A paper on Truncated Density Estimation, authored by statistics institute members, has been recently accepted by the Journal of Machine Learning Research (JMLR)
Analysing the crime pattern of Chicago.
The paper proposes a new approach for estimating density functions for a generic truncated domain. Conventionally, estimating a truncated density requires evaluating a normalizing term, making the estimation intractable, however, in this paper, the authors propose to use a technique called Score Matching (Hyvarinen, 2007, Yu et al., 2020) to match the log-gradients of the model and the data density, thus avoiding the difficult normalization term. The proposed approach has shown promising results in Chicago crime pattern analysis and outlier trimming compensation.
This paper is authored by Song Liu, Lecturer in School of Mathematics, Takafumi Kanamori, Professor at Tokyo Institute of Technology and Daniel Williams, COMPASS PhD student. Its preprint can be found online.
References:
Aapo Hyvarinen, Estimation of Non-Normalized Statistical Models by Score Matching, Journal of Machine Learning Research, 6 (2005) 695–709.
Shiqing Yu, Mathias Drton, Ali Shojaie, Generalized Score Matching for Non-Negative Data, Journal of Machine Learning Research 20 (2019) 1-70
Song Liu, Takafumi Kanamori, Daniel J. Williams, Estimating Density Models with Truncation Boundaries using Score Matching, Journal of Machine Learning Research, to appear, 2022.
