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.

In this article, we present a model for analyzing the cooccurrence count data derived from practical fields such as user-item or item-item data from online shopping platform, cooccurring word-word pairs in sequences of texts. Such data contain important information for developing recommender systems or studying relevance of items or words from non-numerical sources. Different from traditional regression models, there are no observations for covariates. Additionally, the cooccurrence matrix is typically of so high dimension that it does not fit into a computer's memory for modeling. We extract numerical data by defining windows of cooccurrence using weighted count on the continuous scale. Positive probability mass is allowed for zero observations. We present Shared parameter Alternating Tweedie (SA-Tweedie) model and an algorithm to estimate the parameters. We introduce a learning rate adjustment used along with the Fisher scoring method in the inner loop to help the algorithm stay on track of optimizing direction. Gradient descent with Adam update was also considered as an alternative method for the estimation. Simulation studies and an application showed that our algorithm with Fisher scoring and learning rate adjustment outperforms the other two methods. Pseudo-likelihood approach with alternating parameter update was also studied. Numerical studies showed that the pseudo-likelihood approach is not suitable in our shared parameter alternating regression models with unobserved covariates.