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Question 1

2votes

2answers

121views

Symmetry of linear combinations of mean 0 symmetric random vectors

Let $X = (X_1,\ldots,X_n)$ be a random vector with i.i.d. components, each symmetric around $0$, i.e. $X_i \stackrel{d}{=} -\,X_i$ for all $i$.Given two deterministic vectors $a, b \in \mathbb{R}^n$, ...

Alexandre Zwahlen

21

askedJun 23 at 8:22

Question 2

0votes

0answers

40views

Decomposing a Weighted Average of Multiple (96x3) Data Points, Including an Unknown Contribution

I'm working with a dataset where each data point has a shape of (96, 3), with each element being a value between 0 and 1. I have a set of approximately 75 reference data points.My goal is to take a ...

molecularPost

1

askedMar 27 at 20:53

Question 3

2votes

0answers

48views

Interpreting source code for linear discriminant analysis

I am trying to understand the CVA function in the Morpho package in R, which performs canonical variate analysis, aka, linear discriminant analysis. I am confused as to how the canonical variates (CV),...

Patrick

247

askedMar 17 at 8:10

Question 4

0votes

0answers

92views

Construction of the ridge trace hyperellipsoids, equation (3.1) in Hoerl and Kennard (1970)

I would appreciate some clarification on geometric aspects of the hyperellipsoids in the ridge trace in equation $(3.1)$ in Ridge Regression: Biased Estimation of Nonorthogonal Problems, by Hoerl and ...

microhaus

2,834

askedFeb 21 at 23:16

Question 5

2votes

1answer

203views

Dimensionality of the hat matrix in the projection view of the least squares estimator

I would appreciate some clarification on the geometric interpretation of least squares in terms of linear algebra projections and span. Whilst this may be obvious to members of the community, here, it'...

microhaus

2,834

askedFeb 1 at 18:28

Question 6

1vote

0answers

55views

INDSCAL as a special case of CANDELINC

Here is my attempt to show that INDSCAL as a special case of CANDELINC. I am using the following paper as my reference for definitions.Kolda, Tamara G., and Brett W. Bader. "Tensor ...

Omar Shehab

55

askedJan 14 at 19:55

Question 7

3votes

0answers

231views

Deriving the normal equations by differentiating the matrix form

So, if we have $RSS(\beta) = (\mathbf{y}-\mathbf{X}\beta)^T(\mathbf{y}-\mathbf{X}\beta)$ and differentiatiate with respect to $\beta$, and set it to zero in order to minimize it, how do we get $\...

JackOfAllTrades

45

askedDec 15, 2024 at 3:48

Question 8

1vote

2answers

303views

Covariance matrix in terms of $X^TX$

If I have a matrix $X\in \mathbb{R}^{n\times p}$, then I can write the covariance as$$\text{Cov}(X) = \mathbb{E}[(X-\mu_X)(X-\mu_X)^T]$$Now, assuming the data is centered, this becomes $\text{Cov}(X)...

user19904

294

askedDec 11, 2024 at 18:10

Question 9

2votes

1answer

178views

IV Rank/Relevance Condition Linear Algebra Intuition

Consider the following econometric model (IV) : $Y_1 = X'\beta + e$, where $Y_1 \in \mathbb{R}$ is some outcome variable of interest, and we have a set of regressors $X = \begin{bmatrix} Z_1 \\ Y_2 \...

rudinable

375

askedDec 8, 2024 at 11:34

Question 10

2votes

0answers

106views

Least Absolute Deviations – Geometric Intuition

I've recently been exposed to the geometric intuition regarding Least Squares (OLS) regression:The vector of the outcome variable $Y$, is not not in the linear span of $X_1, X_2, ..., X_{p-1}$:The ...

Liam

41

askedDec 2, 2024 at 19:56

Question 11

1vote

1answer

104views

If $n\operatorname{var}( \sum_{ij}M_{ij}v_{i}v_{j}) = (\sum_{i}v_{i}^{2})^{2} - \sum_{i}v_{i}^{4}$ for any $v_i$, what can we say about $M_{ij}$?

Let $M_{ij}$ be a real random matrix, constrained to be symmetric $M_{ij}=M_{ji}$, and with zero diagonal, $M_{ii}=0$.Suppose we know that, for any real vector $v_i$, the following holds:$$\...

a06e

4,666

askedDec 2, 2024 at 9:12

Question 12

4votes

2answers

205views

Avoiding tensors when differentiating with respect to weight matrices in backpropagation

Consider a neural network consisting of only a single affine transformation with no non-linearity. Use the following notation:$\textbf{Inputs}: x \in \mathbb{R}^n$$\textbf{Weights}: W \in \mathbb{R}...

kuzzooroo

181

askedNov 2, 2024 at 18:53

Question 13

4votes

1answer

224views

Closed form solution for bayesian linear regression with 2 responses?

I am thinking about first principles from the point of view of a frequentist moving from regression with 1 response to regression with 2 responses. Reflecting on that I am trying to figure out how to ...

JCWong

1,702

askedNov 2, 2024 at 0:26

Question 14

3votes

0answers

99views

How to show this property of the Covariance matrix? [closed]

Hi all, may I ask how the pink highlighted equation is derived? By expanding the matrix, how does the remaining three terms result in n(avg X)(avg X)T? Apologies for the rather basic question, but am ...

financebro

39

askedOct 27, 2024 at 3:23

Question 15

1vote

0answers

43views

How to implement and notate the replication/transformation of a 2D matrix to a 3D tensor and the summation/transformation of a 3D tensor to 2D matrix?

Background:I have a model with a dimension $T$ representing $time$, a dimension $N$ representing $technologies$ and a dimension $P$ representing $prices$. During calculations in this model, I would ...

tobias hassebrock

123

askedOct 9, 2024 at 0:58

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Stack Exchange Network

Questions tagged [linear-algebra]

Symmetry of linear combinations of mean 0 symmetric random vectors

Decomposing a Weighted Average of Multiple (96x3) Data Points, Including an Unknown Contribution

Interpreting source code for linear discriminant analysis

Construction of the ridge trace hyperellipsoids, equation (3.1) in Hoerl and Kennard (1970)

Dimensionality of the hat matrix in the projection view of the least squares estimator

INDSCAL as a special case of CANDELINC

Deriving the normal equations by differentiating the matrix form

Covariance matrix in terms of $X^TX$

IV Rank/Relevance Condition Linear Algebra Intuition

Least Absolute Deviations – Geometric Intuition

If $n\operatorname{var}( \sum_{ij}M_{ij}v_{i}v_{j}) = (\sum_{i}v_{i}^{2})^{2} - \sum_{i}v_{i}^{4}$ for any $v_i$, what can we say about $M_{ij}$?

Avoiding tensors when differentiating with respect to weight matrices in backpropagation

Closed form solution for bayesian linear regression with 2 responses?

How to show this property of the Covariance matrix? [closed]

How to implement and notate the replication/transformation of a 2D matrix to a 3D tensor and the summation/transformation of a 3D tensor to 2D matrix?

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