\textit{Adaptive importance sampling} (AIS) uses past samples to update the \textit{sampling policy} $q_t$ at each stage $t$. Each stage $t$ is formed with two steps : (i) to explore the space with $n_t$ points according to $q_t$ and (ii) to exploit the current amount of information to update the sampling policy. The very fundamental question raised in this paper concerns the behavior of empirical sums based on AIS. Without making any assumption on the \textit{allocation policy} $n_t$, the theory developed involves no restriction on the split of computational resources between the explore (i) and the exploit (ii) step. It is shown that AIS is asymptotically optimal : the asymptotic behavior of AIS is the same as some ``oracle'' strategy that knows the targeted sampling policy from the beginning. From a practical perspective, weighted AIS is introduced, a new method that allows to forget poor samples from early stages.

Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we derive a general Bayesian network formulation for probability estimation on leaf-labeled trees that enables flexible approximations which can generalize beyond observations. We show that efficient algorithms for learning Bayesian networks can be easily extended to probability estimation on this challenging structured space. Experiments on both synthetic and real data show that our methods greatly outperform the current practice of using the empirical distribution, as well as a previous effort for probability estimation on trees.

We analyze linear independence of rank one tensors produced by tensor powers of randomly perturbed vectors. This enables efficient decomposition of sums of high-order tensors. Our analysis builds upon [BCMV14] but allows for a wider range of perturbation models, including discrete ones. We give an application to recovering assemblies of neurons. Assemblies are large sets of neurons representing specific memories or concepts. The size of the intersection of two assemblies has been shown in experiments to represent the extent to which these memories co-occur or these concepts are related; the phenomenon is called association of assemblies. This suggests that an animal's memory is a complex web of associations, and poses the problem of recovering this representation from cognitive data. Motivated by this problem, we study the following more general question: Can we reconstruct the Venn diagram of a family of sets, given the sizes of their l-wise intersections? We show that as long as the family of sets is randomly perturbed, it is enough for the number of measurements to be polynomially larger than the number of nonempty regions of the Venn diagram to fully reconstruct the diagram.

Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space the time-discretization error can dominate when we are near the boundary of the space. We demonstrate that because of this, current SGMCMC methods for the simplex struggle with sparse simplex spaces; when many of the components are close to zero. Unfortunately, many popular large-scale Bayesian models, such as network or topic models, require inference on sparse simplex spaces. To avoid the biases caused by this discretization error, we propose the stochastic Cox-Ingersoll-Ross process (SCIR), which removes all discretization error and we prove that samples from the SCIR process are asymptotically unbiased. We discuss how this idea can be extended to target other constrained spaces. Use of the SCIR process within a SGMCMC algorithm is shown to give substantially better performance for a topic model and a Dirichlet process mixture model than existing SGMCMC approaches.

Collecting the large datasets needed to train deep neural networks can be very difficult, particularly for the many applications for which sharing and pooling data is complicated by practical, ethical, or legal concerns. However, it may be the case that derivative datasets or predictive models developed within individual sites can be shared and combined with fewer restrictions. Training on distributed data and combining the resulting networks is often viewed as continual learning, but these methods require networks to be trained sequentially. In this paper, we introduce distributed weight consolidation (DWC), a continual learning method to consolidate the weights of separate neural networks, each trained on an independent dataset. We evaluated DWC with a brain segmentation case study, where we consolidated dilated convolutional neural networks trained on independent structural magnetic resonance imaging (sMRI) datasets from different sites. We found that DWC led to increased performance on test sets from the different sites, while maintaining generalization performance for a very large and completely independent multi-site dataset, compared to an ensemble baseline.

Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model complexity, representational capacity and overfitting. In this work, we propose to extend the model's input with latent variables and use Gaussian processes (GP) to map this augmented input onto samples from the conditional distribution. Our Bayesian approach allows for the modeling of small datasets, but we also provide the machinery for it to be applied to big data using stochastic variational inference. Our approach can be used to model densities even in sparse data regions, and allows for sharing learned structure between conditions. We illustrate the effectiveness and wide-reaching applicability of our model on a variety of real-world problems, such as spatio-temporal density estimation of taxi drop-offs, non-Gaussian noise modeling, and few-shot learning on omniglot images.

A fundamental goal of systems neuroscience is to understand how neural activity gives rise to natural behavior. In order to achieve this goal, we must first build comprehensive models that offer quantitative descriptions of behavior. We develop a new class of probabilistic models to tackle this challenge in the study of larval zebrafish, an important model organism for neuroscience. Larval zebrafish locomote via sequences of punctate swim bouts--brief flicks of the tail--which are naturally modeled as a marked point process. However, these sequences of swim bouts belie a set of discrete and continuous internal states, latent variables that are not captured by standard point process models. We incorporate these variables as latent marks of a point process and explore various models for their dynamics. To infer the latent variables and fit the parameters of this model, we develop an amortized variational inference algorithm that targets the collapsed posterior distribution, analytically marginalizing out the discrete latent variables. With a dataset of over 120,000 swim bouts, we show that our models reveal interpretable discrete classes of swim bouts and continuous internal states like hunger that modulate their dynamics. These models are a major step toward understanding the natural behavioral program of the larval zebrafish and, ultimately, its neural underpinnings.

We address the problem of Bayesian structure learning for domains with hundreds of variables by employing non-parametric bootstrap, recursively. We propose a method that covers both model averaging and model selection in the same framework. The proposed method deals with the main weakness of constraint-based learning---sensitivity to errors in the independence tests---by a novel way of combining bootstrap with constraint-based learning. Essentially, we provide an algorithm for learning a tree, in which each node represents a scored CPDAG for a subset of variables and the level of the node corresponds to the maximal order of conditional independencies that are encoded in the graph. As higher order independencies are tested in deeper recursive calls, they benefit from more bootstrap samples, and therefore are more resistant to the curse-of-dimensionality. Moreover, the re-use of stable low order independencies allows greater computational efficiency. We also provide an algorithm for sampling CPDAGs efficiently from their posterior given the learned tree. That is, not from the full posterior, but from a reduced space of CPDAGs encoded in the learned tree. We empirically demonstrate that the proposed algorithm scales well to hundreds of variables, and learns better MAP models and more reliable causal relationships between variables, than other state-of-the-art-methods.

Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adopt a variant of empirical Bayes and show that, by estimating the Gaussian process prior from offline data sampled from the same prior and constructing unbiased estimators of the posterior, variants of both GP-UCB and \emph{probability of improvement} achieve a near-zero regret bound, which decreases to a constant proportional to the observational noise as the number of offline data and the number of online evaluations increase. Empirically, we have verified our approach on challenging simulated robotic problems featuring task and motion planning.

The growing prospect of deep reinforcement learning (DRL) being used in cyber-physical systems has raised concerns around safety and robustness of autonomous agents. Recent work on generating adversarial attacks have shown that it is computationally feasible for a bad actor to fool a DRL policy into behaving sub optimally. Although certain adversarial attacks with specific attack models have been addressed, most studies are only interested in off-line optimization in the data space (e.g., example fitting, distillation). This paper introduces a Meta-Learned Advantage Hierarchy (MLAH) framework that is attack model-agnostic and more suited to reinforcement learning, via handling the attacks in the decision space (as opposed to data space) and directly mitigating learned bias introduced by the adversary. In MLAH, we learn separate sub-policies (nominal and adversarial) in an online manner, as guided by a supervisory master agent that detects the presence of the adversary by leveraging the advantage function for the sub-policies. We demonstrate that the proposed algorithm enables policy learning with significantly lower bias as compared to the state-of-the-art policy learning approaches even in the presence of heavy state information attacks. We present algorithm analysis and simulation results using popular OpenAI Gym environments.