Kernel Density Estimation — mechanism.

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Answer

$(x)\; = \;(1 / (\mathrm{nh}^{d}))$
$K = kernel (Gaussian typical). h = bandwidth (critical hyperparameter).$
$Uses: visualization (smoothed histogram), density-based anomaly detection, generative sampling.$
$Scales poorly to high d (curse of dimensionality — need exponentially more data).$
$Use cross-validation or Silverman's rule for h.$

Check yourself — multiple choice

Random
p̂ $(x)\; = \;(1 / \mathrm{nh}^{d})$ Σ $K((x - x_{i}) / h)$ ; non-parametric; bandwidth h tuned via CV / Silverman; poor in high dim (curse of dim)
Same as GMM
Not real

KDE: non-parametric density; bandwidth h critical; curse of dim.

#density#anomaly-detection

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