Maximum LikelihoodΒΆ

Global Algorithm - One-Dimensional Algorithm

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 \(N\)  
\(\mu\) \(\mu \in \mathbb{R}\)   Mean distribution of \(Y\)  
\(\sigma\) \(\sigma\in \mathbb{R}\)   Standard deviation of \(Y\)  

Output Parameters

Parameter Type Constraint Description Remarks
\(\hat{Y}\) \(\hat{Y} \in \mathbb R^N\)   Values in the \(Y\) list which are outside the region of interest are marked  

Tool Support

  • Matlab

    For details refer to the online documentation of the function ‘mle’.

Single Steps using the Algorithm

References

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