NeurIPS 2016 论文列表

Matrix completion methods can benefit from side information besides the partially observed matrix. The use of side features describing the row and column entities of a matrix has been shown to reduce the sample complexity for completing the matrix. We propose a novel sparse formulation that explicitly models the interaction between the row and column side features to approximate the matrix entries. Unlike early methods, this model does not require the low-rank condition on the model parameter matrix. We prove that when the side features can span the latent feature space of the matrix to be recovered, the number of observed entries needed for an exact recovery is $O(\log N)$ where $N$ is the size of the matrix. When the side features are corrupted latent features of the matrix with a small perturbation, our method can achieve an $\epsilon$-recovery with $O(\log N)$ sample complexity, and maintains a $\O(N^{3/2})$ rate similar to classfic methods with no side information. An efficient linearized Lagrangian algorithm is developed with a strong guarantee of convergence. Empirical results show that our approach outperforms three state-of-the-art methods both in simulations and on real world datasets.

Abstract We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems. Our method has only one parameter (a step size), and is radically simpler than other accelerated methods for finite sums. Additionally it can be applied when the terms are non-smooth, yielding a method applicable in many areas where operator splitting methods would traditionally be applied.

Commonly used in many applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into low rank and sparse components, the latter representing unwanted outliers. Although the resulting problem is typically NP-hard, convex relaxations provide a computationally-expedient alternative with theoretical support. However, in practical regimes performance guarantees break down and a variety of non-convex alternatives, including Bayesian-inspired models, have been proposed to boost estimation quality. Unfortunately though, without additional a priori knowledge none of these methods can significantly expand the critical operational range such that exact principal subspace recovery is possible. Into this mix we propose a novel pseudo-Bayesian algorithm that explicitly compensates for design weaknesses in many existing non-convex approaches leading to state-of-the-art performance with a sound analytical foundation.

Probabilistic techniques are central to data analysis, but different approaches can be challenging to apply, combine, and compare. This paper introduces composable generative population models (CGPMs), a computational abstraction that extends directed graphical models and can be used to describe and compose a broad class of probabilistic data analysis techniques. Examples include discriminative machine learning, hierarchical Bayesian models, multivariate kernel methods, clustering algorithms, and arbitrary probabilistic programs. We demonstrate the integration of CGPMs into BayesDB, a probabilistic programming platform that can express data analysis tasks using a modeling definition language and structured query language. The practical value is illustrated in two ways. First, the paper describes an analysis on a database of Earth satellites, which identifies records that probably violate Kepler’s Third Law by composing causal probabilistic programs with non-parametric Bayes in 50 lines of probabilistic code. Second, it reports the lines of code and accuracy of CGPMs compared with baseline solutions from standard machine learning libraries.

A fundamental problem in cognitive neuroscience is how humans make decisions, act, and behave in relation to other humans. Here we adopt the hypothesis that when we are in an interactive social setting, our brains perform Bayesian inference of the intentions and cooperativeness of others using probabilistic representations. We employ the framework of partially observable Markov decision processes (POMDPs) to model human decision making in a social context, focusing specifically on the volunteer's dilemma in a version of the classic Public Goods Game. We show that the POMDP model explains both the behavior of subjects as well as neural activity recorded using fMRI during the game. The decisions of subjects can be modeled across all trials using two interpretable parameters. Furthermore, the expected reward predicted by the model for each subject was correlated with the activation of brain areas related to reward expectation in social interactions. Our results suggest a probabilistic basis for human social decision making within the framework of expected reward maximization.

We develop a probabilistic framework for deep learning based on the Deep Rendering Mixture Model (DRMM), a new generative probabilistic model that explicitly capture variations in data due to latent task nuisance variables. We demonstrate that max-sum inference in the DRMM yields an algorithm that exactly reproduces the operations in deep convolutional neural networks (DCNs), providing a first principles derivation. Our framework provides new insights into the successes and shortcomings of DCNs as well as a principled route to their improvement. DRMM training via the Expectation-Maximization (EM) algorithm is a powerful alternative to DCN back-propagation, and initial training results are promising. Classification based on the DRMM and other variants outperforms DCNs in supervised digit classification, training 2-3x faster while achieving similar accuracy. Moreover, the DRMM is applicable to semi-supervised and unsupervised learning tasks, achieving results that are state-of-the-art in several categories on the MNIST benchmark and comparable to state of the art on the CIFAR10 benchmark.

To what extent is the success of deep visualization due to the training? Could we do deep visualization using untrained, random weight networks? To address this issue, we explore new and powerful generative models for three popular deep visualization tasks using untrained, random weight convolutional neural networks. First we invert representations in feature spaces and reconstruct images from white noise inputs. The reconstruction quality is statistically higher than that of the same method applied on well trained networks with the same architecture. Next we synthesize textures using scaled correlations of representations in multiple layers and our results are almost indistinguishable with the original natural texture and the synthesized textures based on the trained network. Third, by recasting the content of an image in the style of various artworks, we create artistic images with high perceptual quality, highly competitive to the prior work of Gatys et al. on pretrained networks. To our knowledge this is the first demonstration of image representations using untrained deep neural networks. Our work provides a new and fascinating tool to study the representation of deep network architecture and sheds light on new understandings on deep visualization. It may possibly lead to a way to compare network architectures without training.

Estimating patient's clinical state from multiple concurrent physiological streams plays an important role in determining if a therapeutic intervention is necessary and for triaging patients in the hospital. In this paper we construct a non-parametric learning algorithm to estimate the clinical state of a patient. The algorithm addresses several known challenges with clinical state estimation such as eliminating bias introduced by therapeutic intervention censoring, increasing the timeliness of state estimation while ensuring a sufficient accuracy, and the ability to detect anomalous clinical states. These benefits are obtained by combining the tools of non-parametric Bayesian inference, permutation testing, and generalizations of the empirical Bernstein inequality. The algorithm is validated using real-world data from a cancer ward in a large academic hospital.

We give a novel formal theoretical framework for unsupervised learning with two distinctive characteristics. First, it does not assume any generative model and based on a worst-case performance metric. Second, it is comparative, namely performance is measured with respect to a given hypothesis class. This allows to avoid known computational hardness results and improper algorithms based on convex relaxations. We show how several families of unsupervised learning models, which were previously only analyzed under probabilistic assumptions and are otherwise provably intractable, can be efficiently learned in our framework by convex optimization.

We develop an efficient alternating framework for learning a generalized version of Factorization Machine (gFM) on steaming data with provable guarantees. When the instances are sampled from $d$ dimensional random Gaussian vectors and the target second order coefficient matrix in gFM is of rank $k$, our algorithm converges linearly, achieves $O(\epsilon)$ recovery error after retrieving $O(k^{3}d\log(1/\epsilon))$ training instances, consumes $O(kd)$ memory in one-pass of dataset and only requires matrix-vector product operations in each iteration. The key ingredient of our framework is a construction of an estimation sequence endowed with a so-called Conditionally Independent RIP condition (CI-RIP). As special cases of gFM, our framework can be applied to symmetric or asymmetric rank-one matrix sensing problems, such as inductive matrix completion and phase retrieval.

In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a Lipschitz continuous gradient. We first prove global convergence of the scheme with the help of the Kurdyka–Łojasiewicz property. Then, when the non-smooth part is also partly smooth relative to a smooth submanifold, we establish finite identification of the latter and provide sharp local linear convergence analysis. The proposed method is illustrated on a few problems arising from statistics and machine learning.

The question of how to parallelize the stochastic gradient descent (SGD) method has received much attention in the literature. In this paper, we focus instead on batch methods that use a sizeable fraction of the training set at each iteration to facilitate parallelism, and that employ second-order information. In order to improve the learning process, we follow a multi-batch approach in which the batch changes at each iteration. This can cause difficulties because L-BFGS employs gradient differences to update the Hessian approximations, and when these gradients are computed using different data points the process can be unstable. This paper shows how to perform stable quasi-Newton updating in the multi-batch setting, illustrates the behavior of the algorithm in a distributed computing platform, and studies its convergence properties for both the convex and nonconvex cases.

Given a task of predicting Y from X, a loss function L, and a set of probability distributions Gamma on (X,Y), what is the optimal decision rule minimizing the worst-case expected loss over Gamma? In this paper, we address this question by introducing a generalization of the maximum entropy principle. Applying this principle to sets of distributions with marginal on X constrained to be the empirical marginal, we provide a minimax interpretation of the maximum likelihood problem over generalized linear models as well as some popular regularization schemes. For quadratic and logarithmic loss functions we revisit well-known linear and logistic regression models. Moreover, for the 0-1 loss we derive a classifier which we call the minimax SVM. The minimax SVM minimizes the worst-case expected 0-1 loss over the proposed Gamma by solving a tractable optimization problem. We perform several numerical experiments to show the power of the minimax SVM in outperforming the SVM.

The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing (Riemannian) metric that favors regions of high local density. The resulting locally adaptive normal distribution (LAND) is a generalization of the normal distribution to the "manifold" setting, where data is assumed to lie near a potentially low-dimensional manifold embedded in R^D. The LAND is parametric, depending only on a mean and a covariance, and is the maximum entropy distribution under the given metric. The underlying metric is, however, non-parametric. We develop a maximum likelihood algorithm to infer the distribution parameters that relies on a combination of gradient descent and Monte Carlo integration. We further extend the LAND to mixture models, and provide the corresponding EM algorithm. We demonstrate the efficiency of the LAND to fit non-trivial probability distributions over both synthetic data, and EEG measurements of human sleep.

Many machine learning applications involve jointly predicting multiple mutually dependent output variables. Learning to search is a family of methods where the complex decision problem is cast into a sequence of decisions via a search space. Although these methods have shown promise both in theory and in practice, implementing them has been burdensomely awkward. In this paper, we show the search space can be defined by an arbitrary imperative program, turning learning to search into a credit assignment compiler. Altogether with the algorithmic improvements for the compiler, we radically reduce the complexity of programming and the running time. We demonstrate the feasibility of our approach on multiple joint prediction tasks. In all cases, we obtain accuracies as high as alternative approaches, at drastically reduced execution and programming time.

This paper studies the $k$-means++ algorithm for clustering as well as the class of $D^\ell$ sampling algorithms to which $k$-means++ belongs. It is shown that for any constant factor $\beta > 1$, selecting $\beta k$ cluster centers by $D^\ell$ sampling yields a constant-factor approximation to the optimal clustering with $k$ centers, in expectation and without conditions on the dataset. This result extends the previously known $O(\log k)$ guarantee for the case $\beta = 1$ to the constant-factor bi-criteria regime. It also improves upon an existing constant-factor bi-criteria result that holds only with constant probability.

We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design learning algorithms using a surrogate loss approach and regularization techniques. We prove universal consistency and finite sample bounds characterizing the generalization properties of the proposed method. Experimental results are provided to demonstrate the practical usefulness of the proposed approach.

Asynchronous parallel optimization received substantial successes and extensive attention recently. One of core theoretical questions is how much speedup (or benefit) the asynchronous parallelization can bring to us. This paper provides a comprehensive and generic analysis to study the speedup property for a broad range of asynchronous parallel stochastic algorithms from the zeroth order to the first order methods. Our result recovers or improves existing analysis on special cases, provides more insights for understanding the asynchronous parallel behaviors, and suggests a novel asynchronous parallel zeroth order method for the first time. Our experiments provide novel applications of the proposed asynchronous parallel zeroth order method on hyper parameter tuning and model blending problems.

Decision tree (and its extensions such as Gradient Boosting Decision Trees and Random Forest) is a widely used machine learning algorithm, due to its practical effectiveness and model interpretability. With the emergence of big data, there is an increasing need to parallelize the training process of decision tree. However, most existing attempts along this line suffer from high communication costs. In this paper, we propose a new algorithm, called \emph{Parallel Voting Decision Tree (PV-Tree)}, to tackle this challenge. After partitioning the training data onto a number of (e.g., $M$) machines, this algorithm performs both local voting and global voting in each iteration. For local voting, the top-$k$ attributes are selected from each machine according to its local data. Then, the indices of these top attributes are aggregated by a server, and the globally top-$2k$ attributes are determined by a majority voting among these local candidates. Finally, the full-grained histograms of the globally top-$2k$ attributes are collected from local machines in order to identify the best (most informative) attribute and its split point. PV-Tree can achieve a very low communication cost (independent of the total number of attributes) and thus can scale out very well. Furthermore, theoretical analysis shows that this algorithm can learn a near optimal decision tree, since it can find the best attribute with a large probability. Our experiments on real-world datasets show that PV-Tree significantly outperforms the existing parallel decision tree algorithms in the tradeoff between accuracy and efficiency.