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Questions tagged [reduced-rank-regression]

Multivariate multiple linear regression with a constraint that the coefficient matrix should be of low rank.

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Comparison/Visualisation of Regression Methods

This question follows this question, in particular @amoeba's clarifying answer and the plot from the SAS documentation included. I'm especially interested in knowing if $\mathbf{X}, \mathbf{Y}$ are ...
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Low Rank Gaussian Process vs Bayesian Linear Regression

A main benefit of Gaussian Process Regression is, that we not only get a prediction, but also a variance that we might use as indication of the prediction confidence. While bayesian linear regression ...
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I'd like to do regression using canonical correlation analysis

I got two multidimensional datasets, X and Y. I thought I build the model, which explains the relationship between two datasets, using canonical correlation analysis (CCA). The first correlation ...
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Is low rank finite-iteration manifold identification possible?

In sparse optimization, I am trying to solve the problem $$ \min_{x\in \mathbb R^{n}} \quad f(x) + \|x\|_1 $$ and at optimality, $x^*$ may be sparse. If I define the sparse manifold as $\mathcal M = ...
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how to optimize reduced rank regression with constant diagnoal constraint?

I am trying to optimize a panel regression $G=\beta G+e$. $G \in R^{N\times T}$. $\beta\in R^{N\times N}$ is unknown coefficient, constrained to $diag(\beta)=0$, and reduced rank $rank(\beta)\leq r$. ...
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categorical predictors in partial least squares

I am interested in running a partial least squares analysis using PROC PLS in SAS 9.4. I understand that, by default, the predictors and response variables in PLS are centered to a mean 0 and scaled ...
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Noisy Observation of Matrix of Certain Rank

Consider a rank k matrix, call it M, of size nxm. All the elements are non-negative. Now do a noisy observation of it and assume independent Poissonian errors (the error on element $M_{ij}$ is ...
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1answer
204 views

Is there a way to specify reduced-rank regression using $\mathbf{y} = \mathbf{X}\boldsymbol\beta + \boldsymbol\epsilon$?

In grad school, I was always taught the general linear model $$\mathbf{y} = \mathbf{X}\boldsymbol\beta + \boldsymbol\epsilon\tag{1}$$ where $\mathbf{y}$ is a vector, $\mathbf{X}$ is some matrix, $\...
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1answer
234 views

Reduced rank regression with binary outcome variable

I am trying to find dietary patterns related to a disease outcome. Unfortunately, I only have the binary outcome "disease yes/no" as outcome. I tried to perform PCA on the data, but the dietary ...
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465 views

Definition of “meta-parameter” [duplicate]

What is meant by the term "meta-parameter"? Can a definition, informal and/or formal, be provided? For example, in reduced-rank regression, the rank ($r$) can be referred to as a meta-parameter of ...
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1answer
338 views

Probabilistic models for partial least squares, reduced rank regression, and canonical correlation analysis?

This question results from the discussion following a previous question: What is the connection between partial least squares, reduced rank regression, and principal component regression? For ...
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1answer
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What is the connection between partial least squares, reduced rank regression, and principal component regression?

Are reduced rank regression and principal component regression just special cases of partial least squares? This tutorial (Page 6, "Comparison of Objectives") states that when we do partial least ...
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1answer
1k views

Objective function of canonical correlation analysis (CCA)

Given two vectors of random variables $X$ and $Y$, Canonical Correlation Analysis (CCA) finds the transformation matrices $A$ and $B$ so that $\operatorname{corr}(A_{1*} X, B_{1*} Y)$ is first maximal,...
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2answers
9k views

What is “reduced-rank regression” all about?

I have been reading The Elements of Statistical Learning and I could not understand what Section 3.7 "Multiple outcome shrinkage and selection" is all about. It talks about RRR (reduced-rank ...
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Friendly tutorial or introduction to reduced-rank regression

I am trying to learn Reduced-Rank Regression (RRR) from The Elements of Statistical Learning. I find the writing and them mathematics a little too prohibitive. Does any of you have a resource/text/...
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How to implement reduced-rank regression in R?

How can I fit reduced-rank regression with continuous response in R? I found the package VGAM but it only fits for discrete distributions...
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19k views

What is the relationship between regression and linear discriminant analysis (LDA)?

Is there a relationship between regression and linear discriminant analysis (LDA)? What are their similarities and differences? Does it make any difference if there are two classes or more than two ...