2
votes
0answers
29 views

Smallest set of Liner equations, which exactly fit a set of points

I have a set of 2-d points,(it can be of any arbitrary dimension n). I want to find the minimum set of straight lines(linear equations) which exactly passes through the given 2-d points (unlike ...
0
votes
0answers
8 views

Predict values of some numerical vectors by using other numerical vectors with all these vectors in the same vector set

I need to solve a problem about predicting values of some numerical vectors by using other numerical vectors with all these vectors in the same vector set, which is generated by one or more black box ...
1
vote
1answer
44 views

Inverse of a triangular matrix in a statistical problem

Can any one give to me idea how to solve this problem? Find the inverse of the triangular matrix T, where $ T =\left[ \begin{array}{ccc} I & J & J \\ 0 & I & J \\ 0 & 0 & I ...
0
votes
1answer
45 views

Least Square with homogeneous solution!

I've read somewhere that: $x=A^+b+(I-A^+A)Z$ is a solution for $Ax=b$ ,when is doesn't have a particular solution. where $A^+$ indicates the pseudo-inverse and $Z$ is an arbitrary vector!!! I know ...
1
vote
0answers
48 views

Reformulating objective function of canonical correlation analysis

Given two column vectors $X = (x_1, \dots, x_n)'$ and $Y = (y_1, \dots, y_m)'$ of random variables with finite second moments, canonical-correlation analysis seeks vectors $a$ and $b$ such that the ...
1
vote
0answers
169 views

Weighted linear least squares parameter covariance

I am currently trying to figure out the parameter covariance for a weighted linear least squares problem where $$y = X\beta$$ The parameters for which my objective function is lowest are given by ...
0
votes
1answer
1k views

Covariance Matrix in Weighted Least Square Estimation

I am new to linear algebra and I have the following doubts: In weighted least square estimation of the system $Ax = b$ we minimize the weighted value of the error $e = b - Ax$ and the best $\hat{x}$ ...
5
votes
0answers
70 views

Is there a way to exploit the fact that the covariance matrix has a blocked structure to more easily compute the multivariate normal density?

I'm trying to minimize the (negative) multivariate normal log likelihood (dropping constants): $$ \log |\boldsymbol\Sigma|\,+(\mathbf{x}-\boldsymbol\mu)^{\rm ...
12
votes
3answers
396 views

Fast computation/estimation of the nuclear norm of a matrix

The nuclear norm of a matrix is defined as the sum of its singular values, as given by the Singular Value Decomposition of the matrix itself. It is of central importance in Signal Processing and ...