# Questions tagged [linear-algebra]

A field of mathematics concerned with the study of finite dimensional vector spaces, including matrices and their manipulation, which are important in statistics.

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### Minimizing expected loss in Regression with Rademacher random variables

I am trying to prove the following equality. I am able to solve the terms inside the expectation but I am stuck because of the expectation with respect to $x,y$. I might be wrong in the whole process; ...
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### Implementation of predictive variance in Gaussian process regression of scikit-learn

I'm studying the implementation of Gaussian Process Regression in scikit-learn to get a better understanding of the topic. There I've stumbled upon the following snippet: ...
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### Triangular Markov chain question

A triathlon consists of $3$ disciplines: swimming, cycling and running. A triathlete does a training session every day. However he doesn’t want to pay for professional coaching advice so instead his ...
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### Random matrix theory and research - a lot like doing linear algebra?

I've been searching for a subfield of research to get into and wonder whether random matrix theory could suit me well; it seems like it does, because the stuff I read, and the seminars that I watch ...
1answer
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### If I have only $(\pmb{X}'\pmb{X})^{-1}$, how can I find $\pmb{X}$ (the design matrix)?

My teacher gave me a problem, but he only give me the $(\pmb{X}'\pmb{X})^{-1}$ matrix. If I have only $(\pmb{X}'\pmb{X})^{-1}$, how can I find $\pmb{X}$ (the design matrix)? I think this is an ...
1answer
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### A derivation regarding kernel regression for the support vector machine

THis is from the Elements of Statistical Learning book page 437 in the section of support vector machine. Can anyone give me some hint for the missing derivation steps for why 12.49 is true (as seen ...
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### Expansion of inner product for polynomial kernel for SVMs

On page 424 in "The Elements of Statistical Learning" by Hastie et al (2013) (https://web.stanford.edu/~hastie/Papers/ESLII.pdf), we see the following expansion of a polynomial kernel with degree 2: ...
3answers
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### Intuition for nonmonotonicity of coefficient paths in ridge regression

Intuitively, why may some of the slope coefficients in ridge regression increase in magnitude when the penalty parameter $\lambda$ is increased? Or in other words, why are the coefficient paths ...
1answer
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### Proof $E[Z'TZ]^2=\operatorname{tr}^2(T)+\operatorname{tr}(T^2)$ [duplicate]

How to prove second moment of a quadratic form where $Z$ has normal distribution with mean zero and covariance matrix identical?
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### Chebyshev inequality in terms of RMS

I'm self studying the book Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares In page 48, the author write: "It says,for example, that no more than 1/25 = 4% of the entries ...
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### what is a vector perpendicular to a plane of vectors

I have 3 or 4 vectors connected that forms a plane. How can I find the vector that is perpendicular to this plane? it can be a unit vector as long as it preserves this direction. each vector is on ...
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### Are there extant deep learning analogs to random coefficient (aka mixed) models?

Random coef models, applied to longitudinal data, capture response heterogeneity by cross-sectional unit. I've got a longitudinal prediction problem, in which I know that some "features" (or ...