We formalize the notion of a pseudo-ensemble, a (possibly infinite) collection of child models spawned from a parent model by perturbing it according to some noise process. E.g., dropout (Hinton et al, 2012) in a deep neural network trains a pseudo-ensemble of child subnetworks generated by randomly masking nodes in the parent network. We examine the relationship of pseudo-ensembles, which involve perturbation in model-space, to standard ensemble methods and existing notions of robustness, which focus on perturbation in observation-space. We present a novel regularizer based on making the behavior of a pseudo-ensemble robust with respect to the noise process generating it. In the fully-supervised setting, our regularizer matches the performance of dropout. But, unlike dropout, our regularizer naturally extends to the semi-supervised setting, where it produces state-of-the-art results. We provide a case study in which we transform the Recursive Neural Tensor Network of (Socher et al, 2013) into a pseudo-ensemble, which significantly improves its performance on a real-world sentiment analysis benchmark.

We propose a distributed Markov chain Monte Carlo (MCMC) inference algorithm for large scale Bayesian posterior simulation. We assume that the dataset is partitioned and stored across nodes of a cluster. Our procedure involves an independent MCMC posterior sampler at each node based on its local partition of the data. Moment statistics of the local posteriors are collected from each sampler and propagated across the cluster using expectation propagation message passing with low communication costs. The moment sharing scheme improves posterior estimation quality by enforcing agreement among the samplers. We demonstrate the speed and inference quality of our method with empirical studies on Bayesian logistic regression and sparse linear regression with a spike-and-slab prior.

Despite the prevalence of collaborative filtering in recommendation systems, there has been little theoretical development on why and how well it works, especially in the ``online'' setting, where items are recommended to users over time. We address this theoretical gap by introducing a model for online recommendation systems, cast item recommendation under the model as a learning problem, and analyze the performance of a cosine-similarity collaborative filtering method. In our model, each of $n$ users either likes or dislikes each of $m$ items. We assume there to be $k$ types of users, and all the users of a given type share a common string of probabilities determining the chance of liking each item. At each time step, we recommend an item to each user, where a key distinction from related bandit literature is that once a user consumes an item (e.g., watches a movie), then that item cannot be recommended to the same user again. The goal is to maximize the number of likable items recommended to users over time. Our main result establishes that after nearly $\log(km)$ initial learning time steps, a simple collaborative filtering algorithm achieves essentially optimal performance without knowing $k$. The algorithm has an exploitation step that uses cosine similarity and two types of exploration steps, one to explore the space of items (standard in the literature) and the other to explore similarity between users (novel to this work).

The combination of modern Reinforcement Learning and Deep Learning approaches holds the promise of making significant progress on challenging applications requiring both rich perception and policy-selection. The Arcade Learning Environment (ALE) provides a set of Atari games that represent a useful benchmark set of such applications. A recent breakthrough in combining model-free reinforcement learning with deep learning, called DQN, achieves the best real-time agents thus far. Planning-based approaches achieve far higher scores than the best model-free approaches, but they exploit information that is not available to human players, and they are orders of magnitude slower than needed for real-time play. Our main goal in this work is to build a better real-time Atari game playing agent than DQN. The central idea is to use the slow planning-based agents to provide training data for a deep-learning architecture capable of real-time play. We proposed new agents based on this idea and show that they outperform DQN.

We introduce a framework for unsupervised learning of structured predictors with overlapping, global features. Each input's latent representation is predicted conditional on the observed data using a feature-rich conditional random field (CRF). Then a reconstruction of the input is (re)generated, conditional on the latent structure, using a generative model which factorizes similarly to the CRF. The autoencoder formulation enables efficient exact inference without resorting to unrealistic independence assumptions or restricting the kinds of features that can be used. We illustrate insightful connections to traditional autoencoders, posterior regularization and multi-view learning. Finally, we show competitive results with instantiations of the framework for two canonical tasks in natural language processing: part-of-speech induction and bitext word alignment, and show that training our model can be substantially more efficient than comparable feature-rich baselines.

In this paper, we present a new approach for lifted MAP inference in Markov logic networks (MLNs). The key idea in our approach is to compactly encode the MAP inference problem as an Integer Polynomial Program (IPP) by schematically applying three lifted inference steps to the MLN: lifted decomposition, lifted conditioning, and partial grounding. Our IPP encoding is lifted in the sense that an integer assignment to a variable in the IPP may represent a truth-assignment to multiple indistinguishable ground atoms in the MLN. We show how to solve the IPP by first converting it to an Integer Linear Program (ILP) and then solving the latter using state-of-the-art ILP techniques. Experiments on several benchmark MLNs show that our new algorithm is substantially superior to ground inference and existing methods in terms of computational efficiency and solution quality.

Branch-and-bound is a widely used method in combinatorial optimization, including mixed integer programming, structured prediction and MAP inference. While most work has been focused on developing problem-specific techniques, little is known about how to systematically design the node searching strategy on a branch-and-bound tree. We address the key challenge of learning an adaptive node searching order for any class of problem solvable by branch-and-bound. Our strategies are learned by imitation learning. We apply our algorithm to linear programming based branch-and-bound for solving mixed integer programs (MIP). We compare our method with one of the fastest open-source solvers, SCIP; and a very efficient commercial solver, Gurobi. We demonstrate that our approach achieves better solutions faster on four MIP libraries.

In recent years, distributed representations of inputs have led to performance gains in many applications by allowing statistical information to be shared across inputs. However, the predicted outputs (labels, and more generally structures) are still treated as discrete objects even though outputs are often not discrete units of meaning. In this paper, we present a new formulation for structured prediction where we represent individual labels in a structure as dense vectors and allow semantically similar labels to share parameters. We extend this representation to larger structures by defining compositionality using tensor products to give a natural generalization of standard structured prediction approaches. We define a learning objective for jointly learning the model parameters and the label vectors and propose an alternating minimization algorithm for learning. We show that our formulation outperforms structural SVM baselines in two tasks: multiclass document classification and part-of-speech tagging.

Carl E. Rasmussen Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. Theyhave been applied to both regression and nonlinear dimensionality reduction, and offer desirable properties such as uncertainty estimates, robustness to over-fitting, and principled ways for tuning hyper-parameters. However the scalability of these models to big datasets remains an active topic of research. We introduce a novel re-parametrisation of variational inference for sparse GP regression and latent variable models that allows for an efficient distributed algorithm. Thisis done by exploiting the decoupling of the data given the inducing points to reformulate the evidence lower bound in a Map-Reduce setting. We show that the inference scales well with data and computational resources, while preserving a balanced distribution of the load among the nodes. We further demonstrate the utility in scaling Gaussian processes to big data. We show that GP performance improves with increasing amounts of data in regression (on flight data with 2 million records) and latent variable modelling (on MNIST). The results show that GPs perform better than many common models often used for big data.

We present the Convex Polytope Machine (CPM), a novel non-linear learning algorithm for large-scale binary classification tasks. The CPM finds a large margin convex polytope separator which encloses one class. We develop a stochastic gradient descent based algorithm that is amenable to massive datasets, and augment it with a heuristic procedure to avoid sub-optimal local minima. Our experimental evaluations of the CPM on large-scale datasets from distinct domains (MNIST handwritten digit recognition, text topic, and web security) demonstrate that the CPM trains models faster, sometimes several orders of magnitude, than state-of-the-art similar approaches and kernel-SVM methods while achieving comparable or better classification performance. Our empirical results suggest that, unlike prior similar approaches, we do not need to control the number of sub-classifiers (sides of the polytope) to avoid overfitting.