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4 answers

Feature map for the Gaussian kernel

In SVM, the Gaussian kernel is defined as: $$K(x,y)=\exp\left({-\frac{\|x-y\|_2^2}{2\sigma^2}}\right)=\phi(x)^T\phi(y)$$ where $x, y\in \mathbb{R^n}$. I do not know the explicit equation of $\phi$. I want to know it. I also want to know…
Vivian
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How are the standard errors computed for the fitted values from a logistic regression?

When you predict a fitted value from a logistic regression model, how are standard errors computed? I mean for the fitted values, not for the coefficients (which involves Fishers information matrix). I only found out how to get the numbers with R…
user2457873
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How do I calculate a weighted standard deviation? In Excel?

So, I have a data set of percentages like so: 100 / 10000 = 1% (0.01) 2 / 5 = 40% (0.4) 4 / 3 = 133% (1.3) 1000 / 2000 = 50% (0.5) I want to find the standard deviation of the percentages, but weighted for their…
Yahel
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How to translate the results from lm() to an equation?

We can use lm() to predict a value, but we still need the equation of the result formula in some cases. For example, add the equation to plots.
user27736
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2 answers

How are Bayesian Priors Decided in Real Life?

I always had the following question: How are Bayesian Priors decided in real life? I created the following scenario to pose my question: Suppose you are researcher and you are interested in studying if the age of a giraffe can be predicted by the…
stats_noob
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Reference: who introduced the tilde "~" notation to mean "has probability distribution..."?

[Note: although this question has an accepted answer, the investigation is not finished yet. I encourage you to post your findings.] Who first introduced the notation "$X \sim Q$", meaning that $Q$ is the probability distribution for $X$, and its…
pglpm
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Can AIC compare across different types of model?

I'm using AIC (Akaike's Information Criterion) to compare non-linear models in R. Is it valid to compare the AICs of different types of model? Specifically, I'm comparing a model fitted by glm versus a model with a random effect term fitted by glmer…
Thomas K
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Maximum likelihood estimators for a truncated distribution

Consider $N$ independent samples $S$ obtained from a random variable $X$ that is assumed to follow a truncated distribution (e.g. a truncated normal distribution) of known (finite) minimum and maximum values $a$ and $b$ but of unknown parameters…
a3nm
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Gradient of Hinge loss

I'm trying to implement basic gradient descent and I'm testing it with a hinge loss function i.e. $l_{\text{hinge}} = \max(0,1-y\ \boldsymbol{x}\cdot\boldsymbol{w})$. However, I'm confused about the gradient of the hinge loss. I'm under the…
brcs
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Are the digits of $\pi$ statistically random?

Suppose you observe the sequence: 7, 9, 0, 5, 5, 5, 4, 8, 0, 6, 9, 5, 3, 8, 7, 8, 5, 4, 0, 0, 6, 6, 4, 5 , 3, 3, 7, 5, 9, 8, 1, 8, 6, 2, 8, 4, 6, 4, 1, 9, 9, 0, 5, 2, 2, 0, 4, 5, 2, 8 ... What statistically tests would you apply to determine if this…
Cam.Davidson.Pilon
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Kernel logistic regression vs SVM

As is known to all, SVM can use kernel method to project data points in higher spaces so that points can be separated by a linear space. But we can also use logistic regression to choose this boundary in the kernel space, so what's the advantages…
FindBoat
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How to calculate pooled variance of two or more groups given known group variances, means, and sample sizes?

Say there are $m+n$ elements split into two groups ($m$ and $n$). The variance of the first group is $\sigma_m^2$ and the variance of the second group is $\sigma^2_n$. The elements themselves are assumed to be unknown but I know the means $\mu_m$…
user1809989
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Measuring the "distance" between two multivariate distributions

I'm looking for some good terminology to describe what I'm trying to do, to make it easier to look for resources. So, say I have two clusters of points A and B, each associated to two values, X and Y, and I want to measure the "distance" between A…
Emile
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What if my linear regression data contains several co-mingled linear relationships?

Let's say I am studying how daffodils respond to various soil conditions. I have collected data on the pH of the soil versus the mature height of the daffodil. I'm expecting a linear relationship, so I go about running a linear…
SlowMagic
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How to handle a "self defeating" prediction model?

I was watching a presentation by an ML specialist from a major retailer, where they had developed a model to predict out of stock events. Let's assume for a moment that over time, their model becomes very accurate, wouldn't that somehow be…
Skander H.
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