Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with generalized divergences as a form of estimating the marginal likelihood via biased importance sampling. The choice of divergence determines a bias-variance trade-off between the tightness of a bound on the marginal likelihood (low bias) and the variance of its gradient estimators. Drawing on variational perturbation theory of statistical physics, we use these insights to construct a family of new variational bounds. Enumerated by an odd integer order $K$, this family captures the standard KL bound for $K=1$, and converges to the exact marginal likelihood as $K\to\infty$. Compared to alpha-divergences, our reparameterization gradients have a lower variance. We show in experiments on Gaussian Processes and Variational Autoencoders that the new bounds are more mass covering, and that the resulting posterior covariances are closer to the true posterior and lead to higher likelihoods on held-out data.

We propose a generalized Gibbs sampler algorithm for obtaining samples approximately distributed from a high-dimensional Gaussian distribution. Similarly to Hogwild methods, our approach does not target the original Gaussian distribution of interest, but an approximation to it. Contrary to Hogwild methods, a single parameter allows us to trade bias for variance. We show empirically that our method is very flexible and performs well compared to Hogwild-type algorithms.

In sequential decision making, it is often important and useful for end users to understand the underlying patterns or causes that lead to the corresponding decisions. However, typical deep reinforcement learning algorithms seldom provide such information due to their black-box nature. In this paper, we present a probabilistic model, Q-LDA, to uncover latent patterns in text-based sequential decision processes. The model can be understood as a variant of latent topic models that are tailored to maximize total rewards; we further draw an interesting connection between an approximate maximum-likelihood estimation of Q-LDA and the celebrated Q-learning algorithm. We demonstrate in the text-game domain that our proposed method not only provides a viable mechanism to uncover latent patterns in decision processes, but also obtains state-of-the-art rewards in these games.

Word embeddings are an effective tool to analyze language. They have been recently extended to model other types of data beyond text, such as items in recommendation systems. Embedding models consider the probability of a target observation (a word or an item) conditioned on the elements in the context (other words or items). In this paper, we show that conditioning on all the elements in the context is not optimal. Instead, we model the probability of the target conditioned on a learned subset of the elements in the context. We use amortized variational inference to automatically choose this subset. Compared to standard embedding models, this method improves predictions and the quality of the embeddings.

Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical integration. However, for many real-world applications, only sparse observations are available or even unobserved variables are included in the model description. In these cases most gradient matching methods are difficult to apply or simply do not provide satisfactory results. That is why, despite the high computational cost, numerical integration is still the gold standard in many applications. Using an existing gradient matching approach, we propose a scalable variational inference framework which can infer states and parameters simultaneously, offers computational speedups, improved accuracy and works well even under model misspecifications in a partially observable system.

We study a class of non-parametric density estimators under Bayesian settings. The estimators are obtained by adaptively partitioning the sample space. Under a suitable prior, we analyze the concentration rate of the posterior distribution, and demonstrate that the rate does not directly depend on the dimension of the problem in several special cases. Another advantage of this class of Bayesian density estimators is that it can adapt to the unknown smoothness of the true density function, thus achieving the optimal convergence rate without artificial conditions on the density. We also validate the theoretical results on a variety of simulated data sets.

Catastrophic forgetting is a problem of neural networks that loses the information of the first task after training the second task. Here, we propose a method, i.e. incremental moment matching (IMM), to resolve this problem. IMM incrementally matches the moment of the posterior distribution of the neural network which is trained on the first and the second task, respectively. To make the search space of posterior parameter smooth, the IMM procedure is complemented by various transfer learning techniques including weight transfer, L2-norm of the old and the new parameter, and a variant of dropout with the old parameter. We analyze our approach on a variety of datasets including the MNIST, CIFAR-10, Caltech-UCSD-Birds, and Lifelog datasets. The experimental results show that IMM achieves state-of-the-art performance by balancing the information between an old and a new network.

We propose an efficient method to estimate the accuracy of classifiers using only unlabeled data. We consider a setting with multiple classification problems where the target classes may be tied together through logical constraints. For example, a set of classes may be mutually exclusive, meaning that a data instance can belong to at most one of them. The proposed method is based on the intuition that: (i) when classifiers agree, they are more likely to be correct, and (ii) when the classifiers make a prediction that violates the constraints, at least one classifier must be making an error. Experiments on four real-world data sets produce accuracy estimates within a few percent of the true accuracy, using solely unlabeled data. Our models also outperform existing state-of-the-art solutions in both estimating accuracies, and combining multiple classifier outputs. The results emphasize the utility of logical constraints in estimating accuracy, thus validating our intuition.

We consider the problem of accurately estimating the reliability of workers based on noisy labels they provide, which is a fundamental question in crowdsourcing. We propose a novel lower bound on the minimax estimation error which applies to any estimation procedure. We further propose Triangular Estimation (TE), an algorithm for estimating the reliability of workers. TE has low complexity, may be implemented in a streaming setting when labels are provided by workers in real time, and does not rely on an iterative procedure. We prove that TE is minimax optimal and matches our lower bound. We conclude by assessing the performance of TE and other state-of-the-art algorithms on both synthetic and real-world data.

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It is therefore critical to account for kernel uncertainty in our predictive distributions. We propose a distribution over kernels formed by modelling a spectral mixture density with a Levy process. The resulting distribution has support for all stationary covariances---including the popular RBF, periodic, and Matern kernels---combined with inductive biases which enable automatic and data efficient learning, long-range extrapolation, and state of the art predictive performance. The proposed model also presents an approach to spectral regularization, as the Levy process introduces a sparsity-inducing prior over mixture components, allowing automatic selection over model order and pruning of extraneous components. We exploit the algebraic structure of the proposed process for O(n) training and O(1) predictions. We perform extrapolations having reasonable uncertainty estimates on several benchmarks, show that the proposed model can recover flexible ground truth covariances and that it is robust to errors in initialization.