Deep neural networks (DNNs) are now a central component of nearly all state-of-the-art speech recognition systems. Building neural network acoustic models requires several design decisions including network architecture, size, and training loss function. This paper offers an empirical investigation on which aspects of DNN acoustic model design are most important for speech recognition system performance. We report DNN classifier performance and final speech recognizer word error rates, and compare DNNs using several metrics to quantify factors influencing differences in task performance. Our first set of experiments use the standard Switchboard benchmark corpus, which contains approximately 300 hours of conversational telephone speech. We compare standard DNNs to convolutional networks, and present the first experiments using locally-connected, untied neural networks for acoustic modeling. We additionally build systems on a corpus of 2,100 hours of training data by combining the Switchboard and Fisher corpora. This larger corpus allows us to more thoroughly examine performance of large DNN models -- with up to ten times more parameters than those typically used in speech recognition systems. Our results suggest that a relatively simple DNN architecture and optimization technique produces strong results. These findings, along with previous work, help establish a set of best practices for building DNN hybrid speech recognition systems with maximum likelihood training. Our experiments in DNN optimization additionally serve as a case study for training DNNs with discriminative loss functions for speech tasks, as well as DNN classifiers more generally.

In many applications one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to the challenge, in a compressive sensing framework, one is given only an undersampled set of linear projections of the composite signal. In this paper, we propose using the Dantzig selector model incorporating an overcomplete dictionary to separate a noisy undersampled collection of composite signals, and present an algorithm to efficiently solve the model. The Dantzig selector is a statistical approach to finding a solution to a noisy linear regression problem by minimizing the $\ell_1$ norm of candidate coefficient vectors while constraining the scope of the residuals. If the underlying coefficient vector is sparse, then the Dantzig selector performs well in the recovery and separation of the unknown composite signal. In the following, we propose a proximity operator based algorithm to recover and separate unknown noisy undersampled composite signals through the Dantzig selector. We present numerical simulations comparing the proposed algorithm with the competing Alternating Direction Method, and the proposed algorithm is found to be faster, while producing similar quality results. Additionally, we demonstrate the utility of the proposed algorithm in several experiments by applying it in various domain applications including the recovery of complex-valued coefficient vectors, the removal of impulse noise from smooth signals, and the separation and classification of a composition of handwritten digits.

Multi-output inference tasks, such as multi-label classification, have become increasingly important in recent years. A popular method for multi-label classification is classifier chains, in which the predictions of individual classifiers are cascaded along a chain, thus taking into account inter-label dependencies and improving the overall performance. Several varieties of classifier chain methods have been introduced, and many of them perform very competitively across a wide range of benchmark datasets. However, scalability limitations become apparent on larger datasets when modeling a fully-cascaded chain. In particular, the methods' strategies for discovering and modeling a good chain structure constitutes a mayor computational bottleneck. In this paper, we present the classifier trellis (CT) method for scalable multi-label classification. We compare CT with several recently proposed classifier chain methods to show that it occupies an important niche: it is highly competitive on standard multi-label problems, yet it can also scale up to thousands or even tens of thousands of labels.

In this paper, we present a statistical-mechanical analysis of deep learning. We elucidate some of the essential components of deep learning---pre-training by unsupervised learning and fine tuning by supervised learning. We formulate the extraction of features from the training data as a margin criterion in a high-dimensional feature-vector space. The self-organized classifier is then supplied with small amounts of labelled data, as in deep learning. Although we employ a simple single-layer perceptron model, rather than directly analyzing a multi-layer neural network, we find a nontrivial phase transition that is dependent on the number of unlabelled data in the generalization error of the resultant classifier. In this sense, we evaluate the efficacy of the unsupervised learning component of deep learning. The analysis is performed by the replica method, which is a sophisticated tool in statistical mechanics. We validate our result in the manner of deep learning, using a simple iterative algorithm to learn the weight vector on the basis of belief propagation.

While computer and communication technologies have provided effective means to scale up many aspects of education, the submission and grading of assessments such as homework assignments and tests remains a weak link. In this paper, we study the problem of automatically grading the kinds of open response mathematical questions that figure prominently in STEM (science, technology, engineering, and mathematics) courses. Our data-driven framework for mathematical language processing (MLP) leverages solution data from a large number of learners to evaluate the correctness of their solutions, assign partial-credit scores, and provide feedback to each learner on the likely locations of any errors. MLP takes inspiration from the success of natural language processing for text data and comprises three main steps. First, we convert each solution to an open response mathematical question into a series of numerical features. Second, we cluster the features from several solutions to uncover the structures of correct, partially correct, and incorrect solutions. We develop two different clustering approaches, one that leverages generic clustering algorithms and one based on Bayesian nonparametrics. Third, we automatically grade the remaining (potentially large number of) solutions based on their assigned cluster and one instructor-provided grade per cluster. As a bonus, we can track the cluster assignment of each step of a multistep solution and determine when it departs from a cluster of correct solutions, which enables us to indicate the likely locations of errors to learners. We test and validate MLP on real-world MOOC data to demonstrate how it can substantially reduce the human effort required in large-scale educational platforms.

We study the Bayesian model averaging approach to learning Bayesian network structures (DAGs) from data. We develop new algorithms including the first algorithm that is able to efficiently sample DAGs according to the exact structure posterior. The DAG samples can then be used to construct estimators for the posterior of any feature. We theoretically prove good properties of our estimators and empirically show that our estimators considerably outperform the estimators from the previous state-of-the-art methods.

Applying traditional collaborative filtering to digital publishing is challenging because user data is very sparse due to the high volume of documents relative to the number of users. Content based approaches, on the other hand, is attractive because textual content is often very informative. In this paper we describe large-scale content based collaborative filtering for digital publishing. To solve the digital publishing recommender problem we compare two approaches: latent Dirichlet allocation (LDA) and deep belief nets (DBN) that both find low-dimensional latent representations for documents. Efficient retrieval can be carried out in the latent representation. We work both on public benchmarks and digital media content provided by Issuu, an online publishing platform. This article also comes with a newly developed deep belief nets toolbox for topic modeling tailored towards performance evaluation of the DBN model and comparisons to the LDA model.

While in classical planning the objective is to achieve one of the equally attractive goal states at as low total action cost as possible, the objective in deterministic oversubscription planning (OSP) is to achieve an as valuable as possible subset of goals within a fixed allowance of the total action cost. Although numerous applications in various fields share the latter objective, no substantial algorithmic advances have been made in deterministic OSP. Tracing the key sources of progress in classical planning, we identify a severe lack of effective domain-independent approximations for OSP. With our focus here on optimal planning, our goal is to bridge this gap. Two classes of approximation techniques have been found especially useful in the context of optimal classical planning: those based on state-space abstractions and those based on logical landmarks for goal reachability. The question we study here is whether some similar-in-spirit, yet possibly mathematically different, approximation techniques can be developed for OSP. In the context of abstractions, we define the notion of additive abstractions for OSP, study the complexity of deriving effective abstractions from a rich space of hypotheses, and reveal some substantial, empirically relevant islands of tractability. In the context of landmarks, we show how standard goal-reachability landmarks of certain classical planning tasks can be compiled into the OSP task of interest, resulting in an equivalent OSP task with a lower cost allowance, and thus with a smaller search space. Our empirical evaluation confirms the effectiveness of the proposed techniques, and opens a wide gate for further developments in oversubscription planning.

We obtain an improved finite-sample guarantee on the linear convergence of stochastic gradient descent for smooth and strongly convex objectives, improving from a quadratic dependence on the conditioning $(L/\mu)^2$ (where $L$ is a bound on the smoothness and $\mu$ on the strong convexity) to a linear dependence on $L/\mu$. Furthermore, we show how reweighting the sampling distribution (i.e. importance sampling) is necessary in order to further improve convergence, and obtain a linear dependence in the average smoothness, dominating previous results. We also discuss importance sampling for SGD more broadly and show how it can improve convergence also in other scenarios. Our results are based on a connection we make between SGD and the randomized Kaczmarz algorithm, which allows us to transfer ideas between the separate bodies of literature studying each of the two methods. In particular, we recast the randomized Kaczmarz algorithm as an instance of SGD, and apply our results to prove its exponential convergence, but to the solution of a weighted least squares problem rather than the original least squares problem. We then present a modified Kaczmarz algorithm with partially biased sampling which does converge to the original least squares solution with the same exponential convergence rate.

This paper presents a way of solving Markov Decision Processes that combines state abstraction and temporal abstraction. Specifically, we combine state aggregation with the options framework and demonstrate that they work well together and indeed it is only after one combines the two that the full benefit of each is realized. We introduce a hierarchical value iteration algorithm where we first coarsely solve subgoals and then use these approximate solutions to exactly solve the MDP. This algorithm solved several problems faster than vanilla value iteration.