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Density Estimation under Independent Similarly Distributed Sampling Assumptions
Tony Jebara · Yingbo Song · Kapil Thadani

Tue Dec 04 09:50 AM -- 10:00 AM (PST) @
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A method is proposed for semiparametric estimation where parametric and nonparametric criteria are exploited in density estimation and unsupervised learning. This is accomplished by making sampling assumptions on a dataset that smoothly interpolate between the extreme of independently distributed (or {\em id}) sample data (as in nonparametric kernel density estimators) to the extreme of independent {\em identically} distributed (or {\em iid}) sample data. This article makes independent {\em similarly} distributed (or {\em isd}) sampling assumptions and interpolates between these two using a scalar parameter. The parameter controls a Bhattacharyya affinity penalty between pairs of distributions on samples. Surprisingly, the {\em isd} method maintains certain consistency and unimodality properties akin to maximum likelihood estimation. The proposed {\em isd} scheme is an alternative for handling nonstationarity in data without making drastic hidden variable assumptions which often make estimation difficult and laden with local optima. Experiments in density estimation on a variety of datasets confirm the superiority of {\em isd} over {\em iid} estimation, {\em id} estimation and mixture modeling.

Author Information

Tony Jebara (Spotify)
Yingbo Song (Columbia University)
Kapil Thadani (Columbia University)

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