Stochastic structured prediction under bandit feedback follows a learning protocol where on each of a sequence of iterations, the learner receives an input, predicts an output structure, and receives partial feedback in form of a task loss evaluation of the predicted structure. We present applications of this learning scenario to convex and non-convex objectives for structured prediction and analyze them as stochastic first-order methods. We present an experimental evaluation on problems of natural language processing over exponential output spaces, and compare convergence speed across different objectives under the practical criterion of optimal task performance on development data and the optimization-theoretic criterion of minimal squared gradient norm. Best results under both criteria are obtained for a non-convex objective for pairwise preference learning under bandit feedback.

Towards learning programs from data, we introduce the problem of sampling programs from posterior distributions conditioned on that data. Within this setting, we propose an algorithm that uses a symbolic solver to efficiently sample programs. The proposal combines constraint-based program synthesis with sampling via random parity constraints. We give theoretical guarantees on how well the samples approximate the true posterior, and have empirical results showing the algorithm is efficient in practice, evaluating our approach on 22 program learning problems in the domains of text editing and computer-aided programming.

We propose Sketched Online Newton (SON), an online second order learning algorithm that enjoys substantially improved regret guarantees for ill-conditioned data. SON is an enhanced version of the Online Newton Step, which, via sketching techniques enjoys a running time linear in the dimension and sketch size. We further develop sparse forms of the sketching methods (such as Oja's rule), making the computation linear in the sparsity of features. Together, the algorithm eliminates all computational obstacles in previous second order online learning approaches.

We learn rich natural sound representations by capitalizing on large amounts of unlabeled sound data collected in the wild. We leverage the natural synchronization between vision and sound to learn an acoustic representation using two-million unlabeled videos. Unlabeled video has the advantage that it can be economically acquired at massive scales, yet contains useful signals about natural sound. We propose a student-teacher training procedure which transfers discriminative visual knowledge from well established visual recognition models into the sound modality using unlabeled video as a bridge. Our sound representation yields significant performance improvements over the state-of-the-art results on standard benchmarks for acoustic scene/object classification. Visualizations suggest some high-level semantics automatically emerge in the sound network, even though it is trained without ground truth labels.

A long-term goal of machine learning research is to build an intelligent dialog agent. Most research in natural language understanding has focused on learning from fixed training sets of labeled data, with supervision either at the word level (tagging, parsing tasks) or sentence level (question answering, machine translation). This kind of supervision is not realistic of how humans learn, where language is both learned by, and used for, communication. In this work, we study dialog-based language learning, where supervision is given naturally and implicitly in the response of the dialog partner during the conversation. We study this setup in two domains: the bAbI dataset of (Weston et al., 2015) and large-scale question answering from (Dodge et al., 2015). We evaluate a set of baseline learning strategies on these tasks, and show that a novel model incorporating predictive lookahead is a promising approach for learning from a teacher's response. In particular, a surprising result is that it can learn to answer questions correctly without any reward-based supervision at all.

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (in the sample space) or vertically (in the feature space). While the majority of the literature focuses on sample space partitioning, feature space partitioning is more effective when p >> n. Existing methods for partitioning features, however, are either vulnerable to high correlations or inefficient in reducing the model dimension. In this paper, we solve these problems through a new embarrassingly parallel framework named DECO for distributed variable selection and parameter estimation. In DECO, variables are first partitioned and allocated to m distributed workers. The decorrelated subset data within each worker are then fitted via any algorithm designed for high-dimensional problems. We show that by incorporating the decorrelation step, DECO can achieve consistent variable selection and parameter estimation on each subset with (almost) no assumptions. In addition, the convergence rate is nearly minimax optimal for both sparse and weakly sparse models and does NOT depend on the partition number m. Extensive numerical experiments are provided to illustrate the performance of the new framework.

Binary hashing is a well-known approach for fast approximate nearest-neighbor search in information retrieval. Much work has focused on affinity-based objective functions involving the hash functions or binary codes. These objective functions encode neighborhood information between data points and are often inspired by manifold learning algorithms. They ensure that the hash functions differ from each other through constraints or penalty terms that encourage codes to be orthogonal or dissimilar across bits, but this couples the binary variables and complicates the already difficult optimization. We propose a much simpler approach: we train each hash function (or bit) independently from each other, but introduce diversity among them using techniques from classifier ensembles. Surprisingly, we find that not only is this faster and trivially parallelizable, but it also improves over the more complex, coupled objective function, and achieves state-of-the-art precision and recall in experiments with image retrieval.

The problem of predicting connections between a set of data points finds many applications, in systems biology and social network analysis among others. This paper focuses on the \textit{graph reconstruction} problem, where the prediction rule is obtained by minimizing the average error over all n(n-1)/2 possible pairs of the n nodes of a training graph. Our first contribution is to derive learning rates of order O(log n / n) for this problem, significantly improving upon the slow rates of order O(1/√n) established in the seminal work of Biau & Bleakley (2006). Strikingly, these fast rates are universal, in contrast to similar results known for other statistical learning problems (e.g., classification, density level set estimation, ranking, clustering) which require strong assumptions on the distribution of the data. Motivated by applications to large graphs, our second contribution deals with the computational complexity of graph reconstruction. Specifically, we investigate to which extent the learning rates can be preserved when replacing the empirical reconstruction risk by a computationally cheaper Monte-Carlo version, obtained by sampling with replacement B << n² pairs of nodes. Finally, we illustrate our theoretical results by numerical experiments on synthetic and real graphs.

We study a general adversarial online learning problem, in which we are given a decision set X' in a reflexive Banach space X and a sequence of reward vectors in the dual space of X. At each iteration, we choose an action from X', based on the observed sequence of previous rewards. Our goal is to minimize regret, defined as the gap between the realized reward and the reward of the best fixed action in hindsight. Using results from infinite dimensional convex analysis, we generalize the method of Dual Averaging (or Follow the Regularized Leader) to our setting and obtain upper bounds on the worst-case regret that generalize many previous results. Under the assumption of uniformly continuous rewards, we obtain explicit regret bounds in a setting where the decision set is the set of probability distributions on a compact metric space S. Importantly, we make no convexity assumptions on either the set S or the reward functions. We also prove a general lower bound on the worst-case regret for any online algorithm. We then apply these results to the problem of learning in repeated two-player zero-sum games on compact metric spaces. In doing so, we first prove that if both players play a Hannan-consistent strategy, then with probability 1 the empirical distributions of play weakly converge to the set of Nash equilibria of the game. We then show that, under mild assumptions, Dual Averaging on the (infinite-dimensional) space of probability distributions indeed achieves Hannan-consistency.

In the recent years, a number of parameter-free algorithms have been developed for online linear optimization over Hilbert spaces and for learning with expert advice. These algorithms achieve optimal regret bounds that depend on the unknown competitors, without having to tune the learning rates with oracle choices. We present a new intuitive framework to design parameter-free algorithms for both online linear optimization over Hilbert spaces and for learning with expert advice, based on reductions to betting on outcomes of adversarial coins. We instantiate it using a betting algorithm based on the Krichevsky-Trofimov estimator. The resulting algorithms are simple, with no parameters to be tuned, and they improve or match previous results in terms of regret guarantee and per-round complexity.