New answers tagged covariance-matrix
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How to properly "subtract" a known covariance component from a sample covariance? regression
Consider an additive approach. You know the distribution of $N$. Construct a distribution for $S$ with increasing levels of detail (constraints) until you are satisfied with your model for $S$, and ...
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Concentration inequality of the covariance matrix
Addressing your question 1, $~\Sigma~$ is a statistic of the generative ("true") distribution. $\hat{~\Sigma~}$ is a statistic of the model distribution. $\left\Vert ~\Sigma-\hat{~\Sigma~} \...
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Covariance matrix for p dimensional vector
Let's explore the definitions. This will yield a series of simple, effective characterizations of singular covariance matrices.
Suppose $\Sigma$ is a covariance matrix for a $p$-dimensional random ...
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Examples of positive definite periodic covariance matrices
One non-trivial example can be obtained by taking the outer product of a periodic vector $v \in \mathbb{R}^n$, where $v[i] = v[i+T]$ with itself, to make rank-1 matrix $V = v v^T$. Then you can make ...
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How to properly "subtract" a known covariance component from a sample covariance? regression
[Too long for a comment]
The issue here is that the space of (semi) positive definite matrices is not a vector space.
A first solution would be to compute
$$
\inf_{\Sigma \in \mathcal{S}_+} D\Big( \...
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Is sparse RBF kernel necessarily PSD?
It will typically not be positive definite after this truncation. One previous version of this question is here
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Simple problem of optimizing a positive definite matrix
A covariance matrix estimated with missing data need not be positive definite. That is, suppose you have a data matrix $X$ with observations $x_{ij}$ and for some $ij$ the value of $x_{ij}$ is ...
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How to do gradient descent when parameter is positive definite matrix
Edit: I wrote a blogpost about this problem, see here
Elaborating on the other two answers, one way to achieve this is to not optimize directly over the matrix $\Sigma$ that is constrained to be in ...
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