Combining Bayesian nonparametrics and a forward model selection strategy, we construct parsimonious Bayesian deep networks (PBDNs) that infer capacity-regularized network architectures from the data and require neither cross-validation nor fine-tuning when training the model. One of the two essential components of a PBDN is the development of a special infinite-wide single-hidden-layer neural network, whose number of active hidden units can be inferred from the data. The other one is the construction of a greedy layer-wise learning algorithm that uses a forward model selection criterion to determine when to stop adding another hidden layer. We develop both Gibbs sampling and stochastic gradient descent based maximum a posteriori inference for PBDNs, providing state-of-the-art classification accuracy and interpretable data subtypes near the decision boundaries, while maintaining low computational complexity for out-of-sample prediction.

The variational autoencoder (VAE) is a popular model for density estimation and representation learning. Canonically, the variational principle suggests to prefer an expressive inference model so that the variational approximation is accurate. However, it is often overlooked that an overly-expressive inference model can be detrimental to the test set performance of both the amortized posterior approximator and, more importantly, the generative density estimator. In this paper, we leverage the fact that VAEs rely on amortized inference and propose techniques for amortized inference regularization (AIR) that control the smoothness of the inference model. We demonstrate that, by applying AIR, it is possible to improve VAE generalization on both inference and generative performance. Our paper challenges the belief that amortized inference is simply a mechanism for approximating maximum likelihood training and illustrates that regularization of the amortization family provides a new direction for understanding and improving generalization in VAEs.

We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called "adversarial losses", which, besides classical $\mathcal{L}^p$ losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the losses encoded by discriminator networks in generative adversarial networks (GANs). In a general framework, we study how the choice of loss and the assumed smoothness of the underlying density together determine the minimax rate. We also discuss implications for training GANs based on deep ReLU networks, and more general connections to learning implicit generative models in a minimax statistical sense.

Approximate Bayesian computation is an established and popular method for likelihood-free inference with applications in many disciplines. The effectiveness of the method depends critically on the availability of well performing summary statistics. Summary statistic selection relies heavily on domain knowledge and carefully engineered features, and can be a laborious time consuming process. Since the method is sensitive to data dimensionality, the process of selecting summary statistics must balance the need to include informative statistics and the dimensionality of the feature vector. This paper proposes to treat the problem of dynamically selecting an appropriate summary statistic from a given pool of candidate summary statistics as a multi-armed bandit problem. This allows approximate Bayesian computation rejection sampling to dynamically focus on a distribution over well performing summary statistics as opposed to a fixed set of statistics. The proposed method is unique in that it does not require any pre-processing and is scalable to a large number of candidate statistics. This enables efficient use of a large library of possible time series summary statistics without prior feature engineering. The proposed approach is compared to state-of-the-art methods for summary statistics selection using a challenging test problem from the systems biology literature.

Network embeddings map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the embedding can be used for purposes such as link prediction (if `similar' means being `more likely to be connected') or classification (if `similar' means `being more likely to have the same label'). In recent years various methods for network embedding have been introduced. These methods all follow a similar strategy, defining a notion of similarity between nodes (typically deeming nodes more similar if they are nearby in the network in some metric), a distance measure in the embedding space, and minimizing a loss function that penalizes large distances for similar nodes or small distances for dissimilar nodes. A difficulty faced by existing methods is that certain networks are fundamentally hard to embed due to their structural properties, such as (approximate) multipartiteness, certain degree distributions, or certain kinds of assortativity. Overcoming this difficulty, we introduce a conceptual innovation to the literature on network embedding, proposing to create embeddings that maximally add information with respect to such structural properties (e.g. node degrees, block densities, etc.). We use a simple Bayesian approach to achieve this, and propose a block stochastic gradient descent algorithm for fitting it efficiently. Finally, we demonstrate that the combination of information such structural properties and a Euclidean embedding provides superior performance across a range of link prediction tasks. Moreover, we demonstrate the potential of our approach for network visualization.

Bayesian Optimization (BO) methods are useful for optimizing functions that are expen- sive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the objective function, typically a Gaussian process (GP), upon which an acquisition function is built. The acquisition function guides the optimization process and measures the expected utility of performing an evaluation of the objective at a new point. GPs assume continous input variables. When this is not the case, for example when some of the input variables take categorical or integer values, one has to introduce extra approximations. Consider a suggested input location taking values in the real line. Before doing the evaluation of the objective, a common approach is to use a one hot encoding approximation for categorical variables, or to round to the closest integer, in the case of integer-valued variables. We show that this can lead to problems in the optimization process and describe a more principled approach to account for input variables that are categorical or integer-valued. We illustrate in both synthetic and a real experiments the utility of our approach, which significantly improves the results of standard BO methods using Gaussian processes on problems with categorical or integer-valued variables.

The first time I heard someone use the term maximum likelihood estimation, I went to Google and found out what it meant. Then I went to Wikipedia to find out what it really meant. To spare you the wrestling required to understand and incorporate MLE into your data science workflow, ethos, and projects, I've compiled this guide. This is funny (if you follow this strange domain of humor), and mostly right about the differences between the two camps. Not minding that our Sun going into nova is not really a repeatable experiment -- sorry, frequentists!

In many real-world robotic applications, an autonomous agent must act within and explore a partially observed environment that is unobserved by its human teammate. We consider such a setting in which the agent can, while acting, transmit declarative information to the human that helps them understand aspects of this unseen environment. Importantly, we should expect the human to have preferences about what information they are given and when they are given it. In this work, we adopt an information-theoretic view of the human's preferences: the human scores a piece of information as a function of the induced reduction in weighted entropy of their belief about the environment state. We formulate this setting as a POMDP and give a practical algorithm for solving it approximately. Then, we give an algorithm that allows the agent to sample-efficiently learn the human's preferences online. Finally, we describe an extension in which the human's preferences are time-varying. We validate our approach experimentally in two planning domains: a 2D robot mining task and a more realistic 3D robot fetching task.

Topic models have been widely explored as probabilistic generative models of documents. Traditional inference methods have sought closed-form derivations for updating the models, however as the expressiveness of these models grows, so does the difficulty of performing fast and accurate inference over their parameters. This paper presents alternative neural approaches to topic modelling by providing parameterisable distributions over topics which permit training by backpropagation in the framework of neural variational inference. In addition, with the help of a stick-breaking construction, we propose a recurrent network that is able to discover a notionally unbounded number of topics, analogous to Bayesian non-parametric topic models. Experimental results on the MXM Song Lyrics, 20NewsGroups and Reuters News datasets demonstrate the effectiveness and efficiency of these neural topic models.

MAP perturbation models have emerged as a powerful framework for inference in structured prediction. Such models provide a way to efficiently sample from the Gibbs distribution and facilitate predictions that are robust to random noise. In this paper, we propose a provably polynomial time randomized algorithm for learning the parameters of perturbed MAP predictors. Our approach is based on minimizing a novel Rademacher-based generalization bound on the expected loss of a perturbed MAP predictor, which can be computed in polynomial time. We obtain conditions under which our randomized learning algorithm can guarantee generalization to unseen examples.