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 . 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 multiscale quantization approach for fast similarity search on large, high-dimensional datasets. The key insight of the approach is that quantization methods, in particular product quantization, perform poorly when there is large variance in the norms of the data points. This is a common scenario for realworld datasets, especially when doing product quantization of residuals obtained from coarse vector quantization. To address this issue, we propose a multiscale formulation where we learn a separate scalar quantizer of the residual norm scales. All parameters are learned jointly in a stochastic gradient descent framework to minimize the overall quantization error. We provide theoretical motivation for the proposed technique and conduct comprehensive experiments on two large-scale public datasets, demonstrating substantial improvements in recall over existing state-of-the-art methods.

Discovering statistical structure from links is a fundamental problem in the analysis of social networks. Choosing a misspecified model, or equivalently, an incorrect inference algorithm will result in an invalid analysis or even falsely uncover patterns that are in fact artifacts of the model. This work focuses on unifying two of the most widely used link-formation models: the stochastic blockmodel (SBM) and the small world (or latent space) model (SWM). Integrating techniques from kernel learning, spectral graph theory, and nonlinear dimensionality reduction, we develop the first statistically sound polynomial-time algorithm to discover latent patterns in sparse graphs for both models. When the network comes from an SBM, the algorithm outputs a block structure. When it is from an SWM, the algorithm outputs estimates of each node's latent position.

Neural Information Processing Systems http://nips.cc/

A large body of recent work focuses on methods for extracting low-dimensional latent structure from multi-neuron spike train data. Most such methods employ either linear latent dynamics or linear mappings from latent space to log spike rates. Here we propose a doubly nonlinear latent variable model that can identify low-dimensional structure underlying apparently high-dimensional spike train data. We introduce the Poisson Gaussian-Process Latent Variable Model (P-GPLVM), which consists of Poisson spiking observations and two underlying Gaussian processes--one governing a temporal latent variable and another governing a set of nonlinear tuning curves. The use of nonlinear tuning curves enables discovery of low-dimensional latent structure even when spike responses exhibit high linear dimensionality (e.g., as found in hippocampal place cell codes). To learn the model from data, we introduce the decoupled Laplace approximation, a fast approximate inference method that allows us to efficiently optimize the latent path while marginalizing over tuning curves. We show that this method outperforms previous Laplace-approximation-based inference methods in both the speed of convergence and accuracy. We apply the model to spike trains recorded from hippocampal place cells and show that it compares favorably to a variety of previous methods for latent structure discovery, including variational auto-encoder (VAE) based methods that parametrize the nonlinear mapping from latent space to spike rates with a deep neural network.

Estimating treatment effects from observational data is challenging due to the missing counterfactuals. Matching is an effective strategy to tackle this problem. The widely used matching estimators such as nearest neighbor matching (NNM) pair the treated units with the most similar control units in terms of covariates, and then estimate treatment effects accordingly. However, the existing matching estimators have poor performance when the distributions of control and treatment groups are unbalanced. Moreover, theoretical analysis suggests that the bias of causal effect estimation would increase with the dimension of covariates. In this paper, we aim to address these problems by learning low-dimensional balanced and nonlinear representations (BNR) for observational data. In particular, we convert counterfactual prediction as a classification problem, develop a kernel learning model with domain adaptation constraint, and design a novel matching estimator. The dimension of covariates will be significantly reduced after projecting data to a low-dimensional subspace. Experiments on several synthetic and real-world datasets demonstrate the effectiveness of our approach.

Neural Information Processing Systems http://nips.cc/

Key to multitask learning is exploiting the relationships between different tasks in order to improve prediction performance. Most previous methods have focused on the case where tasks relations can be modeled as linear operators and regularization approaches can be used successfully. However, in practice assuming the tasks to be linearly related is often restrictive, and allowing for nonlinear structures is a challenge. In this paper, we tackle this issue by casting the problem within the framework of structured prediction. Our main contribution is a novel algorithm for learning multiple tasks which are related by a system of nonlinear equations that their joint outputs need to satisfy. We show that our algorithm can be efficiently implemented and study its generalization properties, proving universal consistency and learning rates. Our theoretical analysis highlights the benefits of non-linear multitask learning over learning the tasks independently. Encouraging experimental results show the benefits of the proposed method in practice.

This paper presents a margin-based multiclass generalization bound for neural networks that scales with their margin-normalized spectral complexity: their Lipschitz constant, meaning the product of the spectral norms of the weight matrices, times a certain correction factor. This bound is empirically investigated for a standard AlexNet network trained with SGD on the mnist and cifar10 datasets, with both original and random labels; the bound, the Lipschitz constants, and the excess risks are all in direct correlation, suggesting both that SGD selects predictors whose complexity scales with the difficulty of the learning task, and secondly that the presented bound is sensitive to this complexity.

Contextual bandits are a form of multi-armed bandit in which the agent has access to predictive side information (known as the context) for each arm at each time step, and have been used to model personalized news recommendation, ad placement, and other applications. In this work, we propose a multi-task learning framework for contextual bandit problems. Like multi-task learning in the batch setting, the goal is to leverage similarities in contexts for different arms so as to improve the agent's ability to predict rewards from contexts. We propose an upper confidence bound-based multi-task learning algorithm for contextual bandits, establish a corresponding regret bound, and interpret this bound to quantify the advantages of learning in the presence of high task (arm) similarity. We also describe an effective scheme for estimating task similarity from data, and demonstrate our algorithm's performance on several data sets.