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The keyword to look for is Dudley's chaining integral, see e.g. Vershynin's book "High Dimensional Probability" which contains a chapter on the chaining technique. Chaining allows us to bound the empirical Rademacher complexity in terms of the empirical $L_2$ covering numbers of $\mathcal{A}$. Your result is directly obtained from the chaining ...


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Compute the likelihood of the observed data, for each model. Then higher the likelihood, the better the fit. The likelihood is just the probability that the model assigns to the observed data, which for HMMs can be computed using dynamic programming. Be prepared that the more complex the model, the higher the likelihood will be, but that doesn't ...


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It is not necessary for the activation function to be monotonic. The best example of that is MISHactivation function which is non monotonic activation function and it out performs ReLU activation on various benchmarks.


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If $A$ is an $n \times m$ dense matrix then $AA^T$ is an $n\times n$ matrices given by $$ (AA^T)_{ij} = \sum_{k=1}^m A_{ik} A_{jk}. $$ This gives a $\Theta(n^2m)$ algorithm for computing $AA^T$. If $n \geq m$ then faster algorithms exist, but they are not used in practice (at least in most situations). If $A$ is sparse, that is, stored as a list of non-zero ...


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There's no way to tell for sure without trying out. That said, a crude rule of thumb is that k-d trees tend to be useful when the number of dimensions is up to about 10-20, but in higher dimensions, often they are little better than a naive linear search over all points. See also Is there some theoretical verification or explanation of why KDTree gets ...


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I suspect this paper has typos (see e.g., line 2 of Algorithm 1). If so, you're going to have to guess from context what they might have meant. It's possible that they might have meant to write $$fd_i = \frac{\sqrt{\frac{\sum_j (x_j - \bar{x})^2}{n}}}{\bar{x}}$$ In other words: the ratio between the standard deviation and the mean of that attribute. Who ...


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It is used for: Image analysis, and specially face recognition and search photos library. Language detection, text recognition and analysis ( to identify concepts in a text ). Used for advanced search in text Speech recognition Sound analysis, for efficient filtering and removal of noise in conversations and sound recognition ( Be able to differentiate ...


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