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My goal is to estimate the parameters of a covariance matrix $\Omega$, by maximizing the following log-likelihood function: $$\log L(\vec\tau, \rho, \sigma \mid W, X) = -m\ln(\left | \Omega \right |) ... 2answers 113 views ### Rewrite optimization objective Hi, I wanted to ask, under which conditions can one rewrite the optimization objective \min_x f(x)\;\;\;s.t.\;\;\;g(x) \leq s as \min_x g(x)\;\;\;s.t.\;\;\;f(x) \leq t I have particular ... 0answers 420 views ### Gradient Descent for Primal Kernel SVM with Soft-Margin(Hinge) Loss Given the primal objective$$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 ...
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 ...
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 $(A' A)^{-1}$ ...