mtybilly/Instruct2DS huggingface dataset:
Multi-Step Stochastic ADMM in High Dimensions: Applications to Sparse Optimization and Matrix Decomposition
Authors: Anima Anandkumar, Edmond Jonckheere Hanie Sedghi
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: In this paper, we consider a multi-step version of the stochastic ADMM method with efficient guarantees for high-dimensional problems. We first analyze the simple setting, where the optimization problem consists of a loss function and a single regularizer (e.g. sparse optimization), and then extend to the multi-block setting with multiple regularizers and multiple variables (e.g. matrix decomposition into sparse and low rank components). For the sparse optimization problem, our method achieves the minimax rate of $O(s\log d/T)$ for $s$-sparse problems in $d$ dimensions in $T$ steps, and is thus, unimprovable by any method up to constant factors. For the matrix decomposition problem with a general loss function, we analyze the multi-step ADMM with multiple blocks. We establish $O(1/T)$ rate and efficient scaling as the size of matrix grows. For natural noise models (e.g. independent noise), our convergence rate is minimax-optimal. Thus, we establish tight convergence guarantees for multi-block ADMM in high dimensions. Experiments show that for both sparse optimization and matrix decomposition problems, our algorithm outperforms the state-of-the-art methods.
Spatio-temporal Representations of Uncertainty in Spiking Neural Networks
Authors: Sophie Deneve Cristina Savin
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: It has been long argued that, because of inherent ambiguity and noise, the brain needs to represent uncertainty in the form of probability distributions. The neural encoding of such distributions remains however highly controversial. Here we present a novel circuit model for representing multidimensional real-valued distributions using a spike based spatio-temporal code. Our model combines the computational advantages of the currently competing models for probabilistic codes and exhibits realistic neural responses along a variety of classic measures. Furthermore, the model highlights the challenges associated with interpreting neural activity in relation to behavioral uncertainty and points to alternative population-level approaches for the experimental validation of distributed representations.
Biclustering Using Message Passing
Authors: Soheil Feizi Luke O'Connor
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Biclustering is the analog of clustering on a bipartite graph. Existent methods infer biclusters through local search strategies that find one cluster at a time; a common technique is to update the row memberships based on the current column memberships, and vice versa. We propose a biclustering algorithm that maximizes a global objective function using message passing. Our objective function closely approximates a general likelihood function, separating a cluster size penalty term into row- and column-count penalties. Because we use a global optimization framework, our approach excels at resolving the overlaps between biclusters, which are important features of biclusters in practice. Moreover, Expectation-Maximization can be used to learn the model parameters if they are unknown. In simulations, we find that our method outperforms two of the best existing biclustering algorithms, ISA and LAS, when the planted clusters overlap. Applied to three gene expression datasets, our method finds coregulated gene clusters that have high quality in terms of cluster size and density.
Identifying and attacking the saddle point problem in high-dimensional non-convex optimization
Authors: Razvan Pascanu, Caglar Gulcehre, Kyunghyun Cho, Surya Ganguli, Yoshua Bengio Yann N. Dauphin
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such minimizations, and it is often thought that a main source of difficulty for these local methods to find the global minimum is the proliferation of local minima with much higher error than the global minimum. Here we argue, based on results from statistical physics, random matrix theory, neural network theory, and empirical evidence, that a deeper and more profound difficulty originates from the proliferation of saddle points, not local minima, especially in high dimensional problems of practical interest. Such saddle points are surrounded by high error plateaus that can dramatically slow down learning, and give the illusory impression of the existence of a local minimum. Motivated by these arguments, we propose a new approach to second-order optimization, the saddle-free Newton method, that can rapidly escape high dimensional saddle points, unlike gradient descent and quasi-Newton methods. We apply this algorithm to deep or recurrent neural network training, and provide numerical evidence for its superior optimization performance.
Clustered factor analysis of multineuronal spike data
Authors: Timothy A. Machado, John P. Cunningham, Liam Paninski Lars Buesing
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: High-dimensional, simultaneous recordings of neural spiking activity are often explored, analyzed and visualized with the help of latent variable or factor models. Such models are however ill-equipped to extract structure beyond shared, distributed aspects of firing activity across multiple cells. Here, we extend unstructured factor models by proposing a model that discovers subpopulations or groups of cells from the pool of recorded neurons. The model combines aspects of mixture of factor analyzer models for capturing clustering structure, and aspects of latent dynamical system models for capturing temporal dependencies. In the resulting model, we infer the subpopulations and the latent factors from data using variational inference and model parameters are estimated by Expectation Maximization (EM). We also address the crucial problem of initializing parameters for EM by extending a sparse subspace clustering algorithm to integer-valued spike count observations. We illustrate the merits of the proposed model by applying it to calcium-imaging data from spinal cord neurons, and we show that it uncovers meaningful clustering structure in the data.
Beta-Negative Binomial Process and Exchangeable ￼Random Partitions for Mixed-Membership Modeling
Authors: Mingyuan Zhou
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: The beta-negative binomial process (BNBP), an integer-valued stochastic process, is employed to partition a count vector into a latent random count matrix. As the marginal probability distribution of the BNBP that governs the exchangeable random partitions of grouped data has not yet been developed, current inference for the BNBP has to truncate the number of atoms of the beta process. This paper introduces an exchangeable partition probability function to explicitly describe how the BNBP clusters the data points of each group into a random number of exchangeable partitions, which are shared across all the groups. A fully collapsed Gibbs sampler is developed for the BNBP, leading to a novel nonparametric Bayesian topic model that is distinct from existing ones, with simple implementation, fast convergence, good mixing, and state-of-the-art predictive performance.
Gaussian Process Volatility Model
Authors: José Miguel Hernández Lobato, Zoubin Ghahramani Yue Wu
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: The prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the evolution of the variance. Moreover, functional parameters are usually learned by maximum likelihood, which can lead to overfitting. To address these problems we introduce GP-Vol, a novel non-parametric model for time-changing variances based on Gaussian Processes. This new model can capture highly flexible functional relationships for the variances. Furthermore, we introduce a new online algorithm for fast inference in GP-Vol. This method is much faster than current offline inference procedures and it avoids overfitting problems by following a fully Bayesian approach. Experiments with financial data show that GP-Vol performs significantly better than current standard alternatives.
Distributed Estimation, Information Loss and Exponential Families
Authors: Alexander Ihler Qiang Liu
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum likelihood estimates (MLE) based on the data subsets, and then combines the local MLEs to achieve the best possible approximation to the global MLE, based on the whole dataset jointly. We study the statistical properties of this framework, showing that the loss of efficiency compared to the global setting relates to how much the underlying distribution families deviate from full exponential families, drawing connection to the theory of information loss by Fisher, Rao and Efron. We show that the full-exponential-family-ness" represents the lower bound of the error rate of arbitrary combinations of local MLEs, and is achieved by a KL-divergence-based combination method but not by a more common linear combination method. We also study the empirical properties of the KL and linear combination methods, showing that the KL method significantly outperforms linear combination in practical settings with issues such as model misspecification, non-convexity, and heterogeneous data partitions."
Cone-Constrained Principal Component Analysis
Authors: Andrea Montanari, Emile Richard Yash Deshpande
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Estimating a vector from noisy quadratic observations is a task that arises naturally in many contexts, from dimensionality reduction, to synchronization and phase retrieval problems. It is often the case that additional information is available about the unknown vector (for instance, sparsity, sign or magnitude of its entries). Many authors propose non-convex quadratic optimization problems that aim at exploiting optimally this information. However, solving these problems is typically NP-hard. We consider a simple model for noisy quadratic observation of an unknown vector $\bvz$. The unknown vector is constrained to belong to a cone $\Cone \ni \bvz$. While optimal estimation appears to be intractable for the general problems in this class, we provide evidence that it is tractable when $\Cone$ is a convex cone with an efficient projection. This is surprising, since the corresponding optimization problem is non-convex and --from a worst case perspective-- often NP hard. We characterize the resulting minimax risk in terms of the statistical dimension of the cone $\delta(\Cone)$. This quantity is already known to control the risk of estimation from gaussian observations and random linear measurements. It is rather surprising that the same quantity plays a role in the estimation risk from quadratic measurements.
Dynamic Rank Factor Model for Text Streams
Authors: Lin Du, Esther Salazar, Lawrence Carin Shaobo Han
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We propose a semi-parametric and dynamic rank factor model for topic modeling, capable of (1) discovering topic prevalence over time, and (2) learning contemporary multi-scale dependence structures, providing topic and word correlations as a byproduct. The high-dimensional and time-evolving ordinal/rank observations (such as word counts), after an arbitrary monotone transformation, are well accommodated through an underlying dynamic sparse factor model. The framework naturally admits heavy-tailed innovations, capable of inferring abrupt temporal jumps in the importance of topics. Posterior inference is performed through straightforward Gibbs sampling, based on the forward-filtering backward-sampling algorithm. Moreover, an efficient data subsampling scheme is leveraged to speed up inference on massive datasets. The modeling framework is illustrated on two real datasets: the US State of the Union Address and the JSTOR collection from Science.
Online combinatorial optimization with stochastic decision sets and adversarial losses
Authors: Michal Valko Gergely Neu
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Most work on sequential learning assumes a fixed set of actions that are available all the time. However, in practice, actions can consist of picking subsets of readings from sensors that may break from time to time, road segments that can be blocked or goods that are out of stock. In this paper we study learning algorithms that are able to deal with stochastic availability of such unreliable composite actions. We propose and analyze algorithms based on the Follow-The-Perturbed-Leader prediction method for several learning settings differing in the feedback provided to the learner. Our algorithms rely on a novel loss estimation technique that we call Counting Asleep Times. We deliver regret bounds for our algorithms for the previously studied full information and (semi-)bandit settings, as well as a natural middle point between the two that we call the restricted information setting. A special consequence of our results is a significant improvement of the best known performance guarantees achieved by an efficient algorithm for the sleeping bandit problem with stochastic availability. Finally, we evaluate our algorithms empirically and show their improvement over the known approaches.
Magnitude-sensitive preference formation`
Authors: Edward Vul, Paul R Schrater Nisheeth Srivastava
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Our understanding of the neural computations that underlie the ability of animals to choose among options has advanced through a synthesis of computational modeling, brain imaging and behavioral choice experiments. Yet, there remains a gulf between theories of preference learning and accounts of the real, economic choices that humans face in daily life, choices that are usually between some amount of money and an item. In this paper, we develop a theory of magnitude-sensitive preference learning that permits an agent to rationally infer its preferences for items compared with money options of different magnitudes. We show how this theory yields classical and anomalous supply-demand curves and predicts choices for a large panel of risky lotteries. Accurate replications of such phenomena without recourse to utility functions suggest that the theory proposed is both psychologically realistic and econometrically viable.
Learning convolution filters for inverse covariance estimation of neural network connectivity
Authors: George O. Mohler
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We consider the problem of inferring direct neural network connections from Calcium imaging time series. Inverse covariance estimation has proven to be a fast and accurate method for learning macro- and micro-scale network connectivity in the brain and in a recent Kaggle Connectomics competition inverse covariance was the main component of several top ten solutions, including our own and the winning team's algorithm. However, the accuracy of inverse covariance estimation is highly sensitive to signal preprocessing of the Calcium fluorescence time series. Furthermore, brute force optimization methods such as grid search and coordinate ascent over signal processing parameters is a time intensive process, where learning may take several days and parameters that optimize one network may not generalize to networks with different size and parameters. In this paper we show how inverse covariance estimation can be dramatically improved using a simple convolution filter prior to applying sample covariance. Furthermore, these signal processing parameters can be learned quickly using a supervised optimization algorithm. In particular, we maximize a binomial log-likelihood loss function with respect to a convolution filter of the time series and the inverse covariance regularization parameter. Our proposed algorithm is relatively fast on networks the size of those in the competition (1000 neurons), producing AUC scores with similar accuracy to the winning solution in training time under 2 hours on a cpu. Prediction on new networks of the same size is carried out in less than 15 minutes, the time it takes to read in the data and write out the solution.
Sparse PCA via Covariance Thresholding
Authors: Andrea Montanari Yash Deshpande
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension $n\times p$ and seek to reconstruct it under additional sparsity assumptions. In particular, we assume here that the principal components $\bv_1,\dots,\bv_r$ have at most $k_1, \cdots, k_q$ non-zero entries respectively, and study the high-dimensional regime in which $p$ is of the same order as $n$. In an influential paper, Johnstone and Lu \cite{johnstone2004sparse} introduced a simple algorithm that estimates the support of the principal vectors $\bv_1,\dots,\bv_r$ by the largest entries in the diagonal of the empirical covariance. This method can be shown to succeed with high probability if $k_q \le C_1\sqrt{n/\log p}$, and to fail with high probability if $k_q\ge C_2 \sqrt{n/\log p}$ for two constants $0 < C_1,C_2 < \infty$. Despite a considerable amount of work over the last ten years, no practical algorithm exists with provably better support recovery guarantees. Here we analyze a covariance thresholding algorithm that was recently proposed by Krauthgamer, Nadler and Vilenchik \cite{KrauthgamerSPCA}. We confirm empirical evidence presented by these authors and rigorously prove that the algorithm succeeds with high probability for $k$ of order $\sqrt{n}$. Recent conditional lower bounds \cite{berthet2013computational} suggest that it might be impossible to do significantly better. The key technical component of our analysis develops new bounds on the norm of kernel random matrices, in regimes that were not considered before.
Online Optimization for Max-Norm Regularization
Authors: Huan Xu, Ping Li Jie Shen
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Max-norm regularizer has been extensively studied in the last decade as it promotes an effective low rank estimation of the underlying data. However, max-norm regularized problems are typically formulated and solved in a batch manner, which prevents it from processing big data due to possible memory bottleneck. In this paper, we propose an online algorithm for solving max-norm regularized problems that is scalable to large problems. Particularly, we consider the matrix decomposition problem as an example, although our analysis can also be applied in other problems such as matrix completion. The key technique in our algorithm is to reformulate the max-norm into a matrix factorization form, consisting of a basis component and a coefficients one. In this way, we can solve the optimal basis and coefficients alternatively. We prove that the basis produced by our algorithm converges to a stationary point asymptotically. Experiments demonstrate encouraging results for the effectiveness and robustness of our algorithm. See the full paper at arXiv:1406.3190.
Optimizing Energy Production Using Policy Search and Predictive State Representations
Authors: Doina Precup, Michel Gendreau Yuri Grinberg
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We consider the challenging practical problem of optimizing the power production of a complex of hydroelectric power plants, which involves control over three continuous action variables, uncertainty in the amount of water inflows and a variety of constraints that need to be satisfied. We propose a policy-search-based approach coupled with predictive modelling to address this problem. This approach has some key advantages compared to other alternatives, such as dynamic programming: the policy representation and search algorithm can conveniently incorporate domain knowledge; the resulting policies are easy to interpret, and the algorithm is naturally parallelizable. Our algorithm obtains a policy which outperforms the solution found by dynamic programming both quantitatively and qualitatively.
Dependent nonparametric trees for dynamic hierarchical clustering
Authors: Qirong Ho, Sinead Williamson, Eric P. Xing Avinava Dubey
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Hierarchical clustering methods offer an intuitive and powerful way to model a wide variety of data sets. However, the assumption of a fixed hierarchy is often overly restrictive when working with data generated over a period of time: We expect both the structure of our hierarchy, and the parameters of the clusters, to evolve with time. In this paper, we present a distribution over collections of time-dependent, infinite-dimensional trees that can be used to model evolving hierarchies, and present an efficient and scalable algorithm for performing approximate inference in such a model. We demonstrate the efficacy of our model and inference algorithm on both synthetic data and real-world document corpora.
Kernel Mean Estimation via Spectral Filtering
Authors: Bharath Sriperumbudur, Bernhard Schölkopf Krikamol Muandet
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference step of modern kernel methods (e.g., kernel-based non-parametric tests) that rely on embedding probability distributions in RKHSs. Previous work [1] has shown that shrinkage can help in constructing “better” estimators of the kernel mean than the empirical estimator. The present paper studies the consistency and admissibility of the estimators in [1], and proposes a wider class of shrinkage estimators that improve upon the empirical estimator by considering appropriate basis functions. Using the kernel PCA basis, we show that some of these estimators can be constructed using spectral filtering algorithms which are shown to be consistent under some technical assumptions. Our theoretical analysis also reveals a fundamental connection to the kernel-based supervised learning framework. The proposed estimators are simple to implement and perform well in practice.
Beyond Disagreement-Based Agnostic Active Learning
Authors: Kamalika Chaudhuri Chicheng Zhang
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We study agnostic active learning, where the goal is to learn a classifier in a pre-specified hypothesis class interactively with as few label queries as possible, while making no assumptions on the true function generating the labels. The main algorithms for this problem are {\em{disagreement-based active learning}}, which has a high label requirement, and {\em{margin-based active learning}}, which only applies to fairly restricted settings. A major challenge is to find an algorithm which achieves better label complexity, is consistent in an agnostic setting, and applies to general classification problems. In this paper, we provide such an algorithm. Our solution is based on two novel contributions -- a reduction from consistent active learning to confidence-rated prediction with guaranteed error, and a novel confidence-rated predictor.
Distance-Based Network Recovery under Feature Correlation
Authors: Volker Roth David Adametz
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We present an inference method for Gaussian graphical models when only pairwise distances of n objects are observed. Formally, this is a problem of estimating an n x n covariance matrix from the Mahalanobis distances dMH(xi, xj), where object xi lives in a latent feature space. We solve the problem in fully Bayesian fashion by integrating over the Matrix-Normal likelihood and a Matrix-Gamma prior; the resulting Matrix-T posterior enables network recovery even under strongly correlated features. Hereby, we generalize TiWnet, which assumes Euclidean distances with strict feature independence. In spite of the greatly increased flexibility, our model neither loses statistical power nor entails more computational cost. We argue that the extension is highly relevant as it yields significantly better results in both synthetic and real-world experiments, which is successfully demonstrated for a network of biological pathways in cancer patients.
Inference by Learning: Speeding-up Graphical Model Optimization via a Coarse-to-Fine Cascade of Pruning Classifiers
Authors: Nikos Komodakis, Sebastien Leprince, Jean Philippe Avouac Bruno Conejo
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We propose a general and versatile framework that significantly speeds-up graphical model optimization while maintaining an excellent solution accuracy. The proposed approach, refereed as Inference by Learning or IbyL, relies on a multi-scale pruning scheme that progressively reduces the solution space by use of a coarse-to-fine cascade of learnt classifiers. We thoroughly experiment with classic computer vision related MRF problems, where our novel framework constantly yields a significant time speed-up (with respect to the most efficient inference methods) and obtains a more accurate solution than directly optimizing the MRF. We make our code available on-line.
A Complete Variational Tracker
Authors: Steven Bottone, Bhargav Avasarala Ryan Turner
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We introduce a novel probabilistic tracking algorithm that incorporates combinatorial data association constraints and model-based track management using variational Bayes. We use a Bethe entropy approximation to incorporate data association constraints that are often ignored in previous probabilistic tracking algorithms. Noteworthy aspects of our method include a model-based mechanism to replace heuristic logic typically used to initiate and destroy tracks, and an assignment posterior with linear computation cost in window length as opposed to the exponential scaling of previous MAP-based approaches. We demonstrate the applicability of our method on radar tracking and computer vision problems.
Optimal prior-dependent neural population codes under shared input noise
Authors: Jonathan W. Pillow Agnieszka Grabska-Barwińska
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: The brain uses population codes to form distributed, noise-tolerant representations of sensory and motor variables. Recent work has examined the theoretical optimality of such codes in order to gain insight into the principles governing population codes found in the brain. However, the majority of the population coding literature considers either conditionally independent neurons or neurons with noise governed by a stimulus-independent covariance matrix. Here we analyze population coding under a simple alternative model in which latent input noise" corrupts the stimulus before it is encoded by the population. This provides a convenient and tractable description for irreducible uncertainty that cannot be overcome by adding neurons, and induces stimulus-dependent correlations that mimic certain aspects of the correlations observed in real populations. We examine prior-dependent, Bayesian optimal coding in such populations using exact analyses of cases in which the posterior is approximately Gaussian. These analyses extend previous results on independent Poisson population codes and yield an analytic expression for squared loss and a tight upper bound for mutual information. We show that, for homogeneous populations that tile the input domain, optimal tuning curve width depends on the prior, the loss function, the resource constraint, and the amount of input noise. This framework provides a practical testbed for examining issues of optimality, noise, correlation, and coding fidelity in realistic neural populations."
Conditional Swap Regret and Conditional Correlated Equilibrium
Authors: Scott Yang Mehryar Mohri
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We introduce a natural extension of the notion of swap regret, conditional swap regret, that allows for action modifications conditioned on the player’s action history. We prove a series of new results for conditional swap regret minimization. We present algorithms for minimizing conditional swap regret with bounded conditioning history. We further extend these results to the case where conditional swaps are considered only for a subset of actions. We also define a new notion of equilibrium, conditional correlated equilibrium, that is tightly connected to the notion of conditional swap regret: when all players follow conditional swap regret minimization strategies, then the empirical distribution approaches this equilibrium. Finally, we extend our results to the multi-armed bandit scenario.
Extracting Latent Structure From Multiple Interacting Neural Populations
Authors: Amin Zandvakili, Adam Kohn, Christian K. Machens, Byron M. Yu João D. Semedo
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Developments in neural recording technology are rapidly enabling the recording of populations of neurons in multiple brain areas simultaneously, as well as the identification of the types of neurons being recorded (e.g., excitatory vs. inhibitory). There is a growing need for statistical methods to study the interaction among multiple, labeled populations of neurons. Rather than attempting to identify direct interactions between neurons (where the number of interactions grows with the number of neurons squared), we propose to extract a smaller number of latent variables from each population and study how the latent variables interact. Specifically, we propose extensions to probabilistic canonical correlation analysis (pCCA) to capture the temporal structure of the latent variables, as well as to distinguish within-population dynamics from across-population interactions (termed Group Latent Auto-Regressive Analysis, gLARA). We then applied these methods to populations of neurons recorded simultaneously in visual areas V1 and V2, and found that gLARA provides a better description of the recordings than pCCA. This work provides a foundation for studying how multiple populations of neurons interact and how this interaction supports brain function.
Near-optimal Reinforcement Learning in Factored MDPs
Authors: Benjamin Van Roy Ian Osband
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Any reinforcement learning algorithm that applies to all Markov decision processes (MDPs) will suffer $\Omega(\sqrt{SAT})$ regret on some MDP, where $T$ is the elapsed time and $S$ and $A$ are the cardinalities of the state and action spaces. This implies $T = \Omega(SA)$ time to guarantee a near-optimal policy. In many settings of practical interest, due to the curse of dimensionality, $S$ and $A$ can be so enormous that this learning time is unacceptable. We establish that, if the system is known to be a \emph{factored} MDP, it is possible to achieve regret that scales polynomially in the number of \emph{parameters} encoding the factored MDP, which may be exponentially smaller than $S$ or $A$. We provide two algorithms that satisfy near-optimal regret bounds in this context: posterior sampling reinforcement learning (PSRL) and an upper confidence bound algorithm (UCRL-Factored).
Delay-Tolerant Algorithms for Asynchronous Distributed Online Learning
Authors: Matthew Streeter H. Brendan McMahan
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We analyze new online gradient descent algorithms for distributed systems with large delays between gradient computations and the corresponding updates. Using insights from adaptive gradient methods, we develop algorithms that adapt not only to the sequence of gradients, but also to the precise update delays that occur. We first give an impractical algorithm that achieves a regret bound that precisely quantifies the impact of the delays. We then analyze AdaptiveRevision, an algorithm that is efficiently implementable and achieves comparable guarantees. The key algorithmic technique is appropriately and efficiently revising the learning rate used for previous gradient steps. Experimental results show when the delays grow large (1000 updates or more), our new algorithms perform significantly better than standard adaptive gradient methods.
Difference of Convex Functions Programming for Reinforcement Learning
Authors: Matthieu Geist, Olivier Pietquin Bilal Piot
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Large Markov Decision Processes (MDPs) are usually solved using Approximate Dynamic Programming (ADP) methods such as Approximate Value Iteration (AVI) or Approximate Policy Iteration (API). The main contribution of this paper is to show that, alternatively, the optimal state-action value function can be estimated using Difference of Convex functions (DC) Programming. To do so, we study the minimization of a norm of the Optimal Bellman Residual (OBR) $T^*Q-Q$, where $T^*$ is the so-called optimal Bellman operator. Controlling this residual allows controlling the distance to the optimal action-value function, and we show that minimizing an empirical norm of the OBR is consistant in the Vapnik sense. Finally, we frame this optimization problem as a DC program. That allows envisioning using the large related literature on DC Programming to address the Reinforcement Leaning (RL) problem.
SerialRank: Spectral Ranking using Seriation
Authors: Alexandre d'Aspremont, Milan Vojnovic Fajwel Fogel
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We describe a seriation algorithm for ranking a set of n items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a similarity matrix from pairwise comparisons, using seriation methods to reorder this matrix and construct a ranking. We first show that this spectral seriation algorithm recovers the true ranking when all pairwise comparisons are observed and consistent with a total order. We then show that ranking reconstruction is still exact even when some pairwise comparisons are corrupted or missing, and that seriation based spectral ranking is more robust to noise than other scoring methods. An additional benefit of the seriation formulation is that it allows us to solve semi-supervised ranking problems. Experiments on both synthetic and real datasets demonstrate that seriation based spectral ranking achieves competitive and in some cases superior performance compared to classical ranking methods.
RAAM: The Benefits of Robustness in Approximating Aggregated MDPs in Reinforcement Learning
Authors: Dharmashankar Subramanian Marek Petrik
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We describe how to use robust Markov decision processes for value function approximation with state aggregation. The robustness serves to reduce the sensitivity to the approximation error of sub-optimal policies in comparison to classical methods such as fitted value iteration. This results in reducing the bounds on the gamma-discounted infinite horizon performance loss by a factor of 1/(1-gamma) while preserving polynomial-time computational complexity. Our experimental results show that using the robust representation can significantly improve the solution quality with minimal additional computational cost.
Covariance shrinkage for autocorrelated data
Authors: Klaus-Robert Müller Daniel Bartz
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: The accurate estimation of covariance matrices is essential for many signal processing and machine learning algorithms. In high dimensional settings the sample covariance is known to perform poorly, hence regularization strategies such as analytic shrinkage of Ledoit/Wolf are applied. In the standard setting, i.i.d. data is assumed, however, in practice, time series typically exhibit strong autocorrelation structure, which introduces a pronounced estimation bias. Recent work by Sancetta has extended the shrinkage framework beyond i.i.d. data. We contribute in this work by showing that the Sancetta estimator, while being consistent in the high-dimensional limit, suffers from a high bias in finite sample sizes. We propose an alternative estimator, which is (1) unbiased, (2) less sensitive to hyperparameter choice and (3) yields superior performance in simulations on toy data and on a real world data set from an EEG-based Brain-Computer-Interfacing experiment.
Parallel Successive Convex Approximation for Nonsmooth Nonconvex Optimization
Authors: Mingyi Hong, Zhi-Quan Luo, Jong-Shi Pang Meisam Razaviyayn
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Consider the problem of minimizing the sum of a smooth (possibly non-convex) and a convex (possibly nonsmooth) function involving a large number of variables. A popular approach to solve this problem is the block coordinate descent (BCD) method whereby at each iteration only one variable block is updated while the remaining variables are held fixed. With the recent advances in the developments of the multi-core parallel processing technology, it is desirable to parallelize the BCD method by allowing multiple blocks to be updated simultaneously at each iteration of the algorithm. In this work, we propose an inexact parallel BCD approach where at each iteration, a subset of the variables is updated in parallel by minimizing convex approximations of the original objective function. We investigate the convergence of this parallel BCD method for both randomized and cyclic variable selection rules. We analyze the asymptotic and non-asymptotic convergence behavior of the algorithm for both convex and non-convex objective functions. The numerical experiments suggest that for a special case of Lasso minimization problem, the cyclic block selection rule can outperform the randomized rule.
Exact Post Model Selection Inference for Marginal Screening
Authors: Jonathan E. Taylor Jason D. Lee
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We develop a framework for post model selection inference, via marginal screening, in linear regression. At the core of this framework is a result that characterizes the exact distribution of linear functions of the response $y$, conditional on the model being selected (``condition on selection framework). This allows us to construct valid confidence intervals and hypothesis tests for regression coefficients that account for the selection procedure. In contrast to recent work in high-dimensional statistics, our results are exact (non-asymptotic) and require no eigenvalue-like assumptions on the design matrix $X$. Furthermore, the computational cost of marginal regression, constructing confidence intervals and hypothesis testing is negligible compared to the cost of linear regression, thus making our methods particularly suitable for extremely large datasets. Although we focus on marginal screening to illustrate the applicability of the condition on selection framework, this framework is much more broadly applicable. We show how to apply the proposed framework to several other selection procedures including orthogonal matching pursuit and marginal screening+Lasso."
Capturing Semantically Meaningful Word Dependencies with an Admixture of Poisson MRFs
Authors: Pradeep Ravikumar, Inderjit S. Dhillon David I. Inouye
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We develop a fast algorithm for the Admixture of Poisson MRFs (APM) topic model and propose a novel metric to directly evaluate this model. The APM topic model recently introduced by Inouye et al. (2014) is the first topic model that allows for word dependencies within each topic unlike in previous topic models like LDA that assume independence between words within a topic. Research in both the semantic coherence of a topic models (Mimno et al. 2011, Newman et al. 2010) and measures of model fitness (Mimno & Blei 2011) provide strong support that explicitly modeling word dependencies---as in APM---could be both semantically meaningful and essential for appropriately modeling real text data. Though APM shows significant promise for providing a better topic model, APM has a high computational complexity because $O(p^2)$ parameters must be estimated where $p$ is the number of words (Inouye et al. could only provide results for datasets with $p = 200$). In light of this, we develop a parallel alternating Newton-like algorithm for training the APM model that can handle $p = 10^4$ as an important step towards scaling to large datasets. In addition, Inouye et al. only provided tentative and inconclusive results on the utility of APM. Thus, motivated by simple intuitions and previous evaluations of topic models, we propose a novel evaluation metric based on human evocation scores between word pairs (i.e. how much one word brings to mind" another word (Boyd-Graber et al. 2006)). We provide compelling quantitative and qualitative results on the BNC corpus that demonstrate the superiority of APM over previous topic models for identifying semantically meaningful word dependencies. (MATLAB code available at: http://bigdata.ices.utexas.edu/software/apm/)"
Sequential Monte Carlo for Graphical Models
Authors: Fredrik Lindsten, Thomas B. Schön Christian A. Naesseth
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a monotonically increasing sequence of probability spaces. By targeting these auxiliary distributions using SMC we are able to approximate the full joint distribution defined by the PGM. One of the key merits of the SMC sampler is that it provides an unbiased estimate of the partition function of the model. We also show how it can be used within a particle Markov chain Monte Carlo framework in order to construct high-dimensional block-sampling algorithms for general PGMs.
Multilabel Structured Output Learning with Random Spanning Trees of Max-Margin Markov Networks
Authors: Hongyu Su, Emilie Morvant, Juho Rousu, John Shawe-Taylor Mario Marchand
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: We show that the usual score function for conditional Markov networks can be written as the expectation over the scores of their spanning trees. We also show that a small random sample of these output trees can attain a significant fraction of the margin obtained by the complete graph and we provide conditions under which we can perform tractable inference. The experimental results confirm that practical learning is scalable to realistic datasets using this approach.
Dimensionality Reduction with Subspace Structure Preservation
Authors: Ifeoma Nwogu, Venu Govindaraju Devansh Arpit
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that $2K$ projection vectors are sufficient for the independence preservation of any $K$ class data sampled from a union of independent subspaces. It is this non-trivial observation that we use for designing our dimensionality reduction technique. In this paper, we propose a novel dimensionality reduction algorithm that theoretically preserves this structure for a given dataset. We support our theoretical analysis with empirical results on both synthetic and real world data achieving \textit{state-of-the-art} results compared to popular dimensionality reduction techniques.
Compressive Sensing of Signals from a GMM with Sparse Precision Matrices
Authors: Xuejun Liao, Minhua Chen, Lawrence Carin Jianbo Yang
Published in: Advances in Neural Information Processing Systems 27  (NIPS 2014) (Main Conference Track), 2014

Abstract: This paper is concerned with compressive sensing of signals drawn from a Gaussian mixture model (GMM) with sparse precision matrices. Previous work has shown: (i) a signal drawn from a given GMM can be perfectly reconstructed from r noise-free measurements if the (dominant) rank of each covariance matrix is less than r; (ii) a sparse Gaussian graphical model can be efficiently estimated from fully-observed training signals using graphical lasso. This paper addresses a problem more challenging than both (i) and (ii), by assuming that the GMM is unknown and each signal is only partially observed through incomplete linear measurements. Under these challenging assumptions, we develop a hierarchical Bayesian method to simultaneously estimate the GMM and recover the signals using solely the incomplete measurements and a Bayesian shrinkage prior that promotes sparsity of the Gaussian precision matrices. In addition, we provide theoretical performance bounds to relate the reconstruction error to the number of signals for which measurements are available, the sparsity level of precision matrices, and the “incompleteness” of measurements. The proposed method is demonstrated extensively on compressive sensing of imagery and video, and the results with simulated and hardware-acquired real measurements show significant performance improvement over state-of-the-art methods.