Point processes are popular models of neural spiking behavior as they provide a statistical distribution over temporal sequences of spikes and help to reveal the complexities underlying a series of recorded action potentials. However, the most common neural point process models, the Poisson process and the gamma renewal process, do not capture interactions and correlations that are critical to modeling populations of neurons. We develop a novel model based on a determinantal point process over latent embeddings of neurons that effectively captures and helps visualize complex inhibitory and competitive interaction. We show that this model is a natural extension of the popular generalized linear model to sets of interacting neurons. The model is extended to incorporate gain control or divisive normalization, and the modulation of neural spiking based on periodic phenomena. Applied to neural spike recordings from the rat hippocampus, we see that the model captures inhibitory relationships, a dichotomy of classes of neurons, and a periodic modulation by the theta rhythm known to be present in the data.

Discriminative methods for learning structured models have enabled wide-spread use of very rich feature representations. However, the computational cost of feature extraction is prohibitive for large-scale or time-sensitive applications, often dominating the cost of inference in the models. Significant efforts have been devoted to sparsity-based model selection to decrease this cost. Such feature selection methods control computation statically and miss the opportunity to fine-tune feature extraction to each input at run-time. We address the key challenge of learning to control fine-grained feature extraction adaptively, exploiting non-homogeneity of the data. We propose an architecture that uses a rich feedback loop between extraction and prediction. The run-time control policy is learned using efficient value-function approximation, which adaptively determines the value of information of features at the level of individual variables for each input. We demonstrate significant speedups over state-of-the-art methods on two challenging datasets. For articulated pose estimation in video, we achieve a more accurate state-of-the-art model that is simultaneously 4$\times$ faster while using only a small fraction of possible features, with similar results on an OCR task.

The detection of anomalous activity in graphs is a statistical problem that arises in many applications, such as network surveillance, disease outbreak detection, and activity monitoring in social networks. Beyond its wide applicability, graph structured anomaly detection serves as a case study in the difficulty of balancing computational complexity with statistical power. In this work, we develop from first principles the generalized likelihood ratio test for determining if there is a well connected region of activation over the vertices in the graph in Gaussian noise. Because this test is computationally infeasible, we provide a relaxation, called the Lov\'asz extended scan statistic (LESS) that uses submodularity to approximate the intractable generalized likelihood ratio. We demonstrate a connection between LESS and maximum a-posteriori inference in Markov random fields, which provides us with a poly-time algorithm for LESS. Using electrical network theory, we are able to control type 1 error for LESS and prove conditions under which LESS is risk consistent. Finally, we consider specific graph models, the torus, $k$-nearest neighbor graphs, and $\epsilon$-random graphs. We show that on these graphs our results provide near-optimal performance by matching our results to known lower bounds.

Monte-Carlo tree search is drawing great interest in the domain of planning under uncertainty, particularly when little or no domain knowledge is available. One of the central problems is the trade-off between exploration and exploitation. In this paper we present a novel Bayesian mixture modelling and inference based Thompson sampling approach to addressing this dilemma. The proposed Dirichlet-NormalGamma MCTS (DNG-MCTS) algorithm represents the uncertainty of the accumulated reward for actions in the MCTS search tree as a mixture of Normal distributions and inferences on it in Bayesian settings by choosing conjugate priors in the form of combinations of Dirichlet and NormalGamma distributions. Thompson sampling is used to select the best action at each decision node. Experimental results show that our proposed algorithm has achieved the state-of-the-art comparing with popular UCT algorithm in the context of online planning for general Markov decision processes.

Variational inference algorithms provide the most effective framework for large-scale training of Bayesian nonparametric models. Stochastic online approaches are promising, but are sensitive to the chosen learning rate and often converge to poor local optima. We present a new algorithm, memoized online variational inference, which scales to very large (yet finite) datasets while avoiding the complexities of stochastic gradient. Our algorithm maintains finite-dimensional sufficient statistics from batches of the full dataset, requiring some additional memory but still scaling to millions of examples. Exploiting nested families of variational bounds for infinite nonparametric models, we develop principled birth and merge moves allowing non-local optimization. Births adaptively add components to the model to escape local optima, while merges remove redundancy and improve speed. Using Dirichlet process mixture models for image clustering and denoising, we demonstrate major improvements in robustness and accuracy.

Learning a visual concept from a small number of positive examples is a significant challenge for machine learning algorithms. Current methods typically fail to find the appropriate level of generalization in a concept hierarchy for a given set of visual examples. Recent work in cognitive science on Bayesian models of generalization addresses this challenge, but prior results assumed that objects were perfectly recognized. We present an algorithm for learning visual concepts directly from images, using probabilistic predictions generated by visual classifiers as the input to a Bayesian generalization model. As no existing challenge data tests this paradigm, we collect and make available a new, large-scale dataset for visual concept learning using the ImageNet hierarchy as the source of possible concepts, with human annotators to provide ground truth labels as to whether a new image is an instance of each concept using a paradigm similar to that used in experiments studying word learning in children. We compare the performance of our system to several baseline algorithms, and show a significant advantage results from combining visual classifiers with the ability to identify an appropriate level of abstraction using Bayesian generalization.

Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when computing conditional probabilities. The reason is that conditioning on evidence breaks many of the model's symmetries, which preempts standard lifting techniques. Recent theoretical results show, for example, that conditioning on evidence which corresponds to binary relations is #P-hard, suggesting that no lifting is to be expected in the worst case. In this paper, we balance this grim result by identifying the Boolean rank of the evidence as a key parameter for characterizing the complexity of conditioning in lifted inference. In particular, we show that conditioning on binary evidence with bounded Boolean rank is efficient. This opens up the possibility of approximating evidence by a low-rank Boolean matrix factorization, which we investigate both theoretically and empirically.

We consider a number of classical and new computational problems regarding marginal distributions, and inference in models specifying a full joint distribution. We prove general and efficient reductions between a number of these problems, which demonstrate that algorithmic progress in inference automatically yields progress for "pure data" problems. Our main technique involves formulating the problems as linear programs, and proving that the dual separation oracle required by the ellipsoid method is provided by the target problem. This technique may be of independent interest in probabilistic inference.

What if there is a teacher who knows the learning goal and wants to design good training data for a machine learner? We propose an optimal teaching framework aimed at learners who employ Bayesian models. Our framework is expressed as an optimization problem over teaching examples that balance the future loss of the learner and the effort of the teacher. This optimization problem is in general hard. In the case where the learner employs conjugate exponential family models, we present an approximate algorithm for finding the optimal teaching set. Our algorithm optimizes the aggregate sufficient statistics, then unpacks them into actual teaching examples. We give several examples to illustrate our framework.

In large-scale applications of undirected graphical models, such as social networks and biological networks, similar patterns occur frequently and give rise to similar parameters.In this situation, it is beneficial to group the parameters for more efficient learning. We show that even when the grouping is unknown, we can infer theseparameter groups during learning via a Bayesian approach. We impose a Dirichlet process prior on the parameters. Posterior inference usually involves calculating intractableterms, and we propose two approximation algorithms, namely a Metropolis-Hastings algorithm with auxiliary variables and a Gibbs sampling algorithm with"stripped" Beta approximation (Gibbs SBA). Simulations show that both algorithms outperform conventional maximum likelihood estimation (MLE). Gibbs SBA's performance is close to Gibbs sampling with exact likelihood calculation. Modelslearned with Gibbs SBA also generalize better than the models learned by MLE on real-world Senate voting data.