NeurIPS 2016 Papers

One crucial goal in kernel online learning is to bound the model size. Common approaches employ budget maintenance procedures to restrict the model sizes using removal, projection, or merging strategies. Although projection and merging, in the literature, are known to be the most effective strategies, they demand extensive computation whilst removal strategy fails to retain information of the removed vectors. An alternative way to address the model size problem is to apply random features to approximate the kernel function. This allows the model to be maintained directly in the random feature space, hence effectively resolve the curse of kernelization. However, this approach still suffers from a serious shortcoming as it needs to use a high dimensional random feature space to achieve a sufficiently accurate kernel approximation. Consequently, it leads to a significant increase in the computational cost. To address all of these aforementioned challenges, we present in this paper the Dual Space Gradient Descent (DualSGD), a novel framework that utilizes random features as an auxiliary space to maintain information from data points removed during budget maintenance. Consequently, our approach permits the budget to be maintained in a simple, direct and elegant way while simultaneously mitigating the impact of the dimensionality issue on learning performance. We further provide convergence analysis and extensively conduct experiments on five real-world datasets to demonstrate the predictive performance and scalability of our proposed method in comparison with the state-of-the-art baselines.

While neural machine translation (NMT) is making good progress in the past two years, tens of millions of bilingual sentence pairs are needed for its training. However, human labeling is very costly. To tackle this training data bottleneck, we develop a dual-learning mechanism, which can enable an NMT system to automatically learn from unlabeled data through a dual-learning game. This mechanism is inspired by the following observation: any machine translation task has a dual task, e.g., English-to-French translation (primal) versus French-to-English translation (dual); the primal and dual tasks can form a closed loop, and generate informative feedback signals to train the translation models, even if without the involvement of a human labeler. In the dual-learning mechanism, we use one agent to represent the model for the primal task and the other agent to represent the model for the dual task, then ask them to teach each other through a reinforcement learning process. Based on the feedback signals generated during this process (e.g., the language-model likelihood of the output of a model, and the reconstruction error of the original sentence after the primal and dual translations), we can iteratively update the two models until convergence (e.g., using the policy gradient methods). We call the corresponding approach to neural machine translation \emph{dual-NMT}. Experiments show that dual-NMT works very well on English$\leftrightarrow$French translation; especially, by learning from monolingual data (with 10\% bilingual data for warm start), it achieves a comparable accuracy to NMT trained from the full bilingual data for the French-to-English translation task.

Many applications of machine learning involve structured output with large domain, where learning of structured predictor is prohibitive due to repetitive calls to expensive inference oracle. In this work, we show that, by decomposing training of Structural Support Vector Machine (SVM) into a series of multiclass SVM problems connected through messages, one can replace expensive structured oracle with Factorwise Maximization Oracle (FMO) that allows efficient implementation of complexity sublinear to the factor domain. A Greedy Direction Method of Multiplier (GDMM) algorithm is proposed to exploit sparsity of messages which guarantees $\epsilon$ sub-optimality after $O(log(1/\epsilon))$ passes of FMO calls. We conduct experiments on chain-structured problems and fully-connected problems of large output domains. The proposed approach is orders-of-magnitude faster than the state-of-the-art training algorithms for Structural SVM.

Building large models with parameter sharing accounts for most of the success of deep convolutional neural networks (CNNs). In this paper, we propose doubly convolutional neural networks (DCNNs), which significantly improve the performance of CNNs by further exploring this idea. In stead of allocating a set of convolutional filters that are independently learned, a DCNN maintains groups of filters where filters within each group are translated versions of each other. Practically, a DCNN can be easily implemented by a two-step convolution procedure, which is supported by most modern deep learning libraries. We perform extensive experiments on three image classification benchmarks: CIFAR-10, CIFAR-100 and ImageNet, and show that DCNNs consistently outperform other competing architectures. We have also verified that replacing a convolutional layer with a doubly convolutional layer at any depth of a CNN can improve its performance. Moreover, various design choices of DCNNs are demonstrated, which shows that DCNN can serve the dual purpose of building more accurate models and/or reducing the memory footprint without sacrificing the accuracy.

In this paper, we propose a Double Thompson Sampling (D-TS) algorithm for dueling bandit problems. As its name suggests, D-TS selects both the first and the second candidates according to Thompson Sampling. Specifically, D-TS maintains a posterior distribution for the preference matrix, and chooses the pair of arms for comparison according to two sets of samples independently drawn from the posterior distribution. This simple algorithm applies to general Copeland dueling bandits, including Condorcet dueling bandits as its special case. For general Copeland dueling bandits, we show that D-TS achieves $O(K^2 \log T)$ regret. Moreover, using a back substitution argument, we refine the regret to $O(K \log T + K^2 \log \log T)$ in Condorcet dueling bandits and many practical Copeland dueling bandits. In addition, we propose an enhancement of D-TS, referred to as D-TS+, that reduces the regret by carefully breaking ties. Experiments based on both synthetic and real-world data demonstrate that D-TS and D-TS$^+$ significantly improve the overall performance, in terms of regret and robustness.

The cost of large scale data collection and annotation often makes the application of machine learning algorithms to new tasks or datasets prohibitively expensive. One approach circumventing this cost is training models on synthetic data where annotations are provided automatically. Despite their appeal, such models often fail to generalize from synthetic to real images, necessitating domain adaptation algorithms to manipulate these models before they can be successfully applied. Existing approaches focus either on mapping representations from one domain to the other, or on learning to extract features that are invariant to the domain from which they were extracted. However, by focusing only on creating a mapping or shared representation between the two domains, they ignore the individual characteristics of each domain. We hypothesize that explicitly modeling what is unique to each domain can improve a model's ability to extract domain-invariant features. Inspired by work on private-shared component analysis, we explicitly learn to extract image representations that are partitioned into two subspaces: one component which is private to each domain and one which is shared across domains. Our model is trained to not only perform the task we care about in the source domain, but also to use the partitioned representation to reconstruct the images from both domains. Our novel architecture results in a model that outperforms the state-of-the-art on a range of unsupervised domain adaptation scenarios and additionally produces visualizations of the private and shared representations enabling interpretation of the domain adaptation process.

Tensor factorization is a powerful tool to analyse multi-way data. Recently proposed nonlinear factorization methods, although capable of capturing complex relationships, are computationally quite expensive and may suffer a severe learning bias in case of extreme data sparsity. Therefore, we propose a distributed, flexible nonlinear tensor factorization model, which avoids the expensive computations and structural restrictions of the Kronecker-product in the existing TGP formulations, allowing an arbitrary subset of tensor entries to be selected for training. Meanwhile, we derive a tractable and tight variational evidence lower bound (ELBO) that enables highly decoupled, parallel computations and high-quality inference. Based on the new bound, we develop a distributed, key-value-free inference algorithm in the MapReduce framework, which can fully exploit the memory cache mechanism in fast MapReduce systems such as Spark. Experiments demonstrate the advantages of our method over several state-of-the-art approaches, in terms of both predictive performance and computational efficiency.

We propose a deep generative model for learning to distill the hidden factors of variation within a set of labeled observations into two complementary codes. One code describes the factors of variation relevant to solving a specified task. The other code describes the remaining factors of variation that are irrelevant to solving this task. The only available source of supervision during the training process comes from our ability to distinguish among different observations belonging to the same category. Concrete examples include multiple images of the same object from different viewpoints, or multiple speech samples from the same speaker. In both of these instances, the factors of variation irrelevant to classification are implicitly expressed by intra-class variabilities, such as the relative position of an object in an image, or the linguistic content of an utterance. Most existing approaches for solving this problem rely heavily on having access to pairs of observations only sharing a single factor of variation, e.g. different objects observed in the exact same conditions. This assumption is often not encountered in realistic settings where data acquisition is not controlled and labels for the uninformative components are not available. In this work, we propose to overcome this limitation by augmenting deep convolutional autoencoders with a form of adversarial training. Both factors of variation are implicitly captured in the organization of the learned embedding space, and can be used for solving single-image analogies. Experimental results on synthetic and real datasets show that the proposed method is capable of disentangling the influences of style and content factors using a flexible representation, as well as generalizing to unseen styles or content classes.

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 discriminative Gaifman models, a novel family of relational machine learning models. Gaifman models learn feature representations bottom up from representations of locally connected and bounded-size regions of knowledge bases (KBs). Considering local and bounded-size neighborhoods of knowledge bases renders logical inference and learning tractable, mitigates the problem of overfitting, and facilitates weight sharing. Gaifman models sample neighborhoods of knowledge bases so as to make the learned relational models more robust to missing objects and relations which is a common situation in open-world KBs. We present the core ideas of Gaifman models and apply them to large-scale relational learning problems. We also discuss the ways in which Gaifman models relate to some existing relational machine learning approaches.

Artificial neural networks are most commonly trained with the back-propagation algorithm, where the gradient for learning is provided by back-propagating the error, layer by layer, from the output layer to the hidden layers. A recently discovered method called feedback-alignment shows that the weights used for propagating the error backward don't have to be symmetric with the weights used for propagation the activation forward. In fact, random feedback weights work evenly well, because the network learns how to make the feedback useful. In this work, the feedback alignment principle is used for training hidden layers more independently from the rest of the network, and from a zero initial condition. The error is propagated through fixed random feedback connections directly from the output layer to each hidden layer. This simple method is able to achieve zero training error even in convolutional networks and very deep networks, completely without error back-propagation. The method is a step towards biologically plausible machine learning because the error signal is almost local, and no symmetric or reciprocal weights are required. Experiments show that the test performance on MNIST and CIFAR is almost as good as those obtained with back-propagation for fully connected networks. If combined with dropout, the method achieves 1.45% error on the permutation invariant MNIST task.

In this paper we present a practical solution with performance guarantees to the problem of dimensionality reduction for very large scale sparse matrices. We show applications of our approach to computing the Principle Component Analysis (PCA) of any $n\times d$ matrix, using one pass over the stream of its rows. Our solution uses coresets: a scaled subset of the $n$ rows that approximates their sum of squared distances to \emph{every} $k$-dimensional \emph{affine} subspace. An open theoretical problem has been to compute such a coreset that is independent of both $n$ and $d$. An open practical problem has been to compute a non-trivial approximation to the PCA of very large but sparse databases such as the Wikipedia document-term matrix in a reasonable time. We answer both of these questions affirmatively. Our main technical result is a new framework for deterministic coreset constructions based on a reduction to the problem of counting items in a stream.

Many canonical machine learning problems boil down to a convex optimization problem with a finite sum structure. However, whereas much progress has been made in developing faster algorithms for this setting, the inherent limitations of these problems are not satisfactorily addressed by existing lower bounds. Indeed, current bounds focus on first-order optimization algorithms, and only apply in the often unrealistic regime where the number of iterations is less than $\cO(d/n)$ (where $d$ is the dimension and $n$ is the number of samples). In this work, we extend the framework of Arjevani et al. \cite{arjevani2015lower,arjevani2016iteration} to provide new lower bounds, which are dimension-free, and go beyond the assumptions of current bounds, thereby covering standard finite sum optimization methods, e.g., SAG, SAGA, SVRG, SDCA without duality, as well as stochastic coordinate-descent methods, such as SDCA and accelerated proximal SDCA.

We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from graph-structured data and used as an effective basis for node classification. DCNNs have several attractive qualities, including a latent representation for graphical data that is invariant under isomorphism, as well as polynomial-time prediction and learning that can be represented as tensor operations and efficiently implemented on a GPU. Through several experiments with real structured datasets, we demonstrate that DCNNs are able to outperform probabilistic relational models and kernel-on-graph methods at relational node classification tasks.

The exponential mechanism is a general method to construct a randomized estimator that satisfies $(\varepsilon, 0)$-differential privacy. Recently, Wang et al. showed that the Gibbs posterior, which is a data-dependent probability distribution that contains the Bayesian posterior, is essentially equivalent to the exponential mechanism under certain boundedness conditions on the loss function. While the exponential mechanism provides a way to build an $(\varepsilon, 0)$-differential private algorithm, it requires boundedness of the loss function, which is quite stringent for some learning problems. In this paper, we focus on $(\varepsilon, \delta)$-differential privacy of Gibbs posteriors with convex and Lipschitz loss functions. Our result extends the classical exponential mechanism, allowing the loss functions to have an unbounded sensitivity.

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.

Online optimization covers problems such as online resource allocation, online bipartite matching, adwords (a central problem in e-commerce and advertising), and adwords with separable concave returns. We analyze the worst case competitive ratio of two primal-dual algorithms for a class of online convex (conic) optimization problems that contains the previous examples as special cases defined on the positive orthant. We derive a sufficient condition on the objective function that guarantees a constant worst case competitive ratio (greater than or equal to $\frac{1}{2}$) for monotone objective functions. We provide new examples of online problems on the positive orthant % and the positive semidefinite cone that satisfy the sufficient condition. We show how smoothing can improve the competitive ratio of these algorithms, and in particular for separable functions, we show that the optimal smoothing can be derived by solving a convex optimization problem. This result allows us to directly optimize the competitive ratio bound over a class of smoothing functions, and hence design effective smoothing customized for a given cost function.

A single color image can contain many cues informative towards different aspects of local geometric structure. We approach the problem of monocular depth estimation by using a neural network to produce a mid-level representation that summarizes these cues. This network is trained to characterize local scene geometry by predicting, at every image location, depth derivatives of different orders, orientations and scales. However, instead of a single estimate for each derivative, the network outputs probability distributions that allow it to express confidence about some coefficients, and ambiguity about others. Scene depth is then estimated by harmonizing this overcomplete set of network predictions, using a globalization procedure that finds a single consistent depth map that best matches all the local derivative distributions. We demonstrate the efficacy of this approach through evaluation on the NYU v2 depth data set.

Given $iid$ observations from an unknown continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function. Our density estimate is a piecewise constant function defined on a binary partition of $\Omega$. The key ingredient of the algorithm is to use discrepancy, a concept originates from Quasi Monte Carlo analysis, to control the partition process. The resulting algorithm is simple, efficient, and has provable convergence rate. We demonstrate empirically its efficiency as a density estimation method. We also show how it can be utilized to find good initializations for k-means.