ICML 2016 Papers

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models and as such are arguably more flexible, have a greater capacity to generalise, and provide better calibrated uncertainty estimates than alternative deep models. This paper develops a new approximate Bayesian learning scheme that enables DGPs to be applied to a range of medium to large scale regression problems for the first time. The new method uses an approximate Expectation Propagation procedure and a novel and efficient extension of the probabilistic backpropagation algorithm for learning. We evaluate the new method for non-linear regression on eleven real-world datasets, showing that it always outperforms GP regression and is almost always better than state-of-the-art deterministic and sampling-based approximate inference methods for Bayesian neural networks. As a by-product, this work provides a comprehensive analysis of six approximate Bayesian methods for training neural networks.

The Ladder Network is a recent new approach to semi-supervised learning that turned out to be very successful. While showing impressive performance, the Ladder Network has many components intertwined, whose contributions are not obvious in such a complex architecture. This paper presents an extensive experimental investigation of variants of the Ladder Network in which we replaced or removed individual components to learn about their relative importance. For semi-supervised tasks, we conclude that the most important contribution is made by the lateral connections, followed by the application of noise, and the choice of what we refer to as the ‘combinator function’. As the number of labeled training examples increases, the lateral connections and the reconstruction criterion become less important, with most of the generalization improvement coming from the injection of noise in each layer. Finally, we introduce a combinator function that reduces test error rates on Permutation-Invariant MNIST to 0.57% for the supervised setting, and to 0.97% and 1.0% for semi-supervised settings with 1000 and 100 labeled examples, respectively.

Statistical models of student responses on assessment questions, such as those in homeworks and exams, enable educators and computer-based personalized learning systems to gain insights into students’ knowledge using machine learning. Popular student-response models, including the Rasch model and item response theory models, represent the probability of a student answering a question correctly using an affine function of latent factors. While such models can accurately predict student responses, their ability to interpret the underlying knowledge structure (which is certainly nonlinear) is limited. In response, we develop a new, nonlinear latent variable model that we call the dealbreaker model, in which a student’s success probability is determined by their weakest concept mastery. We develop efficient parameter inference algorithms for this model using novel methods for nonconvex optimization. We show that the dealbreaker model achieves comparable or better prediction performance as compared to affine models with real-world educational datasets. We further demonstrate that the parameters learned by the dealbreaker model are interpretable—they provide key insights into which concepts are critical (i.e., the “dealbreaker”) to answering a question correctly. We conclude by reporting preliminary results for a movie-rating dataset, which illustrate the broader applicability of the dealbreaker model.

Rank aggregation systems collect ordinal preferences from individuals to produce a global ranking that represents the social preference. To reduce the computational complexity of learning the global ranking, a common practice is to use rank-breaking. Individuals’ preferences are broken into pairwise comparisons and then applied to efficient algorithms tailored for independent pairwise comparisons. However, due to the ignored dependencies, naive rank-breaking approaches can result in inconsistent estimates. The key idea to produce unbiased and accurate estimates is to treat the paired comparisons outcomes unequally, depending on the topology of the collected data. In this paper, we provide the optimal rank-breaking estimator, which not only achieves consistency but also achieves the best error bound. This allows us to characterize the fundamental tradeoff between accuracy and complexity in some canonical scenarios. Further, we identify how the accuracy depends on the spectral gap of a corresponding comparison graph.

In this paper we present a new way of predicting the performance of a reinforcement learning policy given historical data that may have been generated by a different policy. The ability to evaluate a policy from historical data is important for applications where the deployment of a bad policy can be dangerous or costly. We show empirically that our algorithm produces estimates that often have orders of magnitude lower mean squared error than existing methods—it makes more efficient use of the available data. Our new estimator is based on two advances: an extension of the doubly robust estimator (Jiang & Li, 2015), and a new way to mix between model based and importance sampling based estimates.

Performing exact posterior inference in complex generative models is often difficult or impossible due to an expensive to evaluate or intractable likelihood function. Approximate Bayesian computation (ABC) is an inference framework that constructs an approximation to the true likelihood based on the similarity between the observed and simulated data as measured by a predefined set of summary statistics. Although the choice of informative problem-specific summary statistics crucially influences the quality of the likelihood approximation and hence also the quality of the posterior sample in ABC, there are only few principled general-purpose approaches to the selection or construction of such summary statistics. In this paper, we develop a novel framework for solving this problem. We model the functional relationship between the data and the optimal choice (with respect to a loss function) of summary statistics using kernel-based distribution regression. Furthermore, we extend our approach to incorporate kernel-based regression from conditional distributions, thus appropriately taking into account the specific structure of the posited generative model. We show that our approach can be implemented in a computationally and statistically efficient way using the random Fourier features framework for large-scale kernel learning. In addition to that, our framework outperforms related methods by a large margin on toy and real-world data, including hierarchical and time series models.

A search engine recommends to the user a list of web pages. The user examines this list, from the first page to the last, and clicks on all attractive pages until the user is satisfied. This behavior of the user can be described by the dependent click model (DCM). We propose DCM bandits, an online learning variant of the DCM where the goal is to maximize the probability of recommending satisfactory items, such as web pages. The main challenge of our learning problem is that we do not observe which attractive item is satisfactory. We propose a computationally-efficient learning algorithm for solving our problem, dcmKL-UCB; derive gap-dependent upper bounds on its regret under reasonable assumptions; and also prove a matching lower bound up to logarithmic factors. We evaluate our algorithm on synthetic and real-world problems, and show that it performs well even when our model is misspecified. This work presents the first practical and regret-optimal online algorithm for learning to rank with multiple clicks in a cascade-like click model.

Cumulative prospect theory (CPT) is known to model human decisions well, with substantial empirical evidence supporting this claim. CPT works by distorting probabilities and is more general than the classic expected utility and coherent risk measures. We bring this idea to a risk-sensitive reinforcement learning (RL) setting and design algorithms for both estimation and control. The RL setting presents two particular challenges when CPT is applied: estimating the CPT objective requires estimations of the entire distribution of the value function and finding a randomized optimal policy. The estimation scheme that we propose uses the empirical distribution to estimate the CPT-value of a random variable. We then use this scheme in the inner loop of a CPT-value optimization procedure that is based on the well-known simulation optimization idea of simultaneous perturbation stochastic approximation (SPSA). We provide theoretical convergence guarantees for all the proposed algorithms and also empirically demonstrate the usefulness of our algorithms.

Applying machine learning to a problem which involves medical, financial, or other types of sensitive data, not only requires accurate predictions but also careful attention to maintaining data privacy and security. Legal and ethical requirements may prevent the use of cloud-based machine learning solutions for such tasks. In this work, we will present a method to convert learned neural networks to CryptoNets, neural networks that can be applied to encrypted data. This allows a data owner to send their data in an encrypted form to a cloud service that hosts the network. The encryption ensures that the data remains confidential since the cloud does not have access to the keys needed to decrypt it. Nevertheless, we will show that the cloud service is capable of applying the neural network to the encrypted data to make encrypted predictions, and also return them in encrypted form. These encrypted predictions can be sent back to the owner of the secret key who can decrypt them. Therefore, the cloud service does not gain any information about the raw data nor about the prediction it made. We demonstrate CryptoNets on the MNIST optical character recognition tasks. CryptoNets achieve 99% accuracy and can make around 59000 predictions per hour on a single PC. Therefore, they allow high throughput, accurate, and private predictions.

Cross-graph Relational Learning (CGRL) refers to the problem of predicting the strengths or labels of multi-relational tuples of heterogeneous object types, through the joint inference over multiple graphs which specify the internal connections among each type of objects. CGRL is an open challenge in machine learning due to the daunting number of all possible tuples to deal with when the numbers of nodes in multiple graphs are large, and because the labeled training instances are extremely sparse as typical. Existing methods such as tensor factorization or tensor-kernel machines do not work well because of the lack of convex formulation for the optimization of CGRL models, the poor scalability of the algorithms in handling combinatorial numbers of tuples, and/or the non-transductive nature of the learning methods which limits their ability to leverage unlabeled data in training. This paper proposes a novel framework which formulates CGRL as a convex optimization problem, enables transductive learning using both labeled and unlabeled tuples, and offers a scalable algorithm that guarantees the optimal solution and enjoys a constant time complexity with respect to the sizes of input graphs. In our experiments with a subset of DBLP publication records and an Enzyme multi-source dataset, the proposed method successfully scaled to the large cross-graph inference problem, and outperformed other representative approaches significantly.

We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph G whose edges are labeled with + or -, we wish to partition the graph into clusters while trying to avoid errors: + edges between clusters or - edges within clusters. Classically, one seeks to minimize the total number of such errors. We introduce a new framework that allows the objective to be a more general function of the number of errors at each vertex (for example, we may wish to minimize the number of errors at the worst vertex) and provide a rounding algorithm which converts “fractional clusterings” into discrete clusterings while causing only a constant-factor blowup in the number of errors at each vertex. This rounding algorithm yields constant-factor approximation algorithms for the discrete problem under a wide variety of objective functions.

Automatic forecasting of time series data is a challenging problem in many industries. Current forecast models adopted by businesses do not provide adequate means for including data representing external factors that may have a significant impact on the time series, such as weather, national events, local events, social media trends, promotions, etc. This paper introduces a novel neural network attention mechanism that naturally incorporates data from multiple external sources without the feature engineering needed to get other techniques to work. We demonstrate empirically that the proposed model achieves superior performance for predicting the demand of 20 commodities across 107 stores of one of America’s largest retailers when compared to other baseline models, including neural networks, linear models, certain kernel methods, Bayesian regression, and decision trees. Our method ultimately accounts for a 23.9% relative improvement as a result of the incorporation of external data sources, and provides an unprecedented level of descriptive ability for a neural network forecasting model.

We study the K-armed dueling bandit problem, a variation of the standard stochastic bandit problem where the feedback is limited to relative comparisons of a pair of arms. The hardness of recommending Copeland winners, the arms that beat the greatest number of other arms, is characterized by deriving an asymptotic regret bound. We propose Copeland Winners Deterministic Minimum Empirical Divergence (CW-RMED), an algorithm inspired by the DMED algorithm (Honda and Takemura, 2010), and derive an asymptotically optimal regret bound for it. However, it is not known whether the algorithm can be efficiently computed or not. To address this issue, we devise an efficient version (ECW-RMED) and derive its asymptotic regret bound. Experimental comparisons of dueling bandit algorithms show that ECW-RMED significantly outperforms existing ones.

Convolutional rectifier networks, i.e. convolutional neural networks with rectified linear activation and max or average pooling, are the cornerstone of modern deep learning. However, despite their wide use and success, our theoretical understanding of the expressive properties that drive these networks is partial at best. On the other hand, we have a much firmer grasp of these issues in the world of arithmetic circuits. Specifically, it is known that convolutional arithmetic circuits possess the property of "complete depth efficiency", meaning that besides a negligible set, all functions realizable by a deep network of polynomial size, require exponential size in order to be realized (or approximated) by a shallow network. In this paper we describe a construction based on generalized tensor decompositions, that transforms convolutional arithmetic circuits into convolutional rectifier networks. We then use mathematical tools available from the world of arithmetic circuits to prove new results. First, we show that convolutional rectifier networks are universal with max pooling but not with average pooling. Second, and more importantly, we show that depth efficiency is weaker with convolutional rectifier networks than it is with convolutional arithmetic circuits. This leads us to believe that developing effective methods for training convolutional arithmetic circuits, thereby fulfilling their expressive potential, may give rise to a deep learning architecture that is provably superior to convolutional rectifier networks but has so far been overlooked by practitioners.

We consider the problem of principal component analysis (PCA) in a streaming stochastic setting, where our goal is to find a direction of approximate maximal variance, based on a stream of i.i.d. data points in R^d. A simple and computationally cheap algorithm for this is stochastic gradient descent (SGD), which incrementally updates its estimate based on each new data point. However, due to the non-convex nature of the problem, analyzing its performance has been a challenge. In particular, existing guarantees rely on a non-trivial eigengap assumption on the covariance matrix, which is intuitively unnecessary. In this paper, we provide (to the best of our knowledge) the first eigengap-free convergence guarantees for SGD in the context of PCA. This also partially resolves an open problem posed in (Hardt & Price, 2014). Moreover, under an eigengap assumption, we show that the same techniques lead to new SGD convergence guarantees with better dependence on the eigengap.

Due to its numerous applications, rank aggregation has become a problem of major interest across many fields of the computer science literature. In the vast majority of situations, Kemeny consensus(es) are considered as the ideal solutions. It is however well known that their computation is NP-hard. Many contributions have thus established various results to apprehend this complexity. In this paper we introduce a practical method to predict, for a ranking and a dataset, how close the Kemeny consensus(es) are to this ranking. A major strength of this method is its generality: it does not require any assumption on the dataset nor the ranking. Furthermore, it relies on a new geometric interpretation of Kemeny aggregation that, we believe, could lead to many other results.

In this paper, we introduce a new set of reinforcement learning (RL) tasks in Minecraft (a flexible 3D world). We then use these tasks to systematically compare and contrast existing deep reinforcement learning (DRL) architectures with our new memory-based DRL architectures. These tasks are designed to emphasize, in a controllable manner, issues that pose challenges for RL methods including partial observability (due to first-person visual observations), delayed rewards, high-dimensional visual observations, and the need to use active perception in a correct manner so as to perform well in the tasks. While these tasks are conceptually simple to describe, by virtue of having all of these challenges simultaneously they are difficult for current DRL architectures. Additionally, we evaluate the generalization performance of the architectures on environments not used during training. The experimental results show that our new architectures generalize to unseen environments better than existing DRL architectures.

Model-free reinforcement learning has been successfully applied to a range of challenging problems, and has recently been extended to handle large neural network policies and value functions. However, the sample complexity of model-free algorithms, particularly when using high-dimensional function approximators, tends to limit their applicability to physical systems. In this paper, we explore algorithms and representations to reduce the sample complexity of deep reinforcement learning for continuous control tasks. We propose two complementary techniques for improving the efficiency of such algorithms. First, we derive a continuous variant of the Q-learning algorithm, which we call normalized advantage functions (NAF), as an alternative to the more commonly used policy gradient and actor-critic methods. NAF representation allows us to apply Q-learning with experience replay to continuous tasks, and substantially improves performance on a set of simulated robotic control tasks. To further improve the efficiency of our approach, we explore the use of learned models for accelerating model-free reinforcement learning. We show that iteratively refitted local linear models are especially effective for this, and demonstrate substantially faster learning on domains where such models are applicable.

We propose the contextual combinatorial cascading bandits, a combinatorial online learning game, where at each time step a learning agent is given a set of contextual information, then selects a list of items, and observes stochastic outcomes of a prefix in the selected items by some stopping criterion. In online recommendation, the stopping criterion might be the first item a user selects; in network routing, the stopping criterion might be the first edge blocked in a path. We consider position discounts in the list order, so that the agent’s reward is discounted depending on the position where the stopping criterion is met. We design a UCB-type algorithm, C^3-UCB, for this problem, prove an n-step regret bound \tildeO(\sqrtn) in the general setting, and give finer analysis for two special cases. Our work generalizes existing studies in several directions, including contextual information, position discounts, and a more general cascading bandit model. Experiments on synthetic and real datasets demonstrate the advantage of involving contextual information and position discounts.