#### Communications and Signal Processing Seminar

# Mixture proportion estimation

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ECE Communications and Signal Processing Seminar Series

Mixture proportion estimation is the following statistical inference problem: given a random sample from a distribution $F$, and another random sample from a distribution $H$, find the largest value $\nu \in [0,1]$ such that $F = (1-\nu)G + \nu H$, for some distribution G. I will argue that mixture proportion estimation is a fundamental estimation task that arises naturally in several machine learning problems, and describe a universally consistent estimator. MPE is particularly relevant in pattern recognition problems where class label information is uncertain or missing, including anomaly detection, classification with label noise, classification with unknown class skew, classification with reject option, learning with partial labels, the two sample problem, multiple testing, change detection, and topic modeling. I will discuss as many of these problems as time permits.