Recurrent neural networks are powerful models for processing sequential data, but they are generally plagued by vanishing and exploding gradient problems. Unitary recurrent neural networks (uRNNs), which use unitary recurrence matrices, haverecently been proposed as a means to avoid these issues. However, in previous experiments, the recurrence matrices were restricted to be a product of parameterized unitary matrices, and an open question remains: when does such a parameterization fail to represent all unitary matrices, and how does this restricted representational capacity limit what can be learned? To address this question, we propose full-capacity uRNNs that optimize their recurrence matrix over all unitary matrices, leading to significantly improved performance over uRNNs that use a restricted-capacity recurrence matrix. Our contribution consists of two main components. First, we provide a theoretical argument to determine if a unitary parameterization has restricted capacity. Using this argument, we show that a recently proposed unitary parameterization has restricted capacity for hidden state dimension greater than 7. Second, we show how a complete, full-capacity unitary recurrence matrix can be optimized over the differentiable manifold of unitary matrices. The resulting multiplicative gradient step is very simple and does not require gradient clipping or learning rate adaptation. We confirm the utility of our claims by empirically evaluating our new full-capacity uRNNs on both synthetic and natural data, achieving superior performance compared to both LSTMs and the original restricted-capacity uRNNs.

Accurately measuring the similarity between text documents lies at the core of many real world applications of machine learning. These include web-search ranking, document recommendation, multi-lingual document matching, and article categorization. Recently, a new document metric, the word mover's distance (WMD), has been proposed with unprecedented results on kNN-based document classification. The WMD elevates high quality word embeddings to document metrics by formulating the distance between two documents as an optimal transport problem between the embedded words. However, the document distances are entirely unsupervised and lack a mechanism to incorporate supervision when available. In this paper we propose an efficient technique to learn a supervised metric, which we call the Supervised WMD (S-WMD) metric. Our algorithm learns document distances that measure the underlying semantic differences between documents by leveraging semantic differences between individual words discovered during supervised training. This is achieved with an linear transformation of the underlying word embedding space and tailored word-specific weights, learned to minimize the stochastic leave-one-out nearest neighbor classification error on a per-document level. We evaluate our metric on eight real-world text classification tasks on which S-WMD consistently outperforms almost all of our 26 competitive baselines.

Adaptive schemes, where tasks are assigned based on the data collected thus far, are widely used in practical crowdsourcing systems to efficiently allocate the budget. However, existing theoretical analyses of crowdsourcing systems suggest that the gain of adaptive task assignments is minimal. To bridge this gap, we investigate this question under a strictly more general probabilistic model, which has been recently introduced to model practical crowdsourcing datasets. Under this generalized Dawid-Skene model, we characterize the fundamental tradeoff between budget and accuracy. We introduce a novel adaptive scheme that matches this fundamental limit. A given budget is allocated over multiple rounds. In each round, a subset of tasks with high enough confidence are classified, and increasing budget is allocated on remaining ones that are potentially more difficult. On each round, decisions are made based on the leading eigenvector of (weighted) non-backtracking operator corresponding to the bipartite assignment graph. We further quantify the gain of adaptivity, by comparing the tradeoff with the one for nonadaptive schemes, and confirm that the gain is significant and can be made arbitrarily large depending on the distribution of the difficulty level of the tasks at hand.

Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with functional data. In this context, variable selection techniques are especially attractive because they reduce the dimensionality, facilitate the interpretation and can improve the accuracy of the predictive models. The method, which is a recursive extension of maxima hunting (MH), performs variable selection by identifying the maxima of a relevance function, which measures the strength of the correlation of the predictor functional variable with the class label. At each stage, the information associated with the selected variable is removed by subtracting the conditional expectation of the process. The results of an extensive empirical evaluation are used to illustrate that, in the problems investigated, RMH has comparable or higher predictive accuracy than standard simensionality reduction techniques, such as PCA and PLS, and state-of-the-art feature selection methods for functional data, such as maxima hunting.

We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of the minimax risk. However, when the set is unspecified, designing an estimator that is blind to the hidden structure of the signal remains a challenging problem. We propose a new family of estimators to recover signals observed in Gaussian noise. Instead of specifying the set where the signal lives, we assume the existence of a well-performing linear estimator. Proposed estimators enjoy exact oracle inequalities and can be efficiently computed through convex optimization.

The framework of normalizing flows provides a general strategy for flexible variational inference of posteriors over latent variables. We propose a new type of normalizing flow, inverse autoregressive flow (IAF), that, in contrast to earlier published flows, scales well to high-dimensional latent spaces. The proposed flow consists of a chain of invertible transformations, where each transformation is based on an autoregressive neural network. In experiments, we show that IAF significantly improves upon diagonal Gaussian approximate posteriors. In addition, we demonstrate that a novel type of variational autoencoder, coupled with IAF, is competitive with neural autoregressive models in terms of attained log-likelihood on natural images, while allowing significantly faster synthesis.

Medical researchers are coming to appreciate that many diseases are in fact complex, heterogeneous syndromes composed of subpopulations that express different variants of a related complication. Longitudinal data extracted from individual electronic health records (EHR) offer an exciting new way to study subtle differences in the way these diseases progress over time. In this paper, we focus on answering two questions that can be asked using these databases of longitudinal EHR data. First, we want to understand whether there are individuals with similar disease trajectories and whether there are a small number of degrees of freedom that account for differences in trajectories across the population. Second, we want to understand how important clinical outcomes are associated with disease trajectories. To answer these questions, we propose the Disease Trajectory Map (DTM), a novel probabilistic model that learns low-dimensional representations of sparse and irregularly sampled longitudinal data. We propose a stochastic variational inference algorithm for learning the DTM that allows the model to scale to large modern medical datasets. To demonstrate the DTM, we analyze data collected on patients with the complex autoimmune disease, scleroderma. We find that DTM learns meaningful representations of disease trajectories and that the representations are significantly associated with important clinical outcomes.

We present a scalable and robust Bayesian method for demand forecasting in the context of a large e-commerce platform, paying special attention to intermittent and bursty target statistics. Inference is approximated by the Newton-Raphson algorithm, reduced to linear-time Kalman smoothing, which allows us to operate on several orders of magnitude larger problems than previous related work. In a study on large real-world sales datasets, our method outperforms competing approaches on fast and medium moving items.

This study introduces a novel feature selection approach CMICOT, which is a further evolution of filter methods with sequential forward selection (SFS) whose scoring functions are based on conditional mutual information (MI). We state and study a novel saddle point (max-min) optimization problem to build a scoring function that is able to identify joint interactions between several features. This method fills the gap of MI-based SFS techniques with high-order dependencies. In this high-dimensional case, the estimation of MI has prohibitively high sample complexity. We mitigate this cost using a greedy approximation and binary representatives what makes our technique able to be effectively used. The superiority of our approach is demonstrated by comparison with recently proposed interaction-aware filters and several interaction-agnostic state-of-the-art ones on ten publicly available benchmark datasets.

We propose a multivariate online dictionary-learning method for obtaining decompositions of brain images with structured and sparse components (aka atoms). Sparsity is to be understood in the usual sense: the dictionary atoms are constrained to contain mostly zeros. This is imposed via an $\ell_1$-norm constraint. By "structured", we mean that the atoms are piece-wise smooth and compact, thus making up blobs, as opposed to scattered patterns of activation. We propose to use a Sobolev (Laplacian) penalty to impose this type of structure. Combining the two penalties, we obtain decompositions that properly delineate brain structures from functional images. This non-trivially extends the online dictionary-learning work of Mairal et al. (2010), at the price of only a factor of 2 or 3 on the overall running time. Just like the Mairal et al. (2010) reference method, the online nature of our proposed algorithm allows it to scale to arbitrarily sized datasets. Experiments on brain data show that our proposed method extracts structured and denoised dictionaries that are more intepretable and better capture inter-subject variability in small medium, and large-scale regimes alike, compared to state-of-the-art models.