ICML 2015 Papers

Multi-instance multi-label learning (MIML) is a framework for learning in the presence of label ambiguity. In MIML, experts provide labels for groups of instances (bags), instead of directly providing a label for every instance. When labeling efforts are focused on a set of target classes, instances outside this set will not be appropriately modeled. For example, ornithologists label bird audio recordings with a list of species present. Other additional sound instances, e.g., a rain drop or a moving vehicle sound, are not labeled. The challenge is due to the fact that for a given bag, the presence or absence of novel instances is latent. In this paper, this problem is addressed using a discriminative probabilistic model that accounts for novel instances. We propose an exact and efficient implementation of the maximum likelihood approach to determine the model parameters and consequently learn an instance-level classifier for all classes including the novel class. Experiments on both synthetic and real datasets illustrate the effectiveness of the proposed approach.

Subspace segmentation is the process of clustering a set of data points that are assumed to lie on the union of multiple linear or affine subspaces, and is increasingly being recognized as a fundamental tool for data analysis in high dimensional settings. Arguably one of the most successful approaches is based on the observation that the sparsest representation of a given point with respect to a dictionary formed by the others involves nonzero coefficients associated with points originating in the same subspace. Such sparse representations are computed independently for each data point via \ell_1-norm minimization and then combined into an affinity matrix for use by a final spectral clustering step. The downside of this procedure is two-fold. First, unlike canonical compressive sensing scenarios with ideally-randomized dictionaries, the data-dependent dictionaries here are unavoidably highly structured, disrupting many of the favorable properties of the \ell_1 norm. Secondly, by treating each data point independently, we ignore useful relationships between points that can be leveraged for jointly computing such sparse representations. Consequently, we motivate a multi-task learning-based framework for learning coupled sparse representations leading to a segmentation pipeline that is both robust against correlation structure and tailored to generate an optimal affinity matrix. Theoretical analysis and empirical tests are provided to support these claims.

We consider linear dynamical systems, particularly coupled linear oscillators, where the parameters represent meaningful values in a domain theory and thus learning what affects them contributes to explanation. Rather than allow perturbations of latent states, we assume that temporal variation beyond noise is explained by parameter drift, and variation across coupled systems is a function of moderating variables. This change of focus reduces opportunities for efficient inference, and we propose sampling procedures to learn and fit the models. We test our approach on a real dataset of physiological measures of heterosexual couples engaged in a conversation about a potentially emotional topic, with body mass index (BMI) being considered as a moderator. We evaluate several models on their ability to predict future conversation dynamics (the last 20% of the data for each test couple), with shared parameters being learned using held out data. As proof of concept, we validate the hypothesis that BMI affects the conversation dynamic in the experimentally chosen topic.

Natural Language Processing (NLP) systems commonly leverage bag-of-words co-occurrence techniques to capture semantic and syntactic word relationships. The resulting word-level distributed representations often ignore morphological information, though character-level embeddings have proven valuable to NLP tasks. We propose a new neural language model incorporating both word order and character order in its embedding. The model produces several vector spaces with meaningful substructure, as evidenced by its performance of 85.8% on a recent word-analogy task, exceeding best published syntactic word-analogy scores by a 58% error margin. Furthermore, the model includes several parallel training methods, most notably allowing a skip-gram network with 160 billion parameters to be trained overnight on 3 multi-core CPUs, 14x larger than the previous largest neural network.

Screening rules allow to early discard irrelevant variables from the optimization in Lasso problems, or its derivatives, making solvers faster. In this paper, we propose new versions of the so-called \textitsafe rules for the Lasso. Based on duality gap considerations, our new rules create safe test regions whose diameters converge to zero, provided that one relies on a converging solver. This property helps screening out more variables, for a wider range of regularization parameter values. In addition to faster convergence, we prove that we correctly identify the active sets (supports) of the solutions in finite time. While our proposed strategy can cope with any solver, its performance is demonstrated using a coordinate descent algorithm particularly adapted to machine learning use cases. Significant computing time reductions are obtained with respect to previous safe rules.

Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A side-effect of such high flexibility is that, in data sparsity scenarios, the model is prone to overfit. In reality, relational entities are always associated with meta information, such as user profiles in a social network. In this paper, we propose a metadata dependent Mondrian process (MDMP) to incorporate meta information into the stochastic partition process in the product space and the entity allocation process on the resulting block structure. MDMP can not only encourage homogeneous relational interactions within blocks but also discourage meta-label diversity within blocks. Regularized by meta information, MDMP becomes more robust in data sparsity scenarios and easier to converge in posterior inference. We apply MDMP to link prediction and rating prediction and demonstrate that MDMP is more effective than the baseline models in prediction accuracy with a more parsimonious model structure.

Collective graphical models (CGMs) are a formalism for inference and learning about a population of independent and identically distributed individuals when only noisy aggregate data are available. We highlight a close connection between approximate MAP inference in CGMs and marginal inference in standard graphical models. The connection leads us to derive a novel Belief Propagation (BP) style algorithm for collective graphical models. Mathematically, the algorithm is a strict generalization of BP—it can be viewed as an extension to minimize the Bethe free energy plus additional energy terms that are non-linear functions of the marginals. For CGMs, the algorithm is much more efficient than previous approaches to inference. We demonstrate its performance on two synthetic experiments concerning bird migration and collective human mobility.

We present a Markov mixed membership model (Markov M3) for grouped data that learns a fully connected graph structure among mixing components. A key feature of Markov M3 is that it interprets the mixed membership assignment as a Markov random walk over this graph of nodes. This is in contrast to tree-structured models in which the assignment is done according to a tree structure on the mixing components. The Markov structure results in a simple parametric model that can learn a complex dependency structure between nodes, while still maintaining full conjugacy for closed-form stochastic variational inference. Empirical results demonstrate that Markov M3 performs well compared with tree structured topic models, and can learn meaningful dependency structure between topics.

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of variational inference and Monte Carlo methods where we incorporate one or more steps of MCMC into our variational approximation. By doing so we obtain a rich class of inference algorithms bridging the gap between variational methods and MCMC, and offering the best of both worlds: fast posterior approximation through the maximization of an explicit objective, with the option of trading off additional computation for additional accuracy. We describe the theoretical foundations that make this possible and show some promising first results.

Statistical models for manifold-valued data permit capturing the intrinsic nature of the curved spaces in which the data lie and have been a topic of research for several decades. Typically, these formulations use geodesic curves and distances defined locally for most cases - this makes it hard to design parametric models globally on smooth manifolds. Thus, most (manifold specific) parametric models available today assume that the data lie in a small neighborhood on the manifold. To address this ’locality’ problem, we propose a novel nonparametric model which unifies multivariate general linear models (MGLMs) using multiple tangent spaces. Our framework generalizes existing work on (both Euclidean and non-Euclidean) general linear models providing a recipe to globally extend the locally-defined parametric models (using a mixture of local models). By grouping observations into sub-populations at multiple tangent spaces, our method provides insights into the hidden structure (geodesic relationships) in the data. This yields a framework to group observations and discover geodesic relationships between covariates X and manifold-valued responses Y, which we call Dirichlet process mixtures of multivariate general linear models (DP-MGLM) on Riemannian manifolds. Finally, we present proof of concept experiments to validate our model.

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.

There has been a lot of recent interest in designing neural network models to estimate a distribution from a set of examples. We introduce a simple modification for autoencoder neural networks that yields powerful generative models. Our method masks the autoencoder’s parameters to respect autoregressive constraints: each input is reconstructed only from previous inputs in a given ordering. Constrained this way, the autoencoder outputs can be interpreted as a set of conditional probabilities, and their product, the full joint probability. We can also train a single network that can decompose the joint probability in multiple different orderings. Our simple framework can be applied to multiple architectures, including deep ones. Vectorized implementations, such as on GPUs, are simple and fast. Experiments demonstrate that this approach is competitive with state-of-the-art tractable distribution estimators. At test time, the method is significantly faster and scales better than other autoregressive estimators.

We propose and study a row-and-column affine measurement scheme for low-rank matrix recovery. Each measurement is a linear combination of elements in one row or one column of a matrix X. This setting arises naturally in applications from different domains. However, current algorithms developed for standard matrix recovery problems do not perform well in our case, hence the need for developing new algorithms and theory for our problem. We propose a simple algorithm for the problem based on Singular Value Decomposition (SVD) and least-squares (LS), which we term alg. We prove that (a simplified version of) our algorithm can recover X exactly with the minimum possible number of measurements in the noiseless case. In the general noisy case, we prove performance guarantees on the reconstruction accuracy under the Frobenius norm. In simulations, our row-and-column design and alg algorithm show improved speed, and comparable and in some cases better accuracy compared to standard measurements designs and algorithms. Our theoretical and experimental results suggest that the proposed row-and-column affine measurements scheme, together with our recovery algorithm, may provide a powerful framework for affine matrix reconstruction.

Low-rank matrix approximation is an integral component of tools such as principal component analysis (PCA), as well as is an important instrument used in applications like web search models, text mining and computer vision, e.g., face recognition. Recently, randomized algorithms were proposed to effectively construct low rank approximations of large matrices. In this paper, we show how matrices from error correcting codes can be used to find such low rank approximations. The benefits of using these code matrices are the following: (i) They are easy to generate and they reduce randomness significantly. (ii) Code matrices have low coherence and have a better chance of preserving the geometry of an entire subspace of vectors; (iii) Unlike Fourier transforms or Hadamard matrices, which require sampling O(k\log k) columns for a rank-k approximation, the log factor is not necessary in the case of code matrices. (iv) Under certain conditions, the approximation errors can be better and the singular values obtained can be more accurate, than those obtained using Gaussian random matrices and other structured random matrices.

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.

The manifold of Symmetric Positive Definite (SPD) matrices has been successfully used for data representation in image set classification. By endowing the SPD manifold with Log-Euclidean Metric, existing methods typically work on vector-forms of SPD matrix logarithms. This however not only inevitably distorts the geometrical structure of the space of SPD matrix logarithms but also brings low efficiency especially when the dimensionality of SPD matrix is high. To overcome this limitation, we propose a novel metric learning approach to work directly on logarithms of SPD matrices. Specifically, our method aims to learn a tangent map that can directly transform the matrix logarithms from the original tangent space to a new tangent space of more discriminability. Under the tangent map framework, the novel metric learning can then be formulated as an optimization problem of seeking a Mahalanobis-like matrix, which can take the advantage of traditional metric learning techniques. Extensive evaluations on several image set classification tasks demonstrate the effectiveness of our proposed metric learning method.

Methods for learning to search for structured prediction typically imitate a reference policy, with existing theoretical guarantees demonstrating low regret compared to that reference. This is unsatisfactory in many applications where the reference policy is suboptimal and the goal of learning is to improve upon it. Can learning to search work even when the reference is poor? We provide a new learning to search algorithm, LOLS, which does well relative to the reference policy, but additionally guarantees low regret compared to deviations from the learned policy: a local-optimality guarantee. Consequently, LOLS can improve upon the reference policy, unlike previous algorithms. This enables us to develop structured contextual bandits, a partial information structured prediction setting with many potential applications.

Many supervised learning problems involve learning from samples whose labels are corrupted in some way. For example, each sample may have some constant probability of being incorrectly labelled (learning with label noise), or one may have a pool of unlabelled samples in lieu of negative samples (learning from positive and unlabelled data). This paper uses class-probability estimation to study these and other corruption processes belonging to the mutually contaminated distributions framework (Scott et al., 2013), with three conclusions. First, one can optimise balanced error and AUC without knowledge of the corruption process parameters. Second, given estimates of the corruption parameters, one can minimise a range of classification risks. Third, one can estimate the corruption parameters using only corrupted data. Experiments confirm the efficacy of class-probability estimation in learning from corrupted labels.

We propose a new method for learning word representations using hierarchical regularization in sparse coding inspired by the linguistic study of word meanings. We show an efficient learning algorithm based on stochastic proximal methods that is significantly faster than previous approaches, making it possible to perform hierarchical sparse coding on a corpus of billions of word tokens. Experiments on various benchmark tasks—word similarity ranking, syntactic and semantic analogies, sentence completion, and sentiment analysis—demonstrate that the method outperforms or is competitive with state-of-the-art methods.