mtybilly/Instruct2DS huggingface dataset:
DR-ABC: Approximate Bayesian Computation with Kernel-Based Distribution Regression
Authors: Jovana Mitrovic, Dino Sejdinovic, Yee-Whye Teh
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: 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.
Predictive Entropy Search for Multi-objective Bayesian Optimization
Authors: Daniel Hernandez-Lobato, Jose Hernandez-Lobato, Amar Shah, Ryan Adams
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We present \small PESMO, a Bayesian method for identifying the Pareto set of multi-objective optimization problems, when the functions are expensive to evaluate. \small PESMO chooses the evaluation points to maximally reduce the entropy of the posterior distribution over the Pareto set. The \small PESMO acquisition function is decomposed as a sum of objective-specific acquisition functions, which makes it possible to use the algorithm in \emphdecoupled scenarios in which the objectives can be evaluated separately and perhaps with different costs. This decoupling capability is useful to identify difficult objectives that require more evaluations. \small PESMO also offers gains in efficiency, as its cost scales linearly with the number of objectives, in comparison to the exponential cost of other methods. We compare \small PESMO with other methods on synthetic and real-world problems. The results show that \small PESMO produces better recommendations with a smaller number of evaluations, and that a decoupled evaluation can lead to improvements in performance, particularly when the number of objectives is large.
Rich Component Analysis
Authors: Rong Ge, James Zou
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: In many settings, we have multiple data sets (also called views) that capture different and overlapping aspects of the same phenomenon. We are often interested in finding patterns that are unique to one or to a subset of the views. For example, we might have one set of molecular observations and one set of physiological observations on the same group of individuals, and we want to quantify molecular patterns that are uncorrelated with physiology. Despite being a common problem, this is highly challenging when the correlations come from complex distributions. In this paper, we develop the general framework of Rich Component Analysis (RCA) to model settings where the observations from different views are driven by different sets of latent components, and each component can be a complex, high-dimensional distribution. We introduce algorithms based on cumulant extraction that provably learn each of the components without having to model the other components. We show how to integrate RCA with stochastic gradient descent into a meta-algorithm for learning general models, and demonstrate substantial improvement in accuracy on several synthetic and real datasets in both supervised and unsupervised tasks. Our method makes it possible to learn latent variable models when we don’t have samples from the true model but only samples after complex perturbations.
Black-Box Alpha Divergence Minimization
Authors: Jose Hernandez-Lobato, Yingzhen Li, Mark Rowland, Thang Bui, Daniel Hernandez-Lobato, Richard Turner
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Black-box alpha (BB-α) is a new approximate inference method based on the minimization of α-divergences. BB-αscales to large datasets because it can be implemented using stochastic gradient descent. BB-αcan be applied to complex probabilistic models with little effort since it only requires as input the likelihood function and its gradients. These gradients can be easily obtained using automatic differentiation. By changing the divergence parameter α, the method is able to interpolate between variational Bayes (VB) (α→0) and an algorithm similar to expectation propagation (EP) (α= 1). Experiments on probit regression and neural network regression and classification problems show that BB-αwith non-standard settings of α, such as α= 0.5, usually produces better predictions than with α→0 (VB) or α= 1 (EP).
One-Shot Generalization in Deep Generative Models
Authors: Danilo Rezende,  Shakir, Ivo Danihelka, Karol Gregor, Daan Wierstra
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Humans have an impressive ability to reason about new concepts and experiences from just a single example. In particular, humans have an ability for one-shot generalization: an ability to encounter a new concept, understand its structure, and then be able to generate compelling alternative variations of the concept. We develop machine learning systems with this important capacity by developing new deep generative models, models that combine the representational power of deep learning with the inferential power of Bayesian reasoning. We develop a class of sequential generative models that are built on the principles of feedback and attention. These two characteristics lead to generative models that are among the state-of-the art in density estimation and image generation. We demonstrate the one-shot generalization ability of our models using three tasks: unconditional sampling, generating new exemplars of a given concept, and generating new exemplars of a family of concepts. In all cases our models are able to generate compelling and diverse samples—having seen new examples just once—providing an important class of general-purpose models for one-shot machine learning.
Optimal Classification with Multivariate Losses
Authors: Nagarajan Natarajan, Oluwasanmi Koyejo, Pradeep Ravikumar, Inderjit Dhillon
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Multivariate loss functions are extensively employed in several prediction tasks arising in Information Retrieval. Often, the goal in the tasks is to minimize expected loss when retrieving relevant items from a presented set of items, where the expectation is with respect to the joint distribution over item sets. Our key result is that for most multivariate losses, the expected loss is provably optimized by sorting the items by the conditional probability of label being positive and then selecting top k items. Such a result was previously known only for the F-measure. Leveraging on the optimality characterization, we give an algorithm for estimating optimal predictions in practice with runtime quadratic in size of item sets for many losses. We provide empirical results on benchmark datasets, comparing the proposed algorithm to state-of-the-art methods for optimizing multivariate losses.
A ranking approach to global optimization
Authors: Cedric Malherbe, Emile Contal, Nicolas Vayatis
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We consider the problem of maximizing an unknown function f over a compact and convex set using as few observations f(x) as possible. We observe that the optimization of the function f essentially relies on learning the induced bipartite ranking rule of f. Based on this idea, we relate global optimization to bipartite ranking which allows to address problems with high dimensional input space, as well as cases of functions with weak regularity properties. The paper introduces novel meta-algorithms for global optimization which rely on the choice of any bipartite ranking method. Theoretical properties are provided as well as convergence guarantees and equivalences between various optimization methods are obtained as a by-product. Eventually, numerical evidence is given to show that the main algorithm of the paper which adapts empirically to the underlying ranking structure essentially outperforms existing state-of-the-art global optimization algorithms in typical benchmarks.
Parallel and Distributed Block-Coordinate Frank-Wolfe Algorithms
Authors: Yu-Xiang Wang, Veeranjaneyulu Sadhanala, Wei Dai, Willie Neiswanger, Suvrit Sra, Eric Xing
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We study parallel and distributed Frank-Wolfe algorithms; the former on shared memory machines with mini-batching, and the latter in a delayed update framework. In both cases, we perform computations asynchronously whenever possible. We assume block-separable constraints as in Block-Coordinate Frank-Wolfe (BCFW) method (Lacoste et. al., 2013) , but our analysis subsumes BCFW and reveals problem-dependent quantities that govern the speedups of our methods over BCFW. A notable feature of our algorithms is that they do not depend on worst-case bounded delays, but only (mildly) on **expected** delays, making them robust to stragglers and faulty worker threads. We present experiments on structural SVM and Group Fused Lasso, and observe significant speedups over competing state-of-the-art (and synchronous) methods.
Autoencoding beyond pixels using a learned similarity metric
Authors: Anders Boesen Lindbo Larsen, Søren Kaae Sønderby, Hugo Larochelle, Ole Winther
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We present an autoencoder that leverages learned representations to better measure similarities in data space. By combining a variational autoencoder (VAE) with a generative adversarial network (GAN) we can use learned feature representations in the GAN discriminator as basis for the VAE reconstruction objective. Thereby, we replace element-wise errors with feature-wise errors to better capture the data distribution while offering invariance towards e.g. translation. We apply our method to images of faces and show that it outperforms VAEs with element-wise similarity measures in terms of visual fidelity. Moreover, we show that the method learns an embedding in which high-level abstract visual features (e.g. wearing glasses) can be modified using simple arithmetic.
Ensuring Rapid Mixing and Low Bias for Asynchronous Gibbs Sampling
Authors: Christopher De Sa, Chris Re, Kunle Olukotun
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Gibbs sampling is a Markov chain Monte Carlo technique commonly used for estimating marginal distributions. To speed up Gibbs sampling, there has recently been interest in parallelizing it by executing asynchronously. While empirical results suggest that many models can be efficiently sampled asynchronously, traditional Markov chain analysis does not apply to the asynchronous case, and thus asynchronous Gibbs sampling is poorly understood. In this paper, we derive a better understanding of the two main challenges of asynchronous Gibbs: bias and mixing time. We show experimentally that our theoretical results match practical outcomes.
Simultaneous Safe Screening of Features and Samples in Doubly Sparse Modeling
Authors: Atsushi Shibagaki, Masayuki Karasuyama, Kohei Hatano, Ichiro Takeuchi
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The problem of learning a sparse model is conceptually interpreted as the process of identifying active features/samples and then optimizing the model over them. Recently introduced safe screening allows us to identify a part of non-active features/samples. So far, safe screening has been individually studied either for feature screening or for sample screening. In this paper, we introduce a new approach for safely screening features and samples simultaneously by alternatively iterating feature and sample screening steps. A significant advantage of considering them simultaneously rather than individually is that they have a synergy effect in the sense that the results of the previous safe feature screening can be exploited for improving the next safe sample screening performances, and vice-versa. We first theoretically investigate the synergy effect, and then illustrate the practical advantage through intensive numerical experiments for problems with large numbers of features and samples.
Anytime optimal algorithms in stochastic multi-armed bandits
Authors: Rémy Degenne, Vianney Perchet
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We introduce an anytime algorithm for stochastic multi-armed bandit with optimal distribution free and distribution dependent bounds (for a specific family of parameters). The performances of this algorithm (as well as another one motivated by the conjectured optimal bound) are evaluated empirically. A similar analysis is provided with full information, to serve as a benchmark.
Bounded Off-Policy Evaluation with Missing Data for Course Recommendation and Curriculum Design
Authors: William Hoiles, Mihaela Schaar
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Successfully recommending personalized course schedules is a difficult problem given the diversity of students knowledge, learning behaviour, and goals. This paper presents personalized course recommendation and curriculum design algorithms that exploit logged student data. The algorithms are based on the regression estimator for contextual multi-armed bandits with a penalized variance term. Guarantees on the predictive performance of the algorithms are provided using empirical Bernstein bounds. We also provide guidelines for including expert domain knowledge into the recommendations. Using undergraduate engineering logged data from a post-secondary institution we illustrate the performance of these algorithms.
On collapsed representation of hierarchical Completely Random Measures
Authors: Gaurav Pandey, Ambedkar Dukkipati
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: The aim of the paper is to provide an exact approach for generating a Poisson process sampled from a hierarchical CRM, without having to instantiate the infinitely many atoms of the random measures. We use completely random measures (CRM) and hierarchical CRM to define a prior for Poisson processes. We derive the marginal distribution of the resultant point process, when the underlying CRM is marginalized out. Using well known properties unique to Poisson processes, we were able to derive an exact approach for instantiating a Poisson process with a hierarchical CRM prior. Furthermore, we derive Gibbs sampling strategies for hierarchical CRM models based on Chinese restaurant franchise sampling scheme. As an example, we present the sum of generalized gamma process (SGGP), and show its application in topic-modelling. We show that one can determine the power-law behaviour of the topics and words in a Bayesian fashion, by defining a prior on the parameters of SGGP.
From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification
Authors: Andre Martins, Ramon Astudillo
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose sparsemax, a new activation function similar to the traditional softmax, but able to output sparse probabilities. After deriving its properties, we show how its Jacobian can be efficiently computed, enabling its use in a network trained with backpropagation. Then, we propose a new smooth and convex loss function which is the sparsemax analogue of the logistic loss. We reveal an unexpected connection between this new loss and the Huber classification loss. We obtain promising empirical results in multi-label classification problems and in attention-based neural networks for natural language inference. For the latter, we achieve a similar performance as the traditional softmax, but with a selective, more compact, attention focus.
Black-box Optimization with a Politician
Authors: Sebastien Bubeck, Yin Tat Lee
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose a new framework for black-box convex optimization which is well-suited for situations where gradient computations are expensive. We derive a new method for this framework which leverages several concepts from convex optimization, from standard first-order methods (e.g. gradient descent or quasi-Newton methods) to analytical centers (i.e. minimizers of self-concordant barriers). We demonstrate empirically that our new technique compares favorably with state of the art algorithms (such as BFGS).
Gaussian process nonparametric tensor estimator and its minimax optimality
Authors: Heishiro Kanagawa, Taiji Suzuki, Hayato Kobayashi, Nobuyuki Shimizu, Yukihiro Tagami
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We investigate the statistical efficiency of a nonparametric Gaussian process method for a nonlinear tensor estimation problem. Low-rank tensor estimation has been used as a method to learn higher order relations among several data sources in a wide range of applications, such as multi-task learning, recommendation systems, and spatiotemporal analysis. We consider a general setting where a common linear tensor learning is extended to a nonlinear learning problem in reproducing kernel Hilbert space and propose a nonparametric Bayesian method based on the Gaussian process method. We prove its statistical convergence rate without assuming any strong convexity, such as restricted strong convexity. Remarkably, it is shown that our convergence rate achieves the minimax optimal rate. We apply our proposed method to multi-task learning and show that our method significantly outperforms existing methods through numerical experiments on real-world data sets.
No-Regret Algorithms for Heavy-Tailed Linear Bandits
Authors: Andres Munoz Medina, Scott Yang
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We analyze the problem of linear bandits under heavy tailed noise. Most of of the work on linear bandits has been based on the assumption of bounded or sub-Gaussian noise. However, this assumption is often violated in common scenarios such as financial markets. We present two algorithms to tackle this problem: one based on dynamic truncation and one based on a median of means estimator. We show that, when the noise admits admits only a 1 + εmoment, these algorithms are still able to achieve regret in \widetildeO(T^\frac2 + ε2(1 + ε)) and \widetildeO(T^\frac1+ 2ε1 + 3 ε) respectively. In particular, they guarantee sublinear regret as long as the noise has finite variance. We also present empirical results showing that our algorithms achieve a better performance than the current state of the art for bounded noise when the L_∞bound on the noise is large yet the 1 + εmoment of the noise is small.
Extended and Unscented Kitchen Sinks
Authors: Edwin Bonilla, Daniel Steinberg, Alistair Reid
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We propose a scalable multiple-output generalization of unscented and extended Gaussian processes. These algorithms have been designed to handle general likelihood models by linearizing them using a Taylor series or the Unscented Transform in a variational inference framework. We build upon random feature approximations of Gaussian process covariance functions and show that, on small-scale single-task problems, our methods can attain similar performance as the original algorithms while having less computational cost. We also evaluate our methods at a larger scale on MNIST and on a seismic inversion which is inherently a multi-task problem.
Matrix Eigen-decomposition via Doubly Stochastic Riemannian Optimization
Authors: Zhiqiang Xu, Peilin Zhao, Jianneng Cao, Xiaoli Li
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Matrix eigen-decomposition is a classic and long-standing problem that plays a fundamental role in scientific computing and machine learning. Despite some existing algorithms for this inherently non-convex problem, the study remains inadequate for the need of large data nowadays. To address this gap, we propose a Doubly Stochastic Riemannian Gradient EIGenSolver, DSRG-EIGS, where the double stochasticity comes from the generalization of the stochastic Euclidean gradient ascent and the stochastic Euclidean coordinate ascent to Riemannian manifolds. As a result, it induces a greatly reduced complexity per iteration, enables the algorithm to completely avoid the matrix inversion, and consequently makes it well-suited to large-scale applications. We theoretically analyze its convergence properties and empirically validate it on real-world datasets. Encouraging experimental results demonstrate its advantages over the deterministic counterparts.
Recommendations as Treatments: Debiasing Learning and Evaluation
Authors: Tobias Schnabel, Adith Swaminathan, Ashudeep Singh, Navin Chandak, Thorsten Joachims
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Most data for evaluating and training recommender systems is subject to selection biases, either through self-selection by the users or through the actions of the recommendation system itself. In this paper, we provide a principled approach to handle selection biases by adapting models and estimation techniques from causal inference. The approach leads to unbiased performance estimators despite biased data, and to a matrix factorization method that provides substantially improved prediction performance on real-world data. We theoretically and empirically characterize the robustness of the approach, and find that it is highly practical and scalable.
ForecastICU: A Prognostic Decision Support System for Timely Prediction of Intensive Care Unit Admission
Authors: Jinsung Yoon, Ahmed Alaa, Scott Hu, Mihaela Schaar
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We develop ForecastICU: a prognostic decision support system that monitors hospitalized patients and prompts alarms for intensive care unit (ICU) admissions. ForecastICU is first trained in an offline stage by constructing a Bayesian belief system that corresponds to its belief about how trajectories of physiological data streams of the patient map to a clinical status. After that, ForecastICU monitors a new patient in real-time by observing her physiological data stream, updating its belief about her status over time, and prompting an alarm whenever its belief process hits a predefined threshold (confidence). Using a real-world dataset obtained from UCLA Ronald Reagan Medical Center, we show that ForecastICU can predict ICU admissions 9 hours before a physician’s decision (for a sensitivity of 40% and a precision of 50%). Also, ForecastICU performs consistently better than other state-of-the-art machine learning algorithms in terms of sensitivity, precision, and timeliness: it can predict ICU admissions 3 hours earlier, and offers a 7.8% gain in sensitivity and a 5.1% gain in precision compared to the best state-of-the-art algorithm. Moreover, ForecastICU offers an area under curve (AUC) gain of 22.3% compared to the Rothman index, which is the currently deployed technology in most hospital wards.
An optimal algorithm for the Thresholding Bandit Problem
Authors: Andrea Locatelli, Maurilio Gutzeit, Alexandra Carpentier
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We study a specific combinatorial pure exploration stochastic bandit problem where the learner aims at finding the set of arms whose means are above a given threshold, up to a given precision, and for a fixed time horizon. We propose a parameter-free algorithm based on an original heuristic, and prove that it is optimal for this problem by deriving matching upper and lower bounds. To the best of our knowledge, this is the first non-trivial pure exploration setting with fixed budget for which provably optimal strategies are constructed.
Fast Parameter Inference in Nonlinear Dynamical Systems using Iterative Gradient Matching
Authors: Mu Niu, Simon Rogers, Maurizio Filippone, Dirk Husmeier
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Parameter inference in mechanistic models of coupled differential equations is a topical and challenging problem. We propose a new method based on kernel ridge regression and gradient matching, and an objective function that simultaneously encourages goodness of fit and penalises inconsistencies with the differential equations. Fast minimisation is achieved by exploiting partial convexity inherent in this function, and setting up an iterative algorithm in the vein of the EM algorithm. An evaluation of the proposed method on various benchmark data suggests that it compares favourably with state-of-the-art alternatives.
Structured and Efficient Variational Deep Learning with Matrix Gaussian Posteriors
Authors: Christos Louizos, Max Welling
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian (Gupta & Nagar ’99) parameter posterior distribution where we explicitly model the covariance among the input and output dimensions of each layer. Furthermore, with approximate covariance matrices we can achieve a more efficient way to represent those correlations that is also cheaper than fully factorized parameter posteriors. We further show that with the “local reprarametrization trick" (Kingma & Welling ’15) on this posterior distribution we arrive at a Gaussian Process (Rasmussen ’06) interpretation of the hidden units in each layer and we, similarly with (Gal & Ghahramani ’15), provide connections with deep Gaussian processes. We continue in taking advantage of this duality and incorporate “pseudo-data” (Snelson & Ghahramani ’05) in our model, which in turn allows for more efficient posterior sampling while maintaining the properties of the original model. The validity of the proposed approach is verified through extensive experiments.
Learning Granger Causality for Hawkes Processes
Authors: Hongteng Xu, Mehrdad Farajtabar, Hongyuan Zha
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Learning Granger causality for general point processes is a very challenging task. We propose an effective method learning Granger causality for a special but significant type of point processes — Hawkes processes. Focusing on Hawkes processes, we reveal the relationship between Hawkes process’s impact functions and its Granger causality graph. Specifically, our model represents impact functions using a series of basis functions and recovers the Granger causality graph via group sparsity of the impact functions’ coefficients. We propose an effective learning algorithm combining a maximum likelihood estimator (MLE) with a sparse-group-lasso (SGL) regularizer. Additionally, the pairwise similarity between the dimensions of the process is considered when their clustering structure is available. We analyze our learning method and discuss the selection of the basis functions. Experiments on synthetic data and real-world data show that our method can learn the Granger causality graph and the triggering patterns of Hawkes processes simultaneously.
Neural Variational Inference for Text Processing
Authors: Yishu Miao, Lei Yu, Phil Blunsom
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Recent advances in neural variational inference have spawned a renaissance in deep latent variable models. In this paper we introduce a generic variational inference framework for generative and conditional models of text. While traditional variational methods derive an analytic approximation for the intractable distributions over latent variables, here we construct an inference network conditioned on the discrete text input to provide the variational distribution. We validate this framework on two very different text modelling applications, generative document modelling and supervised question answering. Our neural variational document model combines a continuous stochastic document representation with a bag-of-words generative model and achieves the lowest reported perplexities on two standard test corpora. The neural answer selection model employs a stochastic representation layer within an attention mechanism to extract the semantics between a question and answer pair. On two question answering benchmarks this model exceeds all previous published benchmarks.
Dictionary Learning for Massive Matrix Factorization
Authors: Arthur Mensch, Julien Mairal, Bertrand Thirion, Gael Varoquaux
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized methods, that reduce the complexity in one of the matrix dimension, but not in both of them. In this paper, we tackle very large matrices in both dimensions. We propose a new factorization method that scales gracefully to terabyte-scale datasets. Those could not be processed by previous algorithms in a reasonable amount of time. We demonstrate the efficiency of our approach on massive functional Magnetic Resonance Imaging (fMRI) data, and on matrix completion problems for recommender systems, where we obtain significant speed-ups compared to state-of-the art coordinate descent methods.
Pixel Recurrent Neural Networks
Authors: Aäron van den Oord, Nal Kalchbrenner, Koray Kavukcuoglu
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: Modeling the distribution of natural images is a landmark problem in unsupervised learning. This task requires an image model that is at once expressive, tractable and scalable. We present a deep neural network that sequentially predicts the pixels in an image along the two spatial dimensions. Our method models the discrete probability of the raw pixel values and encodes the complete set of dependencies in the image. Architectural novelties include fast two-dimensional recurrent layers and an effective use of residual connections in deep recurrent networks. We achieve log-likelihood scores on natural images that are considerably better than the previous state of the art. Our main results also provide benchmarks on the diverse ImageNet dataset. Samples generated from the model appear crisp, varied and globally coherent.
Why Most Decisions Are Easy in Tetris---And Perhaps in Other Sequential Decision Problems, As Well
Authors: Özgür Şimşek, Simón Algorta, Amit Kothiyal
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We examined the sequence of decision problems that are encountered in the game of Tetris and found that most of the problems are easy in the following sense: One can choose well among the available actions without knowing an evaluation function that scores well in the game. This is a consequence of three conditions that are prevalent in the game: simple dominance, cumulative dominance, and noncompensation. These conditions can be exploited to develop faster and more effective learning algorithms. In addition, they allow certain types of domain knowledge to be incorporated with ease into a learning algorithm. Among the sequential decision problems we encounter, it is unlikely that Tetris is unique or rare in having these properties.
Gaussian quadrature for matrix inverse forms with applications
Authors: Chengtao Li, Suvrit Sra, Stefanie Jegelka
Published in: Proceedings of The 33rd International Conference on Machine Learning (Main Conference Track), 2016

Abstract: We present a framework for accelerating a spectrum of machine learning algorithms that require computation of \emphbilinear inverse forms u^T A^-1u, where A is a positive definite matrix and u a given vector. Our framework is built on Gauss-type quadrature and easily scales to large, sparse matrices. Further, it allows retrospective computation of lower and upper bounds on u^T A^-1u, which in turn accelerates several algorithms. We prove that these bounds tighten iteratively and converge at a linear (geometric) rate. To our knowledge, ours is the first work to demonstrate these key properties of Gauss-type quadrature, which is a classical and deeply studied topic. We illustrate empirical consequences of our results by using quadrature to accelerate machine learning tasks involving determinantal point processes and submodular optimization, and observe tremendous speedups in several instances.
Train and Test Tightness of LP Relaxations in Structured Prediction
Authors: Ofer Meshi, Mehrdad Mahdavi, Adrian Weller, David Sontag
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: Raman Arora, Poorya Mianjy, Teodor Marinov
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: Mehmet Basbug, Barbara Engelhardt
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, Jordan Boyd-Graber, Kevin Kwok, III, Hal Daumé
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: Xiangyu Wang, David Dunson, Chenlei Leng
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: Zheng Qu, Peter Richtarik, Martin Takac, Olivier Fercoq
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: Elad Hazan, Kfir Yehuda Levy, Shai Shalev-Shwartz
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: Adam Santoro, Sergey Bartunov, Matthew Botvinick, Daan Wierstra, Timothy Lillicrap
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: Ran Dai, Rina Barber
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: Julien Pérolat, Bilal Piot, Matthieu Geist, Bruno Scherrer, Olivier Pietquin
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: Robert Gower, Donald Goldfarb, Peter Richtarik
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.