Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [algebraic-statistics]

Use for questions relating to algebraic statistics, the branch of statistical theory concerned with methods from abstract algebra, especially algebraic geometry and commutative algebra. This tag is not for questions about the applications of linear algebra to statistics, nor for questions about grade school algebra in statistical problems.

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Algebraic Geometry for Statistics

I have heard about uses of Algebraic Geometry in Statistics and Machine Learning. I wanted to try to learn a bit about this topics. I don't know nearly anything about Algebraic Geometry, but I have background in math, and I know about basic group…
sjm.majewski
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What are important pure mathematics courses for a prospective statistics PhD student?

I know that linear algebra and analysis (especially measure theory) are important. Is it helpful to take graduate level courses in real and complex analysis? Should I take courses in abstract algebra beyond the introductory courses, e.g.,…
user36587
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Cases where TDA outperforms public benchmarks?

Precise Question What are some specific examples where topological data analysis (TDA) outperforms other models on publicly available data? Context When new ML algorithms are developed, it seems common practice to apply them to publicly-available…
Quetzalcoatl
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Calculating Formula with logs and Weighted Average

I am trying to figure out an equation from the following paper by Cadena and Kovak (2016): http://pubs.aeaweb.org/doi/pdfplus/10.1257/app.20140095 on pages 264 and 265. I don't think the context is necessarily important for the purposes here, but…
bill999
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R: linear algebra representation of the prediction operator for a mixed effects model

(See edit at the bottom for the bounty) I am trying to learn how to simulate LMM data with matrix linear algebra. So far I've managed to simulate a simple model with a random intercept: library(data.table) library(lmerTest) # Parameters Ngroups …
mat
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How do I check the validity of a set of inequality constraints?

I have a table of inequality constraints, each with an "x < y" relation. How can I check this table for contradictory logic such as a < b, b < c, c < a? For example library(data.table) set.seed(0) ineqs <- unique(data.table( X =…
Ben
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LASSO: Deriving the smallest lambda at which all coefficient are zero

I'am trying to derive mathematically the lowest $\lambda$ at which all coefficients are zero, reffering to the Exercise 2.1 of the book Sparsity with Statistical Learning. The result should be $\lambda_{min}=\max_j |X_j^Ty|$. I hope this isnt a…
rook1996
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Are permutation groups used in statistics?

I was told that there may be a connection between concepts in abstract algebra and applications in statistics (also confirmed by the 'algebraic statistics' tag on this website). I had no idea, so I'm curious. In particular, I wanted to understand…
SumsArentDumb
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Design of Experiments through Algebraic Statistics

I would like to ask you about how to compute a circuit basis of a design matrix in software R. Let me explain you. I have found a software, named Macaulay2, that calculates some algebraic tools, and one of them is circuits. In this programm, first…
Vasilis T.
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Matrix Covariance Algebra

In the structural equation modeling (SEM) context, one of the modeling frameworks is called the reticular action model (RAM). In RAM, the observed variables (y) and latent variables (η) are combined in one vector. v = [y η](transpose of this…
e. erhan
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How to incorporate the uncertainty of the model coefficients in the prediction interval of a multiple linear regression

The question is a bit similar to question 147242 . I'm dealing with a multiple linear regression model, say: $$ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 $$ and I'm looking for an algebraic equation to calculate (numerically) the prediction interval…
DannyVanpoucke
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Determinants of the sum of two matrices and their eigenvalues

I know some basic property of determinant. I read an article and see this formula: \begin{equation} |(\delta-p-1)D+S|=\bigg(\prod_{i=1}^{p}\lambda_{i}(D)\bigg) \bigg(\prod_{i=1}^{p}(\delta-p-1)\lambda_{i}(D^{-1}S)\bigg) \end{equation} $D$ and $S$…
Omid
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Given two related ratios within a population, derive a third ratio (eg. redheads, non-redheads, and skin cancer)

If People X are N times more likely to have attribute A than non-X People X are P percent of the population then What percentage of A's are X? Example (the numbers are just for illustration). If A redhead is 3 times more likely to get skin…
Stephen Hosking
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How To Find The Right Formula

First off, I'm kind of out of my element when it comes to formulas and figuring out how to come up with a formula for what I need. If you need any other information, let me know and I'll add it. Scenario: I need to determine the opacity percentage…
Brandon
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Kernel trick in feature space

I am working on KPCA based fault detection. I have question concerning the kernel trick in the feature space. We all know that the dot product in the feature space is computed using kernel function. I need algebraic explanation how can the kernel…
F. BENCHEIKH
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