3
votes
1answer
142 views

Equivalent method for maximum likelihood estimation of covariance parameters

My goal is to estimate the parameters of a covariance matrix $\Omega$, by maximizing the following log-likelihood function: $$\log L(\vec\tau, \rho, \sigma \mid W, X) = -m\ln(\left | \Omega \right |) ...
0
votes
2answers
113 views

Rewrite optimization objective

Hi, I wanted to ask, under which conditions can one rewrite the optimization objective $\min_x f(x)\;\;\;s.t.\;\;\;g(x) \leq s$ as $\min_x g(x)\;\;\;s.t.\;\;\;f(x) \leq t$ I have particular ...
0
votes
0answers
420 views

Gradient Descent for Primal Kernel SVM with Soft-Margin(Hinge) Loss

Given the primal objective $$F({\bf a})=L\sum_{i,j}a_{i}a_{j}k(x_i,x_j) + \sum_{i}max(0, 1-y_i \sum_{j}a_jk(x_i,x_j)$$ for the soft margin SVM, where ${\bf a}=(a_1,...,a_N)$, N being the number of ...
0
votes
1answer
306 views

Minimum distance between two data sets

Suppose we have two sets of data, $X$ and $Y$, each of which contains $10$ positive numbers. Now let us order the data sets $X=\left\{ x_{1},\cdots,x_{10}\right\}$, $x_{1}\ge\cdots\ge x_{10}>0$ and ...
1
vote
2answers
797 views

Inequality-constrained linear-regression, what is the covariance of the estimator?

If you do a linear regression: $||Ax - e ||^2$, where e is iid Gaussian, mean 0 and variance 1, then your answer is $x_{hat} = (A' A)^{-1} (A' * e)$ and the covariance of $x_{hat}$ is $(A' A)^{-1}$ ...