ICML 2016 论文列表

We consider axiomatically the problem of estimating the strength of a conditional dependence relationship P_Y|X from a random variables X to a random variable Y. This has applications in determining the strength of a known causal relationship, where the strength depends only on the conditional distribution of the effect given the cause (and not on the driving distribution of the cause). Shannon capacity, appropriately regularized, emerges as a natural measure under these axioms. We examine the problem of calculating Shannon capacity from the observed samples and propose a novel fixed-k nearest neighbor estimator, and demonstrate its consistency. Finally, we demonstrate an application to single-cell flow-cytometry, where the proposed estimators significantly reduce sample complexity.

Multi-label classification is an important machine learning task wherein one assigns a subset of candidate labels to an object. In this paper, we propose a new multi-label classification method based on Conditional Bernoulli Mixtures. Our proposed method has several attractive properties: it captures label dependencies; it reduces the multi-label problem to several standard binary and multi-class problems; it subsumes the classic independent binary prediction and power-set subset prediction methods as special cases; and it exhibits accuracy and/or computational complexity advantages over existing approaches. We demonstrate two implementations of our method using logistic regressions and gradient boosted trees, together with a simple training procedure based on Expectation Maximization. We further derive an efficient prediction procedure based on dynamic programming, thus avoiding the cost of examining an exponential number of potential label subsets. Experimental results show the effectiveness of the proposed method against competitive alternatives on benchmark datasets.

Our goal is to improve the \it training and \it prediction time of Nyström method, which is a widely-used technique for generating low-rank kernel matrix approximations. When applying the Nyström approximation for large-scale applications, both training and prediction time is dominated by computing kernel values between a data point and all landmark points. With m landmark points, this computation requires Θ(md) time (flops), where d is the input dimension. In this paper, we propose the use of a family of fast transforms to generate structured landmark points for Nyström approximation. By exploiting fast transforms, e.g., Haar transform and Hadamard transform, our modified Nyström method requires only Θ(m) or Θ(m\log d) time to compute the kernel values between a given data point and m landmark points. This improvement in time complexity can significantly speed up kernel approximation and benefit prediction speed in kernel machines. For instance, on the webspam data (more than 300,000 data points), our proposed algorithm enables kernel SVM prediction to deliver 98% accuracy and the resulting prediction time is 1000 times faster than LIBSVM and only 10 times slower than linear SVM prediction (which yields only 91% accuracy).

Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix to define a feature vector for each object, and run k-means on these features to separate objects into k classes. Each of these three steps becomes computationally intensive for large N and/or k. We propose to speed up the last two steps based on recent results in the emerging field of graph signal processing: graph filtering of random signals, and random sampling of bandlimited graph signals. We prove that our method, with a gain in computation time that can reach several orders of magnitude, is in fact an approximation of spectral clustering, for which we are able to control the error. We test the performance of our method on artificial and real-world network data.

In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here we make use of complex valued embeddings. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. Compared to state-of-the-art models such as Neural Tensor Network and Holographic Embeddings, our approach based on complex embeddings is arguably simpler, as it only uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors. Our approach is scalable to large datasets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.

Motivated by applications in domains such as social networks and computational biology, we study the problem of community recovery in graphs with locality. In this problem, pairwise noisy measurements of whether two nodes are in the same community or different communities come mainly or exclusively from nearby nodes rather than uniformly sampled between all node pairs, as in most existing models. We present two algorithms that run nearly linearly in the number of measurements and which achieve the information limits for exact recovery.

Sum-Product Networks (SPNs) are probabilistic inference machines that admit exact inference in linear time in the size of the network. Existing parameter learning approaches for SPNs are largely based on the maximum likelihood principle and are subject to overfitting compared to more Bayesian approaches. Exact Bayesian posterior inference for SPNs is computationally intractable. Even approximation techniques such as standard variational inference and posterior sampling for SPNs are computationally infeasible even for networks of moderate size due to the large number of local latent variables per instance. In this work, we propose a novel deterministic collapsed variational inference algorithm for SPNs that is computationally efficient, easy to implement and at the same time allows us to incorporate prior information into the optimization formulation. Extensive experiments show a significant improvement in accuracy compared with a maximum likelihood based approach.

Analysis of categorical data is a challenging task. In this paper, we propose to compute topographical features of high-dimensional categorical data. We propose an efficient algorithm to extract modes of the underlying distribution and their attractive basins. These topographical features provide a geometric view of the data and can be applied to visualization and clustering of real world challenging datasets. Experiments show that our principled method outperforms state-of-the-art clustering methods while also admits an embarrassingly parallel property.

Successfully recommending personalized course schedules is a difficult problem given the diversity of students knowledge, learning behaviour, and goals. This paper presents personalized course recommendation and curriculum design algorithms that exploit logged student data. The algorithms are based on the regression estimator for contextual multi-armed bandits with a penalized variance term. Guarantees on the predictive performance of the algorithms are provided using empirical Bernstein bounds. We also provide guidelines for including expert domain knowledge into the recommendations. Using undergraduate engineering logged data from a post-secondary institution we illustrate the performance of these algorithms.

Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as maximum a posteriori inference problems in a graphical model and present a message passing approach that scales linearly with the number of observations and factors. Our empirical study demonstrates that message passing is able to recover low-rank Boolean matrices, in the boundaries of theoretically possible recovery and compares favorably with state-of-the-art in real-world applications, such collaborative filtering with large-scale Boolean data.

We propose a new framework for black-box convex optimization which is well-suited for situations where gradient computations are expensive. We derive a new method for this framework which leverages several concepts from convex optimization, from standard first-order methods (e.g. gradient descent or quasi-Newton methods) to analytical centers (i.e. minimizers of self-concordant barriers). We demonstrate empirically that our new technique compares favorably with state of the art algorithms (such as BFGS).

Black-box alpha (BB-α) is a new approximate inference method based on the minimization of α-divergences. BB-αscales to large datasets because it can be implemented using stochastic gradient descent. BB-αcan be applied to complex probabilistic models with little effort since it only requires as input the likelihood function and its gradients. These gradients can be easily obtained using automatic differentiation. By changing the divergence parameter α, the method is able to interpolate between variational Bayes (VB) (α→0) and an algorithm similar to expectation propagation (EP) (α= 1). Experiments on probit regression and neural network regression and classification problems show that BB-αwith non-standard settings of α, such as α= 0.5, usually produces better predictions than with α→0 (VB) or α= 1 (EP).

We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are independent random variables but instead a fixed “budget of randomness” is distributed across the matrix. Such matrices can be edfficiently stored in sub-quadratic or even linear space, provide reduction in randomness usage (i.e. number of required random values), and very often lead to computational speed ups. We prove several theoretical results showing that projections via various structured matrices followed by nonlinear mappings accurately preserve the angular distance between input high-dimensional vectors. To the best of our knowledge, these results are the first that give theoretical ground for the use of general structured matrices in the nonlinear setting. We empirically verify our theoretical findings and show the dependence of learning via structured hashed projections on the performance of neural network as well as nearest neighbor classifier.

Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine or Variational Autoencoder, involves training a top-down directed generative model together with a bottom-up auxiliary model used for approximate inference. Recent results indicate that better generative models can be obtained with better approximate inference procedures. Instead of improving the inference procedure, we here propose a new model, the bidirectional Helmholtz machine, which guarantees that the top-down and bottom-up distributions can efficiently invert each other. We achieve this by interpreting both the top-down and the bottom-up directed models as approximate inference distributions and by defining the model distribution to be the geometric mean of these two. We present a lower-bound for the likelihood of this model and we show that optimizing this bound regularizes the model so that the Bhattacharyya distance between the bottom-up and top-down approximate distributions is minimized. This approach results in state of the art generative models which prefer significantly deeper architectures while it allows for orders of magnitude more efficient likelihood estimation.

Random projections have played an important role in scaling up machine learning and data mining algorithms. Recently they have also been applied to probabilistic inference to estimate properties of high-dimensional distributions; however, they all rely on the same class of projections based on universal hashing. We provide a general framework to analyze random projections which relates their statistical properties to their Fourier spectrum, which is a well-studied area of theoretical computer science. Using this framework we introduce two new classes of hash functions for probabilistic inference and model counting that show promising performance on synthetic and real-world benchmarks.

We introduce three novel semi-parametric extensions of probabilistic canonical correlation analysis with identifiability guarantees. We consider moment matching techniques for estimation in these models. For that, by drawing explicit links between the new models and a discrete version of independent component analysis (DICA), we first extend the DICA cumulant tensors to the new discrete version of CCA. By further using a close connection with independent component analysis, we introduce generalized covariance matrices, which can replace the cumulant tensors in the moment matching framework, and, therefore, improve sample complexity and simplify derivations and algorithms significantly. As the tensor power method or orthogonal joint diagonalization are not applicable in the new setting, we use non-orthogonal joint diagonalization techniques for matching the cumulants. We demonstrate performance of the proposed models and estimation techniques on experiments with both synthetic and real datasets.

Recently, researchers have made significant progress combining the advances in deep learning for learning feature representations with reinforcement learning. Some notable examples include training agents to play Atari games based on raw pixel data and to acquire advanced manipulation skills using raw sensory inputs. However, it has been difficult to quantify progress in the domain of continuous control due to the lack of a commonly adopted benchmark. In this work, we present a benchmark suite of continuous control tasks, including classic tasks like cart-pole swing-up, tasks with very high state and action dimensionality such as 3D humanoid locomotion, tasks with partial observations, and tasks with hierarchical structure. We report novel findings based on the systematic evaluation of a range of implemented reinforcement learning algorithms. Both the benchmark and reference implementations are released at https://github.com/rllab/rllab in order to facilitate experimental reproducibility and to encourage adoption by other researchers.

We introduce Bayesian Poisson Tucker decomposition (BPTD) for modeling country–country interaction event data. These data consist of interaction events of the form “country i took action a toward country j at time t.” BPTD discovers overlapping country–community memberships, including the number of latent communities. In addition, it discovers directed community–community interaction networks that are specific to “topics” of action types and temporal “regimes.” We show that BPTD yields an efficient MCMC inference algorithm and achieves better predictive performance than related models. We also demonstrate that it discovers interpretable latent structure that agrees with our knowledge of international relations.

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