Tagged Questions

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Deriving the optimal value for the intercept term in SVM

I was reading andrew ng's machine learning lecture notes on SVM. I came across the following equation (finding the optimal value for the intercept term $b$ in the SVM problem): However, I have no ...
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Stochastic gradient descent for convex optimization

What happens if a convex objective is optimized by stochastic gradient descent? Is a global solution achieved?
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machine learning optimization

I was studying SVM and I am having problems in the conversion of this optimization problem into another : and gamma_hat is defined by I had to paste the images because I was having troubles with ...
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How to solve Hinge-loss based training without regularization term?

I'm trying to optimize the following objective function, $$\min_w \sum_{i=1}^{N}loss(y_i,x_i,w)$$ where $x_i$ is the training instance, $y_i$ is it's corresponding class label, $N$ is the number of ...
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Confusion related to least squares

I was reading this paper where they have modeled the ys given some samples xs,ys as The paper states that the above optimization problem is equivalent to a least squares problem. I didn't get how ...
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Confusion related to convexity and concavity of a problem

I was reading this paper http://www.ist.temple.edu/~vucetic/documents/wang11kdd.pdf related to adaptive multi-hyperplane machine for non linear classification In that paper, they have mentioned about ...
235 views

Gradient of log softmax in matrix form

Suppose $J(\mathbf{A})$ is defined as follows $$J=\text{tr}(\log \mathbf{P})$$ $$\mathbf{P}=\frac{e^\mathbf{A}}{\mathbf{1} \mathbf{1}' e^\mathbf{A}}$$ where division, exp and log are taken pointwise, ...
Consider a strictly convex function $f: [0; 1]^n \rightarrow \mathbb{R}$. The question is why people (especially experts in machine learning) use gradient descent in order to find a global minimum of ...
I am studying Machine Learning, but I believe you guys should be able to help me with this! Basically, we have given a set of training data $\{(x_1,y_1), x(x_2,y_2), ..., (x_n, y_n)\}$, and we need ...