mtybilly/Instruct2DS huggingface dataset:
Complex Event Detection using Semantic Saliency and Nearly-Isotonic SVM
Authors: Chang, Xiaojun and Yang, Yi and Xing, Eric and Yu, Yaoliang
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We aim to detect complex events in long Internet videos that may last for hours. A major challenge in this setting is that only a few shots in a long video are relevant to the event of interest while others are irrelevant or even misleading. Instead of indifferently pooling the shots, we first define a novel notion of semantic saliency that assesses the relevance of each shot with the event of interest. We then prioritize the shots according to their saliency scores since shots that are semantically more salient are expected to contribute more to the final event detector. Next, we propose a new isotonic regularizer that is able to exploit the semantic ordering information. The resulting nearly-isotonic SVM classifier exhibits higher discriminative power. Computationally, we develop an efficient implementation using the proximal gradient algorithm, and we prove new, closed-form proximal steps. We conduct extensive experiments on three real-world video datasets and confirm the effectiveness of the proposed approach.
Rebuilding Factorized Information Criterion: Asymptotically Accurate Marginal Likelihood
Authors: Hayashi, Kohei and Maeda, Shin-ichi and Fujimaki, Ryohei
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Factorized information criterion (FIC) is a recently developed approximation technique for the marginal log-likelihood, which provides an automatic model selection framework for a few latent variable models (LVMs) with tractable inference algorithms. This paper reconsiders FIC and fills theoretical gaps of previous FIC studies. First, we reveal the core idea of FIC that allows generalization for a broader class of LVMs, including continuous LVMs, in contrast to previous FICs, which are applicable only to binary LVMs. Second, we investigate the model selection mechanism of the generalized FIC. Our analysis provides a formal justification of FIC as a model selection criterion for LVMs and also a systematic procedure for pruning redundant latent variables that have been removed heuristically in previous studies. Third, we provide an interpretation of FIC as a variational free energy and uncover previously-unknown their relationship. A demonstrative study on Bayesian principal component analysis is provided and numerical experiments support our theoretical results.
Double Nyström Method: An Efficient and Accurate Nystr\m̈ Scheme for Large-Scale Data Sets
Authors: Lim, Woosang and Kim, Minhwan and Park, Haesun and Jung, Kyomin
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: The Nyström method has been one of the most effective techniques for kernel-based approach that scales well to large data sets. Since its introduction, there has been a large body of work that improves the approximation accuracy while maintaining computational efficiency. In this paper, we present a novel Nyström method that improves both accuracy and efficiency based on a new theoretical analysis. We first provide a generalized sampling scheme, CAPS, that minimizes a novel error bound based on the subspace distance. We then present our double Nyström method that reduces the size of the decomposition in two stages. We show that our method is highly efficient and accurate compared to other state-of-the-art Nyström methods by evaluating them on a number of real data sets.
The Composition Theorem for Differential Privacy
Authors: Kairouz, Peter and Oh, Sewoong and Viswanath, Pramod
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Interactive querying of a database degrades the privacy level. In this paper we answer the fundamental question of characterizing the level of privacy degradation as a function of the number of adaptive interactions and the differential privacy levels maintained by the individual queries. Our solution is complete: the privacy degradation guarantee is true for every privacy mechanism, and further, we demonstrate a sequence of privacy mechanisms that do degrade in the characterized manner. The key innovation is the introduction of an operational interpretation (involving hypothesis testing) to differential privacy and the use of the corresponding data processing inequalities. Our result improves over the state of the art and has immediate applications to several problems studied in the literature.
Convex Formulation for Learning from Positive and Unlabeled Data
Authors: Plessis, Marthinus Du and Niu, Gang and Sugiyama, Masashi
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We discuss binary classification from only from positive and unlabeled data (PU classification), which is conceivable in various real-world machine learning problems. Since unlabeled data consists of both positive and negative data, simply separating positive and unlabeled data yields a biased solution. Recently, it was shown that the bias can be canceled by using a particular non-convex loss such as the ramp loss. However, classifier training with a non-convex loss is not straightforward in practice. In this paper, we discuss a convex formulation for PU classification that can still cancel the bias. The key idea is to use different loss functions for positive and unlabeled samples. However, in this setup, the hinge loss is not permissible. As an alternative, we propose the double hinge loss. Theoretically, we prove that the estimators converge to the optimal solutions at the optimal parametric rate. Experimentally, we demonstrate that PU classification with the double hinge loss performs as accurate as the non-convex method, with a much lower computational cost.
Threshold Influence Model for Allocating Advertising Budgets
Authors: Miyauchi, Atsushi and Iwamasa, Yuni and Fukunaga, Takuro and Kakimura, Naonori
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: We propose a new influence model for allocating budgets to advertising channels. Our model captures customer’s sensitivity to advertisements as a threshold behavior; a customer is expected to be influenced if the influence he receives exceeds his threshold. Over the threshold model, we discuss two optimization problems. The first one is the budget-constrained influence maximization. We propose two greedy algorithms based on different strategies, and analyze the performance when the influence is submodular. We then introduce a new characteristic to measure the cost-effectiveness of a marketing campaign, that is, the proportion of the resulting influence to the cost spent. We design an almost linear-time approximation algorithm to maximize the cost-effectiveness. Furthermore, we design a better-approximation algorithm based on linear programming for a special case. We conduct thorough experiments to confirm that our algorithms outperform baseline algorithms.
Strongly Adaptive Online Learning
Authors: Daniely, Amit and Gonen, Alon and Shalev-Shwartz, Shai
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Strongly adaptive algorithms are algorithms whose performance on every time interval is close to optimal. We present a reduction that can transform standard low-regret algorithms to strongly adaptive. As a consequence, we derive simple, yet efficient, strongly adaptive algorithms for a handful of problems.
CUR Algorithm for Partially Observed Matrices
Authors: Xu, Miao and Jin, Rong and Zhou, Zhi-Hua
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for CUR matrix decomposition is that they cannot deal with entries in a ıt partially observed matrix, while incomplete matrices are found in many real world applications. In this work, we alleviate this limitation by developing a CUR decomposition algorithm for partially observed matrices. In particular, the proposed algorithm computes the low rank approximation of the target matrix based on (i) the randomly sampled rows and columns, and (ii) a subset of observed entries that are randomly sampled from the matrix. Our analysis shows the relative error bound, measured by spectral norm, for the proposed algorithm when the target matrix is of full rank. We also show that only O(n rłn r) observed entries are needed by the proposed algorithm to perfectly recover a rank r matrix of size n\times n, which improves the sample complexity of the existing algorithms for matrix completion. Empirical studies on both synthetic and real-world datasets verify our theoretical claims and demonstrate the effectiveness of the proposed algorithm.
A Deterministic Analysis of Noisy Sparse Subspace Clustering for Dimensionality-reduced Data
Authors: Wang, Yining and Wang, Yu-Xiang and Singh, Aarti
Published in: Proceedings of the 32nd International Conference on Machine Learning (Main Conference Track), 2015

Abstract: Subspace clustering groups data into several lowrank subspaces. In this paper, we propose a theoretical framework to analyze a popular optimization-based algorithm, Sparse Subspace Clustering (SSC), when the data dimension is compressed via some random projection algorithms. We show SSC provably succeeds if the random projection is a subspace embedding, which includes random Gaussian projection, uniform row sampling, FJLT, sketching, etc. Our analysis applies to the most general deterministic setting and is able to handle both adversarial and stochastic noise. It also results in the first algorithm for privacy-preserved subspace clustering.
MRA-based Statistical Learning from Incomplete Rankings
Authors: Sibony, Eric and Clemençon, Stéphan and Jakubowicz, Jérémie
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: Huggins, Jonathan and Tenenbaum, Josh
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: Lopez-Paz, David and Muandet, Krikamol and Schölkopf, Bernhard and Tolstikhin, Iliya
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: Gregor, Karol and Danihelka, Ivo and Graves, Alex and Rezende, Danilo and Wierstra, Daan
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: Amid, Ehsan and Ukkonen, Antti
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: Deisenroth, Marc and Ng, Jun Wei
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: Tang, Gongguo and Shah, Parikshit
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: Zhou, Zirui and Zhang, Qi and So, Anthony Man-Cho
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: Han, Qiuyi and Xu, Kevin and Airoldi, Edoardo
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: Tagorti, Manel and Scherrer, Bruno
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: Rezende, Danilo and Mohamed, Shakir
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: Macdonald, Benn and Higham, Catherine and Husmeier, Dirk
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: Ciliberto, Carlo and Mroueh, Youssef and Poggio, Tomaso and Rosasco, Lorenzo
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: Osadchy, Margarita and Hazan, Tamir and Keren, Daniel
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: Lesner, Boris and Scherrer, Bruno
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: Serrurier, Mathieu and Prade, Henri
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: You, Chong and Vidal, Rene
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: Shah, Amar and Knowles, David and Ghahramani, Zoubin
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: Zhu, Xiaodan and Sobihani, Parinaz and Guo, Hongyu
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: Blundell, Charles and Cornebise, Julien and Kavukcuoglu, Koray and Wierstra, Daan
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: Yu, Jiaqian and Blaschko, Matthew
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: Nutini, Julie and Schmidt, Mark and Laradji, Issam and Friedlander, Michael and Koepke, Hoyt
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: Leng, Cong and Wu, Jiaxiang and Cheng, Jian and Zhang, Xi and Lu, Hanqing
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: Hu, Zhiting and Qirong, Ho and Dubey, Avinava and Xing, Eric
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: Szorenyi, Balazs and Busa-Fekete, Robert and Weng, Paul and Hüllermeier, Eyke
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: Xu, Li and Ren, Jimmy and Yan, Qiong and Liao, Renjie and Jia, Jiaya
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: Lim, Shiau Hong and Chen, Yudong and Xu, Huan
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: Xiao, Huang and Biggio, Battista and Brown, Gavin and Fumera, Giorgio and Eckert, Claudia and Roli, Fabio
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: Hernandez-Lobato, Jose Miguel and Gelbart, Michael and Hoffman, Matthew and Adams, Ryan and Ghahramani, Zoubin
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: Perrot, Michaël and Habrard, Amaury
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: Li, Yujia and Swersky, Kevin and Zemel, Rich
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.