Linked Questions

2
votes
0answers
749 views

Is a covariance matrix defined through a Gaussian covariance function always positive-definite? [duplicate]

When using Gaussian processes, the covariance matrix $\mathbf{\Sigma}$ is often defined via a covariance function $K$ as follows $$ \mathbf{\Sigma}_{ij} = K(\underline{x}_i, \underline{x}_j) $$ where $...
0
votes
0answers
360 views

Creating a covariance matrix with specified variances and correlations [duplicate]

I'm trying to generate a covariance matrix between two multivariate vectors with specified variances for each dimension, correlations between dimensions within a single vector, and cross-correlations ...
3
votes
0answers
111 views

Importance of semi-positive definiteness of covariance matrix [duplicate]

Since Covariance matrix is symmetric it is Hermitian (self adjoint) and always diagonalizable. If the matrix has all non zero eigen-values its is a full rank matrix. But what is the importance of the ...
68
votes
18answers
89k views

Statistics interview questions

I am looking for some statistics (and probability, I guess) interview questions, from the most basic through the more advanced. Answers are not necessary (although links to specific questions on this ...
125
votes
6answers
20k views

Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?

For a given data matrix $A$ (with variables in columns and data points in rows), it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical ...
86
votes
1answer
93k views

What correlation makes a matrix singular and what are implications of singularity or near-singularity?

I am doing some calculations on different matrices (mainly in logistic regression) and I commonly get the error "Matrix is singular", where I have to go back and remove the correlated variables. My ...
60
votes
5answers
37k views

Is every covariance matrix positive definite?

I guess the answer should be yes, but I still feel something is not right. There should be some general results in the literature, could anyone help me?
38
votes
5answers
20k views

Bound for the correlation of three random variables

There are three random variables, $x,y,z$. The three correlations between the three variables are the same. That is, $$\rho=\textrm{cor}(x,y)=\textrm{cor}(x,z)=\textrm{cor}(y,z)$$ What is the ...
21
votes
6answers
5k views

Completing a 3x3 correlation matrix: two coefficients of the three given

I was asked this question in an interview. Lets say we have a correlation matrix of the form \begin{bmatrix}1&0.6&0.8\\0.6&1&\gamma\\0.8&\gamma&1\end{bmatrix} I was asked to ...
19
votes
4answers
34k views

k-means implementation with custom distance matrix in input

Can anyone point me out a k-means implementation (it would be better if in matlab) that can take the distance matrix in input? The standard matlab implementation needs the observation matrix in input ...
28
votes
1answer
18k views

Converting similarity matrix to (euclidean) distance matrix

In Random forest algorithm, Breiman (author) constructs similarity matrix as follows: Send all learning examples down each tree in the forest If two examples land in the same leaf increment ...
12
votes
3answers
11k views

Is every correlation matrix positive definite?

I'm talking here about matrices of Pearson correlations. I've often heard it said that all correlation matrices must be positive semidefinite. My understanding is that positive definite matrices must ...
7
votes
3answers
3k views

Is every correlation matrix positive semi-definite?

I am generating correlation matrix by some new algorithm. Generated matrix is non positive semi-definite matrix. I'm getting a few negative eigenvalues. The rest of eigenvalues are quite equal to the ...
10
votes
2answers
1k views

Appropriate measure to find smallest covariance matrix

In the textbook I am reading they use positive definiteness (semi-positive definiteness) to compare two covariance matrices. The idea being that if $A-B$ is pd then $B$ is smaller than $A$. But I'm ...
7
votes
1answer
7k views

Standard error for the sum of regression coefficients when the covariance is negative

I have a question about appropriately calculation the standard error for the sum of two coefficients in a linear regression model. My question is similar to this and this, but I can't seem to solve ...

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