User soroosh - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-27T02:56:38Z http://mathoverflow.net/feeds/user/17800 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/113906/two-factor-factor-analysis-model Two-Factor Factor Analysis Model Soroosh 2012-11-20T04:31:00Z 2012-11-20T04:38:38Z <p>Hi everyone,</p> <p>I want to build the following factor analysis model and I've samples observations of data (i.e., $m(s)$), labeled with factor $s$. The observations are affected by both $y(s)$ and also an external factor (i.e., $x$). But, I don't know how to fit the model parameters and also estimate the factors ($x$ and $y$), for a given observation.</p> <p>Thanks for your help.</p> <p>$m(s) = \mu + Vy(s) + Ux$</p> <p>$m(s)_{~n\times 1}$</p> <p>$\mu_{~n\times 1}$</p> <p>$V_{~n\times p}$</p> <p>$y(s)_{~k\times 1}$</p> <p>$U_{~n\times q}$</p> <p>$x_{~q\times 1}$</p> <p>$x,y \sim ~ N(0,I)$</p> <p>$p,q &lt; n$</p> http://mathoverflow.net/questions/95486/deriving-conditional-probability-distribution Deriving Conditional Probability Distribution Soroosh 2012-04-29T04:04:55Z 2012-04-29T04:04:55Z <p>Given the following joint normal PDF of $X \in \mathcal{R}^K$ and $Y,Z \in \mathcal{R}$</p> <p>$p(\begin{bmatrix} X \\ Y \\ Z \end{bmatrix}) = \mathcal{N}(\begin{bmatrix} \mu_X \\ \mu_Y \\ \mu_Z \end{bmatrix},\begin{bmatrix} \Sigma_{XX} \ \Sigma_{XY} \ \Sigma_{XZ} \\ \Sigma_{YX} \ \Sigma_{YY} \ \Sigma_{YZ} \\ \Sigma_{ZX} \ \Sigma_{ZY} \ \Sigma_{ZZ} \end{bmatrix})$</p> <p>Can we derive the closed form expression for the following PDF?</p> <p>$P(X|A)$ (or equivalently $P(X|A^2)$)</p> <p>where, $A = \sqrt{Y^2+Z^2}$</p> http://mathoverflow.net/questions/89987/derivative-in-matrix-calculus Derivative in Matrix Calculus Soroosh 2012-03-01T19:38:29Z 2012-03-01T21:20:15Z <p>Hi everyone, Given the two full rank matrices $X$ and $A$, </p> <p>$X_{n\times n},~~(rank(X) = n)$</p> <p>$A_{m\times n},~~(rank(A) = m \le n)$</p> <p>Can I get a closed form expression for the following derivative? Thanks in advance.</p> <p>$\frac{\partial det(X-XA'(AXA')^{-1}AX)}{\partial A}=?$</p> http://mathoverflow.net/questions/75444/robust-entropy-like-measure-for-analyzing-uncertainity Robust entropy-like measure for analyzing uncertainity Soroosh 2011-09-14T20:39:21Z 2011-10-13T01:22:12Z <p>I'm looking for a measure to analysis the uncertainty observed in a set of variables (with multivariate Gaussian distribution). So, I've tried conventional Shanon entropy (differential entropy) which results into the following equation for MVG distributions:</p> <p><strong>H(s) = ln(sqrt((2πe)^k*det(cov)))</strong></p> <p><strong>H(s) = 0.5*[k*ln(2πe)+sum(log(eigs))]</strong></p> <p>Where, Sigma(Σ) is the covariance matrix. Thus, it's just a constant term plus sum of logarithm of eigenvalues of covariance matrix. But, when I've a small eigenvalue among eigenvalues, the small value affects the whole thing dramatically. In other words, this measure is not robust to small eigenvalues. On the other hand if I use sum of eigenvalues itself (instead of logarithmic scales), I won't face this issue. I was wondering if there is any other measures of uncertainty which may result in to sum of eigs instead of sum of log(eigs)?</p> http://mathoverflow.net/questions/75539/closed-form-expression-for-renyi-entropy-for-multivariate-gaussian-distributions closed form expression for Rényi entropy for multivariate Gaussian distributions Soroosh 2011-09-15T16:30:21Z 2011-09-15T18:29:16Z <p>Is there any closed form expression for Rényi entropy of a set variables with multivariate Gaussian distribution?</p> http://mathoverflow.net/questions/94170/joint-portability-of-a-rayleigh-variable-with-a-gaussian-variable Comment by Soroosh Soroosh 2012-04-29T04:12:38Z 2012-04-29T04:12:38Z You are right. My question was not clear enough. So, I've posted the correct and precise problem (the following link). I'll remove this post. :) <a href="http://mathoverflow.net/questions/95486/deriving-conditional-probability-distribution" rel="nofollow" title="deriving conditional probability distribution">mathoverflow.net/questions/95486/&hellip;</a> http://mathoverflow.net/questions/94170/joint-portability-of-a-rayleigh-variable-with-a-gaussian-variable Comment by Soroosh Soroosh 2012-04-16T02:38:57Z 2012-04-16T02:38:57Z I assume the product measure implies their independence. However, I'm interested in the dependency between the variables. The variable with Rayleigh distribution (i.e., $R$) is actually the magnitude of a complex number with i.i.d imaginary and real parts. $R$ is the variable of interest in my problem. Now, given a set of normally distributed variables (i.e., $X$), I want to estimate $R$. Therefore, I want to build the joint distribution of $R$ and $X$. http://mathoverflow.net/questions/89987/derivative-in-matrix-calculus/89992#89992 Comment by Soroosh Soroosh 2012-03-01T23:22:19Z 2012-03-01T23:22:19Z Thanks for your detailed and helpful response. http://mathoverflow.net/questions/75444/robust-entropy-like-measure-for-analyzing-uncertainity/75457#75457 Comment by Soroosh Soroosh 2011-09-14T23:14:23Z 2011-09-14T23:14:23Z Is this &quot;total variance&quot; measure used as a measure of uncertainty in literature?