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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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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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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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