Kai Fan

Hierarchical Graph-Coupled HMMs for Heterogeneous Personalized Health Data

The purpose of this study is to leverage modern technology (mobile or web apps) to enrich epidemiology data and infer the transmission of disease. We develop hierarchical Graph-Coupled Hidden Markov Models (hGCHMMs) to simultaneously track the spread of infection in a small cell phone community and capture person-specific infection parameters by leveraging a link prior that incorporates additional covariates. In this paper we investigate two link functions, the beta-exponential link and sigmoid link, both of which allow the development of a principled Bayesian hierarchical framework for disease transmission. The results of our model allow us to predict the probability of infection for each persons on each day, and also to infer personal physical vulnerability and the relevant association with covariates. We demonstrate our approach theoretically and experimentally on both simulation data and real epidemiological records.

Learning a generative classifier from label proportions

Learning a classifier when only knowing the features and marginal distribution of class labels in each of the data groups is both theoretically interesting and practically useful. Specifically, we consider the case in which the ratio of the number of data instances to the number of classes is large. We prove sample complexity upper bound in this setting, which is inspired by an analysis of existing algorithms. We further formulate the problem in a density estimation framework to learn a generative classifier. We also develop a practical RBM-based algorithm which shows promising performance on benchmark datasets.

Triply Stochastic Variational Inference for Non-linear Beta Process Factor Analysis

We propose a non-linear extension to factor analysis with beta process priors for improved data representation ability. This non-linear Beta Process Factor Analysis (nBPFA) allows data to be represented as a non-linear transformation of a standard sparse factor decomposition. We develop a scalable variational inference framework, which builds upon the ideas of the variational auto-encoder, by allowing latent variables of the model to be sparse. Our framework can be readily used for real-valued, binary and count data. We show theoretically and with experiments that our training scheme, with additive or multiplicative noise on observations, improves performance and prevents overfitting. We benchmark our algorithms on image, text and collaborative filtering datasets. We demonstrate faster convergence rates and competitive performance compared to standard gradient-based approaches.

Estimation based on RBM from label proportions in large group case

Learning a classifier when only knowing about the features and marginal distribution of class labels in each of the data groups is both theoretically interesting and practically useful. Specifically, we are interested in the case where the ratio of the number of data instances to the number of classes is large. For this problem, we show that the performance of a previously proposed discriminative classifier will deteriorate quickly as the ratio grows. In contrast, we formulate a density estimation framework to learn a generative classifier by RBM in this scenario with guaranteed performance under mild assumption.