Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Matrix Factorization Techniques for Recommender Systems

Upper bound of Bayesian generalization error in non-negative matrix factorization

Advanced database marketing is designed to ascertain individual customers’ market responses with a discount or display of widely various products from transaction data. However, transaction data recorded in a supermarket or electric commerce are fundamentally sparse because most customers purchase only a few products from all products in shops. Existing methods are not applicable to elucidate the personalized response because of a lack of sample size of purchased data. This paper proposes a personalized market response estimation method for a wide set of customers and products from these sparse data. The method compresses a sparse transaction data with information related to response to marketing variables into a reduced-dimensional space for feasible parameter estimation. Then, they are decompressed into original space using augmented latent variables to obtain individual response parameters. Results show that the method can find suitable marketing promotions for individual customers to every analyzed product.

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Personalized market response analysis for a wide variety of products from sparse transaction data

Non-negative matrix factorization (NMF) is now used for knowledge discovery in machine learning, however, its mathematical properties have not yet established, because it is statistically singular. Recently, we derived an upper bound of the real log canonical threshold (RLCT) by using an algebraic geometrical method and used it to clarify the theoretical bound of the Bayesian generalization error of NMF. In this paper, we derive the exact value of the RLCT of NMF in the case that the rank of the matrix is not larger than two, and prove the tighter upper bound for general cases.

Tighter upper bound of real log canonical threshold of non-negative matrix factorization and its application to Bayesian inference

In this paper, we tackle with the problem of analyzing datasets with different resolution such as a pair of user's individual data and user group's data, for example "userA visited shopA 5 times" and "users whose attributes are men purchased itemA 80 times in total". In order to establish a basic approach to this problem, we focus on the simplified scenario and propose a new probabilistic model called probabilistic non-negative inconsistent-resolution matrices factorization (pNimf). pNimf is rigorously derived from the data generative process using latent high-resolution data which underlie low-resolution data. We conduct experiments on real purchase log data and confirm that the proposed model provides superior performance, and that the performance improves as the number of low-resolution data increases. These results imply that our way of modeling using latent high-resolution data can become the basic approach to the problem of analyzing dataset with different resolution.

Probabilistic Non-negative Inconsistent-resolution Matrices Factorization

In this paper, we propose a variational Bayesian algorithm for mixture models that can deal with censored data, which is the data under the situation that the exact value is known only when the value is within a certain range and otherwise only partial information is available. The proposed algorithm can be applied to any mixture model whose component distribution belongs to exponential family; it is a natural generalization of the variational Bayes that deals with “standard” samples whose values are known. We confirm the effectiveness of the proposed algorithm by experiments on synthetic and real world data.

Variational Bayes for Mixture Models with Censored Data.

Brand-Choice Analysis using Non-negative Tensor Factorization

The recent enhancement of taxi dispatch services with information technology has enabled data-driven pricing and dispatch. However, existing studies failed to address differences in individual priorities as regards money savings and time savings, leading to non-optimal taxi pricing and dispatch. In this paper, we formulate a new optimization problem that yields optimized price and time proposals for each requester according to their priorities. To consider the requester’s priorities, we introduce an individual requester’s acceptance probability model for price and required time, which is widely used in transportation economics. The proposals of price and time combinations yielded by our method enhance both the requester’s satisfaction and the service provider’s profit. Since the optimization problem is difficult to solve because its objective values are hard to evaluate and discontinuous, we construct a fast approximation algorithm by utilizing the characteristics of the problem. Simulations using real-world datasets show that the proposed framework increases both the requester’s satisfaction and service provider’s profit.

Price and Time Optimization for Utility-Aware Taxi Dispatching.

Recently, analysis of massive purchase histories is thought to be effective for marketing science. For successful sales strategies and advertisements, understanding of consumer's attitude (motivation toward purchasing) is important. However, marketers could obtain merely static attitude for the limited consumers using subjective questionnaires. We focus on purchase rhythm (regularity) as one approach to automatically extracting dynamic attitude transition. We propose "regular behavior measure" which quantifies how well each purchase corresponds to the user's own daily habits. It considers non-periodic habits as well as periodic habits using multiple probabilistic models, we consider purchase probability and the number of purchased dates simultaneously. We also define "influence weight" to quantify whether each item is purchased on a fixed day of the week (DoW) or year-month (YM) using Normalized Mutual Information. We analyze actual purchase data to show the effectiveness of our visualization that considers consumer's regularity transitions.

Masahiro Kohjima

Papers

Probabilistic Non-negative Inconsistent-resolution Matrices Factorization

Variational Bayes for Mixture Models with Censored Data.

Brand-Choice Analysis using Non-negative Tensor Factorization

Price and Time Optimization for Utility-Aware Taxi Dispatching.

Regularity Measure and Influence Weight for Analysis and Visualization of Consumer's Attitude