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.

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.

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 Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution to approximate, from which we can easily draw samples. Recently discrete approximation by particles has attracted attention because of its expressive ability. An example is Stein variational gradient descent (SVGD), which iteratively optimizes particles. Although SVGD has been shown to be computationally efficient empirically, its theoretical properties have not been clarified yet and no finite sample bound of a convergence rate is known. Another example is Stein points (SP), which minimizes kernelized Stein discrepancy directly. The finite sample bound of SP is $\mathcal{O}(\sqrt{\log{N}/N})$ for $N$ particles, which is computationally inefficient empirically, especially in high-dimensional problems. In this paper, we propose a novel method named \emph{Frank-Wolfe Stein sampling}, which minimizes the maximum mean discrepancy in a greedy way. Our method is computationally efficient empirically and theoretically achieves a faster convergence rate, $\mathcal{O}(e^{-N})$. Numerical experiments show the superiority of our method.

We introduce the Kronecker factored online Laplace approximation for overcoming catastrophic forgetting in neural networks. The method is grounded in a Bayesian online learning framework, where we recursively approximate the posterior after every task with a Gaussian, leading to a quadratic penalty on changes to the weights. The Laplace approximation requires calculating the Hessian around a mode, which is typically intractable for modern architectures. In order to make our method scalable, we leverage recent block-diagonal Kronecker factored approximations to the curvature. Our algorithm achieves over 90% test accuracy across a sequence of 50 instantiations of the permuted MNIST dataset, substantially outperforming related methods for overcoming catastrophic forgetting.

The central problem of this paper is the cost-sensitive binary classification problem, where different costs are associated with different types of mistakes. Several important machine learning applications such as medical decision making, targeted marketing, and intrusion detection can be naturally formalized as costsensitive classification setup ([1]). In these domains, the cost of missing a target is much higher than that of a false-positive, and classifiers that do not take misclassification costs into account do not perform well. The cost-sensitive classification problem has been extensively studied, and people have developed efficient algorithms with provable guarantees on the (generalization) error [6, 9, 26, 27, 11, 4]. These methods primarily take existing classification methods based on empirical risk minimization and try to adapt them in various ways to be sensitive to these misclassification costs. Despite all these efforts, the understanding of the fundamental limits of this problem is still missing. In this paper, we study the hardness of this problem by obtaining minimax lower bounds. In particular, we are interested in understanding how the cost parameter influences the hardness or complexity of the cost-sensitive classification. Minimax Lower Bounds Understanding the hardness or fundamental limits of a learning problem is important for practice for the following reasons: - They give an estimate on the number of samples required for a good performance of a learning algorithm.

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model minimizes the worst case (maximum) of Stein's loss across all normal reference distributions within a prescribed Wasserstein distance from the normal distribution characterized by the sample mean and the sample covariance matrix. We prove that this estimation problem is equivalent to a semidefinite program that is tractable in theory but beyond the reach of general purpose solvers for practically relevant problem dimensions $p$. In the absence of any prior structural information, the estimation problem has an analytical solution that is naturally interpreted as a nonlinear shrinkage estimator. Besides being invertible and well-conditioned even for $p>n$, the new shrinkage estimator is rotation-equivariant and preserves the order of the eigenvalues of the sample covariance matrix. These desirable properties are not imposed ad hoc but emerge naturally from the underlying distributionally robust optimization model. Finally, we develop a sequential quadratic approximation algorithm for efficiently solving the general estimation problem subject to conditional independence constraints typically encountered in Gaussian graphical models.

We address the problem of regret minimization in logistic contextual bandits, where a learner decides among sequential actions or arms given their respective contexts to maximize binary rewards. Using a fast inference procedure with Polya-Gamma distributed augmentation variables, we propose an improved version of Thompson Sampling, a Bayesian formulation of contextual bandits with near-optimal performance. Our approach, Polya-Gamma augmented Thompson Sampling (PG-TS), achieves state-of-the-art performance on simulated and real data. PG-TS explores the action space efficiently and exploits high-reward arms, quickly converging to solutions of low regret. Its explicit estimation of the posterior distribution of the context feature covariance leads to substantial empirical gains over approximate approaches. PG-TS is the first approach to demonstrate the benefits of Polya-Gamma augmentation in bandits and to propose an efficient Gibbs sampler for approximating the analytically unsolvable integral of logistic contextual bandits.

We report an exact likelihood computation for Linear Gaussian Markov processes that is more scalable than existing algorithms for complex models and sparsely sampled signals. Better scaling is achieved through elimination of repeated computations in the Kalman likelihood, and by using the diagonalized form of the state transition equation. Using this efficient computation, we study the accuracy of kernel learning using maximum likelihood and the posterior mean in a simulation experiment. The posterior mean with a reference prior is more accurate for complex models and sparse sampling. Because of its lower computation load, the maximum likelihood estimator is an attractive option for more densely sampled signals and lower order models. We confirm estimator behavior in experimental data through their application to speleothem data.