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Outlier Detection (1): Statistical Methods

Statistical methods (also known as model-based methods) assume that the normal data follow some statistical model (a stochastic model)

The data not following the model are outliers.

Effectiveness of statistical methods: highly depends on whether the assumption of statistical model holds in the real data

There are rich alternatives to use various statistical models

E.g., parametric vs. non-parametric

Example (below figure): First use Gaussian distribution to model the normal data

For each object y in region R, estimate gD(y), the probability of y fits the Gaussian distribution
If gD(y) is very low, y is unlikely generated by the Gaussian model, thus an outlier

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