idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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11,401 | How to find local peaks/valleys in a series of data? | using Numpy
ser = np.random.randint(-40, 40, 100) # 100 points
peak = np.where(np.diff(ser) < 0)[0]
or
double_difference = np.diff(np.sign(np.diff(ser)))
peak = np.where(double_difference == -2)[0]
using Pandas
ser = pd.Series(np.random.randint(2, 5, 100))
peak_df = ser[(ser.shift(1) < ser) & (ser.shift(-1) < ser)]
... | How to find local peaks/valleys in a series of data? | using Numpy
ser = np.random.randint(-40, 40, 100) # 100 points
peak = np.where(np.diff(ser) < 0)[0]
or
double_difference = np.diff(np.sign(np.diff(ser)))
peak = np.where(double_difference == -2)[0]
| How to find local peaks/valleys in a series of data?
using Numpy
ser = np.random.randint(-40, 40, 100) # 100 points
peak = np.where(np.diff(ser) < 0)[0]
or
double_difference = np.diff(np.sign(np.diff(ser)))
peak = np.where(double_difference == -2)[0]
using Pandas
ser = pd.Series(np.random.randint(2, 5, 100))
peak_df... | How to find local peaks/valleys in a series of data?
using Numpy
ser = np.random.randint(-40, 40, 100) # 100 points
peak = np.where(np.diff(ser) < 0)[0]
or
double_difference = np.diff(np.sign(np.diff(ser)))
peak = np.where(double_difference == -2)[0]
|
11,402 | How to find local peaks/valleys in a series of data? | I have not enough reputation to comment direcly on stas-g's answer but this is a comment on an issue i found with stas-g's code
I have vectors with incomplete data
a = c(1.60676107, -1.84154137, -0.03814237, -3.01587711, 6.67004912, NA, NA, -0.94917515)
# Looking at the data find_peaks(a, m=3) should return 5
# and fin... | How to find local peaks/valleys in a series of data? | I have not enough reputation to comment direcly on stas-g's answer but this is a comment on an issue i found with stas-g's code
I have vectors with incomplete data
a = c(1.60676107, -1.84154137, -0.03 | How to find local peaks/valleys in a series of data?
I have not enough reputation to comment direcly on stas-g's answer but this is a comment on an issue i found with stas-g's code
I have vectors with incomplete data
a = c(1.60676107, -1.84154137, -0.03814237, -3.01587711, 6.67004912, NA, NA, -0.94917515)
# Looking at ... | How to find local peaks/valleys in a series of data?
I have not enough reputation to comment direcly on stas-g's answer but this is a comment on an issue i found with stas-g's code
I have vectors with incomplete data
a = c(1.60676107, -1.84154137, -0.03 |
11,403 | How to find local peaks/valleys in a series of data? | I work with long records of integer wind speeds including NAs. The integer values can have flat plateaus which count as peaks and ledges which don't count.
My solution takes only 4.3 seconds to process a 11.5 million element vector on my PC:
indx.localpeaks<-function(x)
{dw1<-sign(diff(x)) # -1=down, 0=flat, 1=up
n... | How to find local peaks/valleys in a series of data? | I work with long records of integer wind speeds including NAs. The integer values can have flat plateaus which count as peaks and ledges which don't count.
My solution takes only 4.3 seconds to proces | How to find local peaks/valleys in a series of data?
I work with long records of integer wind speeds including NAs. The integer values can have flat plateaus which count as peaks and ledges which don't count.
My solution takes only 4.3 seconds to process a 11.5 million element vector on my PC:
indx.localpeaks<-function... | How to find local peaks/valleys in a series of data?
I work with long records of integer wind speeds including NAs. The integer values can have flat plateaus which count as peaks and ledges which don't count.
My solution takes only 4.3 seconds to proces |
11,404 | Generate random correlated data between a binary and a continuous variable | @ocram's approach will certainly work. In terms of the dependence properties it's somewhat restrictive though.
Another method is to use a copula to derive a joint distribution. You can specify marginal distributions for success and age (if you have existing data this is especially simple) and a copula family. Varying ... | Generate random correlated data between a binary and a continuous variable | @ocram's approach will certainly work. In terms of the dependence properties it's somewhat restrictive though.
Another method is to use a copula to derive a joint distribution. You can specify margin | Generate random correlated data between a binary and a continuous variable
@ocram's approach will certainly work. In terms of the dependence properties it's somewhat restrictive though.
Another method is to use a copula to derive a joint distribution. You can specify marginal distributions for success and age (if you... | Generate random correlated data between a binary and a continuous variable
@ocram's approach will certainly work. In terms of the dependence properties it's somewhat restrictive though.
Another method is to use a copula to derive a joint distribution. You can specify margin |
11,405 | Generate random correlated data between a binary and a continuous variable | You can simulate the logistic regression model.
More precisely, you can first generate values for the age variable (for example using a uniform distribution) and then compute probabilities of success using
$$\pi ( x ) = \frac{\exp(\beta_0 + \beta_1 x)}{1 + \exp(\beta_0 + \beta_1 x)}$$
where $\beta_0$ and $\beta_1$ ar... | Generate random correlated data between a binary and a continuous variable | You can simulate the logistic regression model.
More precisely, you can first generate values for the age variable (for example using a uniform distribution) and then compute probabilities of success | Generate random correlated data between a binary and a continuous variable
You can simulate the logistic regression model.
More precisely, you can first generate values for the age variable (for example using a uniform distribution) and then compute probabilities of success using
$$\pi ( x ) = \frac{\exp(\beta_0 + \... | Generate random correlated data between a binary and a continuous variable
You can simulate the logistic regression model.
More precisely, you can first generate values for the age variable (for example using a uniform distribution) and then compute probabilities of success |
11,406 | Generate random correlated data between a binary and a continuous variable | You can first generate the success/failure variable ($X$), and then generate the age ($Y$) with a different distribution depending on the value of $X$. That will give you correlation.
To quantify the correlation, the simplest way is to shift $Y$ according to the value of $X$. The amount by which you shift will be a mea... | Generate random correlated data between a binary and a continuous variable | You can first generate the success/failure variable ($X$), and then generate the age ($Y$) with a different distribution depending on the value of $X$. That will give you correlation.
To quantify the | Generate random correlated data between a binary and a continuous variable
You can first generate the success/failure variable ($X$), and then generate the age ($Y$) with a different distribution depending on the value of $X$. That will give you correlation.
To quantify the correlation, the simplest way is to shift $Y... | Generate random correlated data between a binary and a continuous variable
You can first generate the success/failure variable ($X$), and then generate the age ($Y$) with a different distribution depending on the value of $X$. That will give you correlation.
To quantify the |
11,407 | What is a null model in regression and how does it relate to the null hypothesis? | No, I would say "null model" essentially has the same meaning as "null hypothesis": the model if the null hypothesis is true. What this means, in a particular case, of course depends upon the concrete null hypothesis.
Your interpretations as "the average value" (you probably want to say "the marginal distribution ... | What is a null model in regression and how does it relate to the null hypothesis? | No, I would say "null model" essentially has the same meaning as "null hypothesis": the model if the null hypothesis is true. What this means, in a particular case, of course depends upon the concr | What is a null model in regression and how does it relate to the null hypothesis?
No, I would say "null model" essentially has the same meaning as "null hypothesis": the model if the null hypothesis is true. What this means, in a particular case, of course depends upon the concrete null hypothesis.
Your interpreta... | What is a null model in regression and how does it relate to the null hypothesis?
No, I would say "null model" essentially has the same meaning as "null hypothesis": the model if the null hypothesis is true. What this means, in a particular case, of course depends upon the concr |
11,408 | What is a null model in regression and how does it relate to the null hypothesis? | A null model is related to a null hypothesis. Take the following univariate model:
$Y=\alpha+\beta_{1}X + \epsilon$
My null hypothesis would normally be that $\beta_{1}$ is statistically no different from zero.
$H_{0}: \beta_{1}=0$ (null hypothesis)
$H_{A}: \beta_{1}\neq 0$ (alternative hypothesis)
For a univariate lin... | What is a null model in regression and how does it relate to the null hypothesis? | A null model is related to a null hypothesis. Take the following univariate model:
$Y=\alpha+\beta_{1}X + \epsilon$
My null hypothesis would normally be that $\beta_{1}$ is statistically no different | What is a null model in regression and how does it relate to the null hypothesis?
A null model is related to a null hypothesis. Take the following univariate model:
$Y=\alpha+\beta_{1}X + \epsilon$
My null hypothesis would normally be that $\beta_{1}$ is statistically no different from zero.
$H_{0}: \beta_{1}=0$ (null ... | What is a null model in regression and how does it relate to the null hypothesis?
A null model is related to a null hypothesis. Take the following univariate model:
$Y=\alpha+\beta_{1}X + \epsilon$
My null hypothesis would normally be that $\beta_{1}$ is statistically no different |
11,409 | What is a null model in regression and how does it relate to the null hypothesis? | In regression, as described partially in the other two answers, the null model is the null hypothesis that all the regression parameters are 0. So you can interpret this as saying that under the null hypothesis, there is no trend and the best estimate/predictor of a new observation is the mean, which is 0 in the case o... | What is a null model in regression and how does it relate to the null hypothesis? | In regression, as described partially in the other two answers, the null model is the null hypothesis that all the regression parameters are 0. So you can interpret this as saying that under the null | What is a null model in regression and how does it relate to the null hypothesis?
In regression, as described partially in the other two answers, the null model is the null hypothesis that all the regression parameters are 0. So you can interpret this as saying that under the null hypothesis, there is no trend and the ... | What is a null model in regression and how does it relate to the null hypothesis?
In regression, as described partially in the other two answers, the null model is the null hypothesis that all the regression parameters are 0. So you can interpret this as saying that under the null |
11,410 | Why is logistic regression particularly prone to overfitting in high dimensions? | The existing answers aren't wrong, but I think the explanation could be a little more intuitive. There are three key ideas here.
1. Asymptotic Predictions
In logistic regression we use a linear model to predict $\mu$,
the log-odds that $y=1$
$$
\mu = \beta X
$$
We then use the logistic/inverse logit function to convert... | Why is logistic regression particularly prone to overfitting in high dimensions? | The existing answers aren't wrong, but I think the explanation could be a little more intuitive. There are three key ideas here.
1. Asymptotic Predictions
In logistic regression we use a linear model | Why is logistic regression particularly prone to overfitting in high dimensions?
The existing answers aren't wrong, but I think the explanation could be a little more intuitive. There are three key ideas here.
1. Asymptotic Predictions
In logistic regression we use a linear model to predict $\mu$,
the log-odds that $y=... | Why is logistic regression particularly prone to overfitting in high dimensions?
The existing answers aren't wrong, but I think the explanation could be a little more intuitive. There are three key ideas here.
1. Asymptotic Predictions
In logistic regression we use a linear model |
11,411 | Why is logistic regression particularly prone to overfitting in high dimensions? | The asymptotic nature refers to the logistic curve itself. The optimizer, if not regularized, will enlarge the weights of the logistic regression to put $wx$ as far as possible to the left or right per sample to reduce the loss maximally.
Lets assume one feature that provides perfect separation, one can imagine $wx$ ge... | Why is logistic regression particularly prone to overfitting in high dimensions? | The asymptotic nature refers to the logistic curve itself. The optimizer, if not regularized, will enlarge the weights of the logistic regression to put $wx$ as far as possible to the left or right pe | Why is logistic regression particularly prone to overfitting in high dimensions?
The asymptotic nature refers to the logistic curve itself. The optimizer, if not regularized, will enlarge the weights of the logistic regression to put $wx$ as far as possible to the left or right per sample to reduce the loss maximally.
... | Why is logistic regression particularly prone to overfitting in high dimensions?
The asymptotic nature refers to the logistic curve itself. The optimizer, if not regularized, will enlarge the weights of the logistic regression to put $wx$ as far as possible to the left or right pe |
11,412 | Why is logistic regression particularly prone to overfitting in high dimensions? | This has not to do with that specific log loss function.
That loss function is related to binomial/binary regression and not specifically to the logistic regression. With other loss functions you would get the same 'problem'.
So what is the case instead?
Logistic regression is a special case of this binomial/binary re... | Why is logistic regression particularly prone to overfitting in high dimensions? | This has not to do with that specific log loss function.
That loss function is related to binomial/binary regression and not specifically to the logistic regression. With other loss functions you woul | Why is logistic regression particularly prone to overfitting in high dimensions?
This has not to do with that specific log loss function.
That loss function is related to binomial/binary regression and not specifically to the logistic regression. With other loss functions you would get the same 'problem'.
So what is th... | Why is logistic regression particularly prone to overfitting in high dimensions?
This has not to do with that specific log loss function.
That loss function is related to binomial/binary regression and not specifically to the logistic regression. With other loss functions you woul |
11,413 | Why is logistic regression particularly prone to overfitting in high dimensions? | It seems to me that the answer is much simpler than what has been described so elegantly with others' answers. Overfitting increases when the sample size decreases. Overfitting is a function of the effective sample size. Overfitting is minimal for a given apparent sample size when Y is continuous, i.e., has highest ... | Why is logistic regression particularly prone to overfitting in high dimensions? | It seems to me that the answer is much simpler than what has been described so elegantly with others' answers. Overfitting increases when the sample size decreases. Overfitting is a function of the | Why is logistic regression particularly prone to overfitting in high dimensions?
It seems to me that the answer is much simpler than what has been described so elegantly with others' answers. Overfitting increases when the sample size decreases. Overfitting is a function of the effective sample size. Overfitting is ... | Why is logistic regression particularly prone to overfitting in high dimensions?
It seems to me that the answer is much simpler than what has been described so elegantly with others' answers. Overfitting increases when the sample size decreases. Overfitting is a function of the |
11,414 | Why is logistic regression particularly prone to overfitting in high dimensions? | Logistic regression is a convex optimization problem (the likelihood function is concave), and it's known to not have a finite solution when it can fully separate the data, so the loss function can only reach its lowest value asymptomatically as the weights tend to ± infinity. This has the effect of tightening decisio... | Why is logistic regression particularly prone to overfitting in high dimensions? | Logistic regression is a convex optimization problem (the likelihood function is concave), and it's known to not have a finite solution when it can fully separate the data, so the loss function can on | Why is logistic regression particularly prone to overfitting in high dimensions?
Logistic regression is a convex optimization problem (the likelihood function is concave), and it's known to not have a finite solution when it can fully separate the data, so the loss function can only reach its lowest value asymptomatica... | Why is logistic regression particularly prone to overfitting in high dimensions?
Logistic regression is a convex optimization problem (the likelihood function is concave), and it's known to not have a finite solution when it can fully separate the data, so the loss function can on |
11,415 | Why is logistic regression particularly prone to overfitting in high dimensions? | You give the source’s explanation yourself, where it says in your link:
Imagine that you assign a unique id to each example, and map each id
to its own feature. If you don't specify a regularization function,
the model will become completely overfit. That's because the model
would try to drive loss to zero on all exam... | Why is logistic regression particularly prone to overfitting in high dimensions? | You give the source’s explanation yourself, where it says in your link:
Imagine that you assign a unique id to each example, and map each id
to its own feature. If you don't specify a regularization | Why is logistic regression particularly prone to overfitting in high dimensions?
You give the source’s explanation yourself, where it says in your link:
Imagine that you assign a unique id to each example, and map each id
to its own feature. If you don't specify a regularization function,
the model will become complet... | Why is logistic regression particularly prone to overfitting in high dimensions?
You give the source’s explanation yourself, where it says in your link:
Imagine that you assign a unique id to each example, and map each id
to its own feature. If you don't specify a regularization |
11,416 | Why is logistic regression particularly prone to overfitting in high dimensions? | I would split logistic regression into three cases:
modelling "binomial proportions" with no cell proportions being 0% or 100%
modelling "Bernoulli data"
something in between
What's the difference?
case 1
In case 1, your data cannot be separated using your predictors, because each feature $x_i$ has multiple records, ... | Why is logistic regression particularly prone to overfitting in high dimensions? | I would split logistic regression into three cases:
modelling "binomial proportions" with no cell proportions being 0% or 100%
modelling "Bernoulli data"
something in between
What's the difference?
| Why is logistic regression particularly prone to overfitting in high dimensions?
I would split logistic regression into three cases:
modelling "binomial proportions" with no cell proportions being 0% or 100%
modelling "Bernoulli data"
something in between
What's the difference?
case 1
In case 1, your data cannot be s... | Why is logistic regression particularly prone to overfitting in high dimensions?
I would split logistic regression into three cases:
modelling "binomial proportions" with no cell proportions being 0% or 100%
modelling "Bernoulli data"
something in between
What's the difference?
|
11,417 | Why is logistic regression particularly prone to overfitting in high dimensions? | The overfitting nature of logistic regression is related to the curse of dimensionality in way that I would characterize as inversed curse, and not what your source refers to as asymptotic nature. It's a consequence of Manhattan distance being resistant to the curse of dimensionality. I could also say that it drives th... | Why is logistic regression particularly prone to overfitting in high dimensions? | The overfitting nature of logistic regression is related to the curse of dimensionality in way that I would characterize as inversed curse, and not what your source refers to as asymptotic nature. It' | Why is logistic regression particularly prone to overfitting in high dimensions?
The overfitting nature of logistic regression is related to the curse of dimensionality in way that I would characterize as inversed curse, and not what your source refers to as asymptotic nature. It's a consequence of Manhattan distance b... | Why is logistic regression particularly prone to overfitting in high dimensions?
The overfitting nature of logistic regression is related to the curse of dimensionality in way that I would characterize as inversed curse, and not what your source refers to as asymptotic nature. It' |
11,418 | Positioning the arrows on a PCA biplot | There are many different ways to produce a PCA biplot and so there is no unique answer to your question. Here is a short overview.
We assume that the data matrix $\mathbf X$ has $n$ data points in rows and is centered (i.e. column means are all zero). For now, we do not assume that it was standardized, i.e. we conside... | Positioning the arrows on a PCA biplot | There are many different ways to produce a PCA biplot and so there is no unique answer to your question. Here is a short overview.
We assume that the data matrix $\mathbf X$ has $n$ data points in ro | Positioning the arrows on a PCA biplot
There are many different ways to produce a PCA biplot and so there is no unique answer to your question. Here is a short overview.
We assume that the data matrix $\mathbf X$ has $n$ data points in rows and is centered (i.e. column means are all zero). For now, we do not assume th... | Positioning the arrows on a PCA biplot
There are many different ways to produce a PCA biplot and so there is no unique answer to your question. Here is a short overview.
We assume that the data matrix $\mathbf X$ has $n$ data points in ro |
11,419 | How to show that this integral of the normal distribution is finite? | Intuitively, the result is obvious because (a) $\phi$ is a rapidly decreasing function (its magnitude decreases at a quadratic exponential rate) and (b) $\Phi$ is bounded above and, for negative $x,$ is also rapidly decreasing at essentially the same rate as $\phi.$ Thus the fraction $\phi^2/\Phi$ decreases rapidly fo... | How to show that this integral of the normal distribution is finite? | Intuitively, the result is obvious because (a) $\phi$ is a rapidly decreasing function (its magnitude decreases at a quadratic exponential rate) and (b) $\Phi$ is bounded above and, for negative $x,$ | How to show that this integral of the normal distribution is finite?
Intuitively, the result is obvious because (a) $\phi$ is a rapidly decreasing function (its magnitude decreases at a quadratic exponential rate) and (b) $\Phi$ is bounded above and, for negative $x,$ is also rapidly decreasing at essentially the same ... | How to show that this integral of the normal distribution is finite?
Intuitively, the result is obvious because (a) $\phi$ is a rapidly decreasing function (its magnitude decreases at a quadratic exponential rate) and (b) $\Phi$ is bounded above and, for negative $x,$ |
11,420 | How to show that this integral of the normal distribution is finite? | Here is a self-contained elementary argument, by a comparison with the Laplace distribution. We show
$$\int_{-\infty}^{\infty}\frac{\phi(x)^2}{\Phi(x)}dx<\frac{1}{2\sqrt{\pi}}+\sqrt{\frac\pi2}\simeq 1.535<\infty$$
The positive side of the integral has the bound
$$\int_{0}^{\infty}\frac{\phi(x)^2}{\Phi(x)}dx<
\int_{0}^{... | How to show that this integral of the normal distribution is finite? | Here is a self-contained elementary argument, by a comparison with the Laplace distribution. We show
$$\int_{-\infty}^{\infty}\frac{\phi(x)^2}{\Phi(x)}dx<\frac{1}{2\sqrt{\pi}}+\sqrt{\frac\pi2}\simeq 1 | How to show that this integral of the normal distribution is finite?
Here is a self-contained elementary argument, by a comparison with the Laplace distribution. We show
$$\int_{-\infty}^{\infty}\frac{\phi(x)^2}{\Phi(x)}dx<\frac{1}{2\sqrt{\pi}}+\sqrt{\frac\pi2}\simeq 1.535<\infty$$
The positive side of the integral has... | How to show that this integral of the normal distribution is finite?
Here is a self-contained elementary argument, by a comparison with the Laplace distribution. We show
$$\int_{-\infty}^{\infty}\frac{\phi(x)^2}{\Phi(x)}dx<\frac{1}{2\sqrt{\pi}}+\sqrt{\frac\pi2}\simeq 1 |
11,421 | How to show that this integral of the normal distribution is finite? | The integral relates to the expectation value of the normal hazard function
$$E_X[h(x)] = E_X\left[\dfrac{\phi(x)}{1-\Phi(x)}\right] = \int_{-\infty}^{\infty} \left(\dfrac{\phi(x)}{1-\Phi(x)}\right) \phi(x) dx = \int_{-\infty}^{\infty} \left(\dfrac{\phi(x)}{\Phi(x)}\right) \phi(x) dx$$
The last step is due to the symm... | How to show that this integral of the normal distribution is finite? | The integral relates to the expectation value of the normal hazard function
$$E_X[h(x)] = E_X\left[\dfrac{\phi(x)}{1-\Phi(x)}\right] = \int_{-\infty}^{\infty} \left(\dfrac{\phi(x)}{1-\Phi(x)}\right) \ | How to show that this integral of the normal distribution is finite?
The integral relates to the expectation value of the normal hazard function
$$E_X[h(x)] = E_X\left[\dfrac{\phi(x)}{1-\Phi(x)}\right] = \int_{-\infty}^{\infty} \left(\dfrac{\phi(x)}{1-\Phi(x)}\right) \phi(x) dx = \int_{-\infty}^{\infty} \left(\dfrac{\... | How to show that this integral of the normal distribution is finite?
The integral relates to the expectation value of the normal hazard function
$$E_X[h(x)] = E_X\left[\dfrac{\phi(x)}{1-\Phi(x)}\right] = \int_{-\infty}^{\infty} \left(\dfrac{\phi(x)}{1-\Phi(x)}\right) \ |
11,422 | How to show that this integral of the normal distribution is finite? | Intuitive approach
$\Phi(x)$ is changing in the interval $[0,1]$, whereas $\phi(x)^2$ is itself a normal distribution which is integrable. Thus, the only reason why the integral could not be finite, is because it diverges in the limit $x\rightarrow -\infty$.
By L'Hôpital's rule:
$$
\frac{\phi^2(x)}{\Phi(x)}\sim
\frac{2... | How to show that this integral of the normal distribution is finite? | Intuitive approach
$\Phi(x)$ is changing in the interval $[0,1]$, whereas $\phi(x)^2$ is itself a normal distribution which is integrable. Thus, the only reason why the integral could not be finite, i | How to show that this integral of the normal distribution is finite?
Intuitive approach
$\Phi(x)$ is changing in the interval $[0,1]$, whereas $\phi(x)^2$ is itself a normal distribution which is integrable. Thus, the only reason why the integral could not be finite, is because it diverges in the limit $x\rightarrow -\... | How to show that this integral of the normal distribution is finite?
Intuitive approach
$\Phi(x)$ is changing in the interval $[0,1]$, whereas $\phi(x)^2$ is itself a normal distribution which is integrable. Thus, the only reason why the integral could not be finite, i |
11,423 | How to show that this integral of the normal distribution is finite? | The integral on any interval $[a, \infty)$ is clearly finite. Now $\varphi(x)$ is convex on $(-\infty, -1]$ and so the tangent line to $\varphi$ at any $x < -1$ lies below $\varphi$. This tangent intersects the $x$-axis in $x+x^{-1}$. This gives the lower bound $$\Phi(x) > -\frac1{2x} \varphi(x)$$ for all $x < -1$ and... | How to show that this integral of the normal distribution is finite? | The integral on any interval $[a, \infty)$ is clearly finite. Now $\varphi(x)$ is convex on $(-\infty, -1]$ and so the tangent line to $\varphi$ at any $x < -1$ lies below $\varphi$. This tangent int | How to show that this integral of the normal distribution is finite?
The integral on any interval $[a, \infty)$ is clearly finite. Now $\varphi(x)$ is convex on $(-\infty, -1]$ and so the tangent line to $\varphi$ at any $x < -1$ lies below $\varphi$. This tangent intersects the $x$-axis in $x+x^{-1}$. This gives the ... | How to show that this integral of the normal distribution is finite?
The integral on any interval $[a, \infty)$ is clearly finite. Now $\varphi(x)$ is convex on $(-\infty, -1]$ and so the tangent line to $\varphi$ at any $x < -1$ lies below $\varphi$. This tangent int |
11,424 | What is the difference between SVM and LDA? | LDA:
Assumes: data is Normally distributed. All groups are identically distributed, in case the groups have different covariance matrices, LDA becomes Quadratic Discriminant Analysis. LDA is the best discriminator available in case all assumptions are actually met.
QDA, by the way, is a non-linear classifier.
SVM:
Gene... | What is the difference between SVM and LDA? | LDA:
Assumes: data is Normally distributed. All groups are identically distributed, in case the groups have different covariance matrices, LDA becomes Quadratic Discriminant Analysis. LDA is the best | What is the difference between SVM and LDA?
LDA:
Assumes: data is Normally distributed. All groups are identically distributed, in case the groups have different covariance matrices, LDA becomes Quadratic Discriminant Analysis. LDA is the best discriminator available in case all assumptions are actually met.
QDA, by th... | What is the difference between SVM and LDA?
LDA:
Assumes: data is Normally distributed. All groups are identically distributed, in case the groups have different covariance matrices, LDA becomes Quadratic Discriminant Analysis. LDA is the best |
11,425 | What is the difference between SVM and LDA? | Short and sweet answer:
The answers above are very thorough, so here is a quick description of how LDA and SVM work.
Support vector machines find a linear separator (linear combination, hyperplane) that separates the classes with the least error, and chooses the separator with the maximum margin (the width that the bou... | What is the difference between SVM and LDA? | Short and sweet answer:
The answers above are very thorough, so here is a quick description of how LDA and SVM work.
Support vector machines find a linear separator (linear combination, hyperplane) th | What is the difference between SVM and LDA?
Short and sweet answer:
The answers above are very thorough, so here is a quick description of how LDA and SVM work.
Support vector machines find a linear separator (linear combination, hyperplane) that separates the classes with the least error, and chooses the separator wit... | What is the difference between SVM and LDA?
Short and sweet answer:
The answers above are very thorough, so here is a quick description of how LDA and SVM work.
Support vector machines find a linear separator (linear combination, hyperplane) th |
11,426 | What is the difference between SVM and LDA? | SVM focuses only on the points that are difficult to classify, LDA focuses on all data points. Such difficult points are close to the decision boundary and are called Support Vectors. The decision boundary can be linear, but also e.g. an RBF kernel, or an polynomial kernel. Where LDA is a linear transformation to maxim... | What is the difference between SVM and LDA? | SVM focuses only on the points that are difficult to classify, LDA focuses on all data points. Such difficult points are close to the decision boundary and are called Support Vectors. The decision bou | What is the difference between SVM and LDA?
SVM focuses only on the points that are difficult to classify, LDA focuses on all data points. Such difficult points are close to the decision boundary and are called Support Vectors. The decision boundary can be linear, but also e.g. an RBF kernel, or an polynomial kernel. W... | What is the difference between SVM and LDA?
SVM focuses only on the points that are difficult to classify, LDA focuses on all data points. Such difficult points are close to the decision boundary and are called Support Vectors. The decision bou |
11,427 | What to conclude from this lasso plot (glmnet) | I think when trying to interpret these plots of coefficients by $\lambda$, $\log(\lambda)$, or $\sum_i | \beta_i |$, it helps a lot to know how they look in some simple cases. In particular, how they look when your model design matrix is uncorrelated, vs. when there is correlation in your design.
To that end, I create... | What to conclude from this lasso plot (glmnet) | I think when trying to interpret these plots of coefficients by $\lambda$, $\log(\lambda)$, or $\sum_i | \beta_i |$, it helps a lot to know how they look in some simple cases. In particular, how they | What to conclude from this lasso plot (glmnet)
I think when trying to interpret these plots of coefficients by $\lambda$, $\log(\lambda)$, or $\sum_i | \beta_i |$, it helps a lot to know how they look in some simple cases. In particular, how they look when your model design matrix is uncorrelated, vs. when there is co... | What to conclude from this lasso plot (glmnet)
I think when trying to interpret these plots of coefficients by $\lambda$, $\log(\lambda)$, or $\sum_i | \beta_i |$, it helps a lot to know how they look in some simple cases. In particular, how they |
11,428 | Difference between Primal, Dual and Kernel Ridge Regression | Short answer: no difference between Primal and Dual - it's only about the way of arriving to the solution. Kernel ridge regression is essentially the same as usual ridge regression, but uses the kernel trick to go non-linear.
Linear Regression
First of all, a usual Least Squares Linear Regression tries to fit a straigh... | Difference between Primal, Dual and Kernel Ridge Regression | Short answer: no difference between Primal and Dual - it's only about the way of arriving to the solution. Kernel ridge regression is essentially the same as usual ridge regression, but uses the kerne | Difference between Primal, Dual and Kernel Ridge Regression
Short answer: no difference between Primal and Dual - it's only about the way of arriving to the solution. Kernel ridge regression is essentially the same as usual ridge regression, but uses the kernel trick to go non-linear.
Linear Regression
First of all, a ... | Difference between Primal, Dual and Kernel Ridge Regression
Short answer: no difference between Primal and Dual - it's only about the way of arriving to the solution. Kernel ridge regression is essentially the same as usual ridge regression, but uses the kerne |
11,429 | What exactly is multi-hot encoding and how is it different from one-hot? | Imagine your have five different classes e.g. ['cat', 'dog', 'fish', 'bird', 'ant']. If you would use one-hot-encoding you would represent the presence of 'dog' in a five-dimensional binary vector like [0,1,0,0,0]. If you would use multi-hot-encoding you would first label-encode your classes, thus having only a single ... | What exactly is multi-hot encoding and how is it different from one-hot? | Imagine your have five different classes e.g. ['cat', 'dog', 'fish', 'bird', 'ant']. If you would use one-hot-encoding you would represent the presence of 'dog' in a five-dimensional binary vector lik | What exactly is multi-hot encoding and how is it different from one-hot?
Imagine your have five different classes e.g. ['cat', 'dog', 'fish', 'bird', 'ant']. If you would use one-hot-encoding you would represent the presence of 'dog' in a five-dimensional binary vector like [0,1,0,0,0]. If you would use multi-hot-encod... | What exactly is multi-hot encoding and how is it different from one-hot?
Imagine your have five different classes e.g. ['cat', 'dog', 'fish', 'bird', 'ant']. If you would use one-hot-encoding you would represent the presence of 'dog' in a five-dimensional binary vector lik |
11,430 | What exactly is multi-hot encoding and how is it different from one-hot? | The accepted answer seems rather eccentric to me. I think that is rarely done, if ever, and will usually yield bad results.
There's a much more common, sensible use case for this. "Multi-hot encoding" doesn't seem to be a standard term, but I'm not sure there's any standard term. scikit-learn refers to a multi label bi... | What exactly is multi-hot encoding and how is it different from one-hot? | The accepted answer seems rather eccentric to me. I think that is rarely done, if ever, and will usually yield bad results.
There's a much more common, sensible use case for this. "Multi-hot encoding" | What exactly is multi-hot encoding and how is it different from one-hot?
The accepted answer seems rather eccentric to me. I think that is rarely done, if ever, and will usually yield bad results.
There's a much more common, sensible use case for this. "Multi-hot encoding" doesn't seem to be a standard term, but I'm no... | What exactly is multi-hot encoding and how is it different from one-hot?
The accepted answer seems rather eccentric to me. I think that is rarely done, if ever, and will usually yield bad results.
There's a much more common, sensible use case for this. "Multi-hot encoding" |
11,431 | What exactly is multi-hot encoding and how is it different from one-hot? | I too find the accepted answer likely wrong. I could not find any reference to such an encoding anywhere.
In Tensorflow and in Francois Chollet's (the creator of Keras) book: "Deep learning with python", multi-hot is a binary encoding of multiple tokens in a single vector.
Meaning, you can encode a text in a single vec... | What exactly is multi-hot encoding and how is it different from one-hot? | I too find the accepted answer likely wrong. I could not find any reference to such an encoding anywhere.
In Tensorflow and in Francois Chollet's (the creator of Keras) book: "Deep learning with pytho | What exactly is multi-hot encoding and how is it different from one-hot?
I too find the accepted answer likely wrong. I could not find any reference to such an encoding anywhere.
In Tensorflow and in Francois Chollet's (the creator of Keras) book: "Deep learning with python", multi-hot is a binary encoding of multiple ... | What exactly is multi-hot encoding and how is it different from one-hot?
I too find the accepted answer likely wrong. I could not find any reference to such an encoding anywhere.
In Tensorflow and in Francois Chollet's (the creator of Keras) book: "Deep learning with pytho |
11,432 | In machine learning, why are superscripts used instead of subscripts? | If $x$ denotes a vector $x \in \mathbb R^m$ then $x_i$ is a standard notation for the $i$-th coordinate of $x$, i.e. $$x = (x_1, x_2, \ldots, x_m)\in\mathbb R^m.$$
If you have a collection of $n$ such vectors, how would you denote an $i$-th vector? You cannot write $x_i$, this has other standard meaning. So sometimes p... | In machine learning, why are superscripts used instead of subscripts? | If $x$ denotes a vector $x \in \mathbb R^m$ then $x_i$ is a standard notation for the $i$-th coordinate of $x$, i.e. $$x = (x_1, x_2, \ldots, x_m)\in\mathbb R^m.$$
If you have a collection of $n$ such | In machine learning, why are superscripts used instead of subscripts?
If $x$ denotes a vector $x \in \mathbb R^m$ then $x_i$ is a standard notation for the $i$-th coordinate of $x$, i.e. $$x = (x_1, x_2, \ldots, x_m)\in\mathbb R^m.$$
If you have a collection of $n$ such vectors, how would you denote an $i$-th vector? Y... | In machine learning, why are superscripts used instead of subscripts?
If $x$ denotes a vector $x \in \mathbb R^m$ then $x_i$ is a standard notation for the $i$-th coordinate of $x$, i.e. $$x = (x_1, x_2, \ldots, x_m)\in\mathbb R^m.$$
If you have a collection of $n$ such |
11,433 | In machine learning, why are superscripts used instead of subscripts? | The use of super scripts as you have stated I believe is not very common in machine learning literature. I'd have to review Ng's course notes to confirm, but if he's putting that use there, I would say he would be origin of the proliferation of this notation. This is a possibility. Either way, not to be too unkind, but... | In machine learning, why are superscripts used instead of subscripts? | The use of super scripts as you have stated I believe is not very common in machine learning literature. I'd have to review Ng's course notes to confirm, but if he's putting that use there, I would sa | In machine learning, why are superscripts used instead of subscripts?
The use of super scripts as you have stated I believe is not very common in machine learning literature. I'd have to review Ng's course notes to confirm, but if he's putting that use there, I would say he would be origin of the proliferation of this ... | In machine learning, why are superscripts used instead of subscripts?
The use of super scripts as you have stated I believe is not very common in machine learning literature. I'd have to review Ng's course notes to confirm, but if he's putting that use there, I would sa |
11,434 | In machine learning, why are superscripts used instead of subscripts? | Superscripts are already used for exponentiation.
In mathematics superscripts are used left and right depending on the field. The choice is always historical legacy, nothing more. Whoever first got into the field set the convention of using sub- or superscripts.
Two examples. Superscripts are used to denote derivati... | In machine learning, why are superscripts used instead of subscripts? | Superscripts are already used for exponentiation.
In mathematics superscripts are used left and right depending on the field. The choice is always historical legacy, nothing more. Whoever first got | In machine learning, why are superscripts used instead of subscripts?
Superscripts are already used for exponentiation.
In mathematics superscripts are used left and right depending on the field. The choice is always historical legacy, nothing more. Whoever first got into the field set the convention of using sub- o... | In machine learning, why are superscripts used instead of subscripts?
Superscripts are already used for exponentiation.
In mathematics superscripts are used left and right depending on the field. The choice is always historical legacy, nothing more. Whoever first got |
11,435 | What happens when I include a squared variable in my regression? | Well, first of, the dummy variable is interpreted as a change in intercept. That is, your coefficient $\beta_3$ gives you the difference in the intercept when $D=1$, i.e. when $D=1$, the intercept is $\beta_0 + \beta_3$. That interpretation doesn't change when adding the squared $x_1$.
Now, the point of adding a squar... | What happens when I include a squared variable in my regression? | Well, first of, the dummy variable is interpreted as a change in intercept. That is, your coefficient $\beta_3$ gives you the difference in the intercept when $D=1$, i.e. when $D=1$, the intercept is | What happens when I include a squared variable in my regression?
Well, first of, the dummy variable is interpreted as a change in intercept. That is, your coefficient $\beta_3$ gives you the difference in the intercept when $D=1$, i.e. when $D=1$, the intercept is $\beta_0 + \beta_3$. That interpretation doesn't change... | What happens when I include a squared variable in my regression?
Well, first of, the dummy variable is interpreted as a change in intercept. That is, your coefficient $\beta_3$ gives you the difference in the intercept when $D=1$, i.e. when $D=1$, the intercept is |
11,436 | What happens when I include a squared variable in my regression? | A good example of including square of variable comes from labor economics. If you assume y as wage (or log of wage) and x as an age, then including x^2 means that you are testing the quadratic relationship between an age and wage earning. Wage increases with the age as people become more experienced but at the higher a... | What happens when I include a squared variable in my regression? | A good example of including square of variable comes from labor economics. If you assume y as wage (or log of wage) and x as an age, then including x^2 means that you are testing the quadratic relatio | What happens when I include a squared variable in my regression?
A good example of including square of variable comes from labor economics. If you assume y as wage (or log of wage) and x as an age, then including x^2 means that you are testing the quadratic relationship between an age and wage earning. Wage increases w... | What happens when I include a squared variable in my regression?
A good example of including square of variable comes from labor economics. If you assume y as wage (or log of wage) and x as an age, then including x^2 means that you are testing the quadratic relatio |
11,437 | Monty Hall Problem with a Fallible Monty | Let's start with the regular Monty Hall problem. Three doors, behind one of which is a car. The other two have goats behind them. You pick door number 1 and Monty opens door number 2 to show you there is a goat behind that one. Should you switch your guess to door number 3? (Note that the numbers we use to refer to eac... | Monty Hall Problem with a Fallible Monty | Let's start with the regular Monty Hall problem. Three doors, behind one of which is a car. The other two have goats behind them. You pick door number 1 and Monty opens door number 2 to show you there | Monty Hall Problem with a Fallible Monty
Let's start with the regular Monty Hall problem. Three doors, behind one of which is a car. The other two have goats behind them. You pick door number 1 and Monty opens door number 2 to show you there is a goat behind that one. Should you switch your guess to door number 3? (Not... | Monty Hall Problem with a Fallible Monty
Let's start with the regular Monty Hall problem. Three doors, behind one of which is a car. The other two have goats behind them. You pick door number 1 and Monty opens door number 2 to show you there |
11,438 | Monty Hall Problem with a Fallible Monty | This should be a fairly simple variation of the problem (though I note your limited maths background, so I guess that is relative). I would suggest that you first try to determine the solution conditional on whether Monte is infallible, or fully fallible. The first case is just the ordinary Monte Hall problem, so no ... | Monty Hall Problem with a Fallible Monty | This should be a fairly simple variation of the problem (though I note your limited maths background, so I guess that is relative). I would suggest that you first try to determine the solution condit | Monty Hall Problem with a Fallible Monty
This should be a fairly simple variation of the problem (though I note your limited maths background, so I guess that is relative). I would suggest that you first try to determine the solution conditional on whether Monte is infallible, or fully fallible. The first case is jus... | Monty Hall Problem with a Fallible Monty
This should be a fairly simple variation of the problem (though I note your limited maths background, so I guess that is relative). I would suggest that you first try to determine the solution condit |
11,439 | Monty Hall Problem with a Fallible Monty | Based on the comments on Ben's answer, I am going to offer up two different interpretations of this variant of Monty Hall, differing to Ruben van Bergen's.
The first one I am going to call Liar Monty and the second one Unreliable Monty. In both versions the problem proceeds as follows:
(0) There are three doors, behin... | Monty Hall Problem with a Fallible Monty | Based on the comments on Ben's answer, I am going to offer up two different interpretations of this variant of Monty Hall, differing to Ruben van Bergen's.
The first one I am going to call Liar Monty | Monty Hall Problem with a Fallible Monty
Based on the comments on Ben's answer, I am going to offer up two different interpretations of this variant of Monty Hall, differing to Ruben van Bergen's.
The first one I am going to call Liar Monty and the second one Unreliable Monty. In both versions the problem proceeds as ... | Monty Hall Problem with a Fallible Monty
Based on the comments on Ben's answer, I am going to offer up two different interpretations of this variant of Monty Hall, differing to Ruben van Bergen's.
The first one I am going to call Liar Monty |
11,440 | Monty Hall Problem with a Fallible Monty | For some reason, a moderator decided to delete my own answer to my own question, on the grounds that it contained "discussion." I don't really see HOW I can explain what is the Best Answer without discussing what makes it work for me, and how it can be applied in practice.
I appreciate the insights and formulae which w... | Monty Hall Problem with a Fallible Monty | For some reason, a moderator decided to delete my own answer to my own question, on the grounds that it contained "discussion." I don't really see HOW I can explain what is the Best Answer without dis | Monty Hall Problem with a Fallible Monty
For some reason, a moderator decided to delete my own answer to my own question, on the grounds that it contained "discussion." I don't really see HOW I can explain what is the Best Answer without discussing what makes it work for me, and how it can be applied in practice.
I app... | Monty Hall Problem with a Fallible Monty
For some reason, a moderator decided to delete my own answer to my own question, on the grounds that it contained "discussion." I don't really see HOW I can explain what is the Best Answer without dis |
11,441 | Why is the cost function of neural networks non-convex? | $\sum_i (y_i- \hat y_i)^2$ is indeed convex in $\hat y_i$. But if $\hat y_i = f(x_i ; \theta)$ it may not be convex in $\theta$, which is the situation with most non-linear models, and we actually care about convexity in $\theta$ because that's what we're optimizing the cost function over.
For example, let's consider a... | Why is the cost function of neural networks non-convex? | $\sum_i (y_i- \hat y_i)^2$ is indeed convex in $\hat y_i$. But if $\hat y_i = f(x_i ; \theta)$ it may not be convex in $\theta$, which is the situation with most non-linear models, and we actually car | Why is the cost function of neural networks non-convex?
$\sum_i (y_i- \hat y_i)^2$ is indeed convex in $\hat y_i$. But if $\hat y_i = f(x_i ; \theta)$ it may not be convex in $\theta$, which is the situation with most non-linear models, and we actually care about convexity in $\theta$ because that's what we're optimizi... | Why is the cost function of neural networks non-convex?
$\sum_i (y_i- \hat y_i)^2$ is indeed convex in $\hat y_i$. But if $\hat y_i = f(x_i ; \theta)$ it may not be convex in $\theta$, which is the situation with most non-linear models, and we actually car |
11,442 | How to interpret regression coefficients when response was transformed by the 4th root? | The best solution is, at the outset, to choose a re-expression that has a meaning in the field of study.
(For instance, when regressing body weights against independent factors, it's likely that either a cube root ($1/3$ power) or square root ($1/2$ power) will be indicated. Noting that weight is a good proxy for volu... | How to interpret regression coefficients when response was transformed by the 4th root? | The best solution is, at the outset, to choose a re-expression that has a meaning in the field of study.
(For instance, when regressing body weights against independent factors, it's likely that eithe | How to interpret regression coefficients when response was transformed by the 4th root?
The best solution is, at the outset, to choose a re-expression that has a meaning in the field of study.
(For instance, when regressing body weights against independent factors, it's likely that either a cube root ($1/3$ power) or s... | How to interpret regression coefficients when response was transformed by the 4th root?
The best solution is, at the outset, to choose a re-expression that has a meaning in the field of study.
(For instance, when regressing body weights against independent factors, it's likely that eithe |
11,443 | How to interpret regression coefficients when response was transformed by the 4th root? | An alternative to transformation here is to use a generalised linear model with link function power and power 1/4. What error family to use is open, which gives you more flexibility than you have with linear regression and an assumption of conditional normality. One major advantage of this procedure is that predictions... | How to interpret regression coefficients when response was transformed by the 4th root? | An alternative to transformation here is to use a generalised linear model with link function power and power 1/4. What error family to use is open, which gives you more flexibility than you have with | How to interpret regression coefficients when response was transformed by the 4th root?
An alternative to transformation here is to use a generalised linear model with link function power and power 1/4. What error family to use is open, which gives you more flexibility than you have with linear regression and an assump... | How to interpret regression coefficients when response was transformed by the 4th root?
An alternative to transformation here is to use a generalised linear model with link function power and power 1/4. What error family to use is open, which gives you more flexibility than you have with |
11,444 | How to interpret regression coefficients when response was transformed by the 4th root? | I have seen papers using quartic root regression coefficients in thinking about percentage changes, while avoiding taking logs (and dropping observations).
If we're interested in using quartic roots to calculate percentage changes, we know that:
$\hat{Y} = (\alpha + \hat{\beta}_1 X_1 + \hat{\beta}_2 X_2)^4 \implies ... | How to interpret regression coefficients when response was transformed by the 4th root? | I have seen papers using quartic root regression coefficients in thinking about percentage changes, while avoiding taking logs (and dropping observations).
If we're interested in using quartic roots | How to interpret regression coefficients when response was transformed by the 4th root?
I have seen papers using quartic root regression coefficients in thinking about percentage changes, while avoiding taking logs (and dropping observations).
If we're interested in using quartic roots to calculate percentage changes... | How to interpret regression coefficients when response was transformed by the 4th root?
I have seen papers using quartic root regression coefficients in thinking about percentage changes, while avoiding taking logs (and dropping observations).
If we're interested in using quartic roots |
11,445 | Backpropagation algorithm and error in hidden layer | I figured I'd answer a self-contained post here for anyone that's interested. This will be using the notation described here.
Introduction
The idea behind backpropagation is to have a set of "training examples" that we use to train our network. Each of these has a known answer, so we can plug them into the neural netwo... | Backpropagation algorithm and error in hidden layer | I figured I'd answer a self-contained post here for anyone that's interested. This will be using the notation described here.
Introduction
The idea behind backpropagation is to have a set of "training | Backpropagation algorithm and error in hidden layer
I figured I'd answer a self-contained post here for anyone that's interested. This will be using the notation described here.
Introduction
The idea behind backpropagation is to have a set of "training examples" that we use to train our network. Each of these has a kno... | Backpropagation algorithm and error in hidden layer
I figured I'd answer a self-contained post here for anyone that's interested. This will be using the notation described here.
Introduction
The idea behind backpropagation is to have a set of "training |
11,446 | Backpropagation algorithm and error in hidden layer | I haven't dealt with Neural Networks for some years now, but I think you will find everything you need here:
Neural Networks - A Systematic Introduction, Chapter 7: The backpropagation algorithm
I apologize for not writing the direct answer here, but since I have to look up the details to remember (like you) and given ... | Backpropagation algorithm and error in hidden layer | I haven't dealt with Neural Networks for some years now, but I think you will find everything you need here:
Neural Networks - A Systematic Introduction, Chapter 7: The backpropagation algorithm
I apo | Backpropagation algorithm and error in hidden layer
I haven't dealt with Neural Networks for some years now, but I think you will find everything you need here:
Neural Networks - A Systematic Introduction, Chapter 7: The backpropagation algorithm
I apologize for not writing the direct answer here, but since I have to l... | Backpropagation algorithm and error in hidden layer
I haven't dealt with Neural Networks for some years now, but I think you will find everything you need here:
Neural Networks - A Systematic Introduction, Chapter 7: The backpropagation algorithm
I apo |
11,447 | Backpropagation algorithm and error in hidden layer | I'll address the main confusion first: there is no error of a hidden layer. There's only an error of the output. The backpropagation = "back" (chain rule of differentiation) + "propagation" (information travels between layers). I'll explain.
The backpropagation term comes from the following intuition: your inputs propa... | Backpropagation algorithm and error in hidden layer | I'll address the main confusion first: there is no error of a hidden layer. There's only an error of the output. The backpropagation = "back" (chain rule of differentiation) + "propagation" (informati | Backpropagation algorithm and error in hidden layer
I'll address the main confusion first: there is no error of a hidden layer. There's only an error of the output. The backpropagation = "back" (chain rule of differentiation) + "propagation" (information travels between layers). I'll explain.
The backpropagation term c... | Backpropagation algorithm and error in hidden layer
I'll address the main confusion first: there is no error of a hidden layer. There's only an error of the output. The backpropagation = "back" (chain rule of differentiation) + "propagation" (informati |
11,448 | Explain in layperson's terms why predictive models aren't causally interpretable | First of all, I don't think this should be treated as a strict dichotomy: "predictive models can never establish causal inference." There are various situations in which a predictive model gives us "pretty darn good" confidence that a given causal relationship exists. So what I'd say is that predictive models - no matt... | Explain in layperson's terms why predictive models aren't causally interpretable | First of all, I don't think this should be treated as a strict dichotomy: "predictive models can never establish causal inference." There are various situations in which a predictive model gives us "p | Explain in layperson's terms why predictive models aren't causally interpretable
First of all, I don't think this should be treated as a strict dichotomy: "predictive models can never establish causal inference." There are various situations in which a predictive model gives us "pretty darn good" confidence that a give... | Explain in layperson's terms why predictive models aren't causally interpretable
First of all, I don't think this should be treated as a strict dichotomy: "predictive models can never establish causal inference." There are various situations in which a predictive model gives us "p |
11,449 | Explain in layperson's terms why predictive models aren't causally interpretable | I think this explanation is best approached sequentially. Start with a simple story:
When my dog Winston wags his tail, that indicates he is happy. For instance, he never wags it at the vet, wags it a bit when I get his leash, and wags a whole lot when I also grab a tennis ball. But if I wag Winston's tail for him, it... | Explain in layperson's terms why predictive models aren't causally interpretable | I think this explanation is best approached sequentially. Start with a simple story:
When my dog Winston wags his tail, that indicates he is happy. For instance, he never wags it at the vet, wags it | Explain in layperson's terms why predictive models aren't causally interpretable
I think this explanation is best approached sequentially. Start with a simple story:
When my dog Winston wags his tail, that indicates he is happy. For instance, he never wags it at the vet, wags it a bit when I get his leash, and wags a ... | Explain in layperson's terms why predictive models aren't causally interpretable
I think this explanation is best approached sequentially. Start with a simple story:
When my dog Winston wags his tail, that indicates he is happy. For instance, he never wags it at the vet, wags it |
11,450 | Explain in layperson's terms why predictive models aren't causally interpretable | I don't think you even need to posit a covariate adjustment set $\textbf{Z}$ nor the indexation of black-box models to convey in layman terms the main point. Assume the following:
$y$ is number of people drowning in a given month in a given city
$x$ is number of ice-cream sold in a given month in a given city
$u$ is t... | Explain in layperson's terms why predictive models aren't causally interpretable | I don't think you even need to posit a covariate adjustment set $\textbf{Z}$ nor the indexation of black-box models to convey in layman terms the main point. Assume the following:
$y$ is number of pe | Explain in layperson's terms why predictive models aren't causally interpretable
I don't think you even need to posit a covariate adjustment set $\textbf{Z}$ nor the indexation of black-box models to convey in layman terms the main point. Assume the following:
$y$ is number of people drowning in a given month in a giv... | Explain in layperson's terms why predictive models aren't causally interpretable
I don't think you even need to posit a covariate adjustment set $\textbf{Z}$ nor the indexation of black-box models to convey in layman terms the main point. Assume the following:
$y$ is number of pe |
11,451 | Explain in layperson's terms why predictive models aren't causally interpretable | Correlation does not equal causation. Predictive models using advanced techniques such as machine learning can be quite good at finding associations between predictive variables and an outcome, but this isn't the same as determining the causal relationships between those variables.
For example, as a researcher you may ... | Explain in layperson's terms why predictive models aren't causally interpretable | Correlation does not equal causation. Predictive models using advanced techniques such as machine learning can be quite good at finding associations between predictive variables and an outcome, but th | Explain in layperson's terms why predictive models aren't causally interpretable
Correlation does not equal causation. Predictive models using advanced techniques such as machine learning can be quite good at finding associations between predictive variables and an outcome, but this isn't the same as determining the ca... | Explain in layperson's terms why predictive models aren't causally interpretable
Correlation does not equal causation. Predictive models using advanced techniques such as machine learning can be quite good at finding associations between predictive variables and an outcome, but th |
11,452 | Explain in layperson's terms why predictive models aren't causally interpretable | Oo Oo! I'm a mathematical layperson! Let's see if I can do this:
TLDR: I use predictions (or "predictive models") to prepare for events beyond my control without having to know what actually causes them.
I might posit that a lay predictive model is "whether the weather report says it will rain this weekend". I may no... | Explain in layperson's terms why predictive models aren't causally interpretable | Oo Oo! I'm a mathematical layperson! Let's see if I can do this:
TLDR: I use predictions (or "predictive models") to prepare for events beyond my control without having to know what actually causes t | Explain in layperson's terms why predictive models aren't causally interpretable
Oo Oo! I'm a mathematical layperson! Let's see if I can do this:
TLDR: I use predictions (or "predictive models") to prepare for events beyond my control without having to know what actually causes them.
I might posit that a lay predicti... | Explain in layperson's terms why predictive models aren't causally interpretable
Oo Oo! I'm a mathematical layperson! Let's see if I can do this:
TLDR: I use predictions (or "predictive models") to prepare for events beyond my control without having to know what actually causes t |
11,453 | Explain in layperson's terms why predictive models aren't causally interpretable | The basic problem is that a non-causal predictive model may fail if used for interventions. Start with a very simple example where an important part of the real world has:
$$ Cause \rightarrow \mathit{Effect} \rightarrow Measurement $$
Because we imagine Measurement is nearly perfect, the best predictive model will pre... | Explain in layperson's terms why predictive models aren't causally interpretable | The basic problem is that a non-causal predictive model may fail if used for interventions. Start with a very simple example where an important part of the real world has:
$$ Cause \rightarrow \mathit | Explain in layperson's terms why predictive models aren't causally interpretable
The basic problem is that a non-causal predictive model may fail if used for interventions. Start with a very simple example where an important part of the real world has:
$$ Cause \rightarrow \mathit{Effect} \rightarrow Measurement $$
Bec... | Explain in layperson's terms why predictive models aren't causally interpretable
The basic problem is that a non-causal predictive model may fail if used for interventions. Start with a very simple example where an important part of the real world has:
$$ Cause \rightarrow \mathit |
11,454 | Explain in layperson's terms why predictive models aren't causally interpretable | If it's a person who really knows barely anything about statistics and causation I would provide some examples that are straightforward.
If you have data on the number of bathrooms in someone's largest house, you can classify the person as a billionaire or not, in the sense that billionaire mansions have numerous bathr... | Explain in layperson's terms why predictive models aren't causally interpretable | If it's a person who really knows barely anything about statistics and causation I would provide some examples that are straightforward.
If you have data on the number of bathrooms in someone's larges | Explain in layperson's terms why predictive models aren't causally interpretable
If it's a person who really knows barely anything about statistics and causation I would provide some examples that are straightforward.
If you have data on the number of bathrooms in someone's largest house, you can classify the person as... | Explain in layperson's terms why predictive models aren't causally interpretable
If it's a person who really knows barely anything about statistics and causation I would provide some examples that are straightforward.
If you have data on the number of bathrooms in someone's larges |
11,455 | After bootstrapping regression analysis, all p-values are multiple of 0.001996 | Suppose you have a regression coefficient estimate of 1.2. To compute its p-value, you need to know the probability of observing a coefficient that large (or larger) under the null hypothesis. To do this, you have to know the null distribution of this coefficient. Bootstrap resampling is one way to estimate this null d... | After bootstrapping regression analysis, all p-values are multiple of 0.001996 | Suppose you have a regression coefficient estimate of 1.2. To compute its p-value, you need to know the probability of observing a coefficient that large (or larger) under the null hypothesis. To do t | After bootstrapping regression analysis, all p-values are multiple of 0.001996
Suppose you have a regression coefficient estimate of 1.2. To compute its p-value, you need to know the probability of observing a coefficient that large (or larger) under the null hypothesis. To do this, you have to know the null distributi... | After bootstrapping regression analysis, all p-values are multiple of 0.001996
Suppose you have a regression coefficient estimate of 1.2. To compute its p-value, you need to know the probability of observing a coefficient that large (or larger) under the null hypothesis. To do t |
11,456 | How to perform post-hoc test on lmer model? | You could use emmeans::emmeans() or lmerTest::difflsmeans(), or multcomp::glht().
I prefer emmeans (previously lsmeans).
library(emmeans)
emmeans(model, list(pairwise ~ Group), adjust = "tukey")
The next option is difflsmeans. Note difflsmeans cannot correct for multiple comparisons, and uses the Satterthwaite method ... | How to perform post-hoc test on lmer model? | You could use emmeans::emmeans() or lmerTest::difflsmeans(), or multcomp::glht().
I prefer emmeans (previously lsmeans).
library(emmeans)
emmeans(model, list(pairwise ~ Group), adjust = "tukey")
The | How to perform post-hoc test on lmer model?
You could use emmeans::emmeans() or lmerTest::difflsmeans(), or multcomp::glht().
I prefer emmeans (previously lsmeans).
library(emmeans)
emmeans(model, list(pairwise ~ Group), adjust = "tukey")
The next option is difflsmeans. Note difflsmeans cannot correct for multiple com... | How to perform post-hoc test on lmer model?
You could use emmeans::emmeans() or lmerTest::difflsmeans(), or multcomp::glht().
I prefer emmeans (previously lsmeans).
library(emmeans)
emmeans(model, list(pairwise ~ Group), adjust = "tukey")
The |
11,457 | How to perform post-hoc test on lmer model? | After you've fit your lmer model you can do ANOVA, MANOVA, and multiple comparison procedures on the model object, like this:
library(multcomp)
summary(glht(model, linfct = mcp(Group = "Tukey")), test = adjusted("holm"))
Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: Tukey Contras... | How to perform post-hoc test on lmer model? | After you've fit your lmer model you can do ANOVA, MANOVA, and multiple comparison procedures on the model object, like this:
library(multcomp)
summary(glht(model, linfct = mcp(Group = "Tukey")), test | How to perform post-hoc test on lmer model?
After you've fit your lmer model you can do ANOVA, MANOVA, and multiple comparison procedures on the model object, like this:
library(multcomp)
summary(glht(model, linfct = mcp(Group = "Tukey")), test = adjusted("holm"))
Simultaneous Tests for General Linear Hypotheses
... | How to perform post-hoc test on lmer model?
After you've fit your lmer model you can do ANOVA, MANOVA, and multiple comparison procedures on the model object, like this:
library(multcomp)
summary(glht(model, linfct = mcp(Group = "Tukey")), test |
11,458 | How to perform post-hoc test on lmer model? | Why not just do a pairwise t.test, with either holm or bonferroni correction, between your groups, using the fitted values from the model, since you see that your group2 varies significantly in your linear model? You could then draw a comparison between all 3 groups from your data.
In which case, you could just write:
... | How to perform post-hoc test on lmer model? | Why not just do a pairwise t.test, with either holm or bonferroni correction, between your groups, using the fitted values from the model, since you see that your group2 varies significantly in your l | How to perform post-hoc test on lmer model?
Why not just do a pairwise t.test, with either holm or bonferroni correction, between your groups, using the fitted values from the model, since you see that your group2 varies significantly in your linear model? You could then draw a comparison between all 3 groups from your... | How to perform post-hoc test on lmer model?
Why not just do a pairwise t.test, with either holm or bonferroni correction, between your groups, using the fitted values from the model, since you see that your group2 varies significantly in your l |
11,459 | The paradox of i.i.d. data (at least for me) | I think you are confusing an estimated model of a distribution with a random variable. Let's rewrite the independence assumption as follows:
$$
P(X_n | \theta, X_{i_1}, X_{i_2}, \dots, X_{i_k}) = P(X_n | \theta) \tag{1}
$$
which says that if you know the underlying distribution of $X_n$ (and, for example, can identify ... | The paradox of i.i.d. data (at least for me) | I think you are confusing an estimated model of a distribution with a random variable. Let's rewrite the independence assumption as follows:
$$
P(X_n | \theta, X_{i_1}, X_{i_2}, \dots, X_{i_k}) = P(X_ | The paradox of i.i.d. data (at least for me)
I think you are confusing an estimated model of a distribution with a random variable. Let's rewrite the independence assumption as follows:
$$
P(X_n | \theta, X_{i_1}, X_{i_2}, \dots, X_{i_k}) = P(X_n | \theta) \tag{1}
$$
which says that if you know the underlying distribut... | The paradox of i.i.d. data (at least for me)
I think you are confusing an estimated model of a distribution with a random variable. Let's rewrite the independence assumption as follows:
$$
P(X_n | \theta, X_{i_1}, X_{i_2}, \dots, X_{i_k}) = P(X_ |
11,460 | The paradox of i.i.d. data (at least for me) | If you take a Bayesian approach and treat parameters describing the distribution of $X$ as a random variable/vector, then the observations indeed are not independent, but they would be conditionally independent given knowledge of $\theta$ hence $P(X_n \mid X_{n-1}, \ldots X_1, \theta) = P(X_n \mid \theta)$ would hold.
... | The paradox of i.i.d. data (at least for me) | If you take a Bayesian approach and treat parameters describing the distribution of $X$ as a random variable/vector, then the observations indeed are not independent, but they would be conditionally i | The paradox of i.i.d. data (at least for me)
If you take a Bayesian approach and treat parameters describing the distribution of $X$ as a random variable/vector, then the observations indeed are not independent, but they would be conditionally independent given knowledge of $\theta$ hence $P(X_n \mid X_{n-1}, \ldots X_... | The paradox of i.i.d. data (at least for me)
If you take a Bayesian approach and treat parameters describing the distribution of $X$ as a random variable/vector, then the observations indeed are not independent, but they would be conditionally i |
11,461 | What do the fully connected layers do in CNNs? | The output from the convolutional layers represents high-level features in the data. While that output could be flattened and connected to the output layer, adding a fully-connected layer is a (usually) cheap way of learning non-linear combinations of these features.
Essentially the convolutional layers are providing ... | What do the fully connected layers do in CNNs? | The output from the convolutional layers represents high-level features in the data. While that output could be flattened and connected to the output layer, adding a fully-connected layer is a (usual | What do the fully connected layers do in CNNs?
The output from the convolutional layers represents high-level features in the data. While that output could be flattened and connected to the output layer, adding a fully-connected layer is a (usually) cheap way of learning non-linear combinations of these features.
Esse... | What do the fully connected layers do in CNNs?
The output from the convolutional layers represents high-level features in the data. While that output could be flattened and connected to the output layer, adding a fully-connected layer is a (usual |
11,462 | What do the fully connected layers do in CNNs? | I found this answer by Anil-Sharma on Quora helpful.
We can divide the whole network (for classification) into two parts:
Feature extraction:
In the conventional classification algorithms, like SVMs, we used to extract features from the data to make the classification work. The convolutional layers are serving the sa... | What do the fully connected layers do in CNNs? | I found this answer by Anil-Sharma on Quora helpful.
We can divide the whole network (for classification) into two parts:
Feature extraction:
In the conventional classification algorithms, like SVMs | What do the fully connected layers do in CNNs?
I found this answer by Anil-Sharma on Quora helpful.
We can divide the whole network (for classification) into two parts:
Feature extraction:
In the conventional classification algorithms, like SVMs, we used to extract features from the data to make the classification wo... | What do the fully connected layers do in CNNs?
I found this answer by Anil-Sharma on Quora helpful.
We can divide the whole network (for classification) into two parts:
Feature extraction:
In the conventional classification algorithms, like SVMs |
11,463 | What is the intuition of invertible process in time series? | In the AR($\infty$) representation, the most recent error can be written as a linear function of current and past observations:
$$w_t = \sum_{j=0}^\infty (-\theta)^j x_{t-j}$$
For an invertible process, $|\theta|<1$ and so the most recent observations have higher weight than observations from the more distant past. But... | What is the intuition of invertible process in time series? | In the AR($\infty$) representation, the most recent error can be written as a linear function of current and past observations:
$$w_t = \sum_{j=0}^\infty (-\theta)^j x_{t-j}$$
For an invertible proces | What is the intuition of invertible process in time series?
In the AR($\infty$) representation, the most recent error can be written as a linear function of current and past observations:
$$w_t = \sum_{j=0}^\infty (-\theta)^j x_{t-j}$$
For an invertible process, $|\theta|<1$ and so the most recent observations have hig... | What is the intuition of invertible process in time series?
In the AR($\infty$) representation, the most recent error can be written as a linear function of current and past observations:
$$w_t = \sum_{j=0}^\infty (-\theta)^j x_{t-j}$$
For an invertible proces |
11,464 | What is the intuition of invertible process in time series? | A time series is invertible if errors can be inverted into a representation of past observations.
For the time series data, the error ($\epsilon$) at time $t$ ($\epsilon_t$) can be represented as:
$$\epsilon_t = \sum\limits_{i=0}^{\infty}(-\theta)^i \, y_{t-i}$$
With every lagged value ($y_{t-i})$, its coefficient is $... | What is the intuition of invertible process in time series? | A time series is invertible if errors can be inverted into a representation of past observations.
For the time series data, the error ($\epsilon$) at time $t$ ($\epsilon_t$) can be represented as:
$$\ | What is the intuition of invertible process in time series?
A time series is invertible if errors can be inverted into a representation of past observations.
For the time series data, the error ($\epsilon$) at time $t$ ($\epsilon_t$) can be represented as:
$$\epsilon_t = \sum\limits_{i=0}^{\infty}(-\theta)^i \, y_{t-i}... | What is the intuition of invertible process in time series?
A time series is invertible if errors can be inverted into a representation of past observations.
For the time series data, the error ($\epsilon$) at time $t$ ($\epsilon_t$) can be represented as:
$$\ |
11,465 | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence level? | For the most part, people use probability-symmetric confidence intervals (CIs). For example, a 95% confidence
interval is made by cutting off probability 0.025
from each tail of the relevant distribution.
For CIs based on the symmetrical normal and Student t
distributions, the probability-symmetric interval is
the shor... | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence l | For the most part, people use probability-symmetric confidence intervals (CIs). For example, a 95% confidence
interval is made by cutting off probability 0.025
from each tail of the relevant distribut | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence level?
For the most part, people use probability-symmetric confidence intervals (CIs). For example, a 95% confidence
interval is made by cutting off probability 0.025
from each tail of the relevant distribution.
For CIs b... | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence l
For the most part, people use probability-symmetric confidence intervals (CIs). For example, a 95% confidence
interval is made by cutting off probability 0.025
from each tail of the relevant distribut |
11,466 | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence level? | Some theory on optimal confidence intervals
Confidence intervals are formed from pivotal quantities, which are functions of the data and parameter of interest that have a distribution that does not depend on the parameters of the problem. Confidence "intervals" are a special case of the broader class of confidence set... | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence l | Some theory on optimal confidence intervals
Confidence intervals are formed from pivotal quantities, which are functions of the data and parameter of interest that have a distribution that does not de | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence level?
Some theory on optimal confidence intervals
Confidence intervals are formed from pivotal quantities, which are functions of the data and parameter of interest that have a distribution that does not depend on the pa... | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence l
Some theory on optimal confidence intervals
Confidence intervals are formed from pivotal quantities, which are functions of the data and parameter of interest that have a distribution that does not de |
11,467 | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence level? | Shortest confidence interval is an ambiguous term
There is no such thing as the shortest confidence interval.
This is because the confidence interval is a function of the data $X$. And while you can make the confidence interval shorter for some particular observation, this comes at the cost of increasing the size of in... | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence l | Shortest confidence interval is an ambiguous term
There is no such thing as the shortest confidence interval.
This is because the confidence interval is a function of the data $X$. And while you can m | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence level?
Shortest confidence interval is an ambiguous term
There is no such thing as the shortest confidence interval.
This is because the confidence interval is a function of the data $X$. And while you can make the confid... | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence l
Shortest confidence interval is an ambiguous term
There is no such thing as the shortest confidence interval.
This is because the confidence interval is a function of the data $X$. And while you can m |
11,468 | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence level? | The shortest possible confidence interval for any particular parameter is the empty interval with length 0.
A confidence interval isn't just an interval. It's a procedure for constructing an interval from a sample. So, your procedure can be "For this particular sample, I'll take the empty interval, and then for every o... | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence l | The shortest possible confidence interval for any particular parameter is the empty interval with length 0.
A confidence interval isn't just an interval. It's a procedure for constructing an interval | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence level?
The shortest possible confidence interval for any particular parameter is the empty interval with length 0.
A confidence interval isn't just an interval. It's a procedure for constructing an interval from a sample.... | What is a rigorous, mathematical way to obtain the shortest confidence interval given a confidence l
The shortest possible confidence interval for any particular parameter is the empty interval with length 0.
A confidence interval isn't just an interval. It's a procedure for constructing an interval |
11,469 | How can you visualize the relationship between 3 categorical variables? | This is an interesting data set to try to represent graphically, partly because it's not really categorical. Both 3-level factors are ordinal and there is possible interplay between them (presumably, it's harder for a mild baseline to have substantial improvement -- or maybe substantial improvement means something diff... | How can you visualize the relationship between 3 categorical variables? | This is an interesting data set to try to represent graphically, partly because it's not really categorical. Both 3-level factors are ordinal and there is possible interplay between them (presumably, | How can you visualize the relationship between 3 categorical variables?
This is an interesting data set to try to represent graphically, partly because it's not really categorical. Both 3-level factors are ordinal and there is possible interplay between them (presumably, it's harder for a mild baseline to have substant... | How can you visualize the relationship between 3 categorical variables?
This is an interesting data set to try to represent graphically, partly because it's not really categorical. Both 3-level factors are ordinal and there is possible interplay between them (presumably, |
11,470 | How can you visualize the relationship between 3 categorical variables? | First, here is my reading from the graph provided of the data for those who wish to play (experiment, if you like). NB off-by-one errors are certainly possible, as are gross errors.
improvement treatment baseline frequency
none 0 mild 5
moderate 0 m... | How can you visualize the relationship between 3 categorical variables? | First, here is my reading from the graph provided of the data for those who wish to play (experiment, if you like). NB off-by-one errors are certainly possible, as are gross errors.
improvement | How can you visualize the relationship between 3 categorical variables?
First, here is my reading from the graph provided of the data for those who wish to play (experiment, if you like). NB off-by-one errors are certainly possible, as are gross errors.
improvement treatment baseline frequency
no... | How can you visualize the relationship between 3 categorical variables?
First, here is my reading from the graph provided of the data for those who wish to play (experiment, if you like). NB off-by-one errors are certainly possible, as are gross errors.
improvement |
11,471 | How can you visualize the relationship between 3 categorical variables? | Isn't Mosaic plot specially designed for this purpose?
In R it would be like
library(vcd)
d = read.table("data.dat", header=TRUE)
tab = xtabs(frequency ~ treatment+baseline+improvement, data=d)
mosaic(data=tab,~ treatment+baseline+improvement, shade=TRUE, cex=2.5)
Each categorical variables goes to one edge of the s... | How can you visualize the relationship between 3 categorical variables? | Isn't Mosaic plot specially designed for this purpose?
In R it would be like
library(vcd)
d = read.table("data.dat", header=TRUE)
tab = xtabs(frequency ~ treatment+baseline+improvement, data=d)
mosa | How can you visualize the relationship between 3 categorical variables?
Isn't Mosaic plot specially designed for this purpose?
In R it would be like
library(vcd)
d = read.table("data.dat", header=TRUE)
tab = xtabs(frequency ~ treatment+baseline+improvement, data=d)
mosaic(data=tab,~ treatment+baseline+improvement, sh... | How can you visualize the relationship between 3 categorical variables?
Isn't Mosaic plot specially designed for this purpose?
In R it would be like
library(vcd)
d = read.table("data.dat", header=TRUE)
tab = xtabs(frequency ~ treatment+baseline+improvement, data=d)
mosa |
11,472 | How can you visualize the relationship between 3 categorical variables? | I'm fond of using a 2-level x-axis for data like this. So your x-axis categories for a single chart might be:
Treatment=0, Baseline=Mild
Treatment=0, Baseline=Moderate
Treatment=0, Baseline=Severe
Treatment=1, Baseline=Mild
Treatment=1, Baseline=Moderate
Treatment=1, Baseline=Severe
...with the same counts by catego... | How can you visualize the relationship between 3 categorical variables? | I'm fond of using a 2-level x-axis for data like this. So your x-axis categories for a single chart might be:
Treatment=0, Baseline=Mild
Treatment=0, Baseline=Moderate
Treatment=0, Baseline=Severe
T | How can you visualize the relationship between 3 categorical variables?
I'm fond of using a 2-level x-axis for data like this. So your x-axis categories for a single chart might be:
Treatment=0, Baseline=Mild
Treatment=0, Baseline=Moderate
Treatment=0, Baseline=Severe
Treatment=1, Baseline=Mild
Treatment=1, Baseline=... | How can you visualize the relationship between 3 categorical variables?
I'm fond of using a 2-level x-axis for data like this. So your x-axis categories for a single chart might be:
Treatment=0, Baseline=Mild
Treatment=0, Baseline=Moderate
Treatment=0, Baseline=Severe
T |
11,473 | How can you visualize the relationship between 3 categorical variables? | I sugest use mosaic plot
mosaicplot(table(moz), sort = c(3,1,2), color = T) | How can you visualize the relationship between 3 categorical variables? | I sugest use mosaic plot
mosaicplot(table(moz), sort = c(3,1,2), color = T) | How can you visualize the relationship between 3 categorical variables?
I sugest use mosaic plot
mosaicplot(table(moz), sort = c(3,1,2), color = T) | How can you visualize the relationship between 3 categorical variables?
I sugest use mosaic plot
mosaicplot(table(moz), sort = c(3,1,2), color = T) |
11,474 | How can you visualize the relationship between 3 categorical variables? | The information can also be conveyed using following simple line chart:
The improvement is shown by different line types while the baseline group is shown in colors. These and the x-axis parameter (treatment here) can also be interchanged if desired. | How can you visualize the relationship between 3 categorical variables? | The information can also be conveyed using following simple line chart:
The improvement is shown by different line types while the baseline group is shown in colors. These and the x-axis parameter ( | How can you visualize the relationship between 3 categorical variables?
The information can also be conveyed using following simple line chart:
The improvement is shown by different line types while the baseline group is shown in colors. These and the x-axis parameter (treatment here) can also be interchanged if desi... | How can you visualize the relationship between 3 categorical variables?
The information can also be conveyed using following simple line chart:
The improvement is shown by different line types while the baseline group is shown in colors. These and the x-axis parameter ( |
11,475 | How can you visualize the relationship between 3 categorical variables? | An option I'd consider is to use parallel sets. Some of the comparisons will be easier than others, but you can still see the relations among three categorical variables.
Here it is an example with Titanic Survival data:
In R (given your tags) I have used ggparallel for implementing it. Some folks have discussed here... | How can you visualize the relationship between 3 categorical variables? | An option I'd consider is to use parallel sets. Some of the comparisons will be easier than others, but you can still see the relations among three categorical variables.
Here it is an example with T | How can you visualize the relationship between 3 categorical variables?
An option I'd consider is to use parallel sets. Some of the comparisons will be easier than others, but you can still see the relations among three categorical variables.
Here it is an example with Titanic Survival data:
In R (given your tags) I ... | How can you visualize the relationship between 3 categorical variables?
An option I'd consider is to use parallel sets. Some of the comparisons will be easier than others, but you can still see the relations among three categorical variables.
Here it is an example with T |
11,476 | How can you visualize the relationship between 3 categorical variables? | Similar to parallel sets, as posted by nazareno above, you can use alluvial plots which are available from the alluvial R package. http://www.r-bloggers.com/alluvial-diagrams/ | How can you visualize the relationship between 3 categorical variables? | Similar to parallel sets, as posted by nazareno above, you can use alluvial plots which are available from the alluvial R package. http://www.r-bloggers.com/alluvial-diagrams/ | How can you visualize the relationship between 3 categorical variables?
Similar to parallel sets, as posted by nazareno above, you can use alluvial plots which are available from the alluvial R package. http://www.r-bloggers.com/alluvial-diagrams/ | How can you visualize the relationship between 3 categorical variables?
Similar to parallel sets, as posted by nazareno above, you can use alluvial plots which are available from the alluvial R package. http://www.r-bloggers.com/alluvial-diagrams/ |
11,477 | How to understand that MLE of Variance is biased in a Gaussian distribution? | Intuition
The bias is "coming from" (not at all a technical term) the fact that $E[\bar{x}^2]$ is biased for $\mu^2$. The natural question is, "well, what's the intuition for why $E[\bar{x}^2]$ is biased for $\mu^2$"? The intuition is that in a non-squared sample mean, sometimes we miss the true value $\mu$ by over-est... | How to understand that MLE of Variance is biased in a Gaussian distribution? | Intuition
The bias is "coming from" (not at all a technical term) the fact that $E[\bar{x}^2]$ is biased for $\mu^2$. The natural question is, "well, what's the intuition for why $E[\bar{x}^2]$ is bia | How to understand that MLE of Variance is biased in a Gaussian distribution?
Intuition
The bias is "coming from" (not at all a technical term) the fact that $E[\bar{x}^2]$ is biased for $\mu^2$. The natural question is, "well, what's the intuition for why $E[\bar{x}^2]$ is biased for $\mu^2$"? The intuition is that in ... | How to understand that MLE of Variance is biased in a Gaussian distribution?
Intuition
The bias is "coming from" (not at all a technical term) the fact that $E[\bar{x}^2]$ is biased for $\mu^2$. The natural question is, "well, what's the intuition for why $E[\bar{x}^2]$ is bia |
11,478 | How to understand that MLE of Variance is biased in a Gaussian distribution? | The maximum likelihood estimates of mean and variance for a Gaussian distribution are:
\begin{align*}
\hat{\mu} &= \frac{1}{N} \sum_{i=1}^N x_i \\
\hat{\sigma}^2 &= \frac{1}{N} \sum_{i=1}^N (x_i - \hat{\mu})^2 \\
\end{align*}
Suppose the real mean and variance for the Gaussian distribution is $\mu$ and $\sigma^2$.
Firs... | How to understand that MLE of Variance is biased in a Gaussian distribution? | The maximum likelihood estimates of mean and variance for a Gaussian distribution are:
\begin{align*}
\hat{\mu} &= \frac{1}{N} \sum_{i=1}^N x_i \\
\hat{\sigma}^2 &= \frac{1}{N} \sum_{i=1}^N (x_i - \ha | How to understand that MLE of Variance is biased in a Gaussian distribution?
The maximum likelihood estimates of mean and variance for a Gaussian distribution are:
\begin{align*}
\hat{\mu} &= \frac{1}{N} \sum_{i=1}^N x_i \\
\hat{\sigma}^2 &= \frac{1}{N} \sum_{i=1}^N (x_i - \hat{\mu})^2 \\
\end{align*}
Suppose the real ... | How to understand that MLE of Variance is biased in a Gaussian distribution?
The maximum likelihood estimates of mean and variance for a Gaussian distribution are:
\begin{align*}
\hat{\mu} &= \frac{1}{N} \sum_{i=1}^N x_i \\
\hat{\sigma}^2 &= \frac{1}{N} \sum_{i=1}^N (x_i - \ha |
11,479 | Weakly informative prior distributions for scale parameters | I would recommend using a "Beta distribution of the second kind" (Beta2 for short) for a mildly informative distribution, and to use the conjugate inverse gamma distribution if you have strong prior beliefs. The reason I say this is that the conjugate prior is non-robust in the sense that, if the prior and data confli... | Weakly informative prior distributions for scale parameters | I would recommend using a "Beta distribution of the second kind" (Beta2 for short) for a mildly informative distribution, and to use the conjugate inverse gamma distribution if you have strong prior b | Weakly informative prior distributions for scale parameters
I would recommend using a "Beta distribution of the second kind" (Beta2 for short) for a mildly informative distribution, and to use the conjugate inverse gamma distribution if you have strong prior beliefs. The reason I say this is that the conjugate prior i... | Weakly informative prior distributions for scale parameters
I would recommend using a "Beta distribution of the second kind" (Beta2 for short) for a mildly informative distribution, and to use the conjugate inverse gamma distribution if you have strong prior b |
11,480 | Weakly informative prior distributions for scale parameters | The following paper by Daniels compares a variety of shrinkage priors for the variance. These are proper priors but I am not sure how many could be called non-informative if any. But, he also provides a list of noninformative priors (not all proper). Below is the reference.
M. J. Daniels (1999), A prior for the varia... | Weakly informative prior distributions for scale parameters | The following paper by Daniels compares a variety of shrinkage priors for the variance. These are proper priors but I am not sure how many could be called non-informative if any. But, he also provide | Weakly informative prior distributions for scale parameters
The following paper by Daniels compares a variety of shrinkage priors for the variance. These are proper priors but I am not sure how many could be called non-informative if any. But, he also provides a list of noninformative priors (not all proper). Below is... | Weakly informative prior distributions for scale parameters
The following paper by Daniels compares a variety of shrinkage priors for the variance. These are proper priors but I am not sure how many could be called non-informative if any. But, he also provide |
11,481 | Weakly informative prior distributions for scale parameters | (The question is stale, but the issue is not)
Personally, I think your intuition makes some sense. That is to say, if you don't need the mathematical tidiness of conjugacy, then whatever distribution you would use for a location parameter, you should use the same one for the log of a scale parameter. So, what you're sa... | Weakly informative prior distributions for scale parameters | (The question is stale, but the issue is not)
Personally, I think your intuition makes some sense. That is to say, if you don't need the mathematical tidiness of conjugacy, then whatever distribution | Weakly informative prior distributions for scale parameters
(The question is stale, but the issue is not)
Personally, I think your intuition makes some sense. That is to say, if you don't need the mathematical tidiness of conjugacy, then whatever distribution you would use for a location parameter, you should use the s... | Weakly informative prior distributions for scale parameters
(The question is stale, but the issue is not)
Personally, I think your intuition makes some sense. That is to say, if you don't need the mathematical tidiness of conjugacy, then whatever distribution |
11,482 | Weakly informative prior distributions for scale parameters | For hierarchical model scale parameters, I have mostly ended up using Andrew Gelman's suggestion of using a folded, noncentral t-distribution. This has worked pretty decently for me. | Weakly informative prior distributions for scale parameters | For hierarchical model scale parameters, I have mostly ended up using Andrew Gelman's suggestion of using a folded, noncentral t-distribution. This has worked pretty decently for me. | Weakly informative prior distributions for scale parameters
For hierarchical model scale parameters, I have mostly ended up using Andrew Gelman's suggestion of using a folded, noncentral t-distribution. This has worked pretty decently for me. | Weakly informative prior distributions for scale parameters
For hierarchical model scale parameters, I have mostly ended up using Andrew Gelman's suggestion of using a folded, noncentral t-distribution. This has worked pretty decently for me. |
11,483 | Why do neural networks need feature selection / engineering? | What if the "sufficiently deep" network is intractably huge, either making model training too expensive (AWS fees add up!) or because you need to deploy the network in a resource-constrained environment?
How can you know, a priori that the network is well-parameterized? It can take a lot of experimentation to find a ne... | Why do neural networks need feature selection / engineering? | What if the "sufficiently deep" network is intractably huge, either making model training too expensive (AWS fees add up!) or because you need to deploy the network in a resource-constrained environme | Why do neural networks need feature selection / engineering?
What if the "sufficiently deep" network is intractably huge, either making model training too expensive (AWS fees add up!) or because you need to deploy the network in a resource-constrained environment?
How can you know, a priori that the network is well-par... | Why do neural networks need feature selection / engineering?
What if the "sufficiently deep" network is intractably huge, either making model training too expensive (AWS fees add up!) or because you need to deploy the network in a resource-constrained environme |
11,484 | Why do neural networks need feature selection / engineering? | The key words here are priors and scale. As a simple example, imagine you're trying to predict a person's age from a photograph. With a dataset of images and ages, you could train a deep-learning model to make the predictions. This is objectively really inefficient because 90% of the image is useless, and only the regi... | Why do neural networks need feature selection / engineering? | The key words here are priors and scale. As a simple example, imagine you're trying to predict a person's age from a photograph. With a dataset of images and ages, you could train a deep-learning mode | Why do neural networks need feature selection / engineering?
The key words here are priors and scale. As a simple example, imagine you're trying to predict a person's age from a photograph. With a dataset of images and ages, you could train a deep-learning model to make the predictions. This is objectively really ineff... | Why do neural networks need feature selection / engineering?
The key words here are priors and scale. As a simple example, imagine you're trying to predict a person's age from a photograph. With a dataset of images and ages, you could train a deep-learning mode |
11,485 | Why do neural networks need feature selection / engineering? | My intuition about this phenomenon is connected to the complexity of the model to be learned. A deep neural network can indeed approximate any function in theory, but the dimension of the parameter space can be really large, like in the millions. So, actually finding a good neural network is really difficult. I like to... | Why do neural networks need feature selection / engineering? | My intuition about this phenomenon is connected to the complexity of the model to be learned. A deep neural network can indeed approximate any function in theory, but the dimension of the parameter sp | Why do neural networks need feature selection / engineering?
My intuition about this phenomenon is connected to the complexity of the model to be learned. A deep neural network can indeed approximate any function in theory, but the dimension of the parameter space can be really large, like in the millions. So, actually... | Why do neural networks need feature selection / engineering?
My intuition about this phenomenon is connected to the complexity of the model to be learned. A deep neural network can indeed approximate any function in theory, but the dimension of the parameter sp |
11,486 | Relationship between ridge regression and PCA regression | Let $\mathbf X$ be the centered $n \times p$ predictor matrix and consider its singular value decomposition $\mathbf X = \mathbf{USV}^\top$ with $\mathbf S$ being a diagonal matrix with diagonal elements $s_i$.
The fitted values of ordinary least squares (OLS) regression are given by $$\hat {\mathbf y}_\mathrm{OLS} = ... | Relationship between ridge regression and PCA regression | Let $\mathbf X$ be the centered $n \times p$ predictor matrix and consider its singular value decomposition $\mathbf X = \mathbf{USV}^\top$ with $\mathbf S$ being a diagonal matrix with diagonal eleme | Relationship between ridge regression and PCA regression
Let $\mathbf X$ be the centered $n \times p$ predictor matrix and consider its singular value decomposition $\mathbf X = \mathbf{USV}^\top$ with $\mathbf S$ being a diagonal matrix with diagonal elements $s_i$.
The fitted values of ordinary least squares (OLS) r... | Relationship between ridge regression and PCA regression
Let $\mathbf X$ be the centered $n \times p$ predictor matrix and consider its singular value decomposition $\mathbf X = \mathbf{USV}^\top$ with $\mathbf S$ being a diagonal matrix with diagonal eleme |
11,487 | Relationship between ridge regression and PCA regression | Elements of Statistical Learning has a great discussion on this connection.
The way I interpreted this connection and logic is as follows:
PCA is a Linear Combination of the Feature Variables, attempting to maximize the variance of the data explained by the new space.
Data that suffers from multicollinearity (or more... | Relationship between ridge regression and PCA regression | Elements of Statistical Learning has a great discussion on this connection.
The way I interpreted this connection and logic is as follows:
PCA is a Linear Combination of the Feature Variables, attem | Relationship between ridge regression and PCA regression
Elements of Statistical Learning has a great discussion on this connection.
The way I interpreted this connection and logic is as follows:
PCA is a Linear Combination of the Feature Variables, attempting to maximize the variance of the data explained by the new... | Relationship between ridge regression and PCA regression
Elements of Statistical Learning has a great discussion on this connection.
The way I interpreted this connection and logic is as follows:
PCA is a Linear Combination of the Feature Variables, attem |
11,488 | Relationship between ridge regression and PCA regression | Consider the linear equation
$$
\mathbf X \beta = \mathbf y\,,
$$
and the SVD of $\mathbf X$,
$$
\mathbf X = \mathbf U \,\mathbf S \,\mathbf V^T,
$$
where $\mathbf S = \text{diag}(s_i)$ is the diagonal matrix of singular values.
Ordinary least squares determines the parameter vector $\beta$ as
$$
\beta_{OLS} = \... | Relationship between ridge regression and PCA regression | Consider the linear equation
$$
\mathbf X \beta = \mathbf y\,,
$$
and the SVD of $\mathbf X$,
$$
\mathbf X = \mathbf U \,\mathbf S \,\mathbf V^T,
$$
where $\mathbf S = \text{diag}(s_i)$ is the dia | Relationship between ridge regression and PCA regression
Consider the linear equation
$$
\mathbf X \beta = \mathbf y\,,
$$
and the SVD of $\mathbf X$,
$$
\mathbf X = \mathbf U \,\mathbf S \,\mathbf V^T,
$$
where $\mathbf S = \text{diag}(s_i)$ is the diagonal matrix of singular values.
Ordinary least squares determi... | Relationship between ridge regression and PCA regression
Consider the linear equation
$$
\mathbf X \beta = \mathbf y\,,
$$
and the SVD of $\mathbf X$,
$$
\mathbf X = \mathbf U \,\mathbf S \,\mathbf V^T,
$$
where $\mathbf S = \text{diag}(s_i)$ is the dia |
11,489 | What is a block in experimental design? | The block is a factor. The main aim of blocking is to reduce the unexplained variation $(SS_{Residual})$ of a design -compared to non-blocked design-. We are not interested in the block effect per se , rather we block when we suspect the the background "noise" would counfound the effect of the actual factor.
We group e... | What is a block in experimental design? | The block is a factor. The main aim of blocking is to reduce the unexplained variation $(SS_{Residual})$ of a design -compared to non-blocked design-. We are not interested in the block effect per se | What is a block in experimental design?
The block is a factor. The main aim of blocking is to reduce the unexplained variation $(SS_{Residual})$ of a design -compared to non-blocked design-. We are not interested in the block effect per se , rather we block when we suspect the the background "noise" would counfound the... | What is a block in experimental design?
The block is a factor. The main aim of blocking is to reduce the unexplained variation $(SS_{Residual})$ of a design -compared to non-blocked design-. We are not interested in the block effect per se |
11,490 | What is a block in experimental design? | Here is a concise answer.
A lot of details and examples might be found in most documents treating the design of experiments; especially in agronomy.
Often, the researcher is not interested in the block effect per se, but he only wants to account for the variability in response between blocks. So, I use to view the bloc... | What is a block in experimental design? | Here is a concise answer.
A lot of details and examples might be found in most documents treating the design of experiments; especially in agronomy.
Often, the researcher is not interested in the bloc | What is a block in experimental design?
Here is a concise answer.
A lot of details and examples might be found in most documents treating the design of experiments; especially in agronomy.
Often, the researcher is not interested in the block effect per se, but he only wants to account for the variability in response be... | What is a block in experimental design?
Here is a concise answer.
A lot of details and examples might be found in most documents treating the design of experiments; especially in agronomy.
Often, the researcher is not interested in the bloc |
11,491 | What is a block in experimental design? | Here's a paraphrase of my favorite explanation, from my former teacher Freedom King.
You are studying how bread dough and baking temperature affect the tastiness of bread. You have a rating scale for tastiness. And let's say you're purchasing packaged bread dough from some food company rather than mixing it yourself. E... | What is a block in experimental design? | Here's a paraphrase of my favorite explanation, from my former teacher Freedom King.
You are studying how bread dough and baking temperature affect the tastiness of bread. You have a rating scale for | What is a block in experimental design?
Here's a paraphrase of my favorite explanation, from my former teacher Freedom King.
You are studying how bread dough and baking temperature affect the tastiness of bread. You have a rating scale for tastiness. And let's say you're purchasing packaged bread dough from some food c... | What is a block in experimental design?
Here's a paraphrase of my favorite explanation, from my former teacher Freedom King.
You are studying how bread dough and baking temperature affect the tastiness of bread. You have a rating scale for |
11,492 | What is a block in experimental design? | Experimental designs are a combination of three structures:
The treatment structure: How are treatments formed from factors of interest?
The design structure: How are experimental units grouped and assigned to treatments?
The response structure: How are observations taken?
Blocks are "factors" that belong to the de... | What is a block in experimental design? | Experimental designs are a combination of three structures:
The treatment structure: How are treatments formed from factors of interest?
The design structure: How are experimental units grouped and | What is a block in experimental design?
Experimental designs are a combination of three structures:
The treatment structure: How are treatments formed from factors of interest?
The design structure: How are experimental units grouped and assigned to treatments?
The response structure: How are observations taken?
Bl... | What is a block in experimental design?
Experimental designs are a combination of three structures:
The treatment structure: How are treatments formed from factors of interest?
The design structure: How are experimental units grouped and |
11,493 | What is a block in experimental design? | I think most of the time it’s just a matter of convention, likely proper to each field. I think that in medical context, in a two factors anova one of the factors is almost always called "treatment" and the other "block".
Typically, as ocram says, the block effect will be a random effect, but I don’t think this is syst... | What is a block in experimental design? | I think most of the time it’s just a matter of convention, likely proper to each field. I think that in medical context, in a two factors anova one of the factors is almost always called "treatment" a | What is a block in experimental design?
I think most of the time it’s just a matter of convention, likely proper to each field. I think that in medical context, in a two factors anova one of the factors is almost always called "treatment" and the other "block".
Typically, as ocram says, the block effect will be a rando... | What is a block in experimental design?
I think most of the time it’s just a matter of convention, likely proper to each field. I think that in medical context, in a two factors anova one of the factors is almost always called "treatment" a |
11,494 | What is the importance of probabilistic machine learning? | Contemporary machine learning, as a field, requires more familiarity with Bayesian methods and with probabilistic mathematics than does traditional statistics or even the quantitative social sciences, where frequentist statistical methods still dominate. Those coming from Physics are less likely to be surprised by the... | What is the importance of probabilistic machine learning? | Contemporary machine learning, as a field, requires more familiarity with Bayesian methods and with probabilistic mathematics than does traditional statistics or even the quantitative social sciences, | What is the importance of probabilistic machine learning?
Contemporary machine learning, as a field, requires more familiarity with Bayesian methods and with probabilistic mathematics than does traditional statistics or even the quantitative social sciences, where frequentist statistical methods still dominate. Those ... | What is the importance of probabilistic machine learning?
Contemporary machine learning, as a field, requires more familiarity with Bayesian methods and with probabilistic mathematics than does traditional statistics or even the quantitative social sciences, |
11,495 | Does caret train function for glmnet cross-validate for both alpha and lambda? | train does tune over both.
Basically, you only need alpha when training and can get predictions across different values of lambda using predict.glmnet. Maybe a value of lambda = "all" or something else would be more informative.
Max | Does caret train function for glmnet cross-validate for both alpha and lambda? | train does tune over both.
Basically, you only need alpha when training and can get predictions across different values of lambda using predict.glmnet. Maybe a value of lambda = "all" or something el | Does caret train function for glmnet cross-validate for both alpha and lambda?
train does tune over both.
Basically, you only need alpha when training and can get predictions across different values of lambda using predict.glmnet. Maybe a value of lambda = "all" or something else would be more informative.
Max | Does caret train function for glmnet cross-validate for both alpha and lambda?
train does tune over both.
Basically, you only need alpha when training and can get predictions across different values of lambda using predict.glmnet. Maybe a value of lambda = "all" or something el |
11,496 | Does caret train function for glmnet cross-validate for both alpha and lambda? | Old question, but I recently had to deal with this problem and found this question as a reference.
Here is an alternative approach:
The glmnet vignette (https://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html) specifically addresses this issue, recommending to specify the cross validation folds using the foldids ar... | Does caret train function for glmnet cross-validate for both alpha and lambda? | Old question, but I recently had to deal with this problem and found this question as a reference.
Here is an alternative approach:
The glmnet vignette (https://web.stanford.edu/~hastie/glmnet/glmne | Does caret train function for glmnet cross-validate for both alpha and lambda?
Old question, but I recently had to deal with this problem and found this question as a reference.
Here is an alternative approach:
The glmnet vignette (https://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html) specifically addresses this... | Does caret train function for glmnet cross-validate for both alpha and lambda?
Old question, but I recently had to deal with this problem and found this question as a reference.
Here is an alternative approach:
The glmnet vignette (https://web.stanford.edu/~hastie/glmnet/glmne |
11,497 | How to deal with an error such as "Coefficients: 14 not defined because of singularities" in R? | You're probably getting that error because two or more of your independent variables are perfectly collinear (e.g. mis-coding dummy variables to make identical copies).
Use cor() on your data or alias() on your model for closer inspection. | How to deal with an error such as "Coefficients: 14 not defined because of singularities" in R? | You're probably getting that error because two or more of your independent variables are perfectly collinear (e.g. mis-coding dummy variables to make identical copies).
Use cor() on your data or alia | How to deal with an error such as "Coefficients: 14 not defined because of singularities" in R?
You're probably getting that error because two or more of your independent variables are perfectly collinear (e.g. mis-coding dummy variables to make identical copies).
Use cor() on your data or alias() on your model for cl... | How to deal with an error such as "Coefficients: 14 not defined because of singularities" in R?
You're probably getting that error because two or more of your independent variables are perfectly collinear (e.g. mis-coding dummy variables to make identical copies).
Use cor() on your data or alia |
11,498 | How to deal with an error such as "Coefficients: 14 not defined because of singularities" in R? | Error "not defined because of singularities" will occur due to strong correlation between your independent variables. This can be avoided by having n-1 dummy variables. In your case, for Treatment variable, you should use 3 binary dummy variables (Treat1, Treat2, Treat3).
In R programing, linear regression functin lm(... | How to deal with an error such as "Coefficients: 14 not defined because of singularities" in R? | Error "not defined because of singularities" will occur due to strong correlation between your independent variables. This can be avoided by having n-1 dummy variables. In your case, for Treatment var | How to deal with an error such as "Coefficients: 14 not defined because of singularities" in R?
Error "not defined because of singularities" will occur due to strong correlation between your independent variables. This can be avoided by having n-1 dummy variables. In your case, for Treatment variable, you should use 3 ... | How to deal with an error such as "Coefficients: 14 not defined because of singularities" in R?
Error "not defined because of singularities" will occur due to strong correlation between your independent variables. This can be avoided by having n-1 dummy variables. In your case, for Treatment var |
11,499 | How to deal with an error such as "Coefficients: 14 not defined because of singularities" in R? | In my (somewhat limited) experiece, it is most likely due to high levels of colinearity between two or more varaibles. I would suggest using the VIF function to identify which varaibles are the most significant contributors in this respect, and take this into consideration when selecting the varaibles for elimination i... | How to deal with an error such as "Coefficients: 14 not defined because of singularities" in R? | In my (somewhat limited) experiece, it is most likely due to high levels of colinearity between two or more varaibles. I would suggest using the VIF function to identify which varaibles are the most s | How to deal with an error such as "Coefficients: 14 not defined because of singularities" in R?
In my (somewhat limited) experiece, it is most likely due to high levels of colinearity between two or more varaibles. I would suggest using the VIF function to identify which varaibles are the most significant contributors ... | How to deal with an error such as "Coefficients: 14 not defined because of singularities" in R?
In my (somewhat limited) experiece, it is most likely due to high levels of colinearity between two or more varaibles. I would suggest using the VIF function to identify which varaibles are the most s |
11,500 | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation | Start with the basic idea of variation. Your beginning model is the sum of the squared deviations from the mean. The R^2 value is the proportion of that variation that is accounted for by using an alternative model. For example, R-squared tells you how much of the variation in Y you can get rid of by summing up the ... | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation | Start with the basic idea of variation. Your beginning model is the sum of the squared deviations from the mean. The R^2 value is the proportion of that variation that is accounted for by using an a | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation
Start with the basic idea of variation. Your beginning model is the sum of the squared deviations from the mean. The R^2 value is the proportion of that variation that is accounted for by using an alternative model. For example, R-sq... | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation
Start with the basic idea of variation. Your beginning model is the sum of the squared deviations from the mean. The R^2 value is the proportion of that variation that is accounted for by using an a |
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