Neuroscience is undergoing faster changes than ever before. Over 100 years our field qualitatively described and invasively manipulated single or few organisms to gain anatomical, physiological, and pharmacological insights. In the last 10 years neuroscience spawned quantitative big-sample datasets on microanatomy, synaptic connections, optogenetic brain-behavior assays, and high-level cognition. While growing data availability and information granularity have been amply discussed, we direct attention to a routinely neglected question: How will the unprecedented data richness shape data analysis practices? Statistical reasoning is becoming more central to distill neurobiological knowledge from healthy and pathological brain recordings. We believe that large-scale data analysis will use more models that are non-parametric, generative, mixing frequentist and Bayesian aspects, and grounded in different statistical inferences.

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time spot follows a Gaussian mixture distribution, a fact exploited to softly match, aka register, the states in two HMMs. We refer to such HMMs as Gaussian mixture model-HMM (GMM-HMM). The registration of states is inspired by the intrinsic relationship of optimal transport and the Wasserstein metric between distributions. Specifically, the components of the marginal GMMs are matched by solving an optimal transport problem where the cost between components is the Wasserstein metric for Gaussian distributions. The solution of the optimization problem is a fast approximation to the Wasserstein metric between two GMMs. The new Aggregated Wasserstein distance is a semi-metric and can be computed without generating Monte Carlo samples. It is invariant to relabeling or permutation of the states. This distance quantifies the dissimilarity of GMM-HMMs by measuring both the difference between the two marginal GMMs and the difference between the two transition matrices. Our new distance is tested on the tasks of retrieval and classification of time series. Experiments on both synthetic data and real data have demonstrated its advantages in terms of accuracy as well as efficiency in comparison with existing distances based on the Kullback-Leibler divergence.

In this work, we explore how probabilistic programs can be used to represent policies in sequential decision problems. In this formulation, a probabilistic program is a black-box stochastic simulator for both the problem domain and the agent. We relate classic policy gradient techniques to recently introduced black-box variational methods which generalize to probabilistic program inference. We present case studies in the Canadian traveler problem, Rock Sample, and a benchmark for optimal diagnosis inspired by Guess Who. Each study illustrates how programs can efficiently represent policies using moderate numbers of parameters.

We consider the task of robust non-linear regression in the presence of both inlier noise and outliers. Assuming that the unknown non-linear function belongs to a Reproducing Kernel Hilbert Space (RKHS), our goal is to estimate the set of the associated unknown parameters. Due to the presence of outliers, common techniques such as the Kernel Ridge Regression (KRR) or the Support Vector Regression (SVR) turn out to be inadequate. Instead, we employ sparse modeling arguments to explicitly model and estimate the outliers, adopting a greedy approach. The proposed robust scheme, i.e., Kernel Greedy Algorithm for Robust Denoising (KGARD), is inspired by the classical Orthogonal Matching Pursuit (OMP) algorithm. Specifically, the proposed method alternates between a KRR task and an OMP-like selection step. Theoretical results concerning the identification of the outliers are provided. Moreover, KGARD is compared against other cutting edge methods, where its performance is evaluated via a set of experiments with various types of noise. Finally, the proposed robust estimation framework is applied to the task of image denoising, and its enhanced performance in the presence of outliers is demonstrated.

We propose Bayesian extensions of two nonparametric regression methods which are kernel and mutual $k$-nearest neighbor regression methods. Derived based on Gaussian process models for regression, the extensions provide distributions for target value estimates and the framework to select the hyperparameters. It is shown that both the proposed methods asymptotically converge to kernel and mutual $k$-nearest neighbor regression methods, respectively. The simulation results show that the proposed methods can select proper hyperparameters and are better than or comparable to the former methods for an artificial data set and a real world data set.

Community detection has been an active research area for decades. Among all probabilistic models, Stochastic Block Model has been the most popular one. This paper introduces a novel probabilistic model: RW-HDP, based on random walks and Hierarchical Dirichlet Process, for community extraction. In RW-HDP, random walks conducted in a social network are treated as documents; nodes are treated as words. By using Hierarchical Dirichlet Process, a nonparametric Bayesian model, we are not only able to cluster nodes into different communities, but also determine the number of communities automatically. We use Stochastic Variational Inference for our model inference, which makes our method time efficient and can be easily extended to an online learning algorithm.

The latent Dirichlet allocation (LDA) model is a widely-used latent variable model in machine learning for text analysis. Inference for this model typically involves a single-site collapsed Gibbs sampling step for latent variables associated with observations. The efficiency of the sampling is critical to the success of the model in practical large scale applications. In this article, we introduce a blocking scheme to the collapsed Gibbs sampler for the LDA model which can, with a theoretical guarantee, improve chain mixing efficiency. We develop two procedures, an O(K)-step backward simulation and an O(log K)-step nested simulation, to directly sample the latent variables within each block. We demonstrate that the blocking scheme achieves substantial improvements in chain mixing compared to the state of the art single-site collapsed Gibbs sampler. We also show that when the number of topics is over hundreds, the nested-simulation blocking scheme can achieve a significant reduction in computation time compared to the single-site sampler.

We study indeterminacies in realization of ornaments and how they can be incorporated in a stochastic performance model applicable for music information processing such as score-performance matching. We point out the importance of temporal information, and propose a hidden Markov model which describes it explicitly and represents ornaments with several state types. Following a review of the indeterminacies, they are carefully incorporated into the model through its topology and parameters, and the state construction for quite general polyphonic scores is explained in detail. By analyzing piano performance data, we find significant overlaps in inter-onset-interval distributions of chordal notes, ornaments, and inter-chord events, and the data is used to determine details of the model. The model is applied for score following and offline score-performance matching, yielding highly accurate matching for performances with many ornaments and relatively frequent errors, repeats, and skips.

We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles 2015) to calculate expectations with respect to the invariant measures of ergodic SDEs. In that context, we study the (over-damped) Langevin equations with strongly convex potential. We show that, when appropriate contracting couplings for the numerical integrators are available, one can obtain a time-uniform estimates of the MLMC variance in stark contrast to the majority of the results in the MLMC literature. As a consequence, one can approximate expectations with respect to the invariant measure in an unbiased way without the need of a Metropolis- Hastings step. In addition, a root mean square error of $\mathcal{O}(\epsilon)$ is achieved with $\mathcal{O}(\epsilon^{-2})$ complexity on par with Markov Chain Monte Carlo (MCMC) methods, which however can be computationally intensive when applied to large data sets. Finally, we present a multilevel version of the recently introduced Stochastic Gradient Langevin (SGLD) method (Welling and Teh, 2011) built for large datasets applications. We show that this is the first stochastic gradient MCMC method with complexity $\mathcal{O}(\epsilon^{-2}|\log {\epsilon}|^{3})$, which is asymptotically an order $\epsilon$ lower than the $ \mathcal{O}(\epsilon^{-3})$ complexity of all stochastic gradient MCMC methods that are currently available. Numerical experiments confirm our theoretical findings.

Many aspects of the design of efficient crowdsourcing processes, such as defining workers bonuses, fair prices and time limits of the tasks, involve knowledge of the likely duration of the task at hand. In this work we introduce a new timesensitive Bayesian aggregation method that simultaneously estimates a tasks duration and obtains reliable aggregations of crowdsourced judgments. Our method, called BCCTime, uses latent variables to represent the uncertainty about the workers completion time, the tasks duration and the workers accuracy. To relate the quality of a judgment to the time a worker spends on a task, our model assumes that each task is completed within a latent time window within which all workers with a propensity to genuinely attempt the labelling task (i.e., no spammers) are expected to submit their judgments. In contrast, workers with a lower propensity to valid labelling, such as spammers, bots or lazy labellers, are assumed to perform tasks considerably faster or slower than the time required by normal workers. Specifically, we use efficient message-passing Bayesian inference to learn approximate posterior probabilities of (i) the confusion matrix of each worker, (ii) the propensity to valid labelling of each worker, (iii) the unbiased duration of each task and (iv) the true label of each task. Using two real- world public datasets for entity linking tasks, we show that BCCTime produces up to 11% more accurate classifications and up to 100% more informative estimates of a tasks duration compared to stateoftheart methods.