Maximum Likelihood

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

• Outlier Detection with Maximum Likelihood

References

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