mtybilly/Instruct2DS huggingface dataset:
Median Selection Subset Aggregation for Parallel Inference
Authors: Xiangyu Wang, Peichao Peng, David B. Dunson
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: For massive data sets, efficient computation commonly relies on distributed algorithms that store and process subsets of the data on different machines, minimizing communication costs. Our focus is on regression and classification problems involving many features. A variety of distributed algorithms have been proposed in this context, but challenges arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. We propose a MEdian Selection Subset AGgregation Estimator (message) algorithm, which attempts to solve these problems. The algorithm applies feature selection in parallel for each subset using Lasso or another method, calculates the `median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in both sample and feature size, and has theoretical guarantees. In particular, we show model selection consistency and coefficient estimation efficiency. Extensive experiments show excellent performance in variable selection, estimation, prediction, and computation time relative to usual competitors.
Near-Optimal-Sample Estimators for Spherical Gaussian Mixtures
Authors: Jayadev Acharya, Ashkan Jafarpour, Alon Orlitsky, Ananda Theertha Suresh
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Many important distributions are high dimensional, and often they can be modeled as Gaussian mixtures. We derive the first sample-efficient polynomial-time estimator for high-dimensional spherical Gaussian mixtures. Based on intuitive spectral reasoning, it approximates mixtures of $k$ spherical Gaussians in $d$-dimensions to within$\ell_1$ distance $\epsilon$ using $\mathcal{O}({dk^9(\log^2 d)}/{\epsilon^4})$ samples and $\mathcal{O}_{k,\epsilon}(d^3\log^5 d)$ computation time. Conversely, we show that any estimator requires $\Omega\bigl({dk}/{\epsilon^2}\bigr)$ samples, hence the algorithm's sample complexity is nearly optimal in the dimension. The implied time-complexity factor \mathcal{O}_{k,\epsilon}$ is exponential in $k$, but much smaller than previously known. We also construct a simple estimator for one-dimensional Gaussian mixtures that uses $\tilde\mathcal{O}(k /\epsilon^2)$ samples and $\tilde\mathcal{O}((k/\epsilon)^{3k+1})$ computation time.
Clustering from Labels and Time-Varying Graphs
Authors: Shiau Hong Lim, Yudong Chen, Huan Xu
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We present a general framework for graph clustering where a label is observed to each pair of nodes. This allows a very rich encoding of various types of pairwise interactions between nodes. We propose a new tractable approach to this problem based on maximum likelihood estimator and convex optimization. We analyze our algorithm under a general generative model, and provide both necessary and sufficient conditions for successful recovery of the underlying clusters. Our theoretical results cover and subsume a wide range of existing graph clustering results including planted partition, weighted clustering and partially observed graphs. Furthermore, the result is applicable to novel settings including time-varying graphs such that new insights can be gained on solving these problems. Our theoretical findings are further supported by empirical results on both synthetic and real data.
Incremental Local Gaussian Regression
Authors: Franziska Meier, Philipp Hennig, Stefan Schaal
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Locally weighted regression (LWR) was created as a nonparametric method that can approximate a wide range of functions, is computationally efficient, and can learn continually from very large amounts of incrementally collected data. As an interesting feature, LWR can regress on non-stationary functions, a beneficial property, for instance, in control problems. However, it does not provide a proper generative model for function values, and existing algorithms have a variety of manual tuning parameters that strongly influence bias, variance and learning speed of the results. Gaussian (process) regression, on the other hand, does provide a generative model with rather black-box automatic parameter tuning, but it has higher computational cost, especially for big data sets and if a non-stationary model is required. In this paper, we suggest a path from Gaussian (process) regression to locally weighted regression, where we retain the best of both approaches. Using a localizing function basis and approximate inference techniques, we build a Gaussian (process) regression algorithm of increasingly local nature and similar computational complexity to LWR. Empirical evaluations are performed on several synthetic and real robot datasets of increasing complexity and (big) data scale, and demonstrate that we consistently achieve on par or superior performance compared to current state-of-the-art methods while retaining a principled approach to fast incremental regression with minimal manual tuning parameters.
Bayesian Nonlinear Support Vector Machines and Discriminative Factor Modeling
Authors: Ricardo Henao, Xin Yuan, Lawrence Carin
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: A new Bayesian formulation is developed for nonlinear support vector machines (SVMs), based on a Gaussian process and with the SVM hinge loss expressed as a scaled mixture of normals. We then integrate the Bayesian SVM into a factor model, in which feature learning and nonlinear classifier design are performed jointly; almost all previous work on such discriminative feature learning has assumed a linear classifier. Inference is performed with expectation conditional maximization (ECM) and Markov Chain Monte Carlo (MCMC). An extensive set of experiments demonstrate the utility of using a nonlinear Bayesian SVM within discriminative feature learning and factor modeling, from the standpoints of accuracy and interpretability
Altitude Training: Strong Bounds for Single-Layer Dropout
Authors: Stefan Wager, William Fithian, Sida Wang, Percy Liang
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Dropout training, originally designed for deep neural networks, has been successful on high-dimensional single-layer natural language tasks. This paper proposes a theoretical explanation for this phenomenon: we show that, under a generative Poisson topic model with long documents, dropout training improves the exponent in the generalization bound for empirical risk minimization. Dropout achieves this gain much like a marathon runner who practices at altitude: once a classifier learns to perform reasonably well on training examples that have been artificially corrupted by dropout, it will do very well on the uncorrupted test set. We also show that, under similar conditions, dropout preserves the Bayes decision boundary and should therefore induce minimal bias in high dimensions.
Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature
Authors: Tom Gunter, Michael A. Osborne, Roman Garnett, Philipp Hennig, Stephen J. Roberts
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in probabilistic inference is numerical integration, to average over ensembles of models or unknown (hyper-)parameters (for example to compute marginal likelihood or a partition function). MCMC has provided approaches to numerical integration that deliver state-of-the-art inference, but can suffer from sample inefficiency and poor convergence diagnostics. Bayesian quadrature techniques offer a model-based solution to such problems, but their uptake has been hindered by prohibitive computation costs. We introduce a warped model for probabilistic integrands (likelihoods) that are known to be non-negative, permitting a cheap active learning scheme to optimally select sample locations. Our algorithm is demonstrated to offer faster convergence (in seconds) relative to simple Monte Carlo and annealed importance sampling on both synthetic and real-world examples.
Semi-Separable Hamiltonian Monte Carlo for Inference in Bayesian Hierarchical Models
Authors: Yichuan Zhang, Charles Sutton
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Sampling from hierarchical Bayesian models is often difficult for MCMC methods, because of the strong correlations between the model parameters and the hyperparameters. Recent Riemannian manifold Hamiltonian Monte Carlo (RMHMC) methods have significant potential advantages in this setting, but are computationally expensive. We introduce a new RMHMC method, which we call semi-separable Hamiltonian Monte Carlo, which uses a specially designed mass matrix that allows the joint Hamiltonian over model parameters and hyperparameters to decompose into two simpler Hamiltonians. This structure is exploited by a new integrator which we call the alternating blockwise leapfrog algorithm. The resulting method can mix faster than simpler Gibbs sampling while being simpler and more efficient than previous instances of RMHMC.
Deterministic Symmetric Positive Semidefinite Matrix Completion
Authors: William E. Bishop, Byron M. Yu
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We consider the problem of recovering a symmetric, positive semidefinite (SPSD) matrix from a subset of its entries, possibly corrupted by noise. In contrast to previous matrix recovery work, we drop the assumption of a random sampling of entries in favor of a deterministic sampling of principal submatrices of the matrix. We develop a set of sufficient conditions for the recovery of a SPSD matrix from a set of its principal submatrices, present necessity results based on this set of conditions and develop an algorithm that can exactly recover a matrix when these conditions are met. The proposed algorithm is naturally generalized to the problem of noisy matrix recovery, and we provide a worst-case bound on reconstruction error for this scenario. Finally, we demonstrate the algorithm's utility on noiseless and noisy simulated datasets.
Efficient Inference of Continuous Markov Random Fields with Polynomial Potentials
Authors: Shenlong Wang, Alexander G. Schwing, Raquel Urtasun
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: In this paper, we prove that every multivariate polynomial with even degree can be decomposed into a sum of convex and concave polynomials. Motivated by this property, we exploit the concave-convex procedure to perform inference on continuous Markov random fields with polynomial potentials. In particular, we show that the concave-convex decomposition of polynomials can be expressed as a sum-of-squares optimization, which can be efficiently solved via semidefinite programming. We demonstrate the effectiveness of our approach in the context of 3D reconstruction, shape from shading and image denoising, and show that our approach significantly outperforms existing approaches in terms of efficiency as well as the quality of the retrieved solution.
Inferring synaptic conductances from spike trains with a biophysically inspired point process model
Authors: Kenneth W. Latimer, E. J. Chichilnisky, Fred Rieke, Jonathan W. Pillow
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: A popular approach to neural characterization describes neural responses in terms of a cascade of linear and nonlinear stages: a linear filter to describe stimulus integration, followed by a nonlinear function to convert the filter output to spike rate. However, real neurons respond to stimuli in a manner that depends on the nonlinear integration of excitatory and inhibitory synaptic inputs. Here we introduce a biophysically inspired point process model that explicitly incorporates stimulus-induced changes in synaptic conductance in a dynamical model of neuronal membrane potential. Our work makes two important contributions. First, on a theoretical level, it offers a novel interpretation of the popular generalized linear model (GLM) for neural spike trains. We show that the classic GLM is a special case of our conductance-based model in which the stimulus linearly modulates excitatory and inhibitory conductances in an equal and opposite “push-pull” fashion. Our model can therefore be viewed as a direct extension of the GLM in which we relax these constraints; the resulting model can exhibit shunting as well as hyperpolarizing inhibition, and time-varying changes in both gain and membrane time constant. Second, on a practical level, we show that our model provides a tractable model of spike responses in early sensory neurons that is both more accurate and more interpretable than the GLM. Most importantly, we show that we can accurately infer intracellular synaptic conductances from extracellularly recorded spike trains. We validate these estimates using direct intracellular measurements of excitatory and inhibitory conductances in parasol retinal ganglion cells. We show that the model fit to extracellular spike trains can predict excitatory and inhibitory conductances elicited by novel stimuli with nearly the same accuracy as a model trained directly with intracellular conductances.
Robust Tensor Decomposition with Gross Corruption
Authors: Quanquan Gu, Huan Gui, Jiawei Han
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: In this paper, we study the statistical performance of robust tensor decomposition with gross corruption. The observations are noisy realization of the superposition of a low-rank tensor $\mathcal{W}^*$ and an entrywise sparse corruption tensor $\mathcal{V}^*$. Unlike conventional noise with bounded variance in previous convex tensor decomposition analysis, the magnitude of the gross corruption can be arbitrary large. We show that under certain conditions, the true low-rank tensor as well as the sparse corruption tensor can be recovered simultaneously. Our theory yields nonasymptotic Frobenius-norm estimation error bounds for each tensor separately. We show through numerical experiments that our theory can precisely predict the scaling behavior in practice.
Automatic Discovery of Cognitive Skills to Improve the Prediction of Student Learning
Authors: Robert V. Lindsey, Mohammad Khajah, Michael C. Mozer
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: To master a discipline such as algebra or physics, students must acquire a set of cognitive skills. Traditionally, educators and domain experts manually determine what these skills are and then select practice exercises to hone a particular skill. We propose a technique that uses student performance data to automatically discover the skills needed in a discipline. The technique assigns a latent skill to each exercise such that a student's expected accuracy on a sequence of same-skill exercises improves monotonically with practice. Rather than discarding the skills identified by experts, our technique incorporates a nonparametric prior over the exercise-skill assignments that is based on the expert-provided skills and a weighted Chinese restaurant process. We test our technique on datasets from five different intelligent tutoring systems designed for students ranging in age from middle school through college. We obtain two surprising results. First, in three of the five datasets, the skills inferred by our technique support significantly improved predictions of student performance over the expert-provided skills. Second, the expert-provided skills have little value: our technique predicts student performance nearly as well when it ignores the domain expertise as when it attempts to leverage it. We discuss explanations for these surprising results and also the relationship of our skill-discovery technique to alternative approaches.
Optimal rates for k-NN density and mode estimation
Authors: Sanjoy Dasgupta, Samory Kpotufe
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We present two related contributions of independent interest: (1) high-probability finite sample rates for $k$-NN density estimation, and (2) practical mode estimators -- based on $k$-NN -- which attain minimax-optimal rates under surprisingly general distributional conditions.
Optimization Methods for Sparse Pseudo-Likelihood Graphical Model Selection
Authors: Sang-Yun Oh, Onkar Dalal, Kshitij Khare, Bala Rajaratnam
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$ penalized estimation in the Gaussian framework. Though many of these approaches are demonstrably scalable and have leveraged recent advances in convex optimization, they still depend on the Gaussian functional form. To address this gap, a convex pseudo-likelihood based partial correlation graph estimation method (CONCORD) has been recently proposed. This method uses cyclic coordinate-wise minimization of a regression based pseudo-likelihood, and has been shown to have robust model selection properties in comparison with the Gaussian approach. In direct contrast to the parallel work in the Gaussian setting however, this new convex pseudo-likelihood framework has not leveraged the extensive array of methods that have been proposed in the machine learning literature for convex optimization. In this paper, we address this crucial gap by proposing two proximal gradient methods (CONCORD-ISTA and CONCORD-FISTA) for performing $\ell_1$-regularized inverse covariance matrix estimation in the pseudo-likelihood framework. We present timing comparisons with coordinate-wise minimization and demonstrate that our approach yields tremendous pay offs for $\ell_1$-penalized partial correlation graph estimation outside the Gaussian setting, thus yielding the fastest and most scalable approach for such problems. We undertake a theoretical analysis of our approach and rigorously demonstrate convergence, and also derive rates thereof.
Mind the Nuisance: Gaussian Process Classification using Privileged Noise
Authors: Daniel Hernández-Lobato, Viktoriia Sharmanska, Kristian Kersting, Christoph H. Lampert, Novi Quadrianto
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: The learning with privileged information setting has recently attracted a lot of attention within the machine learning community, as it allows the integration of additional knowledge into the training process of a classifier, even when this comes in the form of a data modality that is not available at test time. Here, we show that privileged information can naturally be treated as noise in the latent function of a Gaussian process classifier (GPC). That is, in contrast to the standard GPC setting, the latent function is not just a nuisance but a feature: it becomes a natural measure of confidence about the training data by modulating the slope of the GPC probit likelihood function. Extensive experiments on public datasets show that the proposed GPC method using privileged noise, called GPC+, improves over a standard GPC without privileged knowledge, and also over the current state-of-the-art SVM-based method, SVM+. Moreover, we show that advanced neural networks and deep learning methods can be compressed as privileged information.
Accelerated Mini-batch Randomized Block Coordinate Descent Method
Authors: Tuo Zhao, Mo Yu, Yiming Wang, Raman Arora, Han Liu
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We consider regularized empirical risk minimization problems. In particular, we minimize the sum of a smooth empirical risk function and a nonsmooth regularization function. When the regularization function is block separable, we can solve the minimization problems in a randomized block coordinate descent (RBCD) manner. Existing RBCD methods usually decrease the objective value by exploiting the partial gradient of a randomly selected block of coordinates in each iteration. Thus they need all data to be accessible so that the partial gradient of the block gradient can be exactly obtained. However, such a ``batch setting may be computationally expensive in practice. In this paper, we propose a mini-batch randomized block coordinate descent (MRBCD) method, which estimates the partial gradient of the selected block based on a mini-batch of randomly sampled data in each iteration. We further accelerate the MRBCD method by exploiting the semi-stochastic optimization scheme, which effectively reduces the variance of the partial gradient estimators. Theoretically, we show that for strongly convex functions, the MRBCD method attains lower overall iteration complexity than existing RBCD methods. As an application, we further trim the MRBCD method to solve the regularized sparse learning problems. Our numerical experiments shows that the MRBCD method naturally exploits the sparsity structure and achieves better computational performance than existing methods."
Global Belief Recursive Neural Networks
Authors: Romain Paulus, Richard Socher, Christopher D. Manning
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Recursive Neural Networks have recently obtained state of the art performance on several natural language processing tasks. However, because of their feedforward architecture they cannot correctly predict phrase or word labels that are determined by context. This is a problem in tasks such as aspect-specific sentiment classification which tries to, for instance, predict that the word Android is positive in the sentence Android beats iOS. We introduce global belief recursive neural networks (GB-RNNs) which are based on the idea of extending purely feedforward neural networks to include one feedbackward step during inference. This allows phrase level predictions and representations to give feedback to words. We show the effectiveness of this model on the task of contextual sentiment analysis. We also show that dropout can improve RNN training and that a combination of unsupervised and supervised word vector representations performs better than either alone. The feedbackward step improves F1 performance by 3% over the standard RNN on this task, obtains state-of-the-art performance on the SemEval 2013 challenge and can accurately predict the sentiment of specific entities.
Fast and Robust Least Squares Estimation in Corrupted Linear Models
Authors: Brian McWilliams, Gabriel Krummenacher, Mario Lucic, Joachim M. Buhmann
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence that was developed for regression diagnostics can be used to detect such corrupted observations as shown in this paper. This property of influence -- for which we also develop a randomized approximation -- motivates our proposed subsampling algorithm for large scale corrupted linear regression which limits the influence of data points since highly influential points contribute most to the residual error. Under a general model of corrupted observations, we show theoretically and empirically on a variety of simulated and real datasets that our algorithm improves over the current state-of-the-art approximation schemes for ordinary least squares.
Ranking via Robust Binary Classification
Authors: Hyokun Yun, Parameswaran Raman, S. V. N. Vishwanathan
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We propose RoBiRank, a ranking algorithm that is motivated by observing a close connection between evaluation metrics for learning to rank and loss functions for robust classification. The algorithm shows a very competitive performance on standard benchmark datasets against other representative algorithms in the literature. Further, in large scale problems where explicit feature vectors and scores are not given, our algorithm can be efficiently parallelized across a large number of machines; for a task that requires 386,133 x 49,824,519 pairwise interactions between items to be ranked, our algorithm finds solutions that are of dramatically higher quality than that can be found by a state-of-the-art competitor algorithm, given the same amount of wall-clock time for computation.
Nonparametric Bayesian inference on multivariate exponential families
Authors: William Vega-Brown, Marek Doniec, Nicholas Roy
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We develop a model by choosing the maximum entropy distribution from the set of models satisfying certain smoothness and independence criteria; we show that inference on this model generalizes local kernel estimation to the context of Bayesian inference on stochastic processes. Our model enables Bayesian inference in contexts when standard techniques like Gaussian process inference are too expensive to apply. Exact inference on our model is possible for any likelihood function from the exponential family. Inference is then highly efficient, requiring only O(log N) time and O(N) space at run time. We demonstrate our algorithm on several problems and show quantifiable improvement in both speed and performance relative to models based on the Gaussian process.
Advances in Learning Bayesian Networks of Bounded Treewidth
Authors: Siqi Nie, Denis D. Mauá, Cassio P. de Campos, Qiang Ji
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: This work presents novel algorithms for learning Bayesian networks of bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in sampling k-trees (maximal graphs of treewidth k), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that k-tree. The approaches are empirically compared to each other and to state-of-the-art methods on a collection of public data sets with up to 100 variables.
Convolutional Neural Network Architectures for Matching Natural Language Sentences
Authors: Baotian Hu, Zhengdong Lu, Hang Li, Qingcai Chen
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Semantic matching is of central importance to many natural language tasks \cite{bordes2014semantic,RetrievalQA}. A successful matching algorithm needs to adequately model the internal structures of language objects and the interaction between them. As a step toward this goal, we propose convolutional neural network models for matching two sentences, by adapting the convolutional strategy in vision and speech. The proposed models not only nicely represent the hierarchical structures of sentences with their layer-by-layer composition and pooling, but also capture the rich matching patterns at different levels. Our models are rather generic, requiring no prior knowledge on language, and can hence be applied to matching tasks of different nature and in different languages. The empirical study on a variety of matching tasks demonstrates the efficacy of the proposed model on a variety of matching tasks and its superiority to competitor models.
Fast Training of Pose Detectors in the Fourier Domain
Authors: João F. Henriques, Pedro Martins, Rui Caseiro, Jorge Batista
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: In many datasets, the samples are related by a known image transformation, such as rotation, or a repeatable non-rigid deformation. This applies to both datasets with the same objects under different viewpoints, and datasets augmented with virtual samples. Such datasets possess a high degree of redundancy, because geometrically-induced transformations should preserve intrinsic properties of the objects. Likewise, ensembles of classifiers used for pose estimation should also share many characteristics, since they are related by a geometric transformation. By assuming that this transformation is norm-preserving and cyclic, we propose a closed-form solution in the Fourier domain that can eliminate most redundancies. It can leverage off-the-shelf solvers with no modification (e.g. libsvm), and train several pose classifiers simultaneously at no extra cost. Our experiments show that training a sliding-window object detector and pose estimator can be sped up by orders of magnitude, for transformations as diverse as planar rotation, the walking motion of pedestrians, and out-of-plane rotations of cars.
Modeling Deep Temporal Dependencies with Recurrent Grammar Cells""
Authors: Vincent Michalski, Roland Memisevic, Kishore Konda
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We propose modeling time series by representing the transformations that take a frame at time t to a frame at time t+1. To this end we show how a bi-linear model of transformations, such as a gated autoencoder, can be turned into a recurrent network, by training it to predict future frames from the current one and the inferred transformation using backprop-through-time. We also show how stacking multiple layers of gating units in a recurrent pyramid makes it possible to represent the ”syntax” of complicated time series, and that it can outperform standard recurrent neural networks in terms of prediction accuracy on a variety of tasks.
Subspace Embeddings for the Polynomial Kernel
Authors: Haim Avron, Huy L. Nguyễn, David P. Woodruff
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Sketching is a powerful dimensionality reduction tool for accelerating statistical learning algorithms. However, its applicability has been limited to a certain extent since the crucial ingredient, the so-called oblivious subspace embedding, can only be applied to data spaces with an explicit representation as the column span or row span of a matrix, while in many settings learning is done in a high-dimensional space implicitly defined by the data matrix via a kernel transformation. We propose the first {\em fast} oblivious subspace embeddings that are able to embed a space induced by a non-linear kernel {\em without} explicitly mapping the data to the high-dimensional space. In particular, we propose an embedding for mappings induced by the polynomial kernel. Using the subspace embeddings, we obtain the fastest known algorithms for computing an implicit low rank approximation of the higher-dimension mapping of the data matrix, and for computing an approximate kernel PCA of the data, as well as doing approximate kernel principal component regression.
Scale Adaptive Blind Deblurring
Authors: Haichao Zhang, Jianchao Yang
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: The presence of noise and small scale structures usually leads to large kernel estimation errors in blind image deblurring empirically, if not a total failure. We present a scale space perspective on blind deblurring algorithms, and introduce a cascaded scale space formulation for blind deblurring. This new formulation suggests a natural approach robust to noise and small scale structures through tying the estimation across multiple scales and balancing the contributions of different scales automatically by learning from data. The proposed formulation also allows to handle non-uniform blur with a straightforward extension. Experiments are conducted on both benchmark dataset and real-world images to validate the effectiveness of the proposed method. One surprising finding based on our approach is that blur kernel estimation is not necessarily best at the finest scale.
Iterative Neural Autoregressive Distribution Estimator NADE-k
Authors: Tapani Raiko, Li Yao, KyungHyun Cho, Yoshua Bengio
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Training of the neural autoregressive density estimator (NADE) can be viewed as doing one step of probabilistic inference on missing values in data. We propose a new model that extends this inference scheme to multiple steps, arguing that it is easier to learn to improve a reconstruction in $k$ steps rather than to learn to reconstruct in a single inference step. The proposed model is an unsupervised building block for deep learning that combines the desirable properties of NADE and multi-predictive training: (1) Its test likelihood can be computed analytically, (2) it is easy to generate independent samples from it, and (3) it uses an inference engine that is a superset of variational inference for Boltzmann machines. The proposed NADE-k is competitive with the state-of-the-art in density estimation on the two datasets tested.
Model-based Reinforcement Learning and the Eluder Dimension
Authors: Ian Osband, Benjamin Van Roy
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We consider the problem of learning to optimize an unknown Markov decision process (MDP). We show that, if the MDP can be parameterized within some known function class, we can obtain regret bounds that scale with the dimensionality, rather than cardinality, of the system. We characterize this dependence explicitly as $\tilde{O}(\sqrt{d_K d_E T})$ where $T$ is time elapsed, $d_K$ is the Kolmogorov dimension and $d_E$ is the \emph{eluder dimension}. These represent the first unified regret bounds for model-based reinforcement learning and provide state of the art guarantees in several important settings. Moreover, we present a simple and computationally efficient algorithm \emph{posterior sampling for reinforcement learning} (PSRL) that satisfies these bounds.
Do Deep Nets Really Need to be Deep?
Authors: Lei Jimmy Ba, Rich Caruana
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Currently, deep neural networks are the state of the art on problems such as speech recognition and computer vision. In this paper we empirically demonstrate that shallow feed-forward nets can learn the complex functions previously learned by deep nets and achieve accuracies previously only achievable with deep models. Moreover, in some cases the shallow nets can learn these deep functions using the same number of parameters as the original deep models. On the TIMIT phoneme recognition and CIFAR-10 image recognition tasks, shallow nets can be trained that perform similarly to complex, well-engineered, deeper convolutional models.
A State-Space Model for Decoding Auditory Attentional Modulation from MEG in a Competing-Speaker Environment
Authors: Sahar Akram, Jonathan Z. Simon, Shihab Shamma, Behtash Babadi
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Humans are able to segregate auditory objects in a complex acoustic scene, through an interplay of bottom-up feature extraction and top-down selective attention in the brain. The detailed mechanism underlying this process is largely unknown and the ability to mimic this procedure is an important problem in artificial intelligence and computational neuroscience. We consider the problem of decoding the attentional state of a listener in a competing-speaker environment from magnetoencephalographic (MEG) recordings from the human brain. We develop a behaviorally inspired state-space model to account for the modulation of the MEG with respect to attentional state of the listener. We construct a decoder based on the maximum a posteriori (MAP) estimate of the state parameters via the Expectation-Maximization (EM) algorithm. The resulting decoder is able to track the attentional modulation of the listener with multi-second resolution using only the envelopes of the two speech streams as covariates. We present simulation studies as well as application to real MEG data from two human subjects. Our results reveal that the proposed decoder provides substantial gains in terms of temporal resolution, complexity, and decoding accuracy.
Probabilistic Differential Dynamic Programming
Authors: Yunpeng Pan, Evangelos A. Theodorou
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We present a data-driven, probabilistic trajectory optimization framework for systems with unknown dynamics, called Probabilistic Differential Dynamic Programming (PDDP). PDDP takes into account uncertainty explicitly for dynamics models using Gaussian processes (GPs). Based on the second-order local approximation of the value function, PDDP performs Dynamic Programming around a nominal trajectory in Gaussian belief spaces. Different from typical gradient-based policy search methods, PDDP does not require a policy parameterization and learns a locally optimal, time-varying control policy. We demonstrate the effectiveness and efficiency of the proposed algorithm using two nontrivial tasks. Compared with the classical DDP and a state-of-the-art GP-based policy search method, PDDP offers a superior combination of data-efficiency, learning speed, and applicability.
Smoothed Gradients for Stochastic Variational Inference
Authors: Stephan Mandt, David Blei
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Stochastic variational inference (SVI) lets us scale up Bayesian computation to massive data. It uses stochastic optimization to fit a variational distribution, following easy-to-compute noisy natural gradients. As with most traditional stochastic optimization methods, SVI takes precautions to use unbiased stochastic gradients whose expectations are equal to the true gradients. In this paper, we explore the idea of following biased stochastic gradients in SVI. Our method replaces the natural gradient with a similarly constructed vector that uses a fixed-window moving average of some of its previous terms. We will demonstrate the many advantages of this technique. First, its computational cost is the same as for SVI and storage requirements only multiply by a constant factor. Second, it enjoys significant variance reduction over the unbiased estimates, smaller bias than averaged gradients, and leads to smaller mean-squared error against the full gradient. We test our method on latent Dirichlet allocation with three large corpora.
Conditional Random Field Autoencoders for Unsupervised Structured Prediction
Authors: Waleed Ammar, Chris Dyer, Noah A. Smith
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We introduce a framework for unsupervised learning of structured predictors with overlapping, global features. Each input's latent representation is predicted conditional on the observed data using a feature-rich conditional random field (CRF). Then a reconstruction of the input is (re)generated, conditional on the latent structure, using a generative model which factorizes similarly to the CRF. The autoencoder formulation enables efficient exact inference without resorting to unrealistic independence assumptions or restricting the kinds of features that can be used. We illustrate insightful connections to traditional autoencoders, posterior regularization and multi-view learning. Finally, we show competitive results with instantiations of the framework for two canonical tasks in natural language processing: part-of-speech induction and bitext word alignment, and show that training our model can be substantially more efficient than comparable feature-rich baselines.
Stochastic Gradient Descent, Weighted Sampling, and the Randomized Kaczmarz algorithm
Authors: Deanna Needell, Nathan Srebro, Rachel Ward
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We improve a recent gurantee of Bach and Moulines on the linear convergence of SGD for smooth and strongly convex objectives, reducing a quadratic dependence on the strong convexity to a linear dependence. Furthermore, we show how reweighting the sampling distribution (i.e. importance sampling) is necessary in order to further improve convergence, and obtain a linear dependence on average smoothness, dominating previous results, and more broadly discus how importance sampling for SGD can improve convergence also in other scenarios. Our results are based on a connection we make between SGD and the randomized Kaczmarz algorithm, which allows us to transfer ideas between the separate bodies of literature studying each of the two methods.
Learning Mixed Multinomial Logit Model from Ordinal Data
Authors: Sewoong Oh, Devavrat Shah
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Motivated by generating personalized recommendations using ordinal (or preference) data, we study the question of learning a mixture of MultiNomial Logit (MNL) model, a parameterized class of distributions over permutations, from partial ordinal or preference data (e.g. pair-wise comparisons). Despite its long standing importance across disciplines including social choice, operations research and revenue management, little is known about this question. In case of single MNL models (no mixture), computationally and statistically tractable learning from pair-wise comparisons is feasible. However, even learning mixture of two MNL model is infeasible in general. Given this state of affairs, we seek conditions under which it is feasible to learn the mixture model in both computationally and statistically efficient manner. To that end, we present a sufficient condition as well as an efficient algorithm for learning mixed MNL models from partial preferences/comparisons data. In particular, a mixture of $r$ MNL components over $n$ objects can be learnt using samples whose size scales polynomially in $n$ and $r$ (concretely, $n^3 r^{3.5} \log^4 n$, with $r \ll n^{2/7}$ when the model parameters are sufficiently {\em incoherent}). The algorithm has two phases: first, learn the pair-wise marginals for each component using tensor decomposition; second, learn the model parameters for each component using RankCentrality introduced by Negahban et al. In the process of proving these results, we obtain a generalization of existing analysis for tensor decomposition to a more realistic regime where only partial information about each sample is available.
Multiscale Fields of Patterns
Authors: Pedro F. Felzenszwalb, John G. Oberlin
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We describe a framework for defining high-order image models that can be used in a variety of applications. The approach involves modeling local patterns in a multiscale representation of an image. Local properties of a coarsened image reflect non-local properties of the original image. In the case of binary images local properties are defined by the binary patterns observed over small neighborhoods around each pixel. With the multiscale representation we capture the frequency of patterns observed at different scales of resolution. This framework leads to expressive priors that depend on a relatively small number of parameters. For inference and learning we use an MCMC method for block sampling with very large blocks. We evaluate the approach with two example applications. One involves contour detection. The other involves binary segmentation.
Robust Kernel Density Estimation by Scaling and Projection in Hilbert Space
Authors: Robert A. Vandermeulen, Clayton D. Scott
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel density estimator (KDE). As with other estimators, a robust version of the KDE is useful since sample contamination is a common issue with datasets. What ``robustness'' means for a nonparametric density estimate is not straightforward and is a topic we explore in this paper. To construct a robust KDE we scale the traditional KDE and project it to its nearest weighted KDE in the $L^2$ norm. Because the squared $L^2$ norm penalizes point-wise errors superlinearly this causes the weighted KDE to allocate more weight to high density regions. We demonstrate the robustness of the SPKDE with numerical experiments and a consistency result which shows that asymptotically the SPKDE recovers the uncontaminated density under sufficient conditions on the contamination.
Bayesian Sampling Using Stochastic Gradient Thermostats
Authors: Nan Ding, Youhan Fang, Ryan Babbush, Changyou Chen, Robert D. Skeel, Hartmut Neven
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Dynamics-based sampling methods, such as Hybrid Monte Carlo (HMC) and Langevin dynamics (LD), are commonly used to sample target distributions. Recently, such approaches have been combined with stochastic gradient techniques to increase sampling efficiency when dealing with large datasets. An outstanding problem with this approach is that the stochastic gradient introduces an unknown amount of noise which can prevent proper sampling after discretization. To remedy this problem, we show that one can leverage a small number of additional variables in order to stabilize momentum fluctuations induced by the unknown noise. Our method is inspired by the idea of a thermostat in statistical physics and is justified by a general theory.
A Multi-World Approach to Question Answering about Real-World Scenes based on Uncertain Input
Authors: Mateusz Malinowski, Mario Fritz
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We propose a method for automatically answering questions about images by bringing together recent advances from natural language processing and computer vision. We combine discrete reasoning with uncertain predictions by a multi-world approach that represents uncertainty about the perceived world in a bayesian framework. Our approach can handle human questions of high complexity about realistic scenes and replies with range of answer like counts, object classes, instances and lists of them. The system is directly trained from question-answer pairs. We establish a first benchmark for this task that can be seen as a modern attempt at a visual turing test.