Genetic sequence data are well described by hidden Markov models (HMMs) in which latent states correspond to clusters of similar mutation patterns. Theory from statistical genetics suggests that these HMMs are nonhomogeneous (their transition probabilities vary along the chromosome) and have large support for self transitions. We develop a new nonparametric model of genetic sequence data, based on the hierarchical Dirichlet process, which supports these self transitions and nonhomogeneity. Our model provides a parameterization of the genetic process that is more parsimonious than other more general nonparametric models which have previously been applied to population genetics. We provide truncation-free MCMC inference for our model using a new auxiliary sampling scheme for Bayesian nonparametric HMMs. In a series of experiments on male X chromosome data from the Thousand Genomes Project and also on data simulated from a population bottleneck we show the benefits of our model over the popular finite model fastPHASE, which can itself be seen as a parametric truncation of our model. We find that the number of HMM states found by our model is correlated with the time to the most recent common ancestor in population bottlenecks. This work demonstrates the flexibility of Bayesian nonparametrics applied to large and complex genetic data.

Recent progress in artificial intelligence (AI) has renewed interest in building systems that learn and think like people. Many advances have come from using deep neural networks trained end-to-end in tasks such as object recognition, video games, and board games, achieving performance that equals or even beats humans in some respects. Despite their biological inspiration and performance achievements, these systems differ from human intelligence in crucial ways. We review progress in cognitive science suggesting that truly human-like learning and thinking machines will have to reach beyond current engineering trends in both what they learn, and how they learn it. Specifically, we argue that these machines should (a) build causal models of the world that support explanation and understanding, rather than merely solving pattern recognition problems; (b) ground learning in intuitive theories of physics and psychology, to support and enrich the knowledge that is learned; and (c) harness compositionality and learning-to-learn to rapidly acquire and generalize knowledge to new tasks and situations. We suggest concrete challenges and promising routes towards these goals that can combine the strengths of recent neural network advances with more structured cognitive models.

Reconstruction of the tridimensional geometry of a visual scene using the binocular disparity information is an important issue in computer vision and mobile robotics, which can be formulated as a Bayesian inference problem. However, computation of the full disparity distribution with an advanced Bayesian model is usually an intractable problem, and proves computationally challenging even with a simple model. In this paper, we show how probabilistic hardware using distributed memory and alternate representation of data as stochastic bitstreams can solve that problem with high performance and energy efficiency. We put forward a way to express discrete probability distributions using stochastic data representations and perform Bayesian fusion using those representations, and show how that approach can be applied to diparity computation. We evaluate the system using a simulated stochastic implementation and discuss possible hardware implementations of such architectures and their potential for sensorimotor processing and robotics.

One of the central themes in Sum-Product networks (SPNs) is the interpretation of sum nodes as marginalized latent variables (LVs). This interpretation yields an increased syntactic or semantic structure, allows the application of the EM algorithm and to efficiently perform MPE inference. In literature, the LV interpretation was justified by explicitly introducing the indicator variables corresponding to the LVs' states. However, as pointed out in this paper, this approach is in conflict with the completeness condition in SPNs and does not fully specify the probabilistic model. We propose a remedy for this problem by modifying the original approach for introducing the LVs, which we call SPN augmentation. We discuss conditional independencies in augmented SPNs, formally establish the probabilistic interpretation of the sum-weights and give an interpretation of augmented SPNs as Bayesian networks. Based on these results, we find a sound derivation of the EM algorithm for SPNs. Furthermore, the Viterbi-style algorithm for MPE proposed in literature was never proven to be correct. We show that this is indeed a correct algorithm, when applied to selective SPNs, and in particular when applied to augmented SPNs. Our theoretical results are confirmed in experiments on synthetic data and 103 real-world datasets.

We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the optimization of a geometric loss function, which is a surrogate to the LDA's likelihood. Our method involves a fast optimization based weighted clustering procedure augmented with geometric corrections, which overcomes the computational and statistical inefficiencies encountered by other techniques based on Gibbs sampling and variational inference, while achieving the accuracy comparable to that of a Gibbs sampler. The topic estimates produced by our method are shown to be statistically consistent under some conditions. The algorithm is evaluated with extensive experiments on simulated and real data.

Non-negative Matrix Factorization (NMF) is a popular tool for data exploration. Bayesian NMF promises to also characterize uncertainty in the factorization. Unfortunately, current inference approaches such as MCMC mix slowly and tend to get stuck on single modes. We introduce a novel approach using rapidly-exploring random trees (RRTs) to asymptotically cover regions of high posterior density. These are placed in a principled Bayesian framework via an online extension to nonparametric variational inference. On experiments on real and synthetic data, we obtain greater coverage of the posterior and higher ELBO values than standard NMF inference approaches.

The problem of forecasting conditional probabilities of the next event given the past is considered in a general probabilistic setting. Given an arbitrary (large, uncountable) set C of predictors, we would like to construct a single predictor that performs asymptotically as well as the best predictor in C, on any data. Here we show that there are sets C for which such predictors exist, but none of them is a Bayesian predictor with a prior concentrated on C. In other words, there is a predictor with sublinear regret, but every Bayesian predictor must have a linear regret. This negative finding is in sharp contrast with previous results that establish the opposite for the case when one of the predictors in $C$ achieves asymptotically vanishing error. In such a case, if there is a predictor that achieves asymptotically vanishing error for any measure in C, then there is a Bayesian predictor that also has this property, and whose prior is concentrated on (a countable subset of) C.

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments that are each explained by simpler dynamic units. Building on switching linear dynamical systems (SLDS), we present a new model class that not only discovers these dynamical units, but also explains how their switching behavior depends on observations or continuous latent states. These "recurrent" switching linear dynamical systems provide further insight by discovering the conditions under which each unit is deployed, something that traditional SLDS models fail to do. We leverage recent algorithmic advances in approximate inference to make Bayesian inference in these models easy, fast, and scalable.

Neural circuits contain heterogeneous groups of neurons that differ in type, location, connectivity, and basic response properties. However, traditional methods for dimensionality reduction and clustering are ill-suited to recovering the structure underlying the organization of neural circuits. In particular, they do not take advantage of the rich temporal dependencies in multi-neuron recordings and fail to account for the noise in neural spike trains. Here we describe new tools for inferring latent structure from simultaneously recorded spike train data using a hierarchical extension of a multi-neuron point process model commonly known as the generalized linear model (GLM). Our approach combines the GLM with flexible graph-theoretic priors governing the relationship between latent features and neural connectivity patterns. Fully Bayesian inference via P\'olya-gamma augmentation of the resulting model allows us to classify neurons and infer latent dimensions of circuit organization from correlated spike trains. We demonstrate the effectiveness of our method with applications to synthetic data and multi-neuron recordings in primate retina, revealing latent patterns of neural types and locations from spike trains alone.

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian inference. Moreover, the optimization problem induces a new regularization for the posterior embedding estimator, which is faster and has comparable performance to the squared regularization in kernel Bayes' rule. This regularization coincides with a former thresholding approach used in kernel POMDPs whose consistency remains to be established. Our theoretical work solves this open problem and provides consistency analysis in regression settings. Based on our optimizational formulation, we propose a flexible Bayesian posterior regularization framework which for the first time enables us to put regularization at the distribution level. We apply this method to nonparametric state-space filtering tasks with extremely nonlinear dynamics and show performance gains over all other baselines.