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Another method is Bayesian Blocks from Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations by Scargle et al. Bayesian Blocks is a dynamic histogramming method which optimizes one of several possible fitness functions to determine an optimal binning for data, where the bins are not necessarily uniform width. Bayesian Blocks for ...

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Yes - it is $d\times l$. There would be 6 $β$ coefficients for 2*3: $β_1x_1 + β_2x_1^2 + β_3x_2 + β_4x_2^2 + β_5x_3 + β_6x_3^2$ That does not include an intercept or any interaction terms.

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One option would be look at conditional probability based on percentiles. First, find percentiles based on all the data. For example, 99th percentile is 1432 milliseconds. Then, find percent of a specific user request above that threshold. For example U1 has 50% of requests above 99th percentile. This could be made into a cross-tabs table for easier ...

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Make sure you transformed back your predictions and actual values before calculating MAPE. You can check which observations contributed the most to high MAPE. MAPE is very sensitive to prediction errors at small actual values. Most likely worst performing observations ("from MAPE perspective") are those with small actual values. Depending on the ...

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You first create inverted indexes or postings list. Then, using the term frequency and document frequency you calculate tf idf with the formula $tf* log({N \over df})$. For more details check this blog.

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The notation $D_\mathrm{KL}(P \| Q)$ is pretty much standard for the Kullback-Leibler divergence. There is an interesting discussion on Mathematics SE on the reasons for the fairly unusual notation used for divergences. In general, $x \sim G(z, c)$ means "$x$ is a random variable distributed according to $G(z, c)$". In the subscript the author ...

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Heteroskedasticity is relevant in cases in which you calculate a standard error for the estimated coefficients. For instance for a regression model with a single independent variable this would be for the slope coefficient: $$SE(\hat{\beta_1}) = \sigma \left(\frac{1}{\sum_i(x_i - \bar{x})^2}\right)$$ with (see this for more details)  \hat{\sigma}^2 = \frac{...

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It also applies to other methods, i.e. not just linear regression. For example, ANOVA and T-test also depend on homogeneity of variance. One method to check the homogeneity of variance, compatible with the one-way ANOVA, is the Barlett's test.

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If you're trying too hard, ask yourself if you're enjoying it. If you're asking yourself if you're enjoying it, then maybe you should ask yourself what it is that you really enjoy. Otherwise, try the Schaum series in Calculus, Linear Algebra, Statistics. Those are excellent books for beginners: https://www.amazon.com/Schaums-Outline-Linear-Algebra-Outlines/...

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