Sparse encoding for more-interpretable feature-selecting representations in probabilistic matrix factorization

Fuente: arXiv
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Main Authors: Chang, Joshua C., Fletcher, Patrick, Han, Jungmin, Chang, Ted L., Vattikuti, Shashaank, Desmet, Bart, Zirikly, Ayah, Chow, Carson C.
Format: Preprint
Published: 2020
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author Chang, Joshua C.
Fletcher, Patrick
Han, Jungmin
Chang, Ted L.
Vattikuti, Shashaank
Desmet, Bart
Zirikly, Ayah
Chow, Carson C.
author_facet Chang, Joshua C.
Fletcher, Patrick
Han, Jungmin
Chang, Ted L.
Vattikuti, Shashaank
Desmet, Bart
Zirikly, Ayah
Chow, Carson C.
contents Dimensionality reduction methods for count data are critical to a wide range of applications in medical informatics and other fields where model interpretability is paramount. For such data, hierarchical Poisson matrix factorization (HPF) and other sparse probabilistic non-negative matrix factorization (NMF) methods are considered to be interpretable generative models. They consist of sparse transformations for decoding their learned representations into predictions. However, sparsity in representation decoding does not necessarily imply sparsity in the encoding of representations from the original data features. HPF is often incorrectly interpreted in the literature as if it possesses encoder sparsity. The distinction between decoder sparsity and encoder sparsity is subtle but important. Due to the lack of encoder sparsity, HPF does not possess the column-clustering property of classical NMF -- the factor loading matrix does not sufficiently define how each factor is formed from the original features. We address this deficiency by self-consistently enforcing encoder sparsity, using a generalized additive model (GAM), thereby allowing one to relate each representation coordinate to a subset of the original data features. In doing so, the method also gains the ability to perform feature selection. We demonstrate our method on simulated data and give an example of how encoder sparsity is of practical use in a concrete application of representing inpatient comorbidities in Medicare patients.
format Preprint
id arxiv_https___arxiv_org_abs_2012_04171
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Sparse encoding for more-interpretable feature-selecting representations in probabilistic matrix factorization
Chang, Joshua C.
Fletcher, Patrick
Han, Jungmin
Chang, Ted L.
Vattikuti, Shashaank
Desmet, Bart
Zirikly, Ayah
Chow, Carson C.
Machine Learning
Quantitative Methods
Dimensionality reduction methods for count data are critical to a wide range of applications in medical informatics and other fields where model interpretability is paramount. For such data, hierarchical Poisson matrix factorization (HPF) and other sparse probabilistic non-negative matrix factorization (NMF) methods are considered to be interpretable generative models. They consist of sparse transformations for decoding their learned representations into predictions. However, sparsity in representation decoding does not necessarily imply sparsity in the encoding of representations from the original data features. HPF is often incorrectly interpreted in the literature as if it possesses encoder sparsity. The distinction between decoder sparsity and encoder sparsity is subtle but important. Due to the lack of encoder sparsity, HPF does not possess the column-clustering property of classical NMF -- the factor loading matrix does not sufficiently define how each factor is formed from the original features. We address this deficiency by self-consistently enforcing encoder sparsity, using a generalized additive model (GAM), thereby allowing one to relate each representation coordinate to a subset of the original data features. In doing so, the method also gains the ability to perform feature selection. We demonstrate our method on simulated data and give an example of how encoder sparsity is of practical use in a concrete application of representing inpatient comorbidities in Medicare patients.
title Sparse encoding for more-interpretable feature-selecting representations in probabilistic matrix factorization
topic Machine Learning
Quantitative Methods
url https://arxiv.org/abs/2012.04171