Matrix factorization and prediction for high dimensional co-occurrence count data via shared parameter alternating zero inflated Gamma model

TL;DR

This paper introduces a novel shared parameter alternating zero-inflated Gamma model for high-dimensional sparse co-occurrence count data, enabling effective prediction of item or user relevance by modeling counts with zero-inflation and Gamma distributions.

Contribution

It develops the SA-ZIG model with two link functions, proposes parameter updating schemes, and provides convergence analysis, advancing methods for high-dimensional sparse count data analysis.

Findings

SA-ZIG with Fisher scoring and learning rate adjustment performs well in simulations.

The model effectively captures zero-inflation and skewness in co-occurrence data.

Numerical studies validate the proposed estimation algorithms.

Abstract

High-dimensional sparse matrix data frequently arise in various applications. A notable example is the weighted word-word co-occurrence count data, which summarizes the weighted frequency of word pairs appearing within the same context window. This type of data typically contains highly skewed non-negative values with an abundance of zeros. Another example is the co-occurrence of item-item or user-item pairs in e-commerce, which also generates high-dimensional data. The objective is to utilize this data to predict the relevance between items or users. In this paper, we assume that items or users can be represented by unknown dense vectors. The model treats the co-occurrence counts as arising from zero-inflated Gamma random variables and employs cosine similarity between the unknown vectors to summarize item-item relevance. The unknown values are estimated using the shared parameter alternating zero-inflated Gamma regression models (SA-ZIG). Both canonical link and log link models are considered. Two parameter updating schemes are proposed, along with an algorithm to estimate the unknown parameters. Convergence analysis is presented analytically. Numerical studies demonstrate that the SA-ZIG using Fisher scoring without learning rate adjustment may fail to fi nd the maximum likelihood estimate. However, the SA-ZIG with learning rate adjustment performs satisfactorily in our simulation studies.