mtybilly/Instruct2DS huggingface dataset:
A Data-Driven Approach to Modeling Choice
Authors: Vivek Farias, Srikanth Jagabathula, Devavrat Shah
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: We visit the following fundamental problem: For a `generic model of consumer choice (namely, distributions over preference lists) and a limited amount of data on how consumers actually make decisions (such as marginal preference information), how may one predict revenues from offering a particular assortment of choices? This problem is central to areas within operations research, marketing and econometrics. We present a framework to answer such questions and design a number of tractable algorithms (from a data and computational standpoint) for the same.
Anomaly Detection with Score functions based on Nearest Neighbor Graphs
Authors: Manqi Zhao, Venkatesh Saligrama
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on score functions derived from nearest neighbor graphs on n-point nominal data. Anomalies are declared whenever the score of a test sample falls below q, which is supposed to be the desired false alarm level. The resulting anomaly detector is shown to be asymptotically optimal in that it is uniformly most powerful for the specified false alarm level, q, for the case when the anomaly density is a mixture of the nominal and a known density. Our algorithm is computationally efficient, being linear in dimension and quadratic in data size. It does not require choosing complicated tuning parameters or function approximation classes and it can adapt to local structure such as local change in dimensionality. We demonstrate the algorithm on both artificial and real data sets in high dimensional feature spaces.
Submodularity Cuts and Applications
Authors: Yoshinobu Kawahara, Kiyohito Nagano, Koji Tsuda, Jeff A. Bilmes
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: Several key problems in machine learning, such as feature selection and active learning, can be formulated as submodular set function maximization.  We present herein a novel algorithm for maximizing a submodular set function under a cardinality constraint --- the algorithm is based on a cutting-plane method and is implemented as an iterative small-scale binary-integer linear programming procedure. It is well known that this problem is NP-hard, and the approximation factor achieved by the greedy algorithm is the theoretical limit for polynomial time. As for (non-polynomial time) exact algorithms that perform reasonably in practice, there has been very little in the literature although the problem is quite important for many applications. Our algorithm is guaranteed to find the exact solution in finite iterations, and it converges fast in practice due to the efficiency of the cutting-plane mechanism. Moreover, we also provide a method that produces successively decreasing upper-bounds of the optimal solution, while our algorithm provides successively increasing lower-bounds.  Thus, the accuracy of the current solution can be estimated at any point, and the algorithm can be stopped early once a desired degree of tolerance is met.  We evaluate our algorithm on sensor placement and feature selection applications showing good performance.
Bayesian Sparse Factor Models and DAGs Inference and Comparison
Authors: Ricardo Henao, Ole Winther
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: In this paper we present a novel approach to learn directed acyclic graphs (DAG) and factor models within the same framework while also allowing for model comparison between them. For this purpose, we exploit the connection between factor models and DAGs to propose Bayesian hierarchies based on spike and slab priors to promote sparsity, heavy-tailed priors to ensure identifiability and predictive densities to perform the model comparison. We require identifiability to be able to produce variable orderings leading to valid DAGs and sparsity to learn the structures. The effectiveness of our approach is demonstrated through extensive experiments on artificial and biological data showing that our approach outperform a number of state of the art methods.
A Sparse Non-Parametric Approach for Single Channel Separation of Known Sounds
Authors: Paris Smaragdis, Madhusudana Shashanka, Bhiksha Raj
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: In this paper we present an algorithm for separating mixed sounds from  a monophonic recording. Our approach makes use of training data which  allows us to learn representations of the types of sounds that compose the  mixture. In contrast to popular methods that attempt to extract com-  pact generalizable models for each sound from training data, we employ  the training data itself as a representation of the sources in the mixture.  We show that mixtures of known sounds can be described as sparse com-  binations of the training data itself, and in doing so produce signiﬁcantly  better separation results as compared to similar systems based on compact  statistical models.
Data-driven calibration of linear estimators with minimal penalties
Authors: Sylvain Arlot, Francis R. Bach
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression or spline smoothing, and the choice of a kernel in multiple kernel learning. We propose a new algorithm which first estimates consistently the variance of the noise, based upon the concept of minimal penalty which was previously introduced in the context of model selection. Then, plugging our variance estimate in Mallows $C_L$ penalty is proved to lead to an algorithm satisfying an oracle inequality. Simulation experiments with kernel ridge regression and multiple kernel learning show that the proposed algorithm often improves significantly existing calibration procedures such as 10-fold cross-validation or generalized cross-validation.
fMRI-Based Inter-Subject Cortical Alignment Using Functional Connectivity
Authors: Bryan Conroy, Ben Singer, James Haxby, Peter J. Ramadge
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: The inter-subject alignment of functional MRI (fMRI) data is important for improving the statistical power of fMRI group analyses. In contrast to existing anatomically-based methods, we propose a novel multi-subject algorithm that derives a functional correspondence by aligning spatial patterns of functional connectivity across a set of subjects. We test our method on fMRI data collected during a movie viewing experiment. By cross-validating the results of our algorithm, we show that the correspondence successfully generalizes to a secondary movie dataset not used to derive the alignment.
Unsupervised feature learning for audio classification using convolutional deep belief networks
Authors: Honglak Lee, Peter Pham, Yan Largman, Andrew Y. Ng
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: In recent years, deep learning approaches have gained significant interest as a way of building hierarchical representations from unlabeled data. However, to our knowledge, these deep learning approaches have not been extensively studied for auditory data. In this paper, we apply convolutional deep belief networks to audio data and empirically evaluate them on various audio classification tasks. For the case of speech data, we show that the learned features correspond to phones/phonemes. In addition, our feature representations trained from unlabeled audio data show very good performance for multiple audio classification tasks. We hope that this paper will inspire more research on deep learning approaches applied to a wide range of audio recognition tasks.
Accelerating Bayesian Structural Inference for Non-Decomposable Gaussian Graphical Models
Authors: Baback Moghaddam, Mohammad Emtiyaz Khan, Kevin P. Murphy, Benjamin M. Marlin
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: In this paper we make several contributions towards accelerating approximate Bayesian structural inference for non-decomposable GGMs. Our first contribution is to show how to efficiently compute a BIC or Laplace approximation to the marginal likelihood of non-decomposable graphs using convex methods for precision matrix estimation. This optimization technique can be used as a fast scoring function inside standard Stochastic Local Search (SLS) for generating posterior samples. Our second contribution is a novel framework for efficiently generating large sets of high-quality graph topologies without performing local search. This graph proposal method, which we call Neighborhood Fusion" (NF), samples candidate Markov blankets at each node using sparse regression techniques. Our final contribution is a hybrid method combining the complementary strengths of NF and SLS. Experimental results in structural recovery and prediction tasks demonstrate that NF and hybrid NF/SLS out-perform state-of-the-art local search methods, on both synthetic and real-world datasets, when realistic computational limits are imposed."
Learning transport operators for image manifolds
Authors: Benjamin Culpepper, Bruno A. Olshausen
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: We describe a method for learning a group of continuous transformation operators  to traverse smooth nonlinear manifolds. The method is applied to model how  natural images change over time and scale. The group of continuous transform  operators is represented by a basis that is adapted to the statistics of the data so  that the inﬁnitesimal generator for a measurement orbit can be produced by a  linear combination of a few basis elements. We illustrate how the method can be  used to efﬁciently code time-varying images by describing changes across time  and scale in terms of the learned operators.
Manifold Embeddings for Model-Based Reinforcement Learning under Partial Observability
Authors: Keith Bush, Joelle Pineau
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: Interesting real-world datasets often exhibit nonlinear, noisy, continuous-valued states that are unexplorable, are poorly described by first principles, and are only partially observable. If partial observability can be overcome, these constraints suggest the use of model-based reinforcement learning.  We experiment with manifold embeddings as the reconstructed observable state-space of an off-line, model-based reinforcement learning approach to control. We demonstrate the embedding of a system changes as a result of learning and that the best performing embeddings well-represent the dynamics of both the uncontrolled and adaptively controlled system.  We apply this approach in simulation to learn a neurostimulation policy that is more efficient in treating epilepsy than conventional policies.  We then demonstrate the learned policy completely suppressing seizures in real-world neurostimulation experiments on actual animal brain slices.
Ensemble Nystrom Method
Authors: Sanjiv Kumar, Mehryar Mohri, Ameet Talwalkar
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: A crucial technique for scaling kernel methods to very large data sets reaching or exceeding millions of instances is based on low-rank approximation of kernel matrices. We introduce a new family of algorithms based on mixtures of Nystrom approximations, ensemble Nystrom algorithms, that yield more accurate low-rank approximations than the standard Nystrom method. We give a detailed study of multiple variants of these algorithms based on simple averaging, an exponential weight method, or regression-based methods. We also present a theoretical analysis of these algorithms, including novel error bounds guaranteeing a better convergence rate than the standard Nystrom method. Finally, we report the results of extensive experiments with several data sets containing up to 1M points demonstrating the signiﬁcant performance improvements gained over the standard Nystrom approximation.
Manifold Regularization for SIR with Rate Root-n Convergence
Authors: Wei Bian, Dacheng Tao
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: In this paper, we study the manifold regularization for the Sliced Inverse Regression (SIR). The manifold regularization improves the standard SIR in two aspects: 1) it encodes the local geometry for SIR and 2) it enables SIR to deal with transductive and semi-supervised learning problems. We prove that the proposed graph Laplacian based regularization is convergent at rate root-n. The projection directions of the regularized SIR are optimized by using a conjugate gradient method on the Grassmann manifold. Experimental results support our theory.
STDP enables spiking neurons to detect hidden causes of their inputs
Authors: Bernhard Nessler, Michael Pfeiffer, Wolfgang Maass
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: The principles by which spiking neurons contribute to the astounding computational power of generic cortical microcircuits, and how spike-timing-dependent plasticity (STDP) of synaptic weights could generate and maintain  this computational function, are unknown. We show here that STDP, in conjunction with a stochastic soft winner-take-all (WTA) circuit, induces spiking neurons to generate through their synaptic weights implicit internal models for subclasses (or causes") of the high-dimensional spike patterns of hundreds of pre-synaptic neurons. Hence these  neurons will fire after learning whenever the current input best matches their internal model. The resulting computational function of soft WTA circuits, a common network motif of cortical microcircuits, could therefore be a drastic dimensionality reduction of information streams, together with the autonomous creation of internal models for the probability distributions of their input patterns. We show that the autonomous generation and maintenance of this computational function can be explained on the basis of rigorous mathematical principles. In particular, we show that STDP is able to approximate a stochastic online Expectation-Maximization (EM) algorithm for modeling the input data. A corresponding result is shown for Hebbian learning in artificial neural networks."
Locality-sensitive binary codes from shift-invariant kernels
Authors: Maxim Raginsky, Svetlana Lazebnik
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: This paper addresses the problem of designing binary codes for high-dimensional data such that vectors that are similar in the original space map to similar binary strings. We introduce a simple distribution-free encoding scheme based on random projections, such that the expected Hamming distance between the binary codes of two vectors is related to the value of a shift-invariant kernel (e.g., a Gaussian kernel) between the vectors. We present a full theoretical analysis of the convergence properties of the proposed scheme, and report favorable experimental performance as compared to a recent state-of-the-art method, spectral hashing.
Regularized Distance Metric Learning:Theory and Algorithm
Authors: Rong Jin, Shijun Wang, Yang Zhou
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: In this paper, we examine the generalization error of regularized distance metric learning. We show that with appropriate constraints, the generalization error of regularized distance metric learning could be independent from the dimensionality, making it suitable for handling high dimensional data. In addition, we present an efficient online learning algorithm for regularized distance metric learning. Our empirical studies with data classification and face recognition show that the proposed algorithm is (i) effective for distance metric learning when compared to the state-of-the-art methods, and (ii) efficient and robust for high dimensional data.
Time-Varying Dynamic Bayesian Networks
Authors: Le Song, Mladen Kolar, Eric P. Xing
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: Directed graphical models such as Bayesian networks are a favored formalism to model the dependency structures in complex multivariate systems such as those encountered in biology and neural sciences. When the system is undergoing dynamic transformation, often a temporally rewiring network is needed for capturing the dynamic causal influences between covariates. In this paper, we propose a time-varying dynamic Bayesian network (TV-DBN) for modeling the structurally varying directed dependency structures underlying non-stationary biological/neural time series. This is a challenging problem due the non-stationarity and sample scarcity of the time series. We present a kernel reweighted $\ell_1$ regularized auto-regressive procedure for learning the TV-DBN model. Our method enjoys nice properties such as computational efficiency and provable asymptotic consistency. Applying TV-DBN to time series measurements during yeast cell cycle and brain response to visual stimuli reveals interesting dynamics underlying the respective biological systems.
A General Projection Property for Distribution Families
Authors: Yao-liang Yu, Yuxi Li, Dale Schuurmans, Csaba Szepesvári
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: We prove that linear projections between distribution families with fixed first and second moments are surjective, regardless of dimension. We further extend this result to families that respect additional constraints, such as symmetry, unimodality and log-concavity. By combining our results with classic univariate inequalities, we provide new worst-case analyses for natural risk criteria arising in different fields. One discovery is that portfolio selection under the worst-case value-at-risk and conditional value-at-risk criteria yields identical portfolios.
Region-based Segmentation and Object Detection
Authors: Stephen Gould, Tianshi Gao, Daphne Koller
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: Object detection and multi-class image segmentation are two closely related tasks that can be greatly improved when solved jointly by feeding information from one task to the other. However, current state-of-the-art models use a separate representation for each task making joint inference clumsy and leaving classification of many parts of the scene ambiguous. In this work, we propose a hierarchical region-based approach to joint object detection and image segmentation. Our approach reasons about pixels, regions and objects in a coherent probabilistic model. Importantly, our model gives a single unified description of the scene. We explain every pixel in the image and enforce global consistency between all variables in our model. We run experiments on challenging vision datasets and show significant improvement over state-of-the-art object detection accuracy.
Hierarchical Mixture of Classification Experts Uncovers Interactions between Brain Regions
Authors: Bangpeng Yao, Dirk Walther, Diane Beck, Li Fei-fei
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: The human brain can be described as containing a number of functional regions. For a given task, these regions, as well as the connections between them, play a key role in information processing in the brain. However, most existing multi-voxel pattern analysis approaches either treat multiple functional regions as one large uniform region or several independent regions, ignoring the connections between regions. In this paper, we propose to model such connections in an Hidden Conditional Random Field (HCRF) framework, where the classifier of one region of interest (ROI) makes predictions based on not only its voxels but also the classifier predictions from ROIs that it connects to. Furthermore, we propose a structural learning method in the HCRF framework to automatically uncover the connections between ROIs. Experiments on fMRI data acquired while human subjects viewing images of natural scenes show that our model can improve the top-level (the classifier combining information from all ROIs) and ROI-level prediction accuracy, as well as uncover some meaningful connections between ROIs.
Unsupervised Detection of Regions of Interest Using Iterative Link Analysis
Authors: Gunhee Kim, Antonio Torralba
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: This paper proposes a fast and scalable alternating optimization technique to detect regions of interest (ROIs) in cluttered Web images without labels. The proposed approach discovers highly probable regions of  object instances by iteratively repeating the following two functions: (1) choose the exemplar set (i.e. small number of high ranked reference ROIs) across the dataset and (2) refine the ROIs of each image with respect to the exemplar set. These two subproblems are formulated as ranking in two different similarity networks of ROI hypotheses by link analysis. The experiments with the PASCAL 06 dataset show that our unsupervised localization performance is better than one of state-of-the-art techniques and comparable to supervised methods. Also, we test the scalability of our approach with five objects in Flickr dataset consisting of more than 200,000 images.
Fast Learning from Non-i.i.d. Observations
Authors: Ingo Steinwart, Andreas Christmann
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: We prove an oracle inequality for generic regularized empirical risk minimization algorithms learning from  $\a$-mixing processes. To illustrate this oracle inequality, we use it to derive learning rates for some learning methods including least squares SVMs. Since the proof of the oracle inequality uses recent localization ideas developed for independent and identically distributed (i.i.d.) processes, it turns out that these learning rates are close to the optimal rates known in the i.i.d. case.
Evaluating multi-class learning strategies in a generative hierarchical framework for object detection
Authors: Sanja Fidler, Marko Boben, Ales Leonardis
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: Multiple object class learning and detection is a challenging problem due to the large number of object classes and their high visual variability. Specialized detectors usually excel in performance, while joint representations optimize sharing and reduce inference time --- but are complex to train. Conveniently, sequential learning of categories cuts down training time by transferring existing knowledge to novel classes, but cannot fully exploit the richness of shareability and might depend on ordering in learning. In hierarchical frameworks these issues have been little explored. In this paper, we show how different types of multi-class learning can be done within one generative hierarchical framework and provide a rigorous experimental analysis of various object class learning strategies as the number of classes grows. Specifically, we propose, evaluate and compare three important types of multi-class learning: 1.) independent training of individual categories, 2.) joint training of classes, 3.) sequential learning of classes. We explore and compare their computational behavior (space and time) and detection performance as a function of the number of learned classes on several recognition data sets.
Optimal Scoring for Unsupervised Learning
Authors: Zhihua Zhang, Guang Dai
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: We are often interested in casting classification and clustering problems in a regression framework, because it is feasible to achieve some statistical properties in this framework by imposing some penalty criteria. In this paper we illustrate optimal scoring, which was originally proposed for performing Fisher linear discriminant analysis by regression, in the application of unsupervised learning. In particular, we devise a novel clustering algorithm that we call optimal discriminant clustering (ODC). We associate our algorithm with the existing unsupervised learning algorithms such as spectral clustering, discriminative clustering and sparse principal component analysis. Thus, our work shows that optimal scoring  provides a new approach to the implementation of  unsupervised learning. This approach facilitates the development of new unsupervised learning algorithms.
Matrix Completion from Noisy Entries
Authors: Raghunandan Keshavan, Andrea Montanari, Sewoong Oh
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the ‘Netflix problem’) to structure-from-motion and positioning. We study a low complexity algorithm introduced in [1], based on a combination of spectral techniques and manifold optimization, that we call here OPTSPACE. We prove performance guarantees that are order-optimal in a number of circumstances.
A Generalized Natural Actor-Critic Algorithm
Authors: Tetsuro Morimura, Eiji Uchibe, Junichiro Yoshimoto, Kenji Doya
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: Policy gradient Reinforcement Learning (RL) algorithms have received much attention in seeking stochastic policies that maximize the average rewards.  In addition, extensions based on the concept of the Natural Gradient (NG) show promising learning efficiency because these regard metrics for the task. Though there are two candidate metrics, Kakades Fisher Information Matrix (FIM) and Morimuras FIM, all RL algorithms with NG have followed the Kakades approach. In this paper, we describe a generalized Natural Gradient (gNG) by linearly interpolating the two FIMs and propose an efficient implementation for the gNG learning based on a theory of the estimating function, generalized Natural Actor-Critic (gNAC). The gNAC algorithm involves a near optimal auxiliary function to reduce the variance of the gNG estimates. Interestingly, the gNAC can be regarded as a natural extension of the current state-of-the-art NAC algorithm, as long as the interpolating parameter is appropriately selected. Numerical experiments showed that the proposed gNAC algorithm can estimate gNG efficiently and outperformed the NAC algorithm.
Efficient Moments-based Permutation Tests
Authors: Chunxiao Zhou, Huixia J. Wang, Yongmei M. Wang
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: In this paper, we develop an efficient moments-based permutation test approach to improve the system’s efficiency by approximating the permutation distribution of the test statistic with Pearson distribution series. This approach involves the calculation of the first four moments of the permutation distribution. We propose a novel recursive method to derive these moments theoretically and analytically without any permutation.  Experimental results using different test statistics are demonstrated using simulated data and real data. The proposed strategy takes advantage of nonparametric permutation tests and parametric Pearson distribution approximation to achieve both accuracy and efficiency.
Lower bounds on minimax rates for nonparametric regression with additive sparsity and smoothness
Authors: Garvesh Raskutti, Bin Yu, Martin J. Wainwright
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: This paper uses information-theoretic techniques to determine minimax rates for estimating nonparametric sparse additive regression models under high-dimensional scaling.  We assume an additive decomposition of the form $f^*(X_1, \ldots, X_p) = \sum_{j \in S} h_j(X_j)$, where each component function $h_j$ lies in some Hilbert Space $\Hilb$ and $S \subset \{1, \ldots, \pdim \}$ is an unknown subset with cardinality $\s = |S$.  Given $\numobs$ i.i.d. observations of $f^*(X)$ corrupted with white Gaussian noise where the covariate vectors $(X_1, X_2, X_3,...,X_{\pdim})$ are drawn with i.i.d. components from some distribution $\mP$, we determine tight lower bounds on the minimax rate for estimating the regression function with respect to squared $\LTP$ error. The main result shows that the minimax rates are $\max{\big(\frac{\s \log \pdim / \s}{n}, \LowerRateSq \big)}$.  The first term reflects the difficulty of performing \emph{subset selection} and is independent of the Hilbert space $\Hilb$; the second term $\LowerRateSq$ is an \emph{\s-dimensional estimation} term, depending only on the low dimension $\s$ but not the ambient dimension $\pdim$, that captures the difficulty of estimating a sum of $\s$ univariate functions in the Hilbert space $\Hilb$.  As a special case, if $\Hilb$ corresponds to the $\m$-th order Sobolev space $\SobM$ of functions that are $m$-times differentiable, the $\s$-dimensional estimation term takes the form $\LowerRateSq \asymp \s \; n^{-2\m/(2\m+1)}$. The minimax rates are compared with rates achieved by an $\ell_1$-penalty based approach, it can be shown that a certain $\ell_1$-based approach achieves the minimax optimal rate.
The Ordered Residual Kernel for Robust Motion Subspace Clustering
Authors: Tat-jun Chin, Hanzi Wang, David Suter
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: We present a novel and highly effective approach for multi-body motion segmentation. Drawing inspiration from robust statistical model fitting, we estimate putative subspace hypotheses from the data. However, instead of ranking them we encapsulate the hypotheses in a novel Mercer kernel which elicits the potential of two point trajectories to have emerged from the same subspace. The kernel permits the application of well-established statistical learning methods for effective outlier rejection, automatic recovery of the number of motions and accurate segmentation of the point trajectories. The method operates well under severe outliers arising from spurious trajectories or mistracks. Detailed experiments on a recent benchmark dataset (Hopkins 155) show that our method is superior to other state-of-the-art approaches in terms of recovering the number of motions, segmentation accuracy, robustness against gross outliers and computational efficiency.
Learning to Rank by Optimizing NDCG Measure
Authors: Hamed Valizadegan, Rong Jin, Ruofei Zhang, Jianchang Mao
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: Learning to rank is a relatively new field of study, aiming to learn a ranking function from a set of training data with relevancy labels. The ranking algorithms are often evaluated using Information Retrieval measures, such as Normalized Discounted Cumulative Gain [1] and Mean Average Precision [2]. Until recently, most learning to rank algorithms were not using a loss function related to the above mentioned evaluation measures. The main difficulty in direct optimization of these measures is that they depend on the ranks of documents, not the numerical values output by the ranking function. We propose a probabilistic framework that addresses this challenge by optimizing the expectation of NDCG over all the possible permutations of documents. A relaxation strategy is used to approximate the average of NDCG over the space of permutation, and a bound optimization approach is proposed to make the computation efficient. Extensive experiments show that the proposed algorithm outperforms state-of-the-art ranking algorithms on several benchmark data sets.
Slow Learners are Fast
Authors: Martin Zinkevich, John Langford, Alex J. Smola
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: Online learning algorithms have impressive convergence properties   when it comes to risk minimization and convex games on very large   problems. However, they are inherently sequential in their design   which prevents them from taking advantage of modern multi-core   architectures. In this paper we prove that online learning with   delayed updates converges well, thereby facilitating parallel online   learning.
Tracking Dynamic Sources of Malicious Activity at Internet Scale
Authors: Shobha Venkataraman, Avrim Blum, Dawn Song, Subhabrata Sen, Oliver Spatscheck
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: We formulate and address the problem of discovering dynamic malicious regions on the Internet. We model this problem as one of adaptively pruning a known decision tree, but with additional challenges: (1) severe space requirements, since the underlying decision tree has over 4 billion leaves, and (2) a changing target function, since malicious activity on the Internet is dynamic. We present a novel algorithm that addresses this problem, by putting together a number of different ``experts algorithms and online paging algorithms. We prove guarantees on our algorithms performance as a function of the best possible pruning of a similar size, and our experiments show that our algorithm achieves high accuracy on large real-world data sets, with significant improvements over existing approaches.
Graph Zeta Function in the Bethe Free Energy and Loopy Belief Propagation
Authors: Yusuke Watanabe, Kenji Fukumizu
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: We propose a new approach to the analysis of Loopy Belief Propagation (LBP) by establishing a formula that connects the Hessian of the Bethe free energy with the edge zeta function. The formula has a number of theoretical implications on LBP. It is applied to give a sufficient condition that the Hessian of the Bethe free energy is positive definite, which shows non-convexity for graphs with multiple cycles. The formula clarifies the relation between the local stability of a fixed point of LBP and local minima of the Bethe free energy. We also propose a new approach to the uniqueness of LBP fixed point, and show various conditions of uniqueness.
Statistical Consistency of Top-k Ranking
Authors: Fen Xia, Tie-yan Liu, Hang Li
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: This paper is concerned with the consistency analysis on listwise ranking methods. Among various ranking methods, the listwise methods have competitive performances on benchmark datasets and are regarded as one of the state-of-the-art approaches. Most listwise ranking methods manage to optimize ranking on the whole list (permutation) of objects, however, in practical applications such as information retrieval, correct ranking at the top k positions is much more important. This paper aims to analyze whether existing listwise ranking methods are statistically consistent in the top-k setting. For this purpose, we define a top-k ranking framework, where the true loss (and thus the risks) are defined on the basis of top-k subgroup of permutations. This framework can include the permutation-level ranking framework proposed in previous work as a special case. Based on the new framework, we derive sufficient conditions for a listwise ranking method to be consistent with the top-k true loss, and show an effective way of modifying the surrogate loss functions in existing methods to satisfy these conditions. Experimental results show that after the modifications, the methods can work significantly better than their original versions.
Speaker Comparison with Inner Product Discriminant Functions
Authors: Zahi Karam, Douglas Sturim, William M. Campbell
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: Speaker comparison, the process of finding the speaker similarity between two speech signals, occupies a central role in a variety of applications---speaker verification, clustering, and identification. Speaker comparison can be placed in a geometric framework by casting the problem as a model comparison process.  For a given speech signal, feature vectors are produced and used to adapt a Gaussian mixture model (GMM).  Speaker comparison can then be viewed as the process of compensating and finding metrics on the space of adapted models.  We propose a framework, inner product discriminant functions (IPDFs), which extends many common techniques for speaker comparison: support vector machines, joint factor analysis, and linear scoring.  The framework uses inner products between the parameter vectors of GMM models motivated by several statistical methods.  Compensation of nuisances is performed via linear transforms on GMM parameter vectors.  Using the IPDF framework, we show that many current techniques are simple variations of each other.  We demonstrate, on a 2006 NIST speaker recognition evaluation task, new scoring methods using IPDFs which produce excellent error rates and require significantly less computation than current techniques.
Asymptotic Analysis of MAP Estimation via the Replica Method and Compressed Sensing
Authors: Sundeep Rangan, Vivek Goyal, Alyson K. Fletcher
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: The replica method is a non-rigorous but widely-used technique from statistical physics used in the asymptotic analysis of many large random nonlinear problems.  This paper applies the replica method to non-Gaussian MAP estimation.  It is shown that with large random linear measurements and Gaussian noise, the asymptotic behavior of the MAP estimate of an n-dimensional vector ``decouples as n scalar MAP estimators.  The result is a counterpart to Guo and Verdus replica analysis on MMSE estimation. The replica MAP analysis can be readily applied to many estimators used in compressed sensing, including basis pursuit, lasso, linear estimation with thresholding and zero-norm estimation.  In the case of lasso estimation, the scalar estimator reduces to a soft-thresholding operator and for zero-norm estimation it reduces to a hard-threshold.  Among other benefits, the replica method provides a computationally tractable method for exactly computing various performance metrics including MSE and sparsity recovery.
Statistical Models of Linear and Nonlinear Contextual Interactions in Early Visual Processing
Authors: Ruben Coen-cagli, Peter Dayan, Odelia Schwartz
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: A central hypothesis about early visual processing is that it represents inputs in a coordinate system matched to the statistics of natural scenes. Simple versions of this lead to Gabor-like receptive fields and divisive gain modulation from local surrounds; these have led to influential neural and psychological models of visual processing. However, these accounts are based on an incomplete view of the visual context surrounding each point. Here, we consider an approximate model of linear and non-linear correlations between the responses of spatially distributed Gabor-like receptive fields, which, when trained on an ensemble of natural scenes, unifies a range of spatial context effects. The full model accounts for neural surround data in primary visual cortex (V1), provides a statistical foundation for perceptual phenomena associated with Lis (2002) hypothesis that V1 builds a saliency map, and fits data on the tilt illusion.
A joint maximum-entropy model for binary neural population patterns and continuous signals
Authors: Sebastian Gerwinn, Philipp Berens, Matthias Bethge
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: Second-order maximum-entropy models have recently gained much interest for describing the statistics of binary spike trains. Here, we extend this approach to take continuous stimuli into account as well. By constraining  the joint second-order statistics, we obtain a joint Gaussian-Boltzmann distribution of continuous stimuli and binary neural firing patterns, for which we also compute marginal and conditional distributions. This model has the same computational complexity as pure binary models and fitting it to data is a convex problem. We show that the model can be seen as an extension to the classical spike-triggered average/covariance analysis and can be used as a non-linear method for extracting features which a neural population is sensitive to. Further, by calculating the posterior distribution of stimuli given an observed neural response, the model can be used to decode stimuli and yields a natural spike-train metric. Therefore, extending the framework of maximum-entropy models to continuous variables allows us to gain novel insights into the relationship between the firing patterns of neural ensembles and the stimuli they are processing.
Hierarchical Modeling of Local Image Features through $L_p$-Nested Symmetric Distributions
Authors: Matthias Bethge, Eero P. Simoncelli, Fabian H. Sinz
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: We introduce a new family of distributions, called $L_p${\em -nested symmetric distributions}, whose densities access the data exclusively through a hierarchical cascade of $L_p$-norms. This class generalizes the family of spherically and $L_p$-spherically symmetric distributions which have recently been successfully used for natural image modeling. Similar to those distributions it allows for a nonlinear mechanism to reduce the dependencies between its variables. With suitable choices of the parameters and norms, this family also includes the Independent Subspace Analysis (ISA) model, which has been proposed as a means of deriving filters that mimic complex cells found in mammalian primary visual cortex. $L_p$-nested distributions are easy to estimate and allow us to explore the variety of models between ISA and the $L_p$-spherically symmetric models. Our main findings are that, without a preprocessing step of contrast gain control, the independent subspaces of ISA are in fact more dependent than the individual filter coefficients within a subspace and, with contrast gain control, where ISA finds more than one subspace, the filter responses were almost independent anyway.
Optimizing Multi-Class Spatio-Spectral Filters via Bayes Error Estimation for EEG Classification
Authors: Wenming Zheng, Zhouchen Lin
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: The method of common spatio-spectral patterns (CSSPs) is an extension of common spatial patterns (CSPs) by utilizing the technique of delay embedding to alleviate the adverse effects of noises and artifacts on the electroencephalogram (EEG) classification. Although the CSSPs method has shown to be more powerful than the CSPs method in the EEG classification, this method is only suitable for two-class EEG classification problems. In this paper, we generalize the two-class CSSPs method to multi-class cases. To this end, we first develop a novel theory of multi-class Bayes error estimation and then present the multi-class CSSPs (MCSSPs) method based on this Bayes error theoretical framework. By minimizing the estimated closed-form Bayes error, we obtain the optimal spatio-spectral filters of MCSSPs. To demonstrate the effectiveness of the proposed method, we conduct extensive experiments on the data set of BCI competition 2005. The experimental results show that our method significantly outperforms the previous multi-class CSPs (MCSPs) methods in the EEG classification.
Nash Equilibria of Static Prediction Games
Authors: Michael Brückner, Tobias Scheffer
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: The standard assumption of identically distributed training and test data can be violated when an adversary can exercise some control over the generation of the test data. In a prediction game, a learner produces a predictive model while an adversary may alter the distribution of input data. We study single-shot prediction games in which the cost functions of learner and adversary are not necessarily antagonistic. We identify conditions under which the prediction game has a unique Nash equilibrium, and derive algorithms that will find the equilibrial prediction models. In a case study, we explore properties of Nash-equilibrial prediction models for email spam filtering empirically.
Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization
Authors: John Wright, Arvind Ganesh, Shankar Rao, Yigang Peng, Yi Ma
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: Principal component analysis is a fundamental operation in computational data analysis, with myriad applications ranging from web search to bioinformatics to computer vision and image analysis. However, its performance and applicability in real scenarios are limited by a lack of robustness to outlying or corrupted observations. This paper considers the idealized “robust principal component analysis” problem of recovering a low rank matrix A from corrupted observations D = A + E. Here, the error entries E can be arbitrarily large (modeling grossly corrupted observations common in visual and bioinformatic data), but are assumed to be sparse. We prove that most matrices A can be efficiently and exactly recovered from most error sign-and-support patterns, by solving a simple convex program. Our result holds even when the rank of A grows nearly proportionally (up to a logarithmic factor) to the dimensionality of the observation space and the number of errors E grows in proportion to the total number of entries in the matrix. A by-product of our analysis is the first proportional growth results for the related problem of completing a low-rank matrix from a small fraction of its entries. Simulations and real-data examples corroborate the theoretical results, and suggest potential applications in computer vision.
Unsupervised Feature Selection for the $k$-means Clustering Problem
Authors: Christos Boutsidis, Petros Drineas, Michael W. Mahoney
Published in: Advances in Neural Information Processing Systems 22  (NIPS 2009) (Main Conference Track), 2009

Abstract: We present a novel feature selection algorithm for the $k$-means clustering problem. Our algorithm is randomized and, assuming an accuracy parameter $\epsilon \in (0,1)$, selects and appropriately rescales in an unsupervised manner $\Theta(k \log(k / \epsilon) / \epsilon^2)$ features from a dataset of arbitrary dimensions. We prove that, if we run any $\gamma$-approximate $k$-means algorithm ($\gamma \geq 1$) on the features selected using our method, we can find a $(1+(1+\epsilon)\gamma)$-approximate partition with high probability.