mtybilly/Instruct2DS huggingface dataset:
Train and Test Tightness of LP Relaxations in Structured Prediction
Authors: Meshi, Ofer and Mahdavi, Mehrdad and Weller, Adrian and Sontag, David
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Structured prediction is used in areas such as computer vision and natural language processing to predict structured outputs such as segmentations or parse trees. In these settings, prediction is performed by MAP inference or, equivalently, by solving an integer linear program. Because of the complex scoring functions required to obtain accurate predictions, both learning and inference typically require the use of approximate solvers. We propose a theoretical explanation to the striking observation that approximations based on linear programming (LP) relaxations are often tight on real-world instances. In particular, we show that learning with LP relaxed inference encourages integrality of training instances, and that tightness generalizes from train to test data.
Stochastic Optimization for Multiview Representation Learning using Partial Least Squares
Authors: Arora, Raman and Mianjy, Poorya and Marinov, Teodor
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Partial Least Squares (PLS) is a ubiquitous statistical technique for bilinear factor analysis. It is used in many data analysis, machine learning, and information retrieval applications to model the covariance structure between a pair of data matrices. In this paper, we consider PLS for representation learning in a multiview setting where we have more than one view in data at training time. Furthermore, instead of framing PLS as a problem about a fixed given data set, we argue that PLS should be studied as a stochastic optimization problem, especially in a "big data" setting, with the goal of optimizing a population objective based on sample. This view suggests using Stochastic Approximation (SA) approaches, such as Stochastic Gradient Descent (SGD) and enables a rigorous analysis of their benefits. In this paper, we develop SA approaches to PLS and provide iteration complexity bounds for the proposed algorithms.
Hierarchical Compound Poisson Factorization
Authors: Basbug, Mehmet and Engelhardt, Barbara
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Non-negative matrix factorization models based on a hierarchical Gamma-Poisson structure capture user and item behavior effectively in extremely sparse data sets, making them the ideal choice for collaborative filtering applications. Hierarchical Poisson factorization (HPF) in particular has proved successful for scalable recommendation systems with extreme sparsity. HPF, however, suffers from a tight coupling of sparsity model (absence of a rating) and response model (the value of the rating), which limits the expressiveness of the latter. Here, we introduce hierarchical compound Poisson factorization (HCPF) that has the favorable Gamma-Poisson structure and scalability of HPF to high-dimensional extremely sparse matrices. More importantly, HCPF decouples the sparsity model from the response model, allowing us to choose the most suitable distribution for the response. HCPF can capture binary, non-negative discrete, non-negative continuous, and zero-inflated continuous responses. We compare HCPF with HPF on nine discrete and three continuous data sets and conclude that HCPF captures the relationship between sparsity and response better than HPF.
Opponent Modeling in Deep Reinforcement Learning
Authors: He, He and Boyd-Graber, Jordan and Kwok, Kevin and Daumé, III, Hal
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Opponent modeling is necessary in multi-agent settings where secondary agents with competing goals also adapt their strategies, yet it remains challenging because of strategies’ complex interaction and the non-stationary nature. Most previous work focuses on developing probabilistic models or parameterized strategies for specific applications. Inspired by the recent success of deep reinforcement learning, we present neural-based models that jointly learn a policy and the behavior of opponents. Instead of explicitly predicting the opponent’s action, we encode observation of the opponents into a deep Q-Network (DQN), while retaining explicit modeling under multitasking. By using a Mixture-of-Experts architecture, our model automatically discovers different strategy patterns of opponents even without extra supervision. We evaluate our models on a simulated soccer game and a popular trivia game, showing superior performance over DQN and its variants.
No penalty no tears: Least squares in high-dimensional linear models
Authors: Wang, Xiangyu and Dunson, David and Leng, Chenlei
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Ordinary least squares (OLS) is the default method for fitting linear models, but is not applicable for problems with dimensionality larger than the sample size. For these problems, we advocate the use of a generalized version of OLS motivated by ridge regression, and propose two novel three-step algorithms involving least squares fitting and hard thresholding. The algorithms are methodologically simple to understand intuitively, computationally easy to implement efficiently, and theoretically appealing for choosing models consistently. Numerical exercises comparing our methods with penalization-based approaches in simulations and data analyses illustrate the great potential of the proposed algorithms.
SDNA: Stochastic Dual Newton Ascent for Empirical Risk Minimization
Authors: Qu, Zheng and Richtarik, Peter and Takac, Martin and Fercoq, Olivier
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose a new algorithm for minimizing regularized empirical loss: Stochastic Dual Newton Ascent (SDNA). Our method is dual in nature: in each iteration we update a random subset of the dual variables. However, unlike existing methods such as stochastic dual coordinate ascent, SDNA is capable of utilizing all local curvature information contained in the examples, which leads to striking improvements in both theory and practice – sometimes by orders of magnitude. In the special case when an L2-regularizer is used in the primal, the dual problem is a concave quadratic maximization problem plus a separable term. In this regime, SDNA in each step solves a proximal subproblem involving a random principal submatrix of the Hessian of the quadratic function; whence the name of the method.
On Graduated Optimization for Stochastic Non-Convex Problems
Authors: Hazan, Elad and Levy, Kfir Yehuda and Shalev-Shwartz, Shai
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade.Despite being popular, very little is known in terms of its theoretical convergence analysis. In this paper we describe a new first-order algorithm based on graduated optimization and analyze its performance. We characterize a family of non-convex functions for which this algorithm provably converges to a global optimum. In particular, we prove that the algorithm converges to an ε-approximate solution within O(1 / ε^2) gradient-based steps. We extend our algorithm and analysis to the setting of stochastic non-convex optimization with noisy gradient feedback, attaining the same convergence rate. Additionally, we discuss the setting of “zero-order optimization", and devise a variant of our algorithm which converges at rate of O(d^2/ ε^4).
Meta-Learning with Memory-Augmented Neural Networks
Authors: Santoro, Adam and Bartunov, Sergey and Botvinick, Matthew and Wierstra, Daan and Lillicrap, Timothy
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Despite recent breakthroughs in the applications of deep neural networks, one setting that presents a persistent challenge is that of "one-shot learning." Traditional gradient-based networks require a lot of data to learn, often through extensive iterative training. When new data is encountered, the models must inefficiently relearn their parameters to adequately incorporate the new information without catastrophic interference. Architectures with augmented memory capacities, such as Neural Turing Machines (NTMs), offer the ability to quickly encode and retrieve new information, and hence can potentially obviate the downsides of conventional models. Here, we demonstrate the ability of a memory-augmented neural network to rapidly assimilate new data, and leverage this data to make accurate predictions after only a few samples. We also introduce a new method for accessing an external memory that focuses on memory content, unlike previous methods that additionally use memory location-based focusing mechanisms.
The knockoff filter for FDR control in group-sparse and multitask regression
Authors: Dai, Ran and Barber, Rina
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose the group knockoff filter, a method for false discovery rate control in a linear regression setting where the features are grouped, and we would like to select a set of relevant groups which have a nonzero effect on the response. By considering the set of true and false discoveries at the group level, this method gains power relative to sparse regression methods. We also apply our method to the multitask regression problem where multiple response variables share similar sparsity patterns across the set of possible features. Empirically, the group knockoff filter successfully controls false discoveries at the group level in both settings, with substantially more discoveries made by leveraging the group structure.
Softened Approximate Policy Iteration for Markov Games
Authors: Pérolat, Julien and Piot, Bilal and Geist, Matthieu and Scherrer, Bruno and Pietquin, Olivier
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: This paper reports theoretical and empirical investigations on the use of quasi-Newton methods to minimize the Optimal Bellman Residual (OBR) of zero-sum two-player Markov Games. First, it reveals that state-of-the-art algorithms can be derived by the direct application of Newton’s method to different norms of the OBR. More precisely, when applied to the norm of the OBR, Newton’s method results in the Bellman Residual Minimization Policy Iteration (BRMPI) and, when applied to the norm of the Projected OBR (POBR), it results into the standard Least Squares Policy Iteration (LSPI) algorithm. Consequently, new algorithms are proposed, making use of quasi-Newton methods to minimize the OBR and the POBR so as to take benefit of enhanced empirical performances at low cost. Indeed, using a quasi-Newton method approach introduces slight modifications in term of coding of LSPI and BRMPI but improves significantly both the stability and the performance of those algorithms. These phenomena are illustrated on an experiment conducted on artificially constructed games called Garnets.
Stochastic Block BFGS: Squeezing More Curvature out of Data
Authors: Gower, Robert and Goldfarb, Donald and Richtarik, Peter
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose a novel limited-memory stochastic block BFGS update for incorporating enriched curvature information in stochastic approximation methods. In our method, the estimate of the inverse Hessian matrix that is maintained by it, is updated at each iteration using a sketch of the Hessian, i.e., a randomly generated compressed form of the Hessian. We propose several sketching strategies, present a new quasi-Newton method that uses stochastic block BFGS updates combined with the variance reduction approach SVRG to compute batch stochastic gradients, and prove linear convergence of the resulting method. Numerical tests on large-scale logistic regression problems reveal that our method is more robust and substantially outperforms current state-of-the-art methods.
Differential Geometric Regularization for Supervised Learning of Classifiers
Authors: Bai, Qinxun and Rosenberg, Steven and Wu, Zheng and Sclaroff, Stan
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to an estimator of the class probability P(y|ěc x). The regularization term measures the volume of this submanifold, based on the intuition that overfitting produces rapid local oscillations and hence large volume of the estimator. This technique can be applied to regularize any classification function that satisfies two requirements: firstly, an estimator of the class probability can be obtained; secondly, first and second derivatives of the class probability estimator can be calculated. In experiments, we apply our regularization technique to standard loss functions for classification, our RBF-based implementation compares favorably to widely used regularization methods for both binary and multiclass classification.
Exploiting Cyclic Symmetry in Convolutional Neural Networks
Authors: Dieleman, Sander and Fauw, Jeffrey De and Kavukcuoglu, Koray
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Many classes of images exhibit rotational symmetry. Convolutional neural networks are sometimes trained using data augmentation to exploit this, but they are still required to learn the rotation equivariance properties from the data. Encoding these properties into the network architecture, as we are already used to doing for translation equivariance by using convolutional layers, could result in a more efficient use of the parameter budget by relieving the model from learning them. We introduce four operations which can be inserted into neural network models as layers, and which can be combined to make these models partially equivariant to rotations. They also enable parameter sharing across different orientations. We evaluate the effect of these architectural modifications on three datasets which exhibit rotational symmetry and demonstrate improved performance with smaller models.
Graying the black box: Understanding DQNs
Authors: Zahavy, Tom and Ben-Zrihem, Nir and Mannor, Shie
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: In recent years there is a growing interest in using deep representations for reinforcement learning. In this paper, we present a methodology and tools to analyze Deep Q-networks (DQNs) in a non-blind matter. Using our tools we reveal that the features learned by DQNs aggregate the state space in a hierarchical fashion, explaining its success. Moreover we are able to understand and describe the policies learned by DQNs for three different Atari2600 games and suggest ways to interpret, debug and optimize of deep neural networks in Reinforcement Learning.
The Sum-Product Theorem: A Foundation for Learning Tractable Models
Authors: Friesen, Abram and Domingos, Pedro
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even when an arbitrary number of hidden layers are present. In this paper, we generalize this result to a much broader set of learning problems: all those where inference consists of summing a function over a semiring. This includes satisfiability, constraint satisfaction, optimization, integration, and others. In any semiring, for summation to be tractable it suffices that the factors of every product have disjoint scopes. This unifies and extends many previous results in the literature. Enforcing this condition at learning time thus ensures that the learned models are tractable. We illustrate the power and generality of this approach by applying it to a new type of structured prediction problem: learning a nonconvex function that can be globally optimized in polynomial time. We show empirically that this greatly outperforms the standard approach of learning without regard to the cost of optimization.
Pareto Frontier Learning with Expensive Correlated Objectives
Authors: Shah, Amar and Ghahramani, Zoubin
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: There has been a surge of research interest in developing tools and analysis for Bayesian optimization, the task of finding the global maximizer of an unknown, expensive function through sequential evaluation using Bayesian decision theory. However, many interesting problems involve optimizing multiple, expensive to evaluate objectives simultaneously, and relatively little research has addressed this setting from a Bayesian theoretic standpoint. A prevailing choice when tackling this problem, is to model the multiple objectives as being independent, typically for ease of computation. In practice, objectives are correlated to some extent. In this work, we incorporate the modelling of inter-task correlations, developing an approximation to overcome intractable integrals. We illustrate the power of modelling dependencies between objectives on a range of synthetic and real world multi-objective optimization problems.
Asynchronous Methods for Deep Reinforcement Learning
Authors: Mnih, Volodymyr and Badia, Adria Puigdomenech and Mirza, Mehdi and Graves, Alex and Lillicrap, Timothy and Harley, Tim and Silver, David and Kavukcuoglu, Koray
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose a conceptually simple and lightweight framework for deep reinforcement learning that uses asynchronous gradient descent for optimization of deep neural network controllers. We present asynchronous variants of four standard reinforcement learning algorithms and show that parallel actor-learners have a stabilizing effect on training allowing all four methods to successfully train neural network controllers. The best performing method, an asynchronous variant of actor-critic, surpasses the current state-of-the-art on the Atari domain while training for half the time on a single multi-core CPU instead of a GPU. Furthermore, we show that asynchronous actor-critic succeeds on a wide variety of continuous motor control problems as well as on a new task of navigating random 3D mazes using a visual input.
A Simple and Strongly-Local Flow-Based Method for Cut Improvement
Authors: Veldt, Nate and Gleich, David and Mahoney, Michael
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Many graph-based learning problems can be cast as finding a good set of vertices nearby a seed set, and a powerful methodology for these problems is based on minimum cuts and maximum flows. We introduce and analyze a new method for locally-biased graph-based learning called SimpleLocal, which finds good conductance cuts near a set of seed vertices. An important feature of our algorithm is that it is strongly-local, meaning it does not need to explore the entire graph to find cuts that are locally optimal. This method is related to other strongly-local flow-based methods, but it enables a simple implementation. We also show how it achieves localization through an implicit l1-norm penalty term. As a flow-based method, our algorithm exhibits several advantages in terms of cut optimality and accurate identification of target regions in a graph. We demonstrate the power of SimpleLocal solving segmentation problems on a 467 million edge graph based on an MRI scan.
Nonlinear Statistical Learning with Truncated Gaussian Graphical Models
Authors: Su, Qinliang and Liao, Xuejun and Chen, Changyou and Carin, Lawrence
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The truncated variables are assumed latent and integrated out to induce a marginal model. We show that the variables in the marginal model are non-Gaussian distributed and their expected relations are nonlinear. We use expectation-maximization to break the inference of the nonlinear model into a sequence of TGGM inference problems, each of which is efficiently solved by using the properties and numerical methods of multivariate Gaussian distributions. We use the TGGM to design models for nonlinear regression and classification, with the performances of these models demonstrated on extensive benchmark datasets and compared to state-of-the-art competing results.
Barron and Cover's Theory in Supervised Learning and its Application to Lasso
Authors: Kawakita, Masanori and Takeuchi, Jun’ichi
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We study Barron and Cover’s theory (BC theory) in supervised learning. The original BC theory can be applied to supervised learning only approximately and limitedly. Though Barron (2008) and Chatterjee and Barron (2014) succeeded in removing the approximation, their idea cannot be essentially applied to supervised learning in general. By solving this issue, we propose an extension of BC theory to supervised learning. The extended theory has several advantages inherited from the original BC theory. First, it holds for finite sample number n. Second, it requires remarkably few assumptions. Third, it gives a justification of the MDL principle in supervised learning. We also derive new risk and regret bounds of lasso with random design as its application. The derived risk bound hold for any finite n without boundedness of features in contrast to past work. Behavior of the regret bound is investigated by numerical simulations. We believe that this is the first extension of BC theory to general supervised learning without approximation.
Nonparametric Canonical Correlation Analysis
Authors: Michaeli, Tomer and Wang, Weiran and Livescu, Karen
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep neural network methods. These approaches seek maximally correlated projections among families of functions, which the user specifies (by choosing a kernel or neural network structure), and are computationally demanding. Interestingly, the theory of nonlinear CCA, without functional restrictions, had been studied in the population setting by Lancaster already in the 1950s, but these results have not inspired practical algorithms. We revisit Lancaster’s theory to devise a practical algorithm for nonparametric CCA (NCCA). Specifically, we show that the solution can be expressed in terms of the singular value decomposition of a certain operator associated with the joint density of the views. Thus, by estimating the population density from data, NCCA reduces to solving an eigenvalue system, superficially like kernel CCA but, importantly, without requiring the inversion of any kernel matrix. We also derive a partially linear CCA (PLCCA) variant in which one of the views undergoes a linear projection while the other is nonparametric. Using a kernel density estimate based on a small number of nearest neighbors, our NCCA and PLCCA algorithms are memory-efficient, often run much faster, and perform better than kernel CCA and comparable to deep CCA.
BISTRO: An Efficient Relaxation-Based Method for Contextual Bandits
Authors: Rakhlin, Alexander and Sridharan, Karthik
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We present efficient algorithms for the problem of contextual bandits with i.i.d. covariates, an arbitrary sequence of rewards, and an arbitrary class of policies. Our algorithm BISTRO requires d calls to the empirical risk minimization (ERM) oracle per round, where d is the number of actions. The method uses unlabeled data to make the problem computationally simple. When the ERM problem itself is computationally hard, we extend the approach by employing multiplicative approximation algorithms for the ERM. The integrality gap of the relaxation only enters in the regret bound rather than the benchmark. Finally, we show that the adversarial version of the contextual bandit problem is learnable (and efficient) whenever the full-information supervised online learning problem has a non-trivial regret bound (and efficient).
Associative Long Short-Term Memory
Authors: Danihelka, Ivo and Wayne, Greg and Uria, Benigno and Kalchbrenner, Nal and Graves, Alex
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We investigate a new method to augment recurrent neural networks with extra memory without increasing the number of network parameters. The system has an associative memory based on complex-valued vectors and is closely related to Holographic Reduced Representations and Long Short-Term Memory networks. Holographic Reduced Representations have limited capacity: as they store more information, each retrieval becomes noisier due to interference. Our system in contrast creates redundant copies of stored information, which enables retrieval with reduced noise. Experiments demonstrate faster learning on multiple memorization tasks.
Dueling Network Architectures for Deep Reinforcement Learning
Authors: Wang, Ziyu and Schaul, Tom and Hessel, Matteo and Hasselt, Hado and Lanctot, Marc and Freitas, Nando
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: In recent years there have been many successes of using deep representations in reinforcement learning. Still, many of these applications use conventional architectures, such as convolutional networks, LSTMs, or auto-encoders. In this paper, we present a new neural network architecture for model-free reinforcement learning. Our dueling network represents two separate estimators: one for the state value function and one for the state-dependent action advantage function. The main benefit of this factoring is to generalize learning across actions without imposing any change to the underlying reinforcement learning algorithm. Our results show that this architecture leads to better policy evaluation in the presence of many similar-valued actions. Moreover, the dueling architecture enables our RL agent to outperform the state-of-the-art on the Atari 2600 domain.
Persistence weighted Gaussian kernel for topological data analysis
Authors: Kusano, Genki and Hiraoka, Yasuaki and Fukumizu, Kenji
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy topological properties. This paper proposes a kernel method on persistence diagrams to develop a statistical framework in TDA. The proposed kernel satisfies the stability property and provides explicit control on the effect of persistence. Furthermore, the method allows a fast approximation technique. The method is applied into practical data on proteins and oxide glasses, and the results show the advantage of our method compared to other relevant methods on persistence diagrams.
Learning Convolutional Neural Networks for Graphs
Authors: Niepert, Mathias and Ahmed, Mohamed and Kutzkov, Konstantin
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and edge attributes. Analogous to image-based convolutional networks that operate on locally connected regions of the input, we present a general approach to extracting locally connected regions from graphs. Using established benchmark data sets, we demonstrate that the learned feature representations are competitive with state of the art graph kernels and that their computation is highly efficient.
Persistent RNNs: Stashing Recurrent Weights On-Chip
Authors: Diamos, Greg and Sengupta, Shubho and Catanzaro, Bryan and Chrzanowski, Mike and Coates, Adam and Elsen, Erich and Engel, Jesse and Hannun, Awni and Satheesh, Sanjeev
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: This paper introduces a new technique for mapping Deep Recurrent Neural Networks (RNN) efficiently onto GPUs. We show how it is possi- ble to achieve substantially higher computational throughput at low mini-batch sizes than direct implementations of RNNs based on matrix multiplications. The key to our approach is the use of persistent computational kernels that exploit the GPU’s inverted memory hierarchy to reuse network weights over multiple timesteps. Our initial implementation sustains 2.8 TFLOP/s at a mini-batch size of 4 on an NVIDIA TitanX GPU. This provides a 16x reduction in activation memory footprint, enables model training with 12x more parameters on the same hardware, allows us to strongly scale RNN training to 128 GPUs, and allows us to efficiently explore end-to-end speech recognition models with over 100 layers.
Recurrent Orthogonal Networks and Long-Memory Tasks
Authors: Henaff, Mikael and Szlam, Arthur and LeCun, Yann
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Although RNNs have been shown to be power- ful tools for processing sequential data, finding architectures or optimization strategies that al- low them to model very long term dependencies is still an active area of research. In this work, we carefully analyze two synthetic datasets orig- inally outlined in (Hochreiter & Schmidhuber, 1997) which are used to evaluate the ability of RNNs to store information over many time steps. We explicitly construct RNN solutions to these problems, and using these constructions, illumi- nate both the problems themselves and the way in which RNNs store different types of information in their hidden states. These constructions fur- thermore explain the success of recent methods that specify unitary initializations or constraints on the transition matrices.
The Arrow of Time in Multivariate Time Series
Authors: Bauer, Stefan and Schölkopf, Bernhard and Peters, Jonas
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We prove that a time series satisfying a (linear) multivariate autoregressive moving average (VARMA) model satisfies the same model assumption in the reversed time direction, too, if all innovations are normally distributed. This reversibility breaks down if the innovations are non-Gaussian. This means that under the assumption of a VARMA process with non-Gaussian noise, the arrow of time becomes detectable. Our work thereby provides a theoretic justification of an algorithm that has been used for inferring the direction of video snippets. We present a slightly modified practical algorithm that estimates the time direction for a given sample and prove its consistency. We further investigate how the performance of the algorithm depends on sample size, number of dimensions of the time series and the order of the process. An application to real world data from economics shows that considering multivariate processes instead of univariate processes can be beneficial for estimating the time direction. Our result extends earlier work on univariate time series. It relates to the concept of causal inference, where recent methods exploit non-Gaussianity of the error terms for causal structure learning.
Mixture Proportion Estimation via Kernel Embeddings of Distributions
Authors: Ramaswamy, Harish and Scott, Clayton and Tewari, Ambuj
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Mixture proportion estimation (MPE) is the problem of estimating the weight of a component distribution in a mixture, given samples from the mixture and component. This problem constitutes a key part in many "weakly supervised learning" problems like learning with positive and unlabelled samples, learning with label noise, anomaly detection and crowdsourcing. While there have been several methods proposed to solve this problem, to the best of our knowledge no efficient algorithm with a proven convergence rate towards the true proportion exists for this problem. We fill this gap by constructing a provably correct algorithm for MPE, and derive convergence rates under certain assumptions on the distribution. Our method is based on embedding distributions onto an RKHS, and implementing it only requires solving a simple convex quadratic programming problem a few times. We run our algorithm on several standard classification datasets, and demonstrate that it performs comparably to or better than other algorithms on most datasets.
Fast DPP Sampling for Nystrom with Application to Kernel Methods
Authors: Li, Chengtao and Jegelka, Stefanie and Sra, Suvrit
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The Nystrom method has long been popular for scaling up kernel methods. Its theoretical guarantees and empirical performance rely critically on the quality of the landmarks selected. We study landmark selection for Nystrom using Determinantal Point Processes (DPPs), discrete probability models that allow tractable generation of diverse samples. We prove that landmarks selected via DPPs guarantee bounds on approximation errors; subsequently, we analyze implications for kernel ridge regression. Contrary to prior reservations due to cubic complexity of DPP sampling, we show that (under certain conditions) Markov chain DPP sampling requires only linear time in the size of the data. We present several empirical results that support our theoretical analysis, and demonstrate the superior performance of DPP-based landmark selection compared with existing approaches.
Complex Embeddings for Simple Link Prediction
Authors: Trouillon, Théo and Welbl, Johannes and Riedel, Sebastian and Gaussier, Eric and Bouchard, Guillaume
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here we make use of complex valued embeddings. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. Compared to state-of-the-art models such as Neural Tensor Network and Holographic Embeddings, our approach based on complex embeddings is arguably simpler, as it only uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors. Our approach is scalable to large datasets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.
Interactive Bayesian Hierarchical Clustering
Authors: Vikram, Sharad and Dasgupta, Sanjoy
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Clustering is a powerful tool in data analysis, but it is often difficult to find a grouping that aligns with a user’s needs. To address this, several methods incorporate constraints obtained from users into clustering algorithms, but unfortunately do not apply to hierarchical clustering. We design an interactive Bayesian algorithm that incorporates user interaction into hierarchical clustering while still utilizing the geometry of the data by sampling a constrained posterior distribution over hierarchies. We also suggest several ways to intelligently query a user. The algorithm, along with the querying schemes, shows promising results on real data.
A Convolutional Attention Network for Extreme Summarization of Source Code
Authors: Allamanis, Miltiadis and Peng, Hao and Sutton, Charles
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Attention mechanisms in neural networks have proved useful for problems in which the input and output do not have fixed dimension. Often there exist features that are locally translation invariant and would be valuable for directing the model’s attention, but previous attentional architectures are not constructed to learn such features specifically. We introduce an attentional neural network that employs convolution on the input tokens to detect local time-invariant and long-range topical attention features in a context-dependent way. We apply this architecture to the problem of extreme summarization of source code snippets into short, descriptive function name-like summaries. Using those features, the model sequentially generates a summary by marginalizing over two attention mechanisms: one that predicts the next summary token based on the attention weights of the input tokens and another that is able to copy a code token as-is directly into the summary. We demonstrate our convolutional attention neural network’s performance on 10 popular Java projects showing that it achieves better performance compared to previous attentional mechanisms.
How to Fake Multiply by a Gaussian Matrix
Authors: Kapralov, Michael and Potluru, Vamsi and Woodruff, David
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Have you ever wanted to multiply an n \times d matrix X, with n ≫d, on the left by an m \times n matrix \tilde G of i.i.d. Gaussian random variables, but could not afford to do it because it was too slow? In this work we propose a new randomized m \times n matrix T, for which one can compute T ⋅X in only O(nnz(X)) + \tilde O(m^1.5 ⋅d^3) time, for which the total variation distance between the distributions T ⋅X and \tilde G ⋅X is as small as desired, i.e., less than any positive constant. Here nnz(X) denotes the number of non-zero entries of X. Assuming nnz(X) ≫m^1.5 ⋅d^3, this is a significant savings over the naïve O(nnz(X) m) time to compute \tilde G ⋅X. Moreover, since the total variation distance is small, we can provably use T ⋅X in place of \tilde G ⋅X in any application and have the same guarantees as if we were using \tilde G ⋅X, up to a small positive constant in error probability. We apply this transform to nonnegative matrix factorization (NMF) and support vector machines (SVM).
Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing
Authors: Gaboardi, Marco and Lim, Hyun and Rogers, Ryan and Vadhan, Salil
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Hypothesis testing is a useful statistical tool in determining whether a given model should be rejected based on a sample from the population. Sample data may contain sensitive information about individuals, such as medical information. Thus it is important to design statistical tests that guarantee the privacy of subjects in the data. In this work, we study hypothesis testing subject to differential privacy, specifically chi-squared tests for goodness of fit for multinomial data and independence between two categorical variables.
Pliable Rejection Sampling
Authors: Erraqabi, Akram and Valko, Michal and Carpentier, Alexandra and Maillard, Odalric
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Rejection sampling is a technique for sampling from difficult distributions. However, its use is limited due to a high rejection rate. Common adaptive rejection sampling methods either work only for very specific distributions or without performance guarantees. In this paper, we present pliable rejection sampling (PRS), a new approach to rejection sampling, where we learn the sampling proposal using a kernel estimator. Since our method builds on rejection sampling, the samples obtained are with high probability i.i.d. and distributed according to f. Moreover, PRS comes with a guarantee on the number of accepted samples.
Differentially Private Policy Evaluation
Authors: Balle, Borja and Gomrokchi, Maziar and Precup, Doina
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We present the first differentially private algorithms for reinforcement learning, which apply to the task of evaluating a fixed policy. We establish two approaches for achieving differential privacy, provide a theoretical analysis of the privacy and utility of the two algorithms, and show promising results on simple empirical examples.
Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning
Authors: Thomas, Philip and Brunskill, Emma
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: 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.
Discrete Deep Feature Extraction: A Theory and New Architectures
Authors: Wiatowski, Thomas and Tschannen, Michael and Stanic, Aleksandar and Grohs, Philipp and Boelcskei, Helmut
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made—for the continuous-time case—in Mallat, 2012, and Wiatowski and Bölcskei, 2015. This paper considers the discrete case, introduces new convolutional neural network architectures, and proposes a mathematical framework for their analysis. Specifically, we establish deformation and translation sensitivity results of local and global nature, and we investigate how certain structural properties of the input signal are reflected in the corresponding feature vectors. Our theory applies to general filters and general Lipschitz-continuous non-linearities and pooling operators. Experiments on handwritten digit classification and facial landmark detection—including feature importance evaluation—complement the theoretical findings.
Efficient Algorithms for Adversarial Contextual Learning
Authors: Syrgkanis, Vasilis and Krishnamurthy, Akshay and Schapire, Robert
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We provide the first oracle efficient sublinear regret algorithms for adversarial versions of the contextual bandit problem. In this problem, the learner repeatedly makes an action on the basis of a context and receives reward for the chosen action, with the goal of achieving reward competitive with a large class of policies. We analyze two settings: i) in the transductive setting the learner knows the set of contexts a priori, ii) in the small separator setting, there exists a small set of contexts such that any two policies behave differently on one of the contexts in the set. Our algorithms fall into the Follow-The-Perturbed-Leader family (Kalai and Vempala, 2005) and achieve regret O(T^3/4\sqrtKłog(N)) in the transductive setting and O(T^2/3 d^3/4 K\sqrtłog(N)) in the separator setting, where T is the number of rounds, K is the number of actions, N is the number of baseline policies, and d is the size of the separator. We actually solve the more general adversarial contextual semi-bandit linear optimization problem, whilst in the full information setting we address the even more general contextual combinatorial optimization. We provide several extensions and implications of our algorithms, such as switching regret and efficient learning with predictable sequences.
Training Deep Neural Networks via Direct Loss Minimization
Authors: Song, Yang and Schwing, Alexander and Richard, and Urtasun, Raquel
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Supervised training of deep neural nets typically relies on minimizing cross-entropy. However, in many domains, we are interested in performing well on metrics specific to the application. In this paper we propose a direct loss minimization approach to train deep neural networks, which provably minimizes the application-specific loss function. This is often non-trivial, since these functions are neither smooth nor decomposable and thus are not amenable to optimization with standard gradient-based methods. We demonstrate the effectiveness of our approach in the context of maximizing average precision for ranking problems. Towards this goal, we develop a novel dynamic programming algorithm that can efficiently compute the weight updates. Our approach proves superior to a variety of baselines in the context of action classification and object detection, especially in the presence of label noise.