means that increasing the sample size will not converge to a particular value. The s... | Fitting t-distribution in R: scaling parameter | The parameters of the t-distribution are referred to as the location, scale, and degrees of freedom $\nu$. The location can be estimated by the mean of the samples if $\nu > 1$; otherwise the mean is | Fitting t-distribution in R: scaling parameter
The parameters of the t-distribution are referred to as the location, scale, and degrees of freedom $\nu$. The location can be estimated by the mean of the samples if $\nu > 1$; otherwise the mean is not defined. By not defined, this means that increasing the sample size ... | Fitting t-distribution in R: scaling parameter
The parameters of the t-distribution are referred to as the location, scale, and degrees of freedom $\nu$. The location can be estimated by the mean of the samples if $\nu > 1$; otherwise the mean is |
13,020 | Fitting t-distribution in R: scaling parameter | @SergeyBushmanov points out that sometimes you need to give maximum likelihood estimation a hand by providing appropriate starting point and lower/upper bounds for the optimization algorithm to find the MLE.
Another way to give the likelihood a hand is to augment it with a (weakly) informative prior and do Bayesian est... | Fitting t-distribution in R: scaling parameter | @SergeyBushmanov points out that sometimes you need to give maximum likelihood estimation a hand by providing appropriate starting point and lower/upper bounds for the optimization algorithm to find t | Fitting t-distribution in R: scaling parameter
@SergeyBushmanov points out that sometimes you need to give maximum likelihood estimation a hand by providing appropriate starting point and lower/upper bounds for the optimization algorithm to find the MLE.
Another way to give the likelihood a hand is to augment it with a... | Fitting t-distribution in R: scaling parameter
@SergeyBushmanov points out that sometimes you need to give maximum likelihood estimation a hand by providing appropriate starting point and lower/upper bounds for the optimization algorithm to find t |
13,021 | Can I simply remove one of two predictor variables that are highly linearly correlated? | Both B and E are derived from V. B and E are clearly not truly "independent" variables from each other. The underlying variable that really matters here is V. You should probably disgard both B and E in this case and keep V only.
In a more general situation, when you have two independent variables that are very hi... | Can I simply remove one of two predictor variables that are highly linearly correlated? | Both B and E are derived from V. B and E are clearly not truly "independent" variables from each other. The underlying variable that really matters here is V. You should probably disgard both B and | Can I simply remove one of two predictor variables that are highly linearly correlated?
Both B and E are derived from V. B and E are clearly not truly "independent" variables from each other. The underlying variable that really matters here is V. You should probably disgard both B and E in this case and keep V only.... | Can I simply remove one of two predictor variables that are highly linearly correlated?
Both B and E are derived from V. B and E are clearly not truly "independent" variables from each other. The underlying variable that really matters here is V. You should probably disgard both B and |
13,022 | Can I simply remove one of two predictor variables that are highly linearly correlated? | Here is an answer from the point of view of a machine learner, although I am afraid that I'll be beaten by real statisticians for it.
Is it possible for me to just "throw away" one of the variables?
Well, the question is what type of model you want to use for prediction. It depends e.g. on ...
can the model with corre... | Can I simply remove one of two predictor variables that are highly linearly correlated? | Here is an answer from the point of view of a machine learner, although I am afraid that I'll be beaten by real statisticians for it.
Is it possible for me to just "throw away" one of the variables?
W | Can I simply remove one of two predictor variables that are highly linearly correlated?
Here is an answer from the point of view of a machine learner, although I am afraid that I'll be beaten by real statisticians for it.
Is it possible for me to just "throw away" one of the variables?
Well, the question is what type o... | Can I simply remove one of two predictor variables that are highly linearly correlated?
Here is an answer from the point of view of a machine learner, although I am afraid that I'll be beaten by real statisticians for it.
Is it possible for me to just "throw away" one of the variables?
W |
13,023 | Can I simply remove one of two predictor variables that are highly linearly correlated? | B is a linear transform of V. E represents an interaction between V and D. Have you considered specifying a model that is Y = Intercept + V + D + V:D? As @euphoria83 suggests, it seems likely that there is little variation in D, so it may not solve your problem; however it should at least make the independent contrib... | Can I simply remove one of two predictor variables that are highly linearly correlated? | B is a linear transform of V. E represents an interaction between V and D. Have you considered specifying a model that is Y = Intercept + V + D + V:D? As @euphoria83 suggests, it seems likely that t | Can I simply remove one of two predictor variables that are highly linearly correlated?
B is a linear transform of V. E represents an interaction between V and D. Have you considered specifying a model that is Y = Intercept + V + D + V:D? As @euphoria83 suggests, it seems likely that there is little variation in D, s... | Can I simply remove one of two predictor variables that are highly linearly correlated?
B is a linear transform of V. E represents an interaction between V and D. Have you considered specifying a model that is Y = Intercept + V + D + V:D? As @euphoria83 suggests, it seems likely that t |
13,024 | Can I simply remove one of two predictor variables that are highly linearly correlated? | If D is not a constant, then B and E are effectively two different variables because of the variations in D. The high correlation indicates that D is practically constant throughout the training data. If that is the case, then you can discard either B or E. | Can I simply remove one of two predictor variables that are highly linearly correlated? | If D is not a constant, then B and E are effectively two different variables because of the variations in D. The high correlation indicates that D is practically constant throughout the training data. | Can I simply remove one of two predictor variables that are highly linearly correlated?
If D is not a constant, then B and E are effectively two different variables because of the variations in D. The high correlation indicates that D is practically constant throughout the training data. If that is the case, then you c... | Can I simply remove one of two predictor variables that are highly linearly correlated?
If D is not a constant, then B and E are effectively two different variables because of the variations in D. The high correlation indicates that D is practically constant throughout the training data. |
13,025 | What are the mathematically rigorous data augmentation techniques? | The reason you "wish you had a million observations" is typically because you want to use the data to to infer something that you don't already know. For example, you might want to fit a model, or make predictions. In this context, the data processing inequality implies that, unfortunately, simulating additional data i... | What are the mathematically rigorous data augmentation techniques? | The reason you "wish you had a million observations" is typically because you want to use the data to to infer something that you don't already know. For example, you might want to fit a model, or mak | What are the mathematically rigorous data augmentation techniques?
The reason you "wish you had a million observations" is typically because you want to use the data to to infer something that you don't already know. For example, you might want to fit a model, or make predictions. In this context, the data processing i... | What are the mathematically rigorous data augmentation techniques?
The reason you "wish you had a million observations" is typically because you want to use the data to to infer something that you don't already know. For example, you might want to fit a model, or mak |
13,026 | What are the mathematically rigorous data augmentation techniques? | Are there any proofs that describe the most mathematically precise way to do this?
Any transformation would have some math behind it.
However, I do think image data augmentation would depend on the specific use case / domain knowledge in specific field.
For example, if we want to detect dog or cat, we can flip image... | What are the mathematically rigorous data augmentation techniques? | Are there any proofs that describe the most mathematically precise way to do this?
Any transformation would have some math behind it.
However, I do think image data augmentation would depend on the | What are the mathematically rigorous data augmentation techniques?
Are there any proofs that describe the most mathematically precise way to do this?
Any transformation would have some math behind it.
However, I do think image data augmentation would depend on the specific use case / domain knowledge in specific fiel... | What are the mathematically rigorous data augmentation techniques?
Are there any proofs that describe the most mathematically precise way to do this?
Any transformation would have some math behind it.
However, I do think image data augmentation would depend on the |
13,027 | What are the mathematically rigorous data augmentation techniques? | The question is, why do you want to do data augmentation?
Of course, more data is better, but your augmented dataset is redundant: your million augmented data points are not as good as a million actual data points.
An alternative way of thinking of data augmentation is in terms of teaching invariances.
For example, CNN... | What are the mathematically rigorous data augmentation techniques? | The question is, why do you want to do data augmentation?
Of course, more data is better, but your augmented dataset is redundant: your million augmented data points are not as good as a million actua | What are the mathematically rigorous data augmentation techniques?
The question is, why do you want to do data augmentation?
Of course, more data is better, but your augmented dataset is redundant: your million augmented data points are not as good as a million actual data points.
An alternative way of thinking of data... | What are the mathematically rigorous data augmentation techniques?
The question is, why do you want to do data augmentation?
Of course, more data is better, but your augmented dataset is redundant: your million augmented data points are not as good as a million actua |
13,028 | How to understand the drawbacks of Hierarchical Clustering? | Whereas $k$-means tries to optimize a global goal (variance of the clusters) and achieves a local optimum, agglomerative hierarchical clustering aims at finding the best step at each cluster fusion (greedy algorithm) which is done exactly but resulting in a potentially suboptimal solution.
One should use hierarchical c... | How to understand the drawbacks of Hierarchical Clustering? | Whereas $k$-means tries to optimize a global goal (variance of the clusters) and achieves a local optimum, agglomerative hierarchical clustering aims at finding the best step at each cluster fusion (g | How to understand the drawbacks of Hierarchical Clustering?
Whereas $k$-means tries to optimize a global goal (variance of the clusters) and achieves a local optimum, agglomerative hierarchical clustering aims at finding the best step at each cluster fusion (greedy algorithm) which is done exactly but resulting in a po... | How to understand the drawbacks of Hierarchical Clustering?
Whereas $k$-means tries to optimize a global goal (variance of the clusters) and achieves a local optimum, agglomerative hierarchical clustering aims at finding the best step at each cluster fusion (g |
13,029 | How to understand the drawbacks of Hierarchical Clustering? | Scalability
$k$ means is the clear winner here. $O(n\cdot k\cdot d\cdot i)$ is much better than the $O(n^3 d)$ (in a few cases $O(n^2 d)$) scalability of hierarchical clustering because usually both $k$ and $i$ and $d$ are small (unfortunately, $i$ tends to grow with $n$, so $O(n)$ does not usually hold). Also, memory ... | How to understand the drawbacks of Hierarchical Clustering? | Scalability
$k$ means is the clear winner here. $O(n\cdot k\cdot d\cdot i)$ is much better than the $O(n^3 d)$ (in a few cases $O(n^2 d)$) scalability of hierarchical clustering because usually both $ | How to understand the drawbacks of Hierarchical Clustering?
Scalability
$k$ means is the clear winner here. $O(n\cdot k\cdot d\cdot i)$ is much better than the $O(n^3 d)$ (in a few cases $O(n^2 d)$) scalability of hierarchical clustering because usually both $k$ and $i$ and $d$ are small (unfortunately, $i$ tends to gr... | How to understand the drawbacks of Hierarchical Clustering?
Scalability
$k$ means is the clear winner here. $O(n\cdot k\cdot d\cdot i)$ is much better than the $O(n^3 d)$ (in a few cases $O(n^2 d)$) scalability of hierarchical clustering because usually both $ |
13,030 | How to understand the drawbacks of Hierarchical Clustering? | I just wanted to add to the other answers a bit about how, in some sense, there is a strong theoretical reason to prefer certain hierarchical clustering methods.
A common assumption in cluster analysis is that the data are sampled from some underlying probability density $f$ that we don't have access to. But suppose we... | How to understand the drawbacks of Hierarchical Clustering? | I just wanted to add to the other answers a bit about how, in some sense, there is a strong theoretical reason to prefer certain hierarchical clustering methods.
A common assumption in cluster analysi | How to understand the drawbacks of Hierarchical Clustering?
I just wanted to add to the other answers a bit about how, in some sense, there is a strong theoretical reason to prefer certain hierarchical clustering methods.
A common assumption in cluster analysis is that the data are sampled from some underlying probabil... | How to understand the drawbacks of Hierarchical Clustering?
I just wanted to add to the other answers a bit about how, in some sense, there is a strong theoretical reason to prefer certain hierarchical clustering methods.
A common assumption in cluster analysi |
13,031 | How to understand the drawbacks of Hierarchical Clustering? | An additional practical advantage in hierarchical clustering is the possibility of visualising results using dendrogram. If you don't know in advance what number of clusters you're looking for (as is often the case...), you can the dendrogram plot can help you choose $k$ with no need to create separate clusterings. Ded... | How to understand the drawbacks of Hierarchical Clustering? | An additional practical advantage in hierarchical clustering is the possibility of visualising results using dendrogram. If you don't know in advance what number of clusters you're looking for (as is | How to understand the drawbacks of Hierarchical Clustering?
An additional practical advantage in hierarchical clustering is the possibility of visualising results using dendrogram. If you don't know in advance what number of clusters you're looking for (as is often the case...), you can the dendrogram plot can help you... | How to understand the drawbacks of Hierarchical Clustering?
An additional practical advantage in hierarchical clustering is the possibility of visualising results using dendrogram. If you don't know in advance what number of clusters you're looking for (as is |
13,032 | Do the pdf and the pmf and the cdf contain the same information? | Where a distinction is made between probability function and density*, the pmf applies only to discrete random variables, while the pdf applies to continuous random variables.
* formal approaches can encompass both and use a single term for them
The cdf applies to any random variables, including ones that have neither ... | Do the pdf and the pmf and the cdf contain the same information? | Where a distinction is made between probability function and density*, the pmf applies only to discrete random variables, while the pdf applies to continuous random variables.
* formal approaches can | Do the pdf and the pmf and the cdf contain the same information?
Where a distinction is made between probability function and density*, the pmf applies only to discrete random variables, while the pdf applies to continuous random variables.
* formal approaches can encompass both and use a single term for them
The cdf a... | Do the pdf and the pmf and the cdf contain the same information?
Where a distinction is made between probability function and density*, the pmf applies only to discrete random variables, while the pdf applies to continuous random variables.
* formal approaches can |
13,033 | Do the pdf and the pmf and the cdf contain the same information? | PMFs are associated with discrete random variables, PDFs with continuous random variables. For any type of random of random variable, the CDF always exists (and is unique), defined as $$F_X(x) = P\{X \leq x\}.$$
Now, depending on the support set of the random variable $X$, the density (or mass function) need not exist... | Do the pdf and the pmf and the cdf contain the same information? | PMFs are associated with discrete random variables, PDFs with continuous random variables. For any type of random of random variable, the CDF always exists (and is unique), defined as $$F_X(x) = P\{X | Do the pdf and the pmf and the cdf contain the same information?
PMFs are associated with discrete random variables, PDFs with continuous random variables. For any type of random of random variable, the CDF always exists (and is unique), defined as $$F_X(x) = P\{X \leq x\}.$$
Now, depending on the support set of the r... | Do the pdf and the pmf and the cdf contain the same information?
PMFs are associated with discrete random variables, PDFs with continuous random variables. For any type of random of random variable, the CDF always exists (and is unique), defined as $$F_X(x) = P\{X |
13,034 | Do the pdf and the pmf and the cdf contain the same information? | The other answers point to the fact that CDFs are fundamental and must exist, whereas PDFs and PMFs are not and do not necessarily exist.
This confused and intrigued me (being a non-statistician), as I did not know how to interpret a CDF (or how it might exist) when the sample space was not ordered; think, for example,... | Do the pdf and the pmf and the cdf contain the same information? | The other answers point to the fact that CDFs are fundamental and must exist, whereas PDFs and PMFs are not and do not necessarily exist.
This confused and intrigued me (being a non-statistician), as | Do the pdf and the pmf and the cdf contain the same information?
The other answers point to the fact that CDFs are fundamental and must exist, whereas PDFs and PMFs are not and do not necessarily exist.
This confused and intrigued me (being a non-statistician), as I did not know how to interpret a CDF (or how it might ... | Do the pdf and the pmf and the cdf contain the same information?
The other answers point to the fact that CDFs are fundamental and must exist, whereas PDFs and PMFs are not and do not necessarily exist.
This confused and intrigued me (being a non-statistician), as |
13,035 | Any suggestions for a good undergraduate introductory textbook to statistics? | Statistics, by Freedman, Pisani, & Purves, originated from a popular and successful course taught at U.C. Berkeley. I have used it as an intro stats text for undergraduates, have borrowed some of its ideas when teaching graduate stats courses, and have given away many copies to colleagues and clients. There are many ... | Any suggestions for a good undergraduate introductory textbook to statistics? | Statistics, by Freedman, Pisani, & Purves, originated from a popular and successful course taught at U.C. Berkeley. I have used it as an intro stats text for undergraduates, have borrowed some of its | Any suggestions for a good undergraduate introductory textbook to statistics?
Statistics, by Freedman, Pisani, & Purves, originated from a popular and successful course taught at U.C. Berkeley. I have used it as an intro stats text for undergraduates, have borrowed some of its ideas when teaching graduate stats course... | Any suggestions for a good undergraduate introductory textbook to statistics?
Statistics, by Freedman, Pisani, & Purves, originated from a popular and successful course taught at U.C. Berkeley. I have used it as an intro stats text for undergraduates, have borrowed some of its |
13,036 | Any suggestions for a good undergraduate introductory textbook to statistics? | I read Freedman (almost the entire book) and OpenIntro Statistics (more than a third). Both of these books are quite good.
I eventually found the book that came close to what I was looking for: Learning Statistics with R: A tutorial for psychology students and other beginners by Danielle Navarro. It is freely available... | Any suggestions for a good undergraduate introductory textbook to statistics? | I read Freedman (almost the entire book) and OpenIntro Statistics (more than a third). Both of these books are quite good.
I eventually found the book that came close to what I was looking for: Learni | Any suggestions for a good undergraduate introductory textbook to statistics?
I read Freedman (almost the entire book) and OpenIntro Statistics (more than a third). Both of these books are quite good.
I eventually found the book that came close to what I was looking for: Learning Statistics with R: A tutorial for psych... | Any suggestions for a good undergraduate introductory textbook to statistics?
I read Freedman (almost the entire book) and OpenIntro Statistics (more than a third). Both of these books are quite good.
I eventually found the book that came close to what I was looking for: Learni |
13,037 | Any suggestions for a good undergraduate introductory textbook to statistics? | Thom Baguley, an outgoing editor of The British Journal of Mathematical and Statistical Psychology, published Serious Stats book that you could find useful. It relies on R rather than SPSS, though.
I am suspicious of the books that are in their 7th edition. In my teaching experience, it means that the sections and prob... | Any suggestions for a good undergraduate introductory textbook to statistics? | Thom Baguley, an outgoing editor of The British Journal of Mathematical and Statistical Psychology, published Serious Stats book that you could find useful. It relies on R rather than SPSS, though.
I | Any suggestions for a good undergraduate introductory textbook to statistics?
Thom Baguley, an outgoing editor of The British Journal of Mathematical and Statistical Psychology, published Serious Stats book that you could find useful. It relies on R rather than SPSS, though.
I am suspicious of the books that are in the... | Any suggestions for a good undergraduate introductory textbook to statistics?
Thom Baguley, an outgoing editor of The British Journal of Mathematical and Statistical Psychology, published Serious Stats book that you could find useful. It relies on R rather than SPSS, though.
I |
13,038 | Any suggestions for a good undergraduate introductory textbook to statistics? | Statistics Unplugged is a great book for introductory statistics. The author first introduces the logic of the statistical test and later gives the mathematical formula. This approach helps in digesting the new concepts. There are several examples throughout the book which are presented in the form of a problem require... | Any suggestions for a good undergraduate introductory textbook to statistics? | Statistics Unplugged is a great book for introductory statistics. The author first introduces the logic of the statistical test and later gives the mathematical formula. This approach helps in digesti | Any suggestions for a good undergraduate introductory textbook to statistics?
Statistics Unplugged is a great book for introductory statistics. The author first introduces the logic of the statistical test and later gives the mathematical formula. This approach helps in digesting the new concepts. There are several exa... | Any suggestions for a good undergraduate introductory textbook to statistics?
Statistics Unplugged is a great book for introductory statistics. The author first introduces the logic of the statistical test and later gives the mathematical formula. This approach helps in digesti |
13,039 | Any suggestions for a good undergraduate introductory textbook to statistics? | How about The Statistical Sleuth by Ramsey and Schafer?
I think this book gets at some important points without either a) Too much math or b) dumbing things down.
I would suggest that an intro stats course for psychology and other social science types should emphasize how not to go wrong too much. A survey of methods w... | Any suggestions for a good undergraduate introductory textbook to statistics? | How about The Statistical Sleuth by Ramsey and Schafer?
I think this book gets at some important points without either a) Too much math or b) dumbing things down.
I would suggest that an intro stats c | Any suggestions for a good undergraduate introductory textbook to statistics?
How about The Statistical Sleuth by Ramsey and Schafer?
I think this book gets at some important points without either a) Too much math or b) dumbing things down.
I would suggest that an intro stats course for psychology and other social scie... | Any suggestions for a good undergraduate introductory textbook to statistics?
How about The Statistical Sleuth by Ramsey and Schafer?
I think this book gets at some important points without either a) Too much math or b) dumbing things down.
I would suggest that an intro stats c |
13,040 | Any suggestions for a good undergraduate introductory textbook to statistics? | Check out the introductory statistics book, Making Sense of Data through Statistics: An Introduction (2014) by Dorit Nevo. It is written in an extremely accessible manner and is meant for undergraduate or graduate students in business and in the social sciences. The textbook makes use of examples meaningful to today’... | Any suggestions for a good undergraduate introductory textbook to statistics? | Check out the introductory statistics book, Making Sense of Data through Statistics: An Introduction (2014) by Dorit Nevo. It is written in an extremely accessible manner and is meant for undergradua | Any suggestions for a good undergraduate introductory textbook to statistics?
Check out the introductory statistics book, Making Sense of Data through Statistics: An Introduction (2014) by Dorit Nevo. It is written in an extremely accessible manner and is meant for undergraduate or graduate students in business and in... | Any suggestions for a good undergraduate introductory textbook to statistics?
Check out the introductory statistics book, Making Sense of Data through Statistics: An Introduction (2014) by Dorit Nevo. It is written in an extremely accessible manner and is meant for undergradua |
13,041 | Any suggestions for a good undergraduate introductory textbook to statistics? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Here is a list of books. Puzzles/riddles are a great w... | Any suggestions for a good undergraduate introductory textbook to statistics? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Any suggestions for a good undergraduate introductory textbook to statistics?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | Any suggestions for a good undergraduate introductory textbook to statistics?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
13,042 | Any suggestions for a good undergraduate introductory textbook to statistics? | I have been a TA, observer, or student in a lot of courses involving quantitative methods for psychology, with SPSS as the main program. In all cases it has seemed to me that students have gravitated towards Field (2013), irrespective of whether the course coordinator has mentioned this book or not. In numerous cases s... | Any suggestions for a good undergraduate introductory textbook to statistics? | I have been a TA, observer, or student in a lot of courses involving quantitative methods for psychology, with SPSS as the main program. In all cases it has seemed to me that students have gravitated | Any suggestions for a good undergraduate introductory textbook to statistics?
I have been a TA, observer, or student in a lot of courses involving quantitative methods for psychology, with SPSS as the main program. In all cases it has seemed to me that students have gravitated towards Field (2013), irrespective of whet... | Any suggestions for a good undergraduate introductory textbook to statistics?
I have been a TA, observer, or student in a lot of courses involving quantitative methods for psychology, with SPSS as the main program. In all cases it has seemed to me that students have gravitated |
13,043 | Any suggestions for a good undergraduate introductory textbook to statistics? | Statistics for College Students and Researchers: Grasping the Concepts, Paperback 2010, ISBN-13 : 978-1453604533 is perhaps the easiest and most comprehensive stat book for college students. "grasping the concepts and the logic of Statistics. Formulas do not lead to understanding, they actually prevent it. This book t... | Any suggestions for a good undergraduate introductory textbook to statistics? | Statistics for College Students and Researchers: Grasping the Concepts, Paperback 2010, ISBN-13 : 978-1453604533 is perhaps the easiest and most comprehensive stat book for college students. "graspin | Any suggestions for a good undergraduate introductory textbook to statistics?
Statistics for College Students and Researchers: Grasping the Concepts, Paperback 2010, ISBN-13 : 978-1453604533 is perhaps the easiest and most comprehensive stat book for college students. "grasping the concepts and the logic of Statistics... | Any suggestions for a good undergraduate introductory textbook to statistics?
Statistics for College Students and Researchers: Grasping the Concepts, Paperback 2010, ISBN-13 : 978-1453604533 is perhaps the easiest and most comprehensive stat book for college students. "graspin |
13,044 | Any suggestions for a good undergraduate introductory textbook to statistics? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
http://onlinestatbook.com/index.html is a very nice so... | Any suggestions for a good undergraduate introductory textbook to statistics? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Any suggestions for a good undergraduate introductory textbook to statistics?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | Any suggestions for a good undergraduate introductory textbook to statistics?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
13,045 | Mean and Median properties | This is two questions: one about how the mean and median minimize loss functions and another about the sensitivities of these estimates to the data. The two questions are connected, as we will see.
Minimizing Loss
A summary (or estimator) of the center of a batch of numbers can be created by letting the summary value ... | Mean and Median properties | This is two questions: one about how the mean and median minimize loss functions and another about the sensitivities of these estimates to the data. The two questions are connected, as we will see.
M | Mean and Median properties
This is two questions: one about how the mean and median minimize loss functions and another about the sensitivities of these estimates to the data. The two questions are connected, as we will see.
Minimizing Loss
A summary (or estimator) of the center of a batch of numbers can be created by... | Mean and Median properties
This is two questions: one about how the mean and median minimize loss functions and another about the sensitivities of these estimates to the data. The two questions are connected, as we will see.
M |
13,046 | Mean and Median properties | For the computation of the median, let $x_1,x_2,\ldots,x_n$ be the data. Assume, for simplicity, that $n$ is even, and the points are distinct! Let $y$ be some number. Let $f(y)$ be the 'sum-of-absolute deviations' of $y$ to the points $x_i$. This means that $f(y) = |x_1 - y| + |x_2 - y| + \ldots + |x_n - y|$. Your goa... | Mean and Median properties | For the computation of the median, let $x_1,x_2,\ldots,x_n$ be the data. Assume, for simplicity, that $n$ is even, and the points are distinct! Let $y$ be some number. Let $f(y)$ be the 'sum-of-absolu | Mean and Median properties
For the computation of the median, let $x_1,x_2,\ldots,x_n$ be the data. Assume, for simplicity, that $n$ is even, and the points are distinct! Let $y$ be some number. Let $f(y)$ be the 'sum-of-absolute deviations' of $y$ to the points $x_i$. This means that $f(y) = |x_1 - y| + |x_2 - y| + \l... | Mean and Median properties
For the computation of the median, let $x_1,x_2,\ldots,x_n$ be the data. Assume, for simplicity, that $n$ is even, and the points are distinct! Let $y$ be some number. Let $f(y)$ be the 'sum-of-absolu |
13,047 | Mean and Median properties | Roughly speaking, the median is the "middle value". Now, if you change the highest value (which is supposed to be positive here) from $x_{(n)}$ to $2 * x_{(n)}$, say, it does not change the median. But it does change the arithmetic mean. This shows, in simple terms, that the median does not depend on every value while... | Mean and Median properties | Roughly speaking, the median is the "middle value". Now, if you change the highest value (which is supposed to be positive here) from $x_{(n)}$ to $2 * x_{(n)}$, say, it does not change the median. B | Mean and Median properties
Roughly speaking, the median is the "middle value". Now, if you change the highest value (which is supposed to be positive here) from $x_{(n)}$ to $2 * x_{(n)}$, say, it does not change the median. But it does change the arithmetic mean. This shows, in simple terms, that the median does not ... | Mean and Median properties
Roughly speaking, the median is the "middle value". Now, if you change the highest value (which is supposed to be positive here) from $x_{(n)}$ to $2 * x_{(n)}$, say, it does not change the median. B |
13,048 | Mean and Median properties | Hey here is a contribution, after I read about it a bit. Probably a bit late for the person who asked, but maybe worth for someone else.
For the mean case :
Consider the problem $argmin_x \sum_{i=1}^n (y_i - x)$
Introduce $f(x) = \sum_{i=1}^n(y_i - x)^2$
$f'(x)=0 \Leftrightarrow 2 \sum_{i=1}^n (y_i - x ) = 0$
$f'(x)=0... | Mean and Median properties | Hey here is a contribution, after I read about it a bit. Probably a bit late for the person who asked, but maybe worth for someone else.
For the mean case :
Consider the problem $argmin_x \sum_{i=1}^ | Mean and Median properties
Hey here is a contribution, after I read about it a bit. Probably a bit late for the person who asked, but maybe worth for someone else.
For the mean case :
Consider the problem $argmin_x \sum_{i=1}^n (y_i - x)$
Introduce $f(x) = \sum_{i=1}^n(y_i - x)^2$
$f'(x)=0 \Leftrightarrow 2 \sum_{i=1}... | Mean and Median properties
Hey here is a contribution, after I read about it a bit. Probably a bit late for the person who asked, but maybe worth for someone else.
For the mean case :
Consider the problem $argmin_x \sum_{i=1}^ |
13,049 | Why is GLM different than an LM with transformed variable | Transforming the response prior to doing a linear regression is doing this:
$$E(g(Y)) \sim \beta_0 + \beta_1x_1 + \ldots + \beta_px_p$$
where $g$ is a given function, and we assume that $g(Y)$ has a given distribution (usually normal).
A generalised linear model is doing this:
$$g(E(Y)) \sim \beta_0 + \beta_1x_1 + \ldo... | Why is GLM different than an LM with transformed variable | Transforming the response prior to doing a linear regression is doing this:
$$E(g(Y)) \sim \beta_0 + \beta_1x_1 + \ldots + \beta_px_p$$
where $g$ is a given function, and we assume that $g(Y)$ has a g | Why is GLM different than an LM with transformed variable
Transforming the response prior to doing a linear regression is doing this:
$$E(g(Y)) \sim \beta_0 + \beta_1x_1 + \ldots + \beta_px_p$$
where $g$ is a given function, and we assume that $g(Y)$ has a given distribution (usually normal).
A generalised linear model... | Why is GLM different than an LM with transformed variable
Transforming the response prior to doing a linear regression is doing this:
$$E(g(Y)) \sim \beta_0 + \beta_1x_1 + \ldots + \beta_px_p$$
where $g$ is a given function, and we assume that $g(Y)$ has a g |
13,050 | Why is GLM different than an LM with transformed variable | I'm not sure if this will constitute a complete answer for you, but it may help break free the conceptual logjam.
There seem to be two misconceptions in your account:
Bear in mind that ordinary least squares (OLS--'linear') regression is a special case of the generalized linear model. Thus, when you say "[t]ransformi... | Why is GLM different than an LM with transformed variable | I'm not sure if this will constitute a complete answer for you, but it may help break free the conceptual logjam.
There seem to be two misconceptions in your account:
Bear in mind that ordinary least | Why is GLM different than an LM with transformed variable
I'm not sure if this will constitute a complete answer for you, but it may help break free the conceptual logjam.
There seem to be two misconceptions in your account:
Bear in mind that ordinary least squares (OLS--'linear') regression is a special case of the g... | Why is GLM different than an LM with transformed variable
I'm not sure if this will constitute a complete answer for you, but it may help break free the conceptual logjam.
There seem to be two misconceptions in your account:
Bear in mind that ordinary least |
13,051 | Can I ignore coefficients for non-significant levels of factors in a linear model? | If you are putting in a predictor variable with multiple levels, you either put in the variable or you don't, you can't pick and choose levels. You might want to restructure the levels of your predictor variable to decrease the number of levels (if that makes sense in the context of your analysis.)
However, I'm not su... | Can I ignore coefficients for non-significant levels of factors in a linear model? | If you are putting in a predictor variable with multiple levels, you either put in the variable or you don't, you can't pick and choose levels. You might want to restructure the levels of your predict | Can I ignore coefficients for non-significant levels of factors in a linear model?
If you are putting in a predictor variable with multiple levels, you either put in the variable or you don't, you can't pick and choose levels. You might want to restructure the levels of your predictor variable to decrease the number of... | Can I ignore coefficients for non-significant levels of factors in a linear model?
If you are putting in a predictor variable with multiple levels, you either put in the variable or you don't, you can't pick and choose levels. You might want to restructure the levels of your predict |
13,052 | Can I ignore coefficients for non-significant levels of factors in a linear model? | @Ellie's response is a good one.
If you are putting in a variable with a number of levels, you need to retain all those levels in your analysis. Picking and choosing based on significance level will both bias your results and do very weird things to your inference, even if by some miracle your estimates manage to stay ... | Can I ignore coefficients for non-significant levels of factors in a linear model? | @Ellie's response is a good one.
If you are putting in a variable with a number of levels, you need to retain all those levels in your analysis. Picking and choosing based on significance level will b | Can I ignore coefficients for non-significant levels of factors in a linear model?
@Ellie's response is a good one.
If you are putting in a variable with a number of levels, you need to retain all those levels in your analysis. Picking and choosing based on significance level will both bias your results and do very wei... | Can I ignore coefficients for non-significant levels of factors in a linear model?
@Ellie's response is a good one.
If you are putting in a variable with a number of levels, you need to retain all those levels in your analysis. Picking and choosing based on significance level will b |
13,053 | Can I ignore coefficients for non-significant levels of factors in a linear model? | Expanding on the two good answers you've already gotten, let's look at this substantively. Suppose your dependent variable is (say) income and your independent variable is (say) ethnicity, with levels, per census definitions (White, Black/Afr.Am., Am. Indian/Alaska Native, Asian, Native Hawaii/Pac Islander, other and m... | Can I ignore coefficients for non-significant levels of factors in a linear model? | Expanding on the two good answers you've already gotten, let's look at this substantively. Suppose your dependent variable is (say) income and your independent variable is (say) ethnicity, with levels | Can I ignore coefficients for non-significant levels of factors in a linear model?
Expanding on the two good answers you've already gotten, let's look at this substantively. Suppose your dependent variable is (say) income and your independent variable is (say) ethnicity, with levels, per census definitions (White, Blac... | Can I ignore coefficients for non-significant levels of factors in a linear model?
Expanding on the two good answers you've already gotten, let's look at this substantively. Suppose your dependent variable is (say) income and your independent variable is (say) ethnicity, with levels |
13,054 | Can I ignore coefficients for non-significant levels of factors in a linear model? | To give a different opinion: why not include it as a random effect? That should penalize those levels with weak support and make sure their effect size is minimal. That way you can keep them all in without worrying about getting silly predictions.
And yes, this is more motivated from a Bayesian view of random effect... | Can I ignore coefficients for non-significant levels of factors in a linear model? | To give a different opinion: why not include it as a random effect? That should penalize those levels with weak support and make sure their effect size is minimal. That way you can keep them all in | Can I ignore coefficients for non-significant levels of factors in a linear model?
To give a different opinion: why not include it as a random effect? That should penalize those levels with weak support and make sure their effect size is minimal. That way you can keep them all in without worrying about getting silly... | Can I ignore coefficients for non-significant levels of factors in a linear model?
To give a different opinion: why not include it as a random effect? That should penalize those levels with weak support and make sure their effect size is minimal. That way you can keep them all in |
13,055 | Can I ignore coefficients for non-significant levels of factors in a linear model? | I was also wondering whether I could combine non-significant categories with the reference category. The following statements in the book "Data Mining for Business Intelligence: Concepts, Techniques, and Applications in Microsoft Office Excel® with XLMiner®, 2nd Edition by Galit Shmueli, Nitin R. Patel, Peter C. Bruce... | Can I ignore coefficients for non-significant levels of factors in a linear model? | I was also wondering whether I could combine non-significant categories with the reference category. The following statements in the book "Data Mining for Business Intelligence: Concepts, Techniques, | Can I ignore coefficients for non-significant levels of factors in a linear model?
I was also wondering whether I could combine non-significant categories with the reference category. The following statements in the book "Data Mining for Business Intelligence: Concepts, Techniques, and Applications in Microsoft Office... | Can I ignore coefficients for non-significant levels of factors in a linear model?
I was also wondering whether I could combine non-significant categories with the reference category. The following statements in the book "Data Mining for Business Intelligence: Concepts, Techniques, |
13,056 | Can someone give the intuition behind Mean Absolute Error and the Median? [duplicate] | Here is an intuitive argument with light math. Let's say we have a $d$ claiming to be minimizing the MAE of points $x_i$. And, let's say we have $n_l$ and $n_r$ points on its left and right. If we move $d$ slightly left, i.e. an amount of $\Delta$, then all the absolute differences on the left will decrease by $\Delta$... | Can someone give the intuition behind Mean Absolute Error and the Median? [duplicate] | Here is an intuitive argument with light math. Let's say we have a $d$ claiming to be minimizing the MAE of points $x_i$. And, let's say we have $n_l$ and $n_r$ points on its left and right. If we mov | Can someone give the intuition behind Mean Absolute Error and the Median? [duplicate]
Here is an intuitive argument with light math. Let's say we have a $d$ claiming to be minimizing the MAE of points $x_i$. And, let's say we have $n_l$ and $n_r$ points on its left and right. If we move $d$ slightly left, i.e. an amoun... | Can someone give the intuition behind Mean Absolute Error and the Median? [duplicate]
Here is an intuitive argument with light math. Let's say we have a $d$ claiming to be minimizing the MAE of points $x_i$. And, let's say we have $n_l$ and $n_r$ points on its left and right. If we mov |
13,057 | Can someone give the intuition behind Mean Absolute Error and the Median? [duplicate] | gunes has already presented a wonderful answer with simple formulas. Here is my a numerical example to test it: consider the set {1, 1, 1, 1, 1, 1, 1, 1, 1, 11}; that is, nine 1s and a single 11. The mean is 2, the median is 1.
When you consider the sum of absolute values as the sum of distances, the median will have 0... | Can someone give the intuition behind Mean Absolute Error and the Median? [duplicate] | gunes has already presented a wonderful answer with simple formulas. Here is my a numerical example to test it: consider the set {1, 1, 1, 1, 1, 1, 1, 1, 1, 11}; that is, nine 1s and a single 11. The | Can someone give the intuition behind Mean Absolute Error and the Median? [duplicate]
gunes has already presented a wonderful answer with simple formulas. Here is my a numerical example to test it: consider the set {1, 1, 1, 1, 1, 1, 1, 1, 1, 11}; that is, nine 1s and a single 11. The mean is 2, the median is 1.
When y... | Can someone give the intuition behind Mean Absolute Error and the Median? [duplicate]
gunes has already presented a wonderful answer with simple formulas. Here is my a numerical example to test it: consider the set {1, 1, 1, 1, 1, 1, 1, 1, 1, 11}; that is, nine 1s and a single 11. The |
13,058 | Are there any versions of t-SNE for streaming data? | I had exactly the same question and posted it on a YouTube video of a CS231n lecture given by Andrej Karpathy a few weeks ago. Here is the question I posted followed by Andrej' response:
https://www.youtube.com/watch?v=ta5fdaqDT3M&lc=z12ji3arguzwgxdm422gxnf54xaluzhcx
Q:
Does t-SNE need an entire batch of images (or mo... | Are there any versions of t-SNE for streaming data? | I had exactly the same question and posted it on a YouTube video of a CS231n lecture given by Andrej Karpathy a few weeks ago. Here is the question I posted followed by Andrej' response:
https://www.y | Are there any versions of t-SNE for streaming data?
I had exactly the same question and posted it on a YouTube video of a CS231n lecture given by Andrej Karpathy a few weeks ago. Here is the question I posted followed by Andrej' response:
https://www.youtube.com/watch?v=ta5fdaqDT3M&lc=z12ji3arguzwgxdm422gxnf54xaluzhcx
... | Are there any versions of t-SNE for streaming data?
I had exactly the same question and posted it on a YouTube video of a CS231n lecture given by Andrej Karpathy a few weeks ago. Here is the question I posted followed by Andrej' response:
https://www.y |
13,059 | Are there any versions of t-SNE for streaming data? | When dealing with streaming data, you might not want/need to embed all the points in history in a single t-SNE map. As an alternative, you can perform an online embedding by following these simple steps:
choose a time-window of duration T, long enough so that each pattern of interest appears at least a couple of times... | Are there any versions of t-SNE for streaming data? | When dealing with streaming data, you might not want/need to embed all the points in history in a single t-SNE map. As an alternative, you can perform an online embedding by following these simple ste | Are there any versions of t-SNE for streaming data?
When dealing with streaming data, you might not want/need to embed all the points in history in a single t-SNE map. As an alternative, you can perform an online embedding by following these simple steps:
choose a time-window of duration T, long enough so that each pa... | Are there any versions of t-SNE for streaming data?
When dealing with streaming data, you might not want/need to embed all the points in history in a single t-SNE map. As an alternative, you can perform an online embedding by following these simple ste |
13,060 | Are there any versions of t-SNE for streaming data? | There is a recently published variant, called A-tSNE, which supports dynamically adding new data and refining clusters either based on interest areas or by user input. The paper linked below has some pretty nice examples of this:
Citation: arXiv:1512.01655
Approximated and User Steerable tSNE for Progressive Visual A... | Are there any versions of t-SNE for streaming data? | There is a recently published variant, called A-tSNE, which supports dynamically adding new data and refining clusters either based on interest areas or by user input. The paper linked below has some | Are there any versions of t-SNE for streaming data?
There is a recently published variant, called A-tSNE, which supports dynamically adding new data and refining clusters either based on interest areas or by user input. The paper linked below has some pretty nice examples of this:
Citation: arXiv:1512.01655
Approxima... | Are there any versions of t-SNE for streaming data?
There is a recently published variant, called A-tSNE, which supports dynamically adding new data and refining clusters either based on interest areas or by user input. The paper linked below has some |
13,061 | Are there any versions of t-SNE for streaming data? | The Barnes-Hut approximation makes t-SNE highly scalable (at least, you can use it with 100 000 lines, I tried it). You can call it from R : Rtsne
The complexity of the implemented algorithm is $O(n\log(n))$ whereas the naive implementation had a complexity of $O(n^2)$. The details of the underlying approximation can b... | Are there any versions of t-SNE for streaming data? | The Barnes-Hut approximation makes t-SNE highly scalable (at least, you can use it with 100 000 lines, I tried it). You can call it from R : Rtsne
The complexity of the implemented algorithm is $O(n\l | Are there any versions of t-SNE for streaming data?
The Barnes-Hut approximation makes t-SNE highly scalable (at least, you can use it with 100 000 lines, I tried it). You can call it from R : Rtsne
The complexity of the implemented algorithm is $O(n\log(n))$ whereas the naive implementation had a complexity of $O(n^2)... | Are there any versions of t-SNE for streaming data?
The Barnes-Hut approximation makes t-SNE highly scalable (at least, you can use it with 100 000 lines, I tried it). You can call it from R : Rtsne
The complexity of the implemented algorithm is $O(n\l |
13,062 | Are there any versions of t-SNE for streaming data? | Barnes-Hut approximation is now the default method in scikit-learn as of version 0.17.0:
By default the gradient calculation algorithm uses Barnes-Hut
approximation running in O(NlogN) time. method=’exact’ will run on the
slower, but exact, algorithm in O(N^2) time. The exact algorithm
should be used when neares... | Are there any versions of t-SNE for streaming data? | Barnes-Hut approximation is now the default method in scikit-learn as of version 0.17.0:
By default the gradient calculation algorithm uses Barnes-Hut
approximation running in O(NlogN) time. method | Are there any versions of t-SNE for streaming data?
Barnes-Hut approximation is now the default method in scikit-learn as of version 0.17.0:
By default the gradient calculation algorithm uses Barnes-Hut
approximation running in O(NlogN) time. method=’exact’ will run on the
slower, but exact, algorithm in O(N^2) ti... | Are there any versions of t-SNE for streaming data?
Barnes-Hut approximation is now the default method in scikit-learn as of version 0.17.0:
By default the gradient calculation algorithm uses Barnes-Hut
approximation running in O(NlogN) time. method |
13,063 | Meaning of completeness of a statistic? [duplicate] | This is a very good question and one I've struggled with for quite some time. Here's how I've decided to think about it:
Take the contrapositive of the definition as stated in Wikipedia (which doesn't change the logical meaning at all):
\begin{align}
{\rm If}\quad &\neg\ \forall \theta\ P(g(T(x))=0)=1 \\
{\rm then}\... | Meaning of completeness of a statistic? [duplicate] | This is a very good question and one I've struggled with for quite some time. Here's how I've decided to think about it:
Take the contrapositive of the definition as stated in Wikipedia (which doesn't | Meaning of completeness of a statistic? [duplicate]
This is a very good question and one I've struggled with for quite some time. Here's how I've decided to think about it:
Take the contrapositive of the definition as stated in Wikipedia (which doesn't change the logical meaning at all):
\begin{align}
{\rm If}\quad &... | Meaning of completeness of a statistic? [duplicate]
This is a very good question and one I've struggled with for quite some time. Here's how I've decided to think about it:
Take the contrapositive of the definition as stated in Wikipedia (which doesn't |
13,064 | Meaning of completeness of a statistic? [duplicate] | Geometrically, completeness means something like this: if a vector $g(T)$ is orthogonal to the p.d.f. $f_\theta$ of $T$ for each $\theta$,
$$\mathbb E_\theta g(T) = \langle g(T),f_\theta\rangle=0$$
then $g(T)=0$ i.e., the functions $f_\theta$ for varying $\theta$ span the whole space of functions of $T$. So in a way it... | Meaning of completeness of a statistic? [duplicate] | Geometrically, completeness means something like this: if a vector $g(T)$ is orthogonal to the p.d.f. $f_\theta$ of $T$ for each $\theta$,
$$\mathbb E_\theta g(T) = \langle g(T),f_\theta\rangle=0$$
th | Meaning of completeness of a statistic? [duplicate]
Geometrically, completeness means something like this: if a vector $g(T)$ is orthogonal to the p.d.f. $f_\theta$ of $T$ for each $\theta$,
$$\mathbb E_\theta g(T) = \langle g(T),f_\theta\rangle=0$$
then $g(T)=0$ i.e., the functions $f_\theta$ for varying $\theta$ span... | Meaning of completeness of a statistic? [duplicate]
Geometrically, completeness means something like this: if a vector $g(T)$ is orthogonal to the p.d.f. $f_\theta$ of $T$ for each $\theta$,
$$\mathbb E_\theta g(T) = \langle g(T),f_\theta\rangle=0$$
th |
13,065 | Meaning of completeness of a statistic? [duplicate] | I found this very helpful:
Definition: A statistic $T$ is called complete if $E_\theta[g(T)] = 0$ for all $\theta$ and some function $g$ implies that $P_\theta(g(T) = 0) = 1$ for all $\theta$.
Think of this as analog to vectors and whether or not the vectors {$v_1, \ldots , v_n$} form a complete set (=basis) of the v... | Meaning of completeness of a statistic? [duplicate] | I found this very helpful:
Definition: A statistic $T$ is called complete if $E_\theta[g(T)] = 0$ for all $\theta$ and some function $g$ implies that $P_\theta(g(T) = 0) = 1$ for all $\theta$.
Think | Meaning of completeness of a statistic? [duplicate]
I found this very helpful:
Definition: A statistic $T$ is called complete if $E_\theta[g(T)] = 0$ for all $\theta$ and some function $g$ implies that $P_\theta(g(T) = 0) = 1$ for all $\theta$.
Think of this as analog to vectors and whether or not the vectors {$v_1, ... | Meaning of completeness of a statistic? [duplicate]
I found this very helpful:
Definition: A statistic $T$ is called complete if $E_\theta[g(T)] = 0$ for all $\theta$ and some function $g$ implies that $P_\theta(g(T) = 0) = 1$ for all $\theta$.
Think |
13,066 | What is the difference between online and batch Learning? [duplicate] | To me it looks like they are using batch and online learning correctly. In section 3 they are working on the whole dataset to perform learning, i.e., batch learning, while in section 4 they switch to stochastic gradient following which can be used as an online learning algorithm.
I've never used stochastic gradient fol... | What is the difference between online and batch Learning? [duplicate] | To me it looks like they are using batch and online learning correctly. In section 3 they are working on the whole dataset to perform learning, i.e., batch learning, while in section 4 they switch to | What is the difference between online and batch Learning? [duplicate]
To me it looks like they are using batch and online learning correctly. In section 3 they are working on the whole dataset to perform learning, i.e., batch learning, while in section 4 they switch to stochastic gradient following which can be used as... | What is the difference between online and batch Learning? [duplicate]
To me it looks like they are using batch and online learning correctly. In section 3 they are working on the whole dataset to perform learning, i.e., batch learning, while in section 4 they switch to |
13,067 | What is the difference between online and batch Learning? [duplicate] | In short,
Online: Learning based on each pattern as it is observed.
Batch: Learning over groups of patters. Most algorithms are batch.
Source: http://machinelearningmastery.com/basic-concepts-in-machine-learning/ | What is the difference between online and batch Learning? [duplicate] | In short,
Online: Learning based on each pattern as it is observed.
Batch: Learning over groups of patters. Most algorithms are batch.
Source: http://machinelearningmastery.com/basic-concepts-in-machi | What is the difference between online and batch Learning? [duplicate]
In short,
Online: Learning based on each pattern as it is observed.
Batch: Learning over groups of patters. Most algorithms are batch.
Source: http://machinelearningmastery.com/basic-concepts-in-machine-learning/ | What is the difference between online and batch Learning? [duplicate]
In short,
Online: Learning based on each pattern as it is observed.
Batch: Learning over groups of patters. Most algorithms are batch.
Source: http://machinelearningmastery.com/basic-concepts-in-machi |
13,068 | What is the difference between online and batch Learning? [duplicate] | Batch Versus On-line Learning
The on-line and batch modes are slightly different, although both will perform well for parabolic performance surfaces. One major difference is that the batch algorithm keeps the system weights constant while computing the error associated with each sample in the input. Since the on-line v... | What is the difference between online and batch Learning? [duplicate] | Batch Versus On-line Learning
The on-line and batch modes are slightly different, although both will perform well for parabolic performance surfaces. One major difference is that the batch algorithm k | What is the difference between online and batch Learning? [duplicate]
Batch Versus On-line Learning
The on-line and batch modes are slightly different, although both will perform well for parabolic performance surfaces. One major difference is that the batch algorithm keeps the system weights constant while computing t... | What is the difference between online and batch Learning? [duplicate]
Batch Versus On-line Learning
The on-line and batch modes are slightly different, although both will perform well for parabolic performance surfaces. One major difference is that the batch algorithm k |
13,069 | How to use DLM with Kalman filtering for forecasting | The paper at JSS 39-02 compares 5 different Kalman filtering R packages and gives sample code. | How to use DLM with Kalman filtering for forecasting | The paper at JSS 39-02 compares 5 different Kalman filtering R packages and gives sample code. | How to use DLM with Kalman filtering for forecasting
The paper at JSS 39-02 compares 5 different Kalman filtering R packages and gives sample code. | How to use DLM with Kalman filtering for forecasting
The paper at JSS 39-02 compares 5 different Kalman filtering R packages and gives sample code. |
13,070 | How to use DLM with Kalman filtering for forecasting | DLMs are cool, but they are not as simple as, say, ARIMA or other methods. In other methods, you plug in your data and then tweak some parameters of the algorithm, perhaps referring to various diagnostics to guide your settings.
With a DLM, you are creating a state space machine, which consists of several matrices that... | How to use DLM with Kalman filtering for forecasting | DLMs are cool, but they are not as simple as, say, ARIMA or other methods. In other methods, you plug in your data and then tweak some parameters of the algorithm, perhaps referring to various diagnos | How to use DLM with Kalman filtering for forecasting
DLMs are cool, but they are not as simple as, say, ARIMA or other methods. In other methods, you plug in your data and then tweak some parameters of the algorithm, perhaps referring to various diagnostics to guide your settings.
With a DLM, you are creating a state s... | How to use DLM with Kalman filtering for forecasting
DLMs are cool, but they are not as simple as, say, ARIMA or other methods. In other methods, you plug in your data and then tweak some parameters of the algorithm, perhaps referring to various diagnos |
13,071 | How to use DLM with Kalman filtering for forecasting | I suggest you read the dlm vignette http://cran.r-project.org/web/packages/dlm/vignettes/dlm.pdf especially the chapter 3.3 | How to use DLM with Kalman filtering for forecasting | I suggest you read the dlm vignette http://cran.r-project.org/web/packages/dlm/vignettes/dlm.pdf especially the chapter 3.3 | How to use DLM with Kalman filtering for forecasting
I suggest you read the dlm vignette http://cran.r-project.org/web/packages/dlm/vignettes/dlm.pdf especially the chapter 3.3 | How to use DLM with Kalman filtering for forecasting
I suggest you read the dlm vignette http://cran.r-project.org/web/packages/dlm/vignettes/dlm.pdf especially the chapter 3.3 |
13,072 | Curse of dimensionality- does cosine similarity work better and if so, why? [duplicate] | Contrary to various unproven claims, cosine cannot be significantly better.
It is easy to see that Cosine is essentially the same as Euclidean on normalized data. The normalization takes away one degree of freedom. Thus, cosine on a 1000 dimensional space is about as "cursed" as Euclidean on a 999 dimensional space.
Wh... | Curse of dimensionality- does cosine similarity work better and if so, why? [duplicate] | Contrary to various unproven claims, cosine cannot be significantly better.
It is easy to see that Cosine is essentially the same as Euclidean on normalized data. The normalization takes away one degr | Curse of dimensionality- does cosine similarity work better and if so, why? [duplicate]
Contrary to various unproven claims, cosine cannot be significantly better.
It is easy to see that Cosine is essentially the same as Euclidean on normalized data. The normalization takes away one degree of freedom. Thus, cosine on a... | Curse of dimensionality- does cosine similarity work better and if so, why? [duplicate]
Contrary to various unproven claims, cosine cannot be significantly better.
It is easy to see that Cosine is essentially the same as Euclidean on normalized data. The normalization takes away one degr |
13,073 | Curse of dimensionality- does cosine similarity work better and if so, why? [duplicate] | However, I have read that using different distance metrics, such as a
cosine similarity, performs better with high dimensional data.
Most likely depends on context.
The cosine distance is not impervious to the curse of dimensionality - in high dimensions two randomly picked vectors will be almost orthogonal with hig... | Curse of dimensionality- does cosine similarity work better and if so, why? [duplicate] | However, I have read that using different distance metrics, such as a
cosine similarity, performs better with high dimensional data.
Most likely depends on context.
The cosine distance is not imper | Curse of dimensionality- does cosine similarity work better and if so, why? [duplicate]
However, I have read that using different distance metrics, such as a
cosine similarity, performs better with high dimensional data.
Most likely depends on context.
The cosine distance is not impervious to the curse of dimensiona... | Curse of dimensionality- does cosine similarity work better and if so, why? [duplicate]
However, I have read that using different distance metrics, such as a
cosine similarity, performs better with high dimensional data.
Most likely depends on context.
The cosine distance is not imper |
13,074 | Curse of dimensionality- does cosine similarity work better and if so, why? [duplicate] | Cosine similarity is correlation, which is greater for objects with similar angles from, say, the origin (0,0,0,0,....) over the feature values. So correlation is a similarity index. Euclidean distance is lowest between objects with the same distance and angle from the origin. So, two objects with the same angle (co... | Curse of dimensionality- does cosine similarity work better and if so, why? [duplicate] | Cosine similarity is correlation, which is greater for objects with similar angles from, say, the origin (0,0,0,0,....) over the feature values. So correlation is a similarity index. Euclidean dista | Curse of dimensionality- does cosine similarity work better and if so, why? [duplicate]
Cosine similarity is correlation, which is greater for objects with similar angles from, say, the origin (0,0,0,0,....) over the feature values. So correlation is a similarity index. Euclidean distance is lowest between objects wi... | Curse of dimensionality- does cosine similarity work better and if so, why? [duplicate]
Cosine similarity is correlation, which is greater for objects with similar angles from, say, the origin (0,0,0,0,....) over the feature values. So correlation is a similarity index. Euclidean dista |
13,075 | Is it okay to use cross entropy loss function with soft labels? | The answer is yes, but you have to define it the right way.
Cross entropy is defined on probability distributions, not on single values. For discrete distributions $p$ and $q$, it's:
$$H(p, q) = -\sum_y p(y) \log q(y)$$
When the cross entropy loss is used with 'hard' class labels, what this really amounts to is treatin... | Is it okay to use cross entropy loss function with soft labels? | The answer is yes, but you have to define it the right way.
Cross entropy is defined on probability distributions, not on single values. For discrete distributions $p$ and $q$, it's:
$$H(p, q) = -\sum | Is it okay to use cross entropy loss function with soft labels?
The answer is yes, but you have to define it the right way.
Cross entropy is defined on probability distributions, not on single values. For discrete distributions $p$ and $q$, it's:
$$H(p, q) = -\sum_y p(y) \log q(y)$$
When the cross entropy loss is used ... | Is it okay to use cross entropy loss function with soft labels?
The answer is yes, but you have to define it the right way.
Cross entropy is defined on probability distributions, not on single values. For discrete distributions $p$ and $q$, it's:
$$H(p, q) = -\sum |
13,076 | What is simply meant by reduced form? | To complement Dimitriy's answer (+1), the structural form and the reduced form are two ways of thinking about your system of equations.
The structural form is what your economic theory says the economic relations between the variables are (like consumption and income in the linked Keynesian example). However, getting t... | What is simply meant by reduced form? | To complement Dimitriy's answer (+1), the structural form and the reduced form are two ways of thinking about your system of equations.
The structural form is what your economic theory says the econom | What is simply meant by reduced form?
To complement Dimitriy's answer (+1), the structural form and the reduced form are two ways of thinking about your system of equations.
The structural form is what your economic theory says the economic relations between the variables are (like consumption and income in the linked ... | What is simply meant by reduced form?
To complement Dimitriy's answer (+1), the structural form and the reduced form are two ways of thinking about your system of equations.
The structural form is what your economic theory says the econom |
13,077 | What is simply meant by reduced form? | Take a look at this simple example showing how the Keynesian consumption function and equilibrium condition can be re-written in a reduced form.
The reduced form of a model is the one in which the endogenous variables are expressed as functions of the exogenous variables (and perhaps lagged values of the endogenous var... | What is simply meant by reduced form? | Take a look at this simple example showing how the Keynesian consumption function and equilibrium condition can be re-written in a reduced form.
The reduced form of a model is the one in which the end | What is simply meant by reduced form?
Take a look at this simple example showing how the Keynesian consumption function and equilibrium condition can be re-written in a reduced form.
The reduced form of a model is the one in which the endogenous variables are expressed as functions of the exogenous variables (and perha... | What is simply meant by reduced form?
Take a look at this simple example showing how the Keynesian consumption function and equilibrium condition can be re-written in a reduced form.
The reduced form of a model is the one in which the end |
13,078 | What is simply meant by reduced form? | When you do a regression involving two steps (two-step least squares, or 2sls) you have two equations. The first equations, named the structural equation, looks like any other regression equation. The second equation is the reduced form equation (and looks a lot like any other regression equation). The reason for... | What is simply meant by reduced form? | When you do a regression involving two steps (two-step least squares, or 2sls) you have two equations. The first equations, named the structural equation, looks like any other regression equation. | What is simply meant by reduced form?
When you do a regression involving two steps (two-step least squares, or 2sls) you have two equations. The first equations, named the structural equation, looks like any other regression equation. The second equation is the reduced form equation (and looks a lot like any other ... | What is simply meant by reduced form?
When you do a regression involving two steps (two-step least squares, or 2sls) you have two equations. The first equations, named the structural equation, looks like any other regression equation. |
13,079 | What is simply meant by reduced form? | Jörn-Steffen Pischke provides a very pragmatic explanation of the reduced form in the context of instrumental variables analysis (IV) in his lecture notes.
He essentially distinguishes 3 causal effects of interest:
the causal effect of the instrument (Z) on the endogenous variable (X) - obtained in the first stage;
th... | What is simply meant by reduced form? | Jörn-Steffen Pischke provides a very pragmatic explanation of the reduced form in the context of instrumental variables analysis (IV) in his lecture notes.
He essentially distinguishes 3 causal effect | What is simply meant by reduced form?
Jörn-Steffen Pischke provides a very pragmatic explanation of the reduced form in the context of instrumental variables analysis (IV) in his lecture notes.
He essentially distinguishes 3 causal effects of interest:
the causal effect of the instrument (Z) on the endogenous variable... | What is simply meant by reduced form?
Jörn-Steffen Pischke provides a very pragmatic explanation of the reduced form in the context of instrumental variables analysis (IV) in his lecture notes.
He essentially distinguishes 3 causal effect |
13,080 | What is simply meant by reduced form? | Agree with @user107905, if you use the 2SLS the reduced format equation is used to construct the IV, while the original structural equation can still be fitted through OLS by plugging in the fitted endogenous value. In that way, you can still get INTERPRETABLE parameters for the original/1st structural equation.
see c... | What is simply meant by reduced form? | Agree with @user107905, if you use the 2SLS the reduced format equation is used to construct the IV, while the original structural equation can still be fitted through OLS by plugging in the fitted en | What is simply meant by reduced form?
Agree with @user107905, if you use the 2SLS the reduced format equation is used to construct the IV, while the original structural equation can still be fitted through OLS by plugging in the fitted endogenous value. In that way, you can still get INTERPRETABLE parameters for the or... | What is simply meant by reduced form?
Agree with @user107905, if you use the 2SLS the reduced format equation is used to construct the IV, while the original structural equation can still be fitted through OLS by plugging in the fitted en |
13,081 | Intercept term in logistic regression | $\beta_0$ is not the odds of the event when $x_1 = x_2 = 0$, it is the log of the odds. In addition, it is the log odds only when $x_1 = x_2 = 0$, not when they are at their lowest non-zero values. | Intercept term in logistic regression | $\beta_0$ is not the odds of the event when $x_1 = x_2 = 0$, it is the log of the odds. In addition, it is the log odds only when $x_1 = x_2 = 0$, not when they are at their lowest non-zero values. | Intercept term in logistic regression
$\beta_0$ is not the odds of the event when $x_1 = x_2 = 0$, it is the log of the odds. In addition, it is the log odds only when $x_1 = x_2 = 0$, not when they are at their lowest non-zero values. | Intercept term in logistic regression
$\beta_0$ is not the odds of the event when $x_1 = x_2 = 0$, it is the log of the odds. In addition, it is the log odds only when $x_1 = x_2 = 0$, not when they are at their lowest non-zero values. |
13,082 | Intercept term in logistic regression | There also might be a case when $x_1$ and $x_2$ can not be equal to $0$ at the same time. In this case $\beta_0$ does not have clear interpretation.
Otherwise $\beta_0$ has an interpretation - it shifts the log of the odds to its factual value, if no one variable can not do this. | Intercept term in logistic regression | There also might be a case when $x_1$ and $x_2$ can not be equal to $0$ at the same time. In this case $\beta_0$ does not have clear interpretation.
Otherwise $\beta_0$ has an interpretation - it shi | Intercept term in logistic regression
There also might be a case when $x_1$ and $x_2$ can not be equal to $0$ at the same time. In this case $\beta_0$ does not have clear interpretation.
Otherwise $\beta_0$ has an interpretation - it shifts the log of the odds to its factual value, if no one variable can not do this. | Intercept term in logistic regression
There also might be a case when $x_1$ and $x_2$ can not be equal to $0$ at the same time. In this case $\beta_0$ does not have clear interpretation.
Otherwise $\beta_0$ has an interpretation - it shi |
13,083 | Intercept term in logistic regression | I suggest to look at it a different way ...
In logistic regression we predict some binary class {0 or 1} by calculating the probability of likelihood, which is the actual output of $\text{logit}(p)$.
This, of course, is assuming that the log-odds can reasonably be described by a linear function -- e.g., $\beta_0 + \b... | Intercept term in logistic regression | I suggest to look at it a different way ...
In logistic regression we predict some binary class {0 or 1} by calculating the probability of likelihood, which is the actual output of $\text{logit}(p)$. | Intercept term in logistic regression
I suggest to look at it a different way ...
In logistic regression we predict some binary class {0 or 1} by calculating the probability of likelihood, which is the actual output of $\text{logit}(p)$.
This, of course, is assuming that the log-odds can reasonably be described by a ... | Intercept term in logistic regression
I suggest to look at it a different way ...
In logistic regression we predict some binary class {0 or 1} by calculating the probability of likelihood, which is the actual output of $\text{logit}(p)$. |
13,084 | Transformation to increase kurtosis and skewness of normal r.v | This can be done using the sinh-arcsinh transformation from
Jones, M. C. and Pewsey A. (2009). Sinh-arcsinh distributions. Biometrika 96: 761–780.
The transformation is defined as
$$H(x;\epsilon,\delta)=\sinh[\delta\sinh^{-1}(x)-\epsilon], \tag{$\star$}$$
where $\epsilon \in{\mathbb R}$ and $\delta \in {\mathbb R}_+... | Transformation to increase kurtosis and skewness of normal r.v | This can be done using the sinh-arcsinh transformation from
Jones, M. C. and Pewsey A. (2009). Sinh-arcsinh distributions. Biometrika 96: 761–780.
The transformation is defined as
$$H(x;\epsilon,\d | Transformation to increase kurtosis and skewness of normal r.v
This can be done using the sinh-arcsinh transformation from
Jones, M. C. and Pewsey A. (2009). Sinh-arcsinh distributions. Biometrika 96: 761–780.
The transformation is defined as
$$H(x;\epsilon,\delta)=\sinh[\delta\sinh^{-1}(x)-\epsilon], \tag{$\star$}$... | Transformation to increase kurtosis and skewness of normal r.v
This can be done using the sinh-arcsinh transformation from
Jones, M. C. and Pewsey A. (2009). Sinh-arcsinh distributions. Biometrika 96: 761–780.
The transformation is defined as
$$H(x;\epsilon,\d |
13,085 | Transformation to increase kurtosis and skewness of normal r.v | This can be done using Lambert W x F random variables / distributions. A Lambert W x F random variable (RV) is a non-linearly transformed (RV) X with
distribution F.
For F being the Normal distribution and $\alpha = 1$, they reduce to Tukey's h distribution. The nice property of Lambert W x F distributions is that you... | Transformation to increase kurtosis and skewness of normal r.v | This can be done using Lambert W x F random variables / distributions. A Lambert W x F random variable (RV) is a non-linearly transformed (RV) X with
distribution F.
For F being the Normal distributi | Transformation to increase kurtosis and skewness of normal r.v
This can be done using Lambert W x F random variables / distributions. A Lambert W x F random variable (RV) is a non-linearly transformed (RV) X with
distribution F.
For F being the Normal distribution and $\alpha = 1$, they reduce to Tukey's h distributio... | Transformation to increase kurtosis and skewness of normal r.v
This can be done using Lambert W x F random variables / distributions. A Lambert W x F random variable (RV) is a non-linearly transformed (RV) X with
distribution F.
For F being the Normal distributi |
13,086 | Transformation to increase kurtosis and skewness of normal r.v | One such sequence is exponentiation to various degrees. E.g.
library(moments)
x <- rnorm(1000) #Normal data
x2 <- 2^x #One transformation
x3 <- 2^{x^2} #A stronger transformation
test <- cbind(x, x2, x3)
apply(test, 2, skewness) #Skewness for the three distributions
apply(test, 2, kurtosis) #Kurtosis for the three dis... | Transformation to increase kurtosis and skewness of normal r.v | One such sequence is exponentiation to various degrees. E.g.
library(moments)
x <- rnorm(1000) #Normal data
x2 <- 2^x #One transformation
x3 <- 2^{x^2} #A stronger transformation
test <- cbind(x, x2, | Transformation to increase kurtosis and skewness of normal r.v
One such sequence is exponentiation to various degrees. E.g.
library(moments)
x <- rnorm(1000) #Normal data
x2 <- 2^x #One transformation
x3 <- 2^{x^2} #A stronger transformation
test <- cbind(x, x2, x3)
apply(test, 2, skewness) #Skewness for the three dis... | Transformation to increase kurtosis and skewness of normal r.v
One such sequence is exponentiation to various degrees. E.g.
library(moments)
x <- rnorm(1000) #Normal data
x2 <- 2^x #One transformation
x3 <- 2^{x^2} #A stronger transformation
test <- cbind(x, x2, |
13,087 | Transformation to increase kurtosis and skewness of normal r.v | Same answer as @user10525 but in python
import numpy as np
from scipy.stats import norm
def sinh_archsinh_transformation(x,epsilon,delta):
return norm.pdf(np.sinh(delta*np.arcsinh(x)-epsilon))*delta*np.cosh(delta*np.arcsinh(x)-epsilon)/np.sqrt(1+np.power(x,2))
vec = np.arange(start=-15,stop=15+0.001,step=0.001)
... | Transformation to increase kurtosis and skewness of normal r.v | Same answer as @user10525 but in python
import numpy as np
from scipy.stats import norm
def sinh_archsinh_transformation(x,epsilon,delta):
return norm.pdf(np.sinh(delta*np.arcsinh(x)-epsilon))*del | Transformation to increase kurtosis and skewness of normal r.v
Same answer as @user10525 but in python
import numpy as np
from scipy.stats import norm
def sinh_archsinh_transformation(x,epsilon,delta):
return norm.pdf(np.sinh(delta*np.arcsinh(x)-epsilon))*delta*np.cosh(delta*np.arcsinh(x)-epsilon)/np.sqrt(1+np.powe... | Transformation to increase kurtosis and skewness of normal r.v
Same answer as @user10525 but in python
import numpy as np
from scipy.stats import norm
def sinh_archsinh_transformation(x,epsilon,delta):
return norm.pdf(np.sinh(delta*np.arcsinh(x)-epsilon))*del |
13,088 | Is there a way to maximize/minimize a custom function in R? | I wrote a post listing a few tutorials using optim.
Here is a quote of the relevant section:
"The combination of the R function optim and a custom created objective
function, such as a minus log-likelihood function provides a powerful tool for
parameter estimation of custom models.
Scott Brown's tutorial includes an e... | Is there a way to maximize/minimize a custom function in R? | I wrote a post listing a few tutorials using optim.
Here is a quote of the relevant section:
"The combination of the R function optim and a custom created objective
function, such as a minus log-likel | Is there a way to maximize/minimize a custom function in R?
I wrote a post listing a few tutorials using optim.
Here is a quote of the relevant section:
"The combination of the R function optim and a custom created objective
function, such as a minus log-likelihood function provides a powerful tool for
parameter estima... | Is there a way to maximize/minimize a custom function in R?
I wrote a post listing a few tutorials using optim.
Here is a quote of the relevant section:
"The combination of the R function optim and a custom created objective
function, such as a minus log-likel |
13,089 | Is there a way to maximize/minimize a custom function in R? | In addition to Jeromy Anglim's answer, I have some more links.
Next to optim there is another function in base R that allows for what you want: nlminb. Check ?nlminb and ?optim for examples of the usage.
There are a bunch of packages that can do optimizations. What I found most interesting were the packages optimx and,... | Is there a way to maximize/minimize a custom function in R? | In addition to Jeromy Anglim's answer, I have some more links.
Next to optim there is another function in base R that allows for what you want: nlminb. Check ?nlminb and ?optim for examples of the usa | Is there a way to maximize/minimize a custom function in R?
In addition to Jeromy Anglim's answer, I have some more links.
Next to optim there is another function in base R that allows for what you want: nlminb. Check ?nlminb and ?optim for examples of the usage.
There are a bunch of packages that can do optimizations.... | Is there a way to maximize/minimize a custom function in R?
In addition to Jeromy Anglim's answer, I have some more links.
Next to optim there is another function in base R that allows for what you want: nlminb. Check ?nlminb and ?optim for examples of the usa |
13,090 | Is there a way to maximize/minimize a custom function in R? | Is your function continuous and differentiable? You might be able to use optim, either with user-supplied derivatives or numerically approximated ones. | Is there a way to maximize/minimize a custom function in R? | Is your function continuous and differentiable? You might be able to use optim, either with user-supplied derivatives or numerically approximated ones. | Is there a way to maximize/minimize a custom function in R?
Is your function continuous and differentiable? You might be able to use optim, either with user-supplied derivatives or numerically approximated ones. | Is there a way to maximize/minimize a custom function in R?
Is your function continuous and differentiable? You might be able to use optim, either with user-supplied derivatives or numerically approximated ones. |
13,091 | When did MCMC become commonplace? | This paper by Christian (Xi'an) Robert and George Casella provides a nice summary of the history of MCMC. From the paper (emphasis is mine).
What can be reasonably seen as the first MCMC algorithm is what we now call the Metropolis algorithm, published by Metropolis et al. (1953). It emanates from the same group of s... | When did MCMC become commonplace? | This paper by Christian (Xi'an) Robert and George Casella provides a nice summary of the history of MCMC. From the paper (emphasis is mine).
What can be reasonably seen as the first MCMC algorithm i | When did MCMC become commonplace?
This paper by Christian (Xi'an) Robert and George Casella provides a nice summary of the history of MCMC. From the paper (emphasis is mine).
What can be reasonably seen as the first MCMC algorithm is what we now call the Metropolis algorithm, published by Metropolis et al. (1953). It... | When did MCMC become commonplace?
This paper by Christian (Xi'an) Robert and George Casella provides a nice summary of the history of MCMC. From the paper (emphasis is mine).
What can be reasonably seen as the first MCMC algorithm i |
13,092 | When did MCMC become commonplace? | The excellent answer by knrumsey gives some history on the progression of important academic work in MCMC. One other aspect worth examining is the development of software to facilitate MCMC by the ordinary user. Statistical methods are often used mostly by specialists until they are implemented in software that allow... | When did MCMC become commonplace? | The excellent answer by knrumsey gives some history on the progression of important academic work in MCMC. One other aspect worth examining is the development of software to facilitate MCMC by the or | When did MCMC become commonplace?
The excellent answer by knrumsey gives some history on the progression of important academic work in MCMC. One other aspect worth examining is the development of software to facilitate MCMC by the ordinary user. Statistical methods are often used mostly by specialists until they are ... | When did MCMC become commonplace?
The excellent answer by knrumsey gives some history on the progression of important academic work in MCMC. One other aspect worth examining is the development of software to facilitate MCMC by the or |
13,093 | Tensorflow Cross Entropy for Regression? | No, it doesn't make sense to use TensorFlow functions like tf.nn.sigmoid_cross_entropy_with_logits for a regression task. In TensorFlow, “cross-entropy” is shorthand (or jargon) for “categorical cross entropy.” Categorical cross entropy is an operation on probabilities. A regression problem attempts to predict continuo... | Tensorflow Cross Entropy for Regression? | No, it doesn't make sense to use TensorFlow functions like tf.nn.sigmoid_cross_entropy_with_logits for a regression task. In TensorFlow, “cross-entropy” is shorthand (or jargon) for “categorical cross | Tensorflow Cross Entropy for Regression?
No, it doesn't make sense to use TensorFlow functions like tf.nn.sigmoid_cross_entropy_with_logits for a regression task. In TensorFlow, “cross-entropy” is shorthand (or jargon) for “categorical cross entropy.” Categorical cross entropy is an operation on probabilities. A regres... | Tensorflow Cross Entropy for Regression?
No, it doesn't make sense to use TensorFlow functions like tf.nn.sigmoid_cross_entropy_with_logits for a regression task. In TensorFlow, “cross-entropy” is shorthand (or jargon) for “categorical cross |
13,094 | Tensorflow Cross Entropy for Regression? | The answer given by @Sycorax is correct. However, it is worth mentioning that using (binary) cross-entropy in a regression task where the output values are in the range [0,1] is a valid and reasonable thing to do. Actually, it is used in image autoencoders (e.g. here and this paper). You might be interested to see a si... | Tensorflow Cross Entropy for Regression? | The answer given by @Sycorax is correct. However, it is worth mentioning that using (binary) cross-entropy in a regression task where the output values are in the range [0,1] is a valid and reasonable | Tensorflow Cross Entropy for Regression?
The answer given by @Sycorax is correct. However, it is worth mentioning that using (binary) cross-entropy in a regression task where the output values are in the range [0,1] is a valid and reasonable thing to do. Actually, it is used in image autoencoders (e.g. here and this pa... | Tensorflow Cross Entropy for Regression?
The answer given by @Sycorax is correct. However, it is worth mentioning that using (binary) cross-entropy in a regression task where the output values are in the range [0,1] is a valid and reasonable |
13,095 | Tensorflow Cross Entropy for Regression? | Deep learning frameworks often mix models and losses and refer to the cross-entropy of a multinomial model with softmax nonlinearity by cross_entropy, which is misleading. In general, you can define cross-entropy for arbitrary models.
For a Gaussian model with varying mean but fixed diagonal covariance, it is equivale... | Tensorflow Cross Entropy for Regression? | Deep learning frameworks often mix models and losses and refer to the cross-entropy of a multinomial model with softmax nonlinearity by cross_entropy, which is misleading. In general, you can define c | Tensorflow Cross Entropy for Regression?
Deep learning frameworks often mix models and losses and refer to the cross-entropy of a multinomial model with softmax nonlinearity by cross_entropy, which is misleading. In general, you can define cross-entropy for arbitrary models.
For a Gaussian model with varying mean but ... | Tensorflow Cross Entropy for Regression?
Deep learning frameworks often mix models and losses and refer to the cross-entropy of a multinomial model with softmax nonlinearity by cross_entropy, which is misleading. In general, you can define c |
13,096 | Tensorflow Cross Entropy for Regression? | Unfortunately, the as of now accepted answer by @Sycorax, while detailed, is incorrect.
Actually, a prime example of regression through categorical cross-entropy -- Wavenet -- has been implemented in TensorFlow.
The principle is that you discretize your output space and then your model only predicts the respective bin;... | Tensorflow Cross Entropy for Regression? | Unfortunately, the as of now accepted answer by @Sycorax, while detailed, is incorrect.
Actually, a prime example of regression through categorical cross-entropy -- Wavenet -- has been implemented in | Tensorflow Cross Entropy for Regression?
Unfortunately, the as of now accepted answer by @Sycorax, while detailed, is incorrect.
Actually, a prime example of regression through categorical cross-entropy -- Wavenet -- has been implemented in TensorFlow.
The principle is that you discretize your output space and then you... | Tensorflow Cross Entropy for Regression?
Unfortunately, the as of now accepted answer by @Sycorax, while detailed, is incorrect.
Actually, a prime example of regression through categorical cross-entropy -- Wavenet -- has been implemented in |
13,097 | Tensorflow Cross Entropy for Regression? | I've revisited this question as I now disagree with the answer I previously accepted. Cross entropy loss CAN be used in regression (although it isn't common.)
It comes down to the fact that cross-entropy is a concept that only makes sense when comparing two probability distributions. You could consider a neural network... | Tensorflow Cross Entropy for Regression? | I've revisited this question as I now disagree with the answer I previously accepted. Cross entropy loss CAN be used in regression (although it isn't common.)
It comes down to the fact that cross-entr | Tensorflow Cross Entropy for Regression?
I've revisited this question as I now disagree with the answer I previously accepted. Cross entropy loss CAN be used in regression (although it isn't common.)
It comes down to the fact that cross-entropy is a concept that only makes sense when comparing two probability distribut... | Tensorflow Cross Entropy for Regression?
I've revisited this question as I now disagree with the answer I previously accepted. Cross entropy loss CAN be used in regression (although it isn't common.)
It comes down to the fact that cross-entr |
13,098 | Tensorflow Cross Entropy for Regression? | Yes, sure.
What is Cross-Entropy?
Let's think about what is Cross-Entropy (CE). CE cost in the context of PyTorch or another Frameworks can mean a different thing compare to MATH. Originally cross-entropy is some form of KL-divergence between distributions: https://sites.google.com/site/burlachenkok/articles/properties... | Tensorflow Cross Entropy for Regression? | Yes, sure.
What is Cross-Entropy?
Let's think about what is Cross-Entropy (CE). CE cost in the context of PyTorch or another Frameworks can mean a different thing compare to MATH. Originally cross-ent | Tensorflow Cross Entropy for Regression?
Yes, sure.
What is Cross-Entropy?
Let's think about what is Cross-Entropy (CE). CE cost in the context of PyTorch or another Frameworks can mean a different thing compare to MATH. Originally cross-entropy is some form of KL-divergence between distributions: https://sites.google.... | Tensorflow Cross Entropy for Regression?
Yes, sure.
What is Cross-Entropy?
Let's think about what is Cross-Entropy (CE). CE cost in the context of PyTorch or another Frameworks can mean a different thing compare to MATH. Originally cross-ent |
13,099 | Non-transitivity of correlation: correlations between gender and brain size and between brain size and IQ, but no correlation between gender and IQ | Yes, it would still be a fallacy.
Here is a very simple figure showing four different situations. In each case red dots represent women, blue dot represent men, horizontal axis represents brain size and vertical axis represents IQ. I generated all four datasets such that:
there is always the same difference in mean br... | Non-transitivity of correlation: correlations between gender and brain size and between brain size a | Yes, it would still be a fallacy.
Here is a very simple figure showing four different situations. In each case red dots represent women, blue dot represent men, horizontal axis represents brain size a | Non-transitivity of correlation: correlations between gender and brain size and between brain size and IQ, but no correlation between gender and IQ
Yes, it would still be a fallacy.
Here is a very simple figure showing four different situations. In each case red dots represent women, blue dot represent men, horizontal ... | Non-transitivity of correlation: correlations between gender and brain size and between brain size a
Yes, it would still be a fallacy.
Here is a very simple figure showing four different situations. In each case red dots represent women, blue dot represent men, horizontal axis represents brain size a |
13,100 | Non-transitivity of correlation: correlations between gender and brain size and between brain size and IQ, but no correlation between gender and IQ | Let us define $x_1=\text{IQ}, x_2=\text{gender}$ and $x_3$ be some other variable (like brain volume) correlated to both. Let us assume that
$$
\text{cor}(x_1, x_2)=\lambda, \\
\text{cor}(x_1,x_3)=\text{cor}(x_2, x_3)=\rho=0.9
$$
What is the smallest possible value for $\lambda$? A correlation matrix must be... | Non-transitivity of correlation: correlations between gender and brain size and between brain size a | Let us define $x_1=\text{IQ}, x_2=\text{gender}$ and $x_3$ be some other variable (like brain volume) correlated to both. Let us assume that
$$
\text{cor}(x_1, x_2)=\lambda, \\
\text{cor}(x_1 | Non-transitivity of correlation: correlations between gender and brain size and between brain size and IQ, but no correlation between gender and IQ
Let us define $x_1=\text{IQ}, x_2=\text{gender}$ and $x_3$ be some other variable (like brain volume) correlated to both. Let us assume that
$$
\text{cor}(x_1, x_2)=\l... | Non-transitivity of correlation: correlations between gender and brain size and between brain size a
Let us define $x_1=\text{IQ}, x_2=\text{gender}$ and $x_3$ be some other variable (like brain volume) correlated to both. Let us assume that
$$
\text{cor}(x_1, x_2)=\lambda, \\
\text{cor}(x_1 |
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