Maximum LikelihoodΒΆ

Maximum Likelihood algorithm decides whether a value is a value outside the region of interest based on that value’s distance from the estimated mean distribution. Generally, if

\[|Y_i - \mu| > 3 \cdot \sigma \, \text{,}\]

the data point is considered outside the region of interest. \(\mu\) is the mean distribution, \(Y_i\) is \(i\)th element of \(Y\) and \(\sigma\) denotes the standard deviation. Note that \(\mu \pm 3\sigma\) contains \(99.7%\) data under the assumption of normal distribution.

Input Parameters

Parameter Type Constraint Description Remarks
\(Y\) \(Y \in \mathbb R^N\) \(N \in \mathbb{N}\) Input data sequence of length \(N\) None
\(\mu\) \(\mu \in \mathbb{R}\) None Mean distribution of \(Y\) None
\(\sigma\) \(\sigma\in \mathbb{R}\) None Standard deviation of \(Y\) None

Output Parameters

Parameter Type Constraint Description Remarks
\(\hat{Y}\) \(\hat{Y} \in \mathbb R^N\) None Values in the \(Y\) list which are outside the region of interest are marked None

Single Steps using the Algorithm

References

    1. Han, M. Kamber and J. Pei, Data Mining - Concepts and Techniques, 3rd ed., Amsterdam: Morgan Kaufmann Publishers, 2012.