Bayesian graphical models have been shown to be a powerful tool for discovering uncertainty and causal structure from real-world data in many application fields. Current inference methods primarily follow different kinds of trade-offs between computational complexity and predictive accuracy. At one end of the spectrum, variational inference approaches perform well in computational efficiency, while at the other end, Gibbs sampling approaches are known to be relatively accurate for prediction in practice. In this paper, we extend an existing Gibbs sampling method, and propose a new deterministic Heron inference (Heron) for a family of Bayesian graphical models. In addition to the support for nontrivial distributability, one more benefit of Heron is that it is able to not only allow us to easily assess the convergence status but also largely improve the running efficiency. We evaluate Heron against the standard collapsed Gibbs sampler and state-of-the-art state augmentation method in inference for well-known graphical models. Experimental results using publicly available real-life data have demonstrated that Heron significantly outperforms the baseline methods for inferring Bayesian graphical models.

Online social networks like Twitter and Facebook produce an overwhelming amount of information every day. However, research suggests that much of this content focuses on a reasonably sized set of ongoing events or topics that are both temporally and geographically situated. These patterns are especially observable when the data that is generated contains geospatial information, usually generated by a location enabled device such as a smartphone. In this paper, we consider a data set of 1.4 million geo-tagged tweets from a country during a large social movement, where social events and demonstrations occurred frequently. We use a probabilistic graphical model to discover these events within the data in a way that informs us of their spatial, temporal and topical focus. Quantitative analysis suggests that the streaming algorithm proposed in the paper uncovers both well-known events and lesser-known but important events that occurred within the timeframe of the dataset. In addition, the model can be used to predict the location and time of texts that do not have these pieces of information, which accounts for the much of the data on the web.

In this paper we investigate the geometry of the likelihood of the unknown parameters in a simple class of Bayesian directed graphs with hidden variables. This enables us, before any numerical algorithms are employed, to obtain certain insights in the nature of the unidentifiability inherent in such models, the way posterior densities will be sensitive to prior densities and the typical geometrical form these posterior densities might take. Many of these insights carry over into more complicated Bayesian networks with systematic missing data.

We propose a new probabilistic graphical model that jointly models the difficulties of questions, the abilities of participants and the correct answers to questions in aptitude testing and crowdsourcing settings. We devise an active learning/adaptive testing scheme based on a greedy minimization of expected model entropy, which allows a more efficient resource allocation by dynamically choosing the next question to be asked based on the previous responses. We present experimental results that confirm the ability of our model to infer the required parameters and demonstrate that the adaptive testing scheme requires fewer questions to obtain the same accuracy as a static test scenario.