Breakthroughs in modern technology have allowed more sequential data to be collected in higher resolutions.

Examples of such events include disease transmission, opinion transition in elections, and rumor propagation.

The key idea in this paper is to maintain this property of discrete state space models while relaxing the stationary Markov assumption on the transition probabilities that we typically use to simplify inference. Although this idea is not new (e.g. The variational inference algorithm for this model also seems to be new. In practice, we can relax the "strict" Markov assumption (i.e. the state in year t 1 is conditionally independent of the past given the state at year t) by augmenting the state with the past h 1 years. This keeps the inference exact and relatively easy to implement.

The authors present a variational inference algorithm for continuous time Markov jump processes. Following previous work, they use "uniformization" to produce a discrete time skeleton at which they infer the latent states. Unlike previous work, however, the authors propose to learn this skeleton (a point estimate, via random search) and to integrate out, or collapse, the transition matrix during latent state inference. They compare their algorithm to existing MCMC schemes, which also use uniformization, but which do not collapse out the transition matrix. While this work is well motivated, I found it difficult to tease out which elements of the inference algorithm led to the observed improvement.

Factorial Hidden Markov Models (FHMMs) are powerful models for sequential data but they do not scale well with long sequences. We propose a scalable inference and learning algorithm for FHMMs that draws on ideas from the stochastic variational inference, neural network and copula literatures. Unlike existing approaches, the proposed algorithm requires no message passing procedure among latent variables and can be distributed to a network of computers to speed up learning. Our experiments corroborate that the proposed algorithm does not introduce further approximation bias compared to the proven structured mean-field algorithm, and achieves better performance with long sequences and large FHMMs.

Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the availability of large-scale data from social networks and sensor networks offers an unprecedented opportunity to predict state-changing events at the individual level. Examples of such events include disease transmission, opinion transition in elections, and rumor propagation. Unlike previous research focusing on the collective effects of social systems, this study makes efficient inferences at the individual level. In order to cope with dynamic interactions among a large number of individuals, we introduce the stochastic kinetic model to capture adaptive transition probabilities and propose an efficient variational inference algorithm the complexity of which grows linearly -- rather than exponentially-- with the number of individuals. To validate this method, we have performed epidemic-dynamics experiments on wireless sensor network data collected from more than ten thousand people over three years. The proposed algorithm was used to track disease transmission and predict the probability of infection for each individual. Our results demonstrate that this method is more efficient than sampling while nonetheless achieving high accuracy.

We present a truncation-free online variational inference algorithm for Bayesian nonparametric models. Unlike traditional (online) variational inference algorithms that require truncations for the model or the variational distribution, our method adapts model complexity on the fly. Our experiments for Dirichlet process mixture models and hierarchical Dirichlet process topic models on two large-scale data sets show better performance than previous online variational inference algorithms.

Estimating time-varying graphical models are of paramount importance in various social, financial, biological, and engineering systems, since the evolution of such networks can be utilized for example to spot trends, detect anomalies, predict vulnerability, and evaluate the impact of interventions. Existing methods require extensive tuning of parameters that control the graph sparsity and temporal smoothness. Furthermore, these methods are computationally burdensome with time complexity O(NP^3) for P variables and N time points. As a remedy, we propose a low-complexity tuning-free Bayesian approach, named BADGE. Specifically, we impose temporally-dependent spike-and-slab priors on the graphs such that they are sparse and varying smoothly across time. A variational inference algorithm is then derived to learn the graph structures from the data automatically. Owning to the pseudo-likelihood and the mean-field approximation, the time complexity of BADGE is only O(NP^2). Additionally, by identifying the frequency-domain resemblance to the time-varying graphical models, we show that BADGE can be extended to learning frequency-varying inverse spectral density matrices, and yields graphical models for multivariate stationary time series. Numerical results on both synthetic and real data show that that BADGE can better recover the underlying true graphs, while being more efficient than the existing methods, especially for high-dimensional cases.

We present a truncation-free online variational inference algorithm for Bayesian nonparametric models. Unlike traditional (online) variational inference algorithms that require truncations for the model or the variational distribution, our method adapts model complexity on the fly. Our experiments for Dirichlet process mixture models and hierarchical Dirichlet process topic models on two large-scale data sets show better performance than previous online variational inference algorithms. Papers published at the Neural Information Processing Systems Conference.

Items in modern recommender systems are often organized in hierarchical structures. These hierarchical structures and the data within them provide valuable information for building personalized recommendation systems. In this paper, we propose a general hierarchical Bayesian learning framework, i.e., \emph{HBayes}, to learn both the structures and associated latent factors. Furthermore, we develop a variational inference algorithm that is able to learn model parameters with fast empirical convergence rate. The proposed HBayes is evaluated on two real-world datasets from different domains. The results demonstrate the benefits of our approach on item recommendation tasks, and show that it can outperform the state-of-the-art models in terms of precision, recall, and normalized discounted cumulative gain. To encourage the reproducible results, we make our code public on a git repo: \url{https://tinyurl.com/ycruhk4t}.