mtybilly/Instruct2DS huggingface dataset:
MRA-based Statistical Learning from Incomplete Rankings
Authors: Eric Sibony, Stéphan Clemençon, Jérémie Jakubowicz
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Statistical analysis of rank data describing preferences over small and variable subsets of a potentially large ensemble of items 1, ..., n is a very challenging problem. It is motivated by a wide variety of modern applications, such as recommender systems or search engines. However, very few inference methods have been documented in the literature to learn a ranking model from such incomplete rank data. The goal of this paper is twofold: it develops a rigorous mathematical framework for the problem of learning a ranking model from incomplete rankings and introduces a novel general statistical method to address it. Based on an original concept of multi-resolution analysis (MRA) of incomplete rankings, it finely adapts to any observation setting, leading to a statistical accuracy and an algorithmic complexity that depend directly on the complexity of the observed data. Beyond theoretical guarantees, we also provide experimental results that show its statistical performance.
Risk and Regret of Hierarchical Bayesian Learners
Authors: Jonathan Huggins, Josh Tenenbaum
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Common statistical practice has shown that the full power of Bayesian methods is not realized until hierarchical priors are used, as these allow for greater “robustness” and the ability to “share statistical strength.” Yet it is an ongoing challenge to provide a learning-theoretically sound formalism of such notions that: offers practical guidance concerning when and how best to utilize hierarchical models; provides insights into what makes for a good hierarchical prior; and, when the form of the prior has been chosen, can guide the choice of hyperparameter settings. We present a set of analytical tools for understanding hierarchical priors in both the online and batch learning settings. We provide regret bounds under log-loss, which show how certain hierarchical models compare, in retrospect, to the best single model in the model class. We also show how to convert a Bayesian log-loss regret bound into a Bayesian risk bound for any bounded loss, a result which may be of independent interest. Risk and regret bounds for Student’s t and hierarchical Gaussian priors allow us to formalize the concepts of “robustness” and “sharing statistical strength.” Priors for feature selection are investigated as well. Our results suggest that the learning-theoretic benefits of using hierarchical priors can often come at little cost on practical problems.
Towards a Learning Theory of Cause-Effect Inference
Authors: David Lopez-Paz, Krikamol Muandet, Bernhard Schölkopf, Iliya Tolstikhin
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection (S_i,l_i)_i=1^n, where each S_i is a sample drawn from the probability distribution of X_i \times Y_i, and l_i is a binary label indicating whether “X_i \to Y_i” or “X_i ←Y_i”. Given these data, we build a causal inference rule in two steps. First, we featurize each S_i using the kernel mean embedding associated with some characteristic kernel. Second, we train a binary classifier on such embeddings to distinguish between causal directions. We present generalization bounds showing the statistical consistency and learning rates of the proposed approach, and provide a simple implementation that achieves state-of-the-art cause-effect inference. Furthermore, we extend our ideas to infer causal relationships between more than two variables.
DRAW: A Recurrent Neural Network For Image Generation
Authors: Karol Gregor, Ivo Danihelka, Alex Graves, Danilo Rezende, Daan Wierstra
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: This paper introduces the Deep Recurrent Attentive Writer (DRAW) architecture for image generation with neural networks. DRAW networks combine a novel spatial attention mechanism that mimics the foveation of the human eye, with a sequential variational auto-encoding framework that allows for the iterative construction of complex images. The system substantially improves on the state of the art for generative models on MNIST, and, when trained on the Street View House Numbers dataset, it is able to generate images that are indistinguishable from real data with the naked eye.
Multiview Triplet Embedding: Learning Attributes in Multiple Maps
Authors: Ehsan Amid, Antti Ukkonen
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: For humans, it is usually easier to make statements about the similarity of objects in relative, rather than absolute terms. Moreover, subjective comparisons of objects can be based on a number of different and independent attributes. For example, objects can be compared based on their shape, color, etc. In this paper, we consider the problem of uncovering these hidden attributes given a set of relative distance judgments in the form of triplets. The attribute that was used to generate a particular triplet in this set is unknown. Such data occurs, e.g., in crowdsourcing applications where the triplets are collected from a large group of workers. We propose the Multiview Triplet Embedding (MVTE) algorithm that produces a number of low-dimensional maps, each corresponding to one of the hidden attributes. The method can be used to assess how many different attributes were used to create the triplets, as well as to assess the difficulty of a distance comparison task, and find objects that have multiple interpretations in relation to the other objects.
Distributed Gaussian Processes
Authors: Marc Deisenroth, Jun Wei Ng
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: To scale Gaussian processes (GPs) to large data sets we introduce the robust Bayesian Committee Machine (rBCM), a practical and scalable product-of-experts model for large-scale distributed GP regression. Unlike state-of-the-art sparse GP approximations, the rBCM is conceptually simple and does not rely on inducing or variational parameters. The key idea is to recursively distribute computations to independent computational units and, subsequently, recombine them to form an overall result. Efficient closed-form inference allows for straightforward parallelisation and distributed computations with a small memory footprint. The rBCM is independent of the computational graph and can be used on heterogeneous computing infrastructures, ranging from laptops to clusters. With sufficient computing resources our distributed GP model can handle arbitrarily large data sets.
Guaranteed Tensor Decomposition: A Moment Approach
Authors: Gongguo Tang, Parikshit Shah
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We develop a theoretical and computational framework to perform guaranteed tensor decomposition, which also has the potential to accomplish other tensor tasks such as tensor completion and denoising. We formulate tensor decomposition as a problem of measure estimation from moments. By constructing a dual polynomial, we demonstrate that measure optimization returns the correct CP decomposition under an incoherence condition on the rank-one factors. To address the computational challenge, we present a hierarchy of semidefinite programs based on sums-of-squares relaxations of the measure optimization problem. By showing that the constructed dual polynomial is a sum-of-squares modulo the sphere, we prove that the smallest SDP in the relaxation hierarchy is exact and the decomposition can be extracted from the solution under the same incoherence condition. One implication is that the tensor nuclear norm can be computed exactly using the smallest SDP as long as the rank-one factors of the tensor are incoherent. Numerical experiments are conducted to test the performance of the moment approach.
$\ell_1,p$-Norm Regularization: Error Bounds and Convergence Rate Analysis of First-Order Methods
Authors: Zirui Zhou, Qi Zhang, Anthony Man-Cho So
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Recently, \ell_1,p-regularization has been widely used to induce structured sparsity in the solutions to various optimization problems. Motivated by the desire to analyze the convergence rate of first-order methods, we show that for a large class of \ell_1,p-regularized problems, an error bound condition is satisfied when p∈[1,2] or p=∞but fails to hold for any p∈(2,∞). Based on this result, we show that many first-order methods enjoy an asymptotic linear rate of convergence when applied to \ell_1,p-regularized linear or logistic regression with p∈[1,2] or p=∞. By contrast, numerical experiments suggest that for the same class of problems with p∈(2,∞), the aforementioned methods may not converge linearly.
Consistent estimation of dynamic and multi-layer block models
Authors: Qiuyi Han, Kevin Xu, Edoardo Airoldi
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Significant progress has been made recently on theoretical analysis of estimators for the stochastic block model (SBM). In this paper, we consider the multi-graph SBM, which serves as a foundation for many application settings including dynamic and multi-layer networks. We explore the asymptotic properties of two estimators for the multi-graph SBM, namely spectral clustering and the maximum-likelihood estimate (MLE), as the number of layers of the multi-graph increases. We derive sufficient conditions for consistency of both estimators and propose a variational approximation to the MLE that is computationally feasible for large networks. We verify the sufficient conditions via simulation and demonstrate that they are practical. In addition, we apply the model to two real data sets: a dynamic social network and a multi-layer social network with several types of relations.
On the Rate of Convergence and Error Bounds for LSTD($łambda$)
Authors: Manel Tagorti, Bruno Scherrer
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We consider LSTD(λ), the least-squares temporal-difference algorithm with eligibility traces algorithm proposed by Boyan (2002). It computes a linear approximation of the value function of a fixed policy in a large Markov Decision Process. Under a β-mixing assumption, we derive, for any value of λ∈(0,1), a high-probability bound on the rate of convergence of this algorithm to its limit. We deduce a high-probability bound on the error of this algorithm, that extends (and slightly improves) that derived by Lazaric et al. (2012) in the specific case where λ=0. In the context of temporal-difference algorithms with value function approximation, this analysis is to our knowledge the first to provide insight on the choice of the eligibility-trace parameter λwith respect to the approximation quality of the space and the number of samples.
Variational Inference with Normalizing Flows
Authors: Danilo Rezende, Shakir Mohamed
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: The choice of the approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.
Controversy in mechanistic modelling with Gaussian processes
Authors: Benn Macdonald, Catherine Higham, Dirk Husmeier
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Parameter inference in mechanistic models based on non-affine differential equations is computationally onerous, and various faster alternatives based on gradient matching have been proposed. A particularly promising approach is based on nonparametric Bayesian modelling with Gaussian processes, which exploits the fact that a Gaussian process is closed under differentiation. However, two alternative paradigms have been proposed. The first paradigm, proposed at NIPS 2008 and AISTATS 2013, is based on a product of experts approach and a marginalization over the derivatives of the state variables. The second paradigm, proposed at ICML 2014, is based on a probabilistic generative model and a marginalization over the state variables. The claim has been made that this leads to better inference results. In the present article, we offer a new interpretation of the second paradigm, which highlights the underlying assumptions, approximations and limitations. In particular, we show that the second paradigm suffers from an intrinsic identifiability problem, which the first paradigm is not affected by.
Convex Learning of Multiple Tasks and their Structure
Authors: Carlo Ciliberto, Youssef Mroueh, Tomaso Poggio, Lorenzo Rosasco
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Reducing the amount of human supervision is a key problem in machine learning and a natural approach is that of exploiting the relations (structure) among different tasks. This is the idea at the core of multi-task learning. In this context a fundamental question is how to incorporate the tasks structure in the learning problem. We tackle this question by studying a general computational framework that allows to encode a-priori knowledge of the tasks structure in the form of a convex penalty; in this setting a variety of previously proposed methods can be recovered as special cases, including linear and non-linear approaches. Within this framework, we show that tasks and their structure can be efficiently learned considering a convex optimization problem that can be approached by means of block coordinate methods such as alternating minimization and for which we prove convergence to the global minimum.
K-hyperplane Hinge-Minimax Classifier
Authors: Margarita Osadchy, Tamir Hazan, Daniel Keren
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We explore a novel approach to upper bound the misclassification error for problems with data comprising a small number of positive samples and a large number of negative samples. We assign the hinge-loss to upper bound the misclassification error of the positive examples and use the minimax risk to upper bound the misclassification error with respect to the worst case distribution that generates the negative examples. This approach is computationally appealing since the majority of training examples (belonging to the negative class) are represented by the statistics of their distribution, in contrast to kernel SVM which produces a very large number of support vectors in such settings. We derive empirical risk bounds for linear and non-linear classification and show that they are dimensionally independent and decay as 1/\sqrtm for m samples. We propose an efficient algorithm for training an intersection of finite number of hyperplane and demonstrate its effectiveness on real data, including letter and scene recognition.
Non-Stationary Approximate Modified Policy Iteration
Authors: Boris Lesner, Bruno Scherrer
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We consider the infinite-horizon γ-discounted optimal control problem formalized by Markov Decision Processes. Running any instance of Modified Policy Iteration—a family of algorithms that can interpolate between Value and Policy Iteration—with an error εat each iteration is known to lead to stationary policies that are at least \frac2γε(1-γ)^2-optimal. Variations of Value and Policy Iteration, that build \ell-periodic non-stationary policies, have recently been shown to display a better \frac2γε(1-γ)(1-γ^\ell)-optimality guarantee. Our first contribution is to describe a new algorithmic scheme, Non-Stationary Modified Policy Iteration, a family of algorithms parameterized by two integers m \ge 0 and \ell \ge 1 that generalizes all the above mentionned algorithms. While m allows to interpolate between Value-Iteration-style and Policy-Iteration-style updates, \ell specifies the period of the non-stationary policy that is output. We show that this new family of algorithms also enjoys the improved \frac2γε(1-γ)(1-γ^\ell)-optimality guarantee. Perhaps more importantly, we show, by exhibiting an original problem instance, that this guarantee is tight for all m and \ell; this tightness was to our knowledge only proved two specific cases, Value Iteration (m=0,\ell=1) and Policy Iteration (m=∞,\ell=1).
Entropy evaluation based on confidence intervals of frequency estimates : Application to the learning of decision trees
Authors: Mathieu Serrurier, Henri Prade
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Entropy gain is widely used for learning decision trees. However, as we go deeper downward the tree, the examples become rarer and the faithfulness of entropy decreases. Thus, misleading choices and over-fitting may occur and the tree has to be adjusted by using an early-stop criterion or post pruning algorithms. However, these methods still depends on the choices previously made, which may be unsatisfactory. We propose a new cumulative entropy function based on confidence intervals on frequency estimates that together considers the entropy of the probability distribution and the uncertainty around the estimation of its parameters. This function takes advantage of the ability of a possibility distribution to upper bound a family of probabilities previously estimated from a limited set of examples and of the link between possibilistic specificity order and entropy. The proposed measure has several advantages over the classical one. It performs significant choices of split and provides a statistically relevant stopping criterion that allows the learning of trees whose size is well-suited w.r.t. the available data. On the top of that, it also provides a reasonable estimator of the performances of a decision tree. Finally, we show that it can be used for designing a simple and efficient online learning algorithm.
Geometric Conditions for Subspace-Sparse Recovery
Authors: Chong You, Rene Vidal
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Given a dictionary Π and a signal ξ= Π \mathbf x generated by a few \textitlinearly independent columns of Π, classical sparse recovery theory deals with the problem of uniquely recovering the sparse representation \mathbf x of ξ. In this work, we consider the more general case where ξlies in a low-dimensional subspace spanned by a few columns of Π, which are possibly \textitlinearly dependent. In this case, \mathbf x may not unique, and the goal is to recover any subset of the columns of Π that spans the subspace containing ξ. We call such a representation \mathbf x \textitsubspace-sparse. We study conditions under which existing pursuit methods recover a subspace-sparse representation. Such conditions reveal important geometric insights and have implications for the theory of classical sparse recovery as well as subspace clustering.
An Empirical Study of Stochastic Variational Inference Algorithms for the Beta Bernoulli Process
Authors: Amar Shah, David Knowles, Zoubin Ghahramani
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Stochastic variational inference (SVI) is emerging as the most promising candidate for scaling inference in Bayesian probabilistic models to large datasets. However, the performance of these methods has been assessed primarily in the context of Bayesian topic models, particularly latent Dirichlet allocation (LDA). Deriving several new algorithms, and using synthetic, image and genomic datasets, we investigate whether the understanding gleaned from LDA applies in the setting of sparse latent factor models, specifically beta process factor analysis (BPFA). We demonstrate that the big picture is consistent: using Gibbs sampling within SVI to maintain certain posterior dependencies is extremely effective. However, we also show that different posterior dependencies are important in BPFA relative to LDA.
Long Short-Term Memory Over Recursive Structures
Authors: Xiaodan Zhu, Parinaz Sobihani, Hongyu Guo
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: The chain-structured long short-term memory (LSTM) has showed to be effective in a wide range of problems such as speech recognition and machine translation. In this paper, we propose to extend it to tree structures, in which a memory cell can reflect the history memories of multiple child cells or multiple descendant cells in a recursive process. We call the model S-LSTM, which provides a principled way of considering long-distance interaction over hierarchies, e.g., language or image parse structures. We leverage the models for semantic composition to understand the meaning of text, a fundamental problem in natural language understanding, and show that it outperforms a state-of-the-art recursive model by replacing its composition layers with the S-LSTM memory blocks. We also show that utilizing the given structures is helpful in achieving a performance better than that without considering the structures.
Weight Uncertainty in Neural Network
Authors: Charles Blundell, Julien Cornebise, Koray Kavukcuoglu, Daan Wierstra
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We introduce a new, efficient, principled and backpropagation-compatible algorithm for learning a probability distribution on the weights of a neural network, called Bayes by Backprop. It regularises the weights by minimising a compression cost, known as the variational free energy or the expected lower bound on the marginal likelihood. We show that this principled kind of regularisation yields comparable performance to dropout on MNIST classification. We then demonstrate how the learnt uncertainty in the weights can be used to improve generalisation in non-linear regression problems, and how this weight uncertainty can be used to drive the exploration-exploitation trade-off in reinforcement learning.
Learning Submodular Losses with the Lovasz Hinge
Authors: Jiaqian Yu, Matthew Blaschko
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Learning with non-modular losses is an important problem when sets of predictions are made simultaneously. The main tools for constructing convex surrogate loss functions for set prediction are margin rescaling and slack rescaling. In this work, we show that these strategies lead to tight convex surrogates iff the underlying loss function is increasing in the number of incorrect predictions. However, gradient or cutting-plane computation for these functions is NP-hard for non-supermodular loss functions. We propose instead a novel convex surrogate loss function for submodular losses, the Lovasz hinge, which leads to O(p log p) complexity with O(p) oracle accesses to the loss function to compute a gradient or cutting-plane. As a result, we have developed the first tractable convex surrogates in the literature for submodular losses. We demonstrate the utility of this novel convex surrogate through a real world image labeling task.
Coordinate Descent Converges Faster with the Gauss-Southwell Rule Than Random Selection
Authors: Julie Nutini, Mark Schmidt, Issam Laradji, Michael Friedlander, Hoyt Koepke
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: There has been significant recent work on the theory and application of randomized coordinate descent algorithms, beginning with the work of  Nesterov [SIAM J. Optim., 22(2), 2012], who showed that a random-coordinate selection rule achieves the same convergence rate as the Gauss-Southwell selection rule. This result suggests that we should never use the Gauss-Southwell rule, as it is typically much more expensive than random selection. However, the empirical behaviours of these algorithms contradict this theoretical result: in applications where the computational costs of the selection rules are comparable, the Gauss-Southwell selection rule tends to perform substantially better than random coordinate selection. We give a simple analysis of the Gauss-Southwell rule showing that—except in extreme cases—it’s convergence rate is faster than choosing random coordinates. Further, in this work we (i) show that exact coordinate optimization improves the convergence rate for certain sparse problems, (ii) propose a Gauss-Southwell-Lipschitz rule that gives an even faster convergence rate given knowledge of the Lipschitz constants of the partial derivatives, (iii) analyze the effect of approximate Gauss-Southwell rules, and (iv) analyze proximal-gradient variants of the Gauss-Southwell rule.
Hashing for Distributed Data
Authors: Cong Leng, Jiaxiang Wu, Jian Cheng, Xi Zhang, Hanqing Lu
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Recently, hashing based approximate nearest neighbors search has attracted much attention. Extensive centralized hashing algorithms have been proposed and achieved promising performance. However, due to the large scale of many applications, the data is often stored or even collected in a distributed manner. Learning hash functions by aggregating all the data into a fusion center is infeasible because of the prohibitively expensive communication and computation overhead. In this paper, we develop a novel hashing model to learn hash functions in a distributed setting. We cast a centralized hashing model as a set of subproblems with consensus constraints. We find these subproblems can be analytically solved in parallel on the distributed compute nodes. Since no training data is transmitted across the nodes in the learning process, the communication cost of our model is independent to the data size. Extensive experiments on several large scale datasets containing up to 100 million samples demonstrate the efficacy of our method.
Large-scale Distributed Dependent Nonparametric Trees
Authors: Zhiting Hu, Ho Qirong, Avinava Dubey, Eric Xing
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Practical applications of Bayesian nonparametric (BNP) models have been limited, due to their high computational complexity and poor scaling on large data. In this paper, we consider dependent nonparametric trees (DNTs), a powerful infinite model that captures time-evolving hierarchies, and develop a large-scale distributed training system. Our major contributions include: (1) an effective memoized variational inference for DNTs, with a novel birth-merge strategy for exploring the unbounded tree space; (2) a model-parallel scheme for concurrent tree growing/pruning and efficient model alignment, through conflict-free model partitioning and lightweight synchronization; (3) a data-parallel scheme for variational parameter updates that allows distributed processing of massive data. Using 64 cores in 36 hours, our system learns a 10K-node DNT topic model on 8M documents that captures both high-frequency and long-tail topics. Our data and model scales are orders-of-magnitude larger than recent results on the hierarchical Dirichlet process, and the near-linear scalability indicates great potential for even bigger problem sizes.
Qualitative Multi-Armed Bandits: A Quantile-Based Approach
Authors: Balazs Szorenyi, Robert Busa-Fekete, Paul Weng, Eyke Hüllermeier
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We formalize and study the multi-armed bandit (MAB) problem in a generalized stochastic setting, in which rewards are not assumed to be numerical. Instead, rewards are measured on a qualitative scale that allows for comparison but invalidates arithmetic operations such as averaging. Correspondingly, instead of characterizing an arm in terms of the mean of the underlying distribution, we opt for using a quantile of that distribution as a representative value. We address the problem of quantile-based online learning both for the case of a finite (pure exploration) and infinite time horizon (cumulative regret minimization). For both cases, we propose suitable algorithms and analyze their properties. These properties are also illustrated by means of first experimental studies.
Deep Edge-Aware Filters
Authors: Li Xu, Jimmy Ren, Qiong Yan, Renjie Liao, Jiaya Jia
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: There are many edge-aware filters varying in their construction forms and filtering properties. It seems impossible to uniformly represent and accelerate them in a single framework. We made the attempt to learn a big and important family of edge-aware operators from data. Our method is based on a deep convolutional neural network with a gradient domain training procedure, which gives rise to a powerful tool to approximate various filters without knowing the original models and implementation details. The only difference among these operators in our system becomes merely the learned parameters. Our system enables fast approximation for complex edge-aware filters and achieves up to 200x acceleration, regardless of their originally very different implementation. Fast speed can also be achieved when creating new effects using spatially varying filter or filter combination, bearing out the effectiveness of our deep edge-aware filters.
A Convex Optimization Framework for Bi-Clustering
Authors: Shiau Hong Lim, Yudong Chen, Huan Xu
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We present a framework for biclustering and clustering where the observations are general labels. Our approach is based on the maximum likelihood estimator and its convex relaxation, and generalizes recent works in graph clustering to the biclustering setting. In addition to standard biclustering setting where one seeks to discover clustering structure simultaneously in two domain sets, we show that the same algorithm can be as effective when clustering structure only occurs in one domain. This allows for an alternative approach to clustering that is more natural in some scenarios. We present theoretical results that provide sufficient conditions for the recovery of the true underlying clusters under a generalized stochastic block model. These are further validated by our empirical results on both synthetic and real data.
Is Feature Selection Secure against Training Data Poisoning?
Authors: Huang Xiao, Battista Biggio, Gavin Brown, Giorgio Fumera, Claudia Eckert, Fabio Roli
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Learning in adversarial settings is becoming an important task for application domains where attackers may inject malicious data into the training set to subvert normal operation of data-driven technologies. Feature selection has been widely used in machine learning for security applications to improve generalization and computational efficiency, although it is not clear whether its use may be beneficial or even counterproductive when training data are poisoned by intelligent attackers. In this work, we shed light on this issue by providing a framework to investigate the robustness of popular feature selection methods, including LASSO, ridge regression and the elastic net. Our results on malware detection show that feature selection methods can be significantly compromised under attack (we can reduce LASSO to almost random choices of feature sets by careful insertion of less than 5% poisoned training samples), highlighting the need for specific countermeasures.
Predictive Entropy Search for Bayesian Optimization with Unknown Constraints
Authors: Jose Miguel Hernandez-Lobato, Michael Gelbart, Matthew Hoffman, Ryan Adams, Zoubin Ghahramani
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Unknown constraints arise in many types of expensive black-box optimization problems. Several methods have been proposed recently for performing Bayesian optimization with constraints, based on the expected improvement (EI) heuristic. However, EI can lead to pathologies when used with constraints. For example, in the case of decoupled constraints—i.e., when one can independently evaluate the objective or the constraints—EI can encounter a pathology that prevents exploration. Additionally, computing EI requires a current best solution, which may not exist if none of the data collected so far satisfy the constraints. By contrast, information-based approaches do not suffer from these failure modes. In this paper, we present a new information-based method called Predictive Entropy Search with Constraints (PESC). We analyze the performance of PESC and show that it compares favorably to EI-based approaches on synthetic and benchmark problems, as well as several real-world examples. We demonstrate that PESC is an effective algorithm that provides a promising direction towards a unified solution for constrained Bayesian optimization.
A Theoretical Analysis of Metric Hypothesis Transfer Learning
Authors: Michaël Perrot, Amaury Habrard
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We consider the problem of transferring some a priori knowledge in the context of supervised metric learning approaches. While this setting has been successfully applied in some empirical contexts, no theoretical evidence exists to justify this approach. In this paper, we provide a theoretical justification based on the notion of algorithmic stability adapted to the regularized metric learning setting. We propose an on-average-replace-two-stability model allowing us to prove fast generalization rates when an auxiliary source metric is used to bias the regularizer. Moreover, we prove a consistency result from which we show the interest of considering biased weighted regularized formulations and we provide a solution to estimate the associated weight. We also present some experiments illustrating the interest of the approach in standard metric learning tasks and in a transfer learning problem where few labelled data are available.
Generative Moment Matching Networks
Authors: Yujia Li, Kevin Swersky, Rich Zemel
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We consider the problem of learning deep generative models from data. We formulate a method that generates an independent sample via a single feedforward pass through a multilayer preceptron, as in the recently proposed generative adversarial networks (Goodfellow et al., 2014). Training a generative adversarial network, however, requires careful optimization of a difficult minimax program. Instead, we utilize a technique from statistical hypothesis testing known as maximum mean discrepancy (MMD), which leads to a simple objective that can be interpreted as matching all orders of statistics between a dataset and samples from the model, and can be trained by backpropagation. We further boost the performance of this approach by combining our generative network with an auto-encoder network, using MMD to learn to generate codes that can then be decoded to produce samples. We show that the combination of these techniques yields excellent generative models compared to baseline approaches as measured on MNIST and the Toronto Face Database.
Stay on path: PCA along graph paths
Authors: Megasthenis Asteris, Anastasios Kyrillidis, Alex Dimakis, Han-Gyol Yi, Bharath Chandrasekaran
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We introduce a variant of (sparse) PCA in which the set of feasible support sets is determined by a graph. In particular, we consider the following setting: given a directed acyclic graph G on p vertices corresponding to variables, the non-zero entries of the extracted principal component must coincide with vertices lying along a path in G. From a statistical perspective, information on the underlying network may potentially reduce the number of observations required to recover the population principal component. We consider the canonical estimator which optimally exploits the prior knowledge by solving a non-convex quadratic maximization on the empirical covariance. We introduce a simple network and analyze the estimator under the spiked covariance model for sparse PCA. We show that side information potentially improves the statistical complexity. We propose two algorithms to approximate the solution of the constrained quadratic maximization, and recover a component with the desired properties. We empirically evaluate our schemes on synthetic and real datasets.
Deep Learning with Limited Numerical Precision
Authors: Suyog Gupta, Ankur Agrawal, Kailash Gopalakrishnan, Pritish Narayanan
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Training of large-scale deep neural networks is often constrained by the available computational resources. We study the effect of limited precision data representation and computation on neural network training. Within the context of low-precision fixed-point computations, we observe the rounding scheme to play a crucial role in determining the network’s behavior during training. Our results show that deep networks can be trained using only 16-bit wide fixed-point number representation when using stochastic rounding, and incur little to no degradation in the classification accuracy. We also demonstrate an energy-efficient hardware accelerator that implements low-precision fixed-point arithmetic with stochastic rounding
Safe Screening for Multi-Task Feature Learning with Multiple Data Matrices
Authors: Jie Wang, Jieping Ye
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Multi-task feature learning (MTFL) is a powerful technique in boosting the predictive performance by learning multiple related classification/regression/clustering tasks simultaneously. However, solving the MTFL problem remains challenging when the feature dimension is extremely large. In this paper, we propose a novel screening rule—that is based on the dual projection onto convex sets (DPC)—to quickly identify the inactive features—that have zero coefficients in the solution vectors across all tasks. One of the appealing features of DPC is that: it is safe in the sense that the detected inactive features are guaranteed to have zero coefficients in the solution vectors across all tasks. Thus, by removing the inactive features from the training phase, we may have substantial savings in the computational cost and memory usage without sacrificing accuracy. To the best of our knowledge, it is the first screening rule that is applicable to sparse models with multiple data matrices. A key challenge in deriving DPC is to solve a nonconvex problem. We show that we can solve for the global optimum efficiently via a properly chosen parametrization of the constraint set. Moreover, DPC has very low computational cost and can be integrated with any existing solvers. We have evaluated the proposed DPC rule on both synthetic and real data sets. The experiments indicate that DPC is very effective in identifying the inactive features—especially for high dimensional data—which leads to a speedup up to several orders of magnitude.
Harmonic Exponential Families on Manifolds
Authors: Taco Cohen, Max Welling
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: In a range of fields including the geosciences, molecular biology, robotics and computer vision, one encounters problems that involve random variables on manifolds. Currently, there is a lack of flexible probabilistic models on manifolds that are fast and easy to train. We define an extremely flexible class of exponential family distributions on manifolds such as the torus, sphere, and rotation groups, and show that for these distributions the gradient of the log-likelihood can be computed efficiently using a non-commutative generalization of the Fast Fourier Transform (FFT). We discuss applications to Bayesian camera motion estimation (where harmonic exponential families serve as conjugate priors), and modelling of the spatial distribution of earthquakes on the surface of the earth. Our experimental results show that harmonic densities yield a significantly higher likelihood than the best competing method, while being orders of magnitude faster to train.
Training Deep Convolutional Neural Networks to Play Go
Authors: Christopher Clark, Amos Storkey
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Mastering the game of Go has remained a long-standing challenge to the field of AI. Modern computer Go programs rely on processing millions of possible future positions to play well, but intuitively a stronger and more ’humanlike’ way to play the game would be to rely on pattern recognition rather than brute force computation. Following this sentiment, we train deep convolutional neural networks to play Go by training them to predict the moves made by expert Go players. To solve this problem we introduce a number of novel techniques, including a method of tying weights in the network to ’hard code’ symmetries that are expected to exist in the target function, and demonstrate in an ablation study they considerably improve performance. Our final networks are able to achieve move prediction accuracies of 41.1% and 44.4% on two different Go datasets, surpassing previous state of the art on this task by significant margins. Additionally, while previous move prediction systems have not yielded strong Go playing programs, we show that the networks trained in this work acquired high levels of skill. Our convolutional neural networks can consistently defeat the well known Go program GNU Go and win some games against state of the art Go playing program Fuego while using a fraction of the play time.
Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)
Authors: Andrew Wilson, Hannes Nickisch
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpolation strategy, and GP covariance kernel. SKI also provides a mechanism to create new scalable kernel methods, through choosing different kernel interpolation strategies. Using SKI, with local cubic kernel interpolation, we introduce KISS-GP, which is 1) more scalable than inducing point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for substantial additional gains in scalability, without requiring any grid data, and 3) can be used for fast and expressive kernel learning. KISS-GP costs O(n) time and storage for GP inference. We evaluate KISS-GP for kernel matrix approximation, kernel learning, and natural sound modelling.
Learning Deep Structured Models
Authors: Liang-Chieh Chen, Alexander Schwing, Alan Yuille, Raquel Urtasun
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Many problems in real-world applications involve predicting several random variables that are statistically related. Markov random fields (MRFs) are a great mathematical tool to encode such dependencies. The goal of this paper is to combine MRFs with deep learning to estimate complex representations while taking into account the dependencies between the output random variables. Towards this goal, we propose a training algorithm that is able to learn structured models jointly with deep features that form the MRF potentials. Our approach is efficient as it blends learning and inference and makes use of GPU acceleration. We demonstrate the effectiveness of our algorithm in the tasks of predicting words from noisy images, as well as tagging of Flickr photographs. We show that joint learning of the deep features and the MRF parameters results in significant performance gains.
Community Detection Using Time-Dependent Personalized PageRank
Authors: Haim Avron, Lior Horesh
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Local graph diffusions have proven to be valuable tools for solving various graph clustering problems. As such, there has been much interest recently in efficient local algorithms for computing them. We present an efficient local algorithm for approximating a graph diffusion that generalizes both the celebrated personalized PageRank and its recent competitor/companion - the heat kernel. Our algorithm is based on writing the diffusion vector as the solution of an initial value problem, and then using a waveform relaxation approach to approximate the solution. Our experimental results suggest that it produces rankings that are distinct and competitive with the ones produced by high quality implementations of personalized PageRank and localized heat kernel, and that our algorithm is a useful addition to the toolset of localized graph diffusions.