State Space LSTM Models with Particle MCMC Inference

Long Short-Term Memory (LSTM) is one of the most powerful sequence models. Despite the strong performance, however, it lacks the nice interpretability as in state space models. In this paper, we present a way to combine the best of both worlds by introducing State Space LSTM (SSL) models that generalizes the earlier work \cite{zaheer2017latent} of combining topic models with LSTM. However, unlike \cite{zaheer2017latent}, we do not make any factorization assumptions in our inference algorithm. We present an efficient sampler based on sequential Monte Carlo (SMC) method that draws from the joint posterior directly. Experimental results confirms the superiority and stability of this SMC inference algorithm on a variety of domains

A General Method for Amortizing Variational Filtering

We introduce the variational filtering EM algorithm, a simple, general-purpose method for performing variational inference in dynamical latent variable models using information from only past and present variables, i.e. filtering. The algorithm is derived from the variational objective in the filtering setting and consists of an optimization procedure at each time step. By performing each inference optimization procedure with an iterative amortized inference model, we obtain a computationally efficient implementation of the algorithm, which we call amortized variational filtering. We present experiments demonstrating that this general-purpose method improves performance across several deep dynamical latent variable models.Comment: Advances in Neural Information Processing Systems (NIPS) 201

Gradient Estimation Using Stochastic Computation Graphs

In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external world. Estimating the gradient of this loss function, using samples, lies at the core of gradient-based learning algorithms for these problems. We introduce the formalism of stochastic computation graphs---directed acyclic graphs that include both deterministic functions and conditional probability distributions---and describe how to easily and automatically derive an unbiased estimator of the loss function's gradient. The resulting algorithm for computing the gradient estimator is a simple modification of the standard backpropagation algorithm. The generic scheme we propose unifies estimators derived in variety of prior work, along with variance-reduction techniques therein. It could assist researchers in developing intricate models involving a combination of stochastic and deterministic operations, enabling, for example, attention, memory, and control actions.Comment: Advances in Neural Information Processing Systems 28 (NIPS 2015

A Tutorial on Deep Latent Variable Models of Natural Language

There has been much recent, exciting work on combining the complementary strengths of latent variable models and deep learning. Latent variable modeling makes it easy to explicitly specify model constraints through conditional independence properties, while deep learning makes it possible to parameterize these conditional likelihoods with powerful function approximators. While these "deep latent variable" models provide a rich, flexible framework for modeling many real-world phenomena, difficulties exist: deep parameterizations of conditional likelihoods usually make posterior inference intractable, and latent variable objectives often complicate backpropagation by introducing points of non-differentiability. This tutorial explores these issues in depth through the lens of variational inference.Comment: EMNLP 2018 Tutoria

Advances in Variational Inference

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solving an optimization problem. This approach has been successfully used in various models and large-scale applications. In this review, we give an overview of recent trends in variational inference. We first introduce standard mean field variational inference, then review recent advances focusing on the following aspects: (a) scalable VI, which includes stochastic approximations, (b) generic VI, which extends the applicability of VI to a large class of otherwise intractable models, such as non-conjugate models, (c) accurate VI, which includes variational models beyond the mean field approximation or with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. Finally, we provide a summary of promising future research directions

ZhuSuan: A Library for Bayesian Deep Learning

In this paper we introduce ZhuSuan, a python probabilistic programming library for Bayesian deep learning, which conjoins the complimentary advantages of Bayesian methods and deep learning. ZhuSuan is built upon Tensorflow. Unlike existing deep learning libraries, which are mainly designed for deterministic neural networks and supervised tasks, ZhuSuan is featured for its deep root into Bayesian inference, thus supporting various kinds of probabilistic models, including both the traditional hierarchical Bayesian models and recent deep generative models. We use running examples to illustrate the probabilistic programming on ZhuSuan, including Bayesian logistic regression, variational auto-encoders, deep sigmoid belief networks and Bayesian recurrent neural networks.Comment: The GitHub page is at https://github.com/thu-ml/zhusua

End-to-end Learning of Deterministic Decision Trees

Conventional decision trees have a number of favorable properties, including interpretability, a small computational footprint and the ability to learn from little training data. However, they lack a key quality that has helped fuel the deep learning revolution: that of being end-to-end trainable, and to learn from scratch those features that best allow to solve a given supervised learning problem. Recent work (Kontschieder 2015) has addressed this deficit, but at the cost of losing a main attractive trait of decision trees: the fact that each sample is routed along a small subset of tree nodes only. We here propose a model and Expectation-Maximization training scheme for decision trees that are fully probabilistic at train time, but after a deterministic annealing process become deterministic at test time. We also analyze the learned oblique split parameters on image datasets and show that Neural Networks can be trained at each split node. In summary, we present the first end-to-end learning scheme for deterministic decision trees and present results on par with or superior to published standard oblique decision tree algorithms

Variational Message Passing with Structured Inference Networks

Recent efforts on combining deep models with probabilistic graphical models are promising in providing flexible models that are also easy to interpret. We propose a variational message-passing algorithm for variational inference in such models. We make three contributions. First, we propose structured inference networks that incorporate the structure of the graphical model in the inference network of variational auto-encoders (VAE). Second, we establish conditions under which such inference networks enable fast amortized inference similar to VAE. Finally, we derive a variational message passing algorithm to perform efficient natural-gradient inference while retaining the efficiency of the amortized inference. By simultaneously enabling structured, amortized, and natural-gradient inference for deep structured models, our method simplifies and generalizes existing methods.Comment: Added a missing term in the gradient of the lower boun

When Gaussian Process Meets Big Data: A Review of Scalable GPs

The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process (GP) regression, a well-known non-parametric and interpretable Bayesian model, which suffers from cubic complexity to data size. To improve the scalability while retaining desirable prediction quality, a variety of scalable GPs have been presented. But they have not yet been comprehensively reviewed and analyzed in order to be well understood by both academia and industry. The review of scalable GPs in the GP community is timely and important due to the explosion of data size. To this end, this paper is devoted to the review on state-of-the-art scalable GPs involving two main categories: global approximations which distillate the entire data and local approximations which divide the data for subspace learning. Particularly, for global approximations, we mainly focus on sparse approximations comprising prior approximations which modify the prior but perform exact inference, posterior approximations which retain exact prior but perform approximate inference, and structured sparse approximations which exploit specific structures in kernel matrix; for local approximations, we highlight the mixture/product of experts that conducts model averaging from multiple local experts to boost predictions. To present a complete review, recent advances for improving the scalability and capability of scalable GPs are reviewed. Finally, the extensions and open issues regarding the implementation of scalable GPs in various scenarios are reviewed and discussed to inspire novel ideas for future research avenues.Comment: 20 pages, 6 figure

Reconciling meta-learning and continual learning with online mixtures of tasks

Learning-to-learn or meta-learning leverages data-driven inductive bias to increase the efficiency of learning on a novel task. This approach encounters difficulty when transfer is not advantageous, for instance, when tasks are considerably dissimilar or change over time. We use the connection between gradient-based meta-learning and hierarchical Bayes to propose a Dirichlet process mixture of hierarchical Bayesian models over the parameters of an arbitrary parametric model such as a neural network. In contrast to consolidating inductive biases into a single set of hyperparameters, our approach of task-dependent hyperparameter selection better handles latent distribution shift, as demonstrated on a set of evolving, image-based, few-shot learning benchmarks.Comment: updated experimental result