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21,602
k-NN Regression Adapts to Local Intrinsic Dimension
stat.ML
Many nonparametric regressors were recently shown to converge at rates that depend only on the intrinsic dimension of data. These regressors thus escape the curse of dimension when high-dimensional data has low intrinsic dimension (e.g. a manifold). We show that k-NN regression is also adaptive to intrinsic dimension. ...
computer science
21,603
Is the k-NN classifier in high dimensions affected by the curse of dimensionality?
stat.ML
There is an increasing body of evidence suggesting that exact nearest neighbour search in high-dimensional spaces is affected by the curse of dimensionality at a fundamental level. Does it necessarily mean that the same is true for k nearest neighbours based learning algorithms such as the k-NN classifier? We analyse t...
computer science
21,604
Regression for sets of polynomial equations
stat.ML
We propose a method called ideal regression for approximating an arbitrary system of polynomial equations by a system of a particular type. Using techniques from approximate computational algebraic geometry, we show how we can solve ideal regression directly without resorting to numerical optimization. Ideal regression...
computer science
21,605
Multiple Gaussian Process Models
stat.ML
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data. Sparsity in the kernel weights is obtained by adopting a hierarchical Bayesian approa...
computer science
21,606
A Flexible, Scalable and Efficient Algorithmic Framework for Primal Graphical Lasso
stat.ML
We propose a scalable, efficient and statistically motivated computational framework for Graphical Lasso (Friedman et al., 2007b) - a covariance regularization framework that has received significant attention in the statistics community over the past few years. Existing algorithms have trouble in scaling to dimensions...
computer science
21,607
Structural Similarity and Distance in Learning
stat.ML
We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured by solving a non-linear, low-rank representation problem. We show that this low-...
computer science
21,608
Adaptive Hedge
stat.ML
Most methods for decision-theoretic online learning are based on the Hedge algorithm, which takes a parameter called the learning rate. In most previous analyses the learning rate was carefully tuned to obtain optimal worst-case performance, leading to suboptimal performance on easy instances, for example when there ex...
computer science
21,609
The theory and application of penalized methods or Reproducing Kernel Hilbert Spaces made easy
stat.ML
The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $\sum_j(Y_j - {\mu}(t_j))^2 + {\lambda}\int_a^b [{\mu}"(t)]^2 dt$, where the data are $t_j,Y_j$, $j=1,..., n$. The minimization is taken over an infinite-dimensional function space, the space of ...
computer science
21,610
Estimated VC dimension for risk bounds
stat.ML
Vapnik-Chervonenkis (VC) dimension is a fundamental measure of the generalization capacity of learning algorithms. However, apart from a few special cases, it is hard or impossible to calculate analytically. Vapnik et al. [10] proposed a technique for estimating the VC dimension empirically. While their approach behave...
computer science
21,611
Fast Learning Rate of Non-Sparse Multiple Kernel Learning and Optimal Regularization Strategies
stat.ML
In this paper, we give a new generalization error bound of Multiple Kernel Learning (MKL) for a general class of regularizations, and discuss what kind of regularization gives a favorable predictive accuracy. Our main target in this paper is dense type regularizations including \ellp-MKL. According to the recent numeri...
computer science
21,612
On l_1 Mean and Variance Filtering
stat.ML
This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables with unknown, possibly changing, mean value but fixed variance. The main assumpt...
computer science
21,613
Optimal exponential bounds on the accuracy of classification
stat.ML
We consider a standard binary classification problem. The performance of any binary classifier based on the training data is characterized by the excess risk. We study Bahadur's type exponential bounds on the minimax accuracy confidence function based on the excess risk. We study how this quantity depends on the comple...
computer science
21,614
Additive Covariance Kernels for High-Dimensional Gaussian Process Modeling
stat.ML
Gaussian process models -also called Kriging models- are often used as mathematical approximations of expensive experiments. However, the number of observation required for building an emulator becomes unrealistic when using classical covariance kernels when the dimension of input increases. In oder to get round the cu...
computer science
21,615
Fast, Linear Time, m-Adic Hierarchical Clustering for Search and Retrieval using the Baire Metric, with linkages to Generalized Ultrametrics, Hashing, Formal Concept Analysis, and Precision of Data Measurement
stat.ML
We describe many vantage points on the Baire metric and its use in clustering data, or its use in preprocessing and structuring data in order to support search and retrieval operations. In some cases, we proceed directly to clusters and do not directly determine the distances. We show how a hierarchical clustering can ...
computer science
21,616
Gaussian Probabilities and Expectation Propagation
stat.ML
While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We study the utility of Expectation Propagation (EP) as an approximate integration method for this problem. For rectangular integration regions, the approx...
computer science
21,617
A General Framework of Dual Certificate Analysis for Structured Sparse Recovery Problems
stat.ML
This paper develops a general theoretical framework to analyze structured sparse recovery problems using the notation of dual certificate. Although certain aspects of the dual certificate idea have already been used in some previous work, due to the lack of a general and coherent theory, the analysis has so far only be...
computer science
21,618
A robust and sparse K-means clustering algorithm
stat.ML
In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) might present a serious and sometimes hard-to-assess problem for large and complex datasets. In this pap...
computer science
21,619
Learning a Common Substructure of Multiple Graphical Gaussian Models
stat.ML
Properties of data are frequently seen to vary depending on the sampled situations, which usually changes along a time evolution or owing to environmental effects. One way to analyze such data is to find invariances, or representative features kept constant over changes. The aim of this paper is to identify one such fe...
computer science
21,620
Subspace clustering of high-dimensional data: a predictive approach
stat.ML
In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a new approach for partitioning such high-dimensional data. Our assumption is that...
computer science
21,621
An ADMM Algorithm for a Class of Total Variation Regularized Estimation Problems
stat.ML
We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between consecutive variable blocks. Examples of such problems include Fused Lasso estima...
computer science
21,622
Asymptotic Confidence Sets for General Nonparametric Regression and Classification by Regularized Kernel Methods
stat.ML
Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning asymptotic properties have manly focused on rates of convergence during the last years bu...
computer science
21,623
Polynomial expansion of the binary classification function
stat.ML
This paper describes a novel method to approximate the polynomial coefficients of regression functions, with particular interest on multi-dimensional classification. The derivation is simple, and offers a fast, robust classification technique that is resistant to over-fitting.
computer science
21,624
Empirical Normalization for Quadratic Discriminant Analysis and Classifying Cancer Subtypes
stat.ML
We introduce a new discriminant analysis method (Empirical Discriminant Analysis or EDA) for binary classification in machine learning. Given a dataset of feature vectors, this method defines an empirical feature map transforming the training and test data into new data with components having Gaussian empirical distrib...
computer science
21,625
Application of Bayesian Hierarchical Prior Modeling to Sparse Channel Estimation
stat.ML
Existing methods for sparse channel estimation typically provide an estimate computed as the solution maximizing an objective function defined as the sum of the log-likelihood function and a penalization term proportional to the l1-norm of the parameter of interest. However, other penalization terms have proven to have...
computer science
21,626
Estimation of causal orders in a linear non-Gaussian acyclic model: a method robust against latent confounders
stat.ML
We consider to learn a causal ordering of variables in a linear non-Gaussian acyclic model called LiNGAM. Several existing methods have been shown to consistently estimate a causal ordering assuming that all the model assumptions are correct. But, the estimation results could be distorted if some assumptions actually a...
computer science
21,627
Coherence Functions with Applications in Large-Margin Classification Methods
stat.ML
Support vector machines (SVMs) naturally embody sparseness due to their use of hinge loss functions. However, SVMs can not directly estimate conditional class probabilities. In this paper we propose and study a family of coherence functions, which are convex and differentiable, as surrogates of the hinge function. The ...
computer science
21,628
Learning Sets with Separating Kernels
stat.ML
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of reproducing kernel, that we call separating kernel, plays a crucial role in our...
computer science
21,629
Regularized Partial Least Squares with an Application to NMR Spectroscopy
stat.ML
High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension reduction techniques in the context of supervised data analysis. We introduce a framewo...
computer science
21,630
Semi-Supervised learning with Density-Ratio Estimation
stat.ML
In this paper, we study statistical properties of semi-supervised learning, which is considered as an important problem in the community of machine learning. In the standard supervised learning, only the labeled data is observed. The classification and regression problems are formalized as the supervised learning. In s...
computer science
21,631
EP-GIG Priors and Applications in Bayesian Sparse Learning
stat.ML
In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG is a variant of generalized hyperbolic distributions, and the special cases inclu...
computer science
21,632
Efficient hierarchical clustering for continuous data
stat.ML
We present an new sequential Monte Carlo sampler for coalescent based Bayesian hierarchical clustering. Our model is appropriate for modeling non-i.i.d. data and offers a substantial reduction of computational cost when compared to the original sampler without resorting to approximations. We also propose a quadratic co...
computer science
21,633
Learning Loosely Connected Markov Random Fields
stat.ML
We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test based algorithm for learning the underlying graph structure. The novel maximization ...
computer science
21,634
Learning LiNGAM based on data with more variables than observations
stat.ML
A very important topic in systems biology is developing statistical methods that automatically find causal relations in gene regulatory networks with no prior knowledge of causal connectivity. Many methods have been developed for time series data. However, discovery methods based on steady-state data are often necessar...
computer science
21,635
A non-parametric mixture model for topic modeling over time
stat.ML
A single, stationary topic model such as latent Dirichlet allocation is inappropriate for modeling corpora that span long time periods, as the popularity of topics is likely to change over time. A number of models that incorporate time have been proposed, but in general they either exhibit limited forms of temporal var...
computer science
21,636
On the convergence of maximum variance unfolding
stat.ML
Maximum Variance Unfolding is one of the main methods for (nonlinear) dimensionality reduction. We study its large sample limit, providing specific rates of convergence under standard assumptions. We find that it is consistent when the underlying submanifold is isometric to a convex subset, and we provide some simple e...
computer science
21,637
Seeded Graph Matching
stat.ML
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first given a partial alignment that we are tasked with completing. In this paper, we m...
computer science
21,638
A Bayesian Boosting Model
stat.ML
We offer a novel view of AdaBoost in a statistical setting. We propose a Bayesian model for binary classification in which label noise is modeled hierarchically. Using variational inference to optimize a dynamic evidence lower bound, we derive a new boosting-like algorithm called VIBoost. We show its close connections ...
computer science
21,639
Link Prediction in Graphs with Autoregressive Features
stat.ML
In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure ...
computer science
21,640
Recovering Block-structured Activations Using Compressive Measurements
stat.ML
We consider the problems of detection and localization of a contiguous block of weak activation in a large matrix, from a small number of noisy, possibly adaptive, compressive (linear) measurements. This is closely related to the problem of compressed sensing, where the task is to estimate a sparse vector using a small...
computer science
21,641
Scaling Multidimensional Inference for Structured Gaussian Processes
stat.ML
Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure inherent in particular covariance functions, including GPs with implied Markov st...
computer science
21,642
Variational Inference in Nonconjugate Models
stat.ML
Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization algorithm. When the model is conditionally conjugate, the coordinate updates are easily ...
computer science
21,643
Improving accuracy and power with transfer learning using a meta-analytic database
stat.ML
Typical cohorts in brain imaging studies are not large enough for systematic testing of all the information contained in the images. To build testable working hypotheses, investigators thus rely on analysis of previous work, sometimes formalized in a so-called meta-analysis. In brain imaging, this approach underlies th...
computer science
21,644
A New Geometric Approach to Latent Topic Modeling and Discovery
stat.ML
A new geometrically-motivated algorithm for nonnegative matrix factorization is developed and applied to the discovery of latent "topics" for text and image "document" corpora. The algorithm is based on robustly finding and clustering extreme points of empirical cross-document word-frequencies that correspond to novel ...
computer science
21,645
Efficient Eigen-updating for Spectral Graph Clustering
stat.ML
Partitioning a graph into groups of vertices such that those within each group are more densely connected than vertices assigned to different groups, known as graph clustering, is often used to gain insight into the organisation of large scale networks and for visualisation purposes. Whereas a large number of dedicated...
computer science
21,646
Nonparametric Reduced Rank Regression
stat.ML
We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a $q$-dimensional response, with a shared $p$-dimensional predictor variable. To control the complexity of the model, we employ a functional fo...
computer science
21,647
On the Incommensurability Phenomenon
stat.ML
Suppose that two large, multi-dimensional data sets are each noisy measurements of the same underlying random process, and principle components analysis is performed separately on the data sets to reduce their dimensionality. In some circumstances it may happen that the two lower-dimensional data sets have an inordinat...
computer science
21,648
Spectral Clustering Based on Local PCA
stat.ML
We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weighted according to a discrepancy between the principal subspaces in the neighborhoods, and then applies spectral clustering. ...
computer science
21,649
Perturbative Corrections for Approximate Inference in Gaussian Latent Variable Models
stat.ML
Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact but intractable correcti...
computer science
21,650
A Nested HDP for Hierarchical Topic Models
stat.ML
We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP is a generalization of the nested Chinese restaurant process (nCRP) that allows each word to follow its own path to a topic node according to a document-specific distribution on a shared tree. This alleviates the rigid, ...
computer science
21,651
Jitter-Adaptive Dictionary Learning - Application to Multi-Trial Neuroelectric Signals
stat.ML
Dictionary Learning has proven to be a powerful tool for many image processing tasks, where atoms are typically defined on small image patches. As a drawback, the dictionary only encodes basic structures. In addition, this approach treats patches of different locations in one single set, which means a loss of informati...
computer science
21,652
An Impossibility Result for High Dimensional Supervised Learning
stat.ML
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster than the number of labeled training samples. We show that the Bayes error, namely t...
computer science
21,653
Learning Heteroscedastic Models by Convex Programming under Group Sparsity
stat.ML
Popular sparse estimation methods based on $\ell_1$-relaxation, such as the Lasso and the Dantzig selector, require the knowledge of the variance of the noise in order to properly tune the regularization parameter. This constitutes a major obstacle in applying these methods in several frameworks---such as time series, ...
computer science
21,654
Low-Rank Matrix and Tensor Completion via Adaptive Sampling
stat.ML
We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for learning the column space of the matrix (tensor) and consequently, our results ...
computer science
21,655
Feature Elimination in Kernel Machines in moderately high dimensions
stat.ML
We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features.We present theoretical properties of this method and show that it is uniformly consistent in finding the correct feature space under certain generalized assumptions.We present four cas...
computer science
21,656
Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions
stat.ML
The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this model have been devised, and many of them employ some type of dissimilarity measure...
computer science
21,657
Direct Learning of Sparse Changes in Markov Networks by Density Ratio Estimation
stat.ML
We propose a new method for detecting changes in Markov network structure between two sets of samples. Instead of naively fitting two Markov network models separately to the two data sets and figuring out their difference, we \emph{directly} learn the network structure change by estimating the ratio of Markov network m...
computer science
21,658
The Randomized Dependence Coefficient
stat.ML
We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-R\'enyi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with resp...
computer science
21,659
Generalized Canonical Correlation Analysis for Classification
stat.ML
For multiple multivariate data sets, we derive conditions under which Generalized Canonical Correlation Analysis (GCCA) improves classification performance of the projected datasets, compared to standard Canonical Correlation Analysis (CCA) using only two data sets. We illustrate our theoretical results with simulation...
computer science
21,660
Constructive Setting of the Density Ratio Estimation Problem and its Rigorous Solution
stat.ML
We introduce a general constructive setting of the density ratio estimation problem as a solution of a (multidimensional) integral equation. In this equation, not only its right hand side is known approximately, but also the integral operator is defined approximately. We show that this ill-posed problem has a rigorous ...
computer science
21,661
Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances
stat.ML
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation involves the resolution of a linear program whose cost is prohibitive whenever the hi...
computer science
21,662
Structural Intervention Distance (SID) for Evaluating Causal Graphs
stat.ML
Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-) distance between DAGs, the structural intervention distance (SID). T...
computer science
21,663
Generalized Beta Divergence
stat.ML
This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the exponential dispersion model. This compact integral form simplifies derivations of many pr...
computer science
21,664
Early stopping and non-parametric regression: An optimal data-dependent stopping rule
stat.ML
The strategy of early stopping is a regularization technique based on choosing a stopping time for an iterative algorithm. Focusing on non-parametric regression in a reproducing kernel Hilbert space, we analyze the early stopping strategy for a form of gradient-descent applied to the least-squares loss function. We pro...
computer science
21,665
Bayesian methods for low-rank matrix estimation: short survey and theoretical study
stat.ML
The problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However, only a few papers considered Bayesian estimation. In this paper, we review the ...
computer science
21,666
Group Symmetry and non-Gaussian Covariance Estimation
stat.ML
We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization problems. Recently, it was shown that the underlying principle behind their succ...
computer science
21,667
Optimal computational and statistical rates of convergence for sparse nonconvex learning problems
stat.ML
We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this category, including least squares regression with nonconvex regularization, generalized ...
computer science
21,668
Online dictionary learning for kernel LMS. Analysis and forward-backward splitting algorithm
stat.ML
Adaptive filtering algorithms operating in reproducing kernel Hilbert spaces have demonstrated superiority over their linear counterpart for nonlinear system identification. Unfortunately, an undesirable characteristic of these methods is that the order of the filters grows linearly with the number of input data. This ...
computer science
21,669
Supersparse Linear Integer Models for Predictive Scoring Systems
stat.ML
We introduce Supersparse Linear Integer Models (SLIM) as a tool to create scoring systems for binary classification. We derive theoretical bounds on the true risk of SLIM scoring systems, and present experimental results to show that SLIM scoring systems are accurate, sparse, and interpretable classification models.
computer science
21,670
The nested Chinese restaurant process and Bayesian nonparametric inference of topic hierarchies
stat.ML
We present the nested Chinese restaurant process (nCRP), a stochastic process which assigns probability distributions to infinitely-deep, infinitely-branching trees. We show how this stochastic process can be used as a prior distribution in a Bayesian nonparametric model of document collections. Specifically, we presen...
computer science
21,671
Probabilistic coherence and proper scoring rules
stat.ML
We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results achieved by other investigators.
computer science
21,672
Bayesian Online Changepoint Detection
stat.ML
Changepoints are abrupt variations in the generative parameters of a data sequence. Online detection of changepoints is useful in modelling and prediction of time series in application areas such as finance, biometrics, and robotics. While frequentist methods have yielded online filtering and prediction techniques, mos...
computer science
21,673
Large Scale Variational Inference and Experimental Design for Sparse Generalized Linear Models
stat.ML
Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making problems, such as optimizing imag...
computer science
21,674
Online Coordinate Boosting
stat.ML
We present a new online boosting algorithm for adapting the weights of a boosted classifier, which yields a closer approximation to Freund and Schapire's AdaBoost algorithm than previous online boosting algorithms. We also contribute a new way of deriving the online algorithm that ties together previous online boosting...
computer science
21,675
A non-negative expansion for small Jensen-Shannon Divergences
stat.ML
In this report, we derive a non-negative series expansion for the Jensen-Shannon divergence (JSD) between two probability distributions. This series expansion is shown to be useful for numerical calculations of the JSD, when the probability distributions are nearly equal, and for which, consequently, small numerical er...
computer science
21,676
Kernels for Measures Defined on the Gram Matrix of their Support
stat.ML
We present in this work a new family of kernels to compare positive measures on arbitrary spaces $\Xcal$ endowed with a positive kernel $\kappa$, which translates naturally into kernels between histograms or clouds of points. We first cover the case where $\Xcal$ is Euclidian, and focus on kernels which take into accou...
computer science
21,677
Structured Sparse Principal Component Analysis
stat.ML
We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This \emph{structured sparse PCA} is based on a structured regularization recently introduced by [1]. While classical spa...
computer science
21,678
Telling cause from effect based on high-dimensional observations
stat.ML
We describe a method for inferring linear causal relations among multi-dimensional variables. The idea is to use an asymmetry between the distributions of cause and effect that occurs if both the covariance matrix of the cause and the structure matrix mapping cause to the effect are independently chosen. The method wor...
computer science
21,679
Initialization Free Graph Based Clustering
stat.ML
This paper proposes an original approach to cluster multi-component data sets, including an estimation of the number of clusters. From the construction of a minimal spanning tree with Prim's algorithm, and the assumption that the vertices are approximately distributed according to a Poisson distribution, the number of ...
computer science
21,680
Dirichlet Process Mixtures of Generalized Linear Models
stat.ML
We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean fu...
computer science
21,681
Laplacian Support Vector Machines Trained in the Primal
stat.ML
In the last few years, due to the growing ubiquity of unlabeled data, much effort has been spent by the machine learning community to develop better understanding and improve the quality of classifiers exploiting unlabeled data. Following the manifold regularization approach, Laplacian Support Vector Machines (LapSVMs)...
computer science
21,682
On a Rapid Simulation of the Dirichlet Process
stat.ML
We describe a simple and efficient procedure for approximating the L\'evy measure of a $\text{Gamma}(\alpha,1)$ random variable. We use this approximation to derive a finite sum-representation that converges almost surely to Ferguson's representation of the Dirichlet process based on arrivals of a homogeneous Poisson p...
computer science
21,683
Spectral approximations in machine learning
stat.ML
In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension and a newly introduced algorithm based on random projections. Previous work has c...
computer science
21,684
Robustness of Anytime Bandit Policies
stat.ML
This paper studies the deviations of the regret in a stochastic multi-armed bandit problem. When the total number of plays n is known beforehand by the agent, Audibert et al. (2009) exhibit a policy such that with probability at least 1-1/n, the regret of the policy is of order log(n). They have also shown that such a ...
computer science
21,685
The Group Lasso for Design of Experiments
stat.ML
We introduce an application of the group lasso to design of experiments. Note that we are NOT trying to explain experimental design for the group lasso. Conversely, we explain how we can use the idea of the group lasso in experimental design, showing that the problem of constructing an optimal design matrix can be tran...
computer science
21,686
Challenges of Big Data Analysis
stat.ML
Big Data bring new opportunities to modern society and challenges to data scientists. On one hand, Big Data hold great promises for discovering subtle population patterns and heterogeneities that are not possible with small-scale data. On the other hand, the massive sample size and high dimensionality of Big Data intro...
computer science
21,687
Accuracy of Latent-Variable Estimation in Bayesian Semi-Supervised Learning
stat.ML
Hierarchical probabilistic models, such as Gaussian mixture models, are widely used for unsupervised learning tasks. These models consist of observable and latent variables, which represent the observable data and the underlying data-generation process, respectively. Unsupervised learning tasks, such as cluster analysi...
computer science
21,688
Flexible Low-Rank Statistical Modeling with Side Information
stat.ML
We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly incorporates row and column features, smoothing kernels, and other sources of sid...
computer science
21,689
Frequency Recognition in SSVEP-based BCI using Multiset Canonical Correlation Analysis
stat.ML
Canonical correlation analysis (CCA) has been one of the most popular methods for frequency recognition in steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs). Despite its efficiency, a potential problem is that using pre-constructed sine-cosine waves as the required reference signals in...
computer science
21,690
The Generalized Mean Information Coefficient
stat.ML
Reshef & Reshef recently published a paper in which they present a method called the Maximal Information Coefficient (MIC) that can detect all forms of statistical dependence between pairs of variables as sample size goes to infinity. While this method has been praised by some, it has also been criticized for its lack ...
computer science
21,691
Component models for large networks
stat.ML
Being among the easiest ways to find meaningful structure from discrete data, Latent Dirichlet Allocation (LDA) and related component models have been applied widely. They are simple, computationally fast and scalable, interpretable, and admit nonparametric priors. In the currently popular field of network modeling, re...
computer science
21,692
Missing Data using Decision Forest and Computational Intelligence
stat.ML
Autoencoder neural network is implemented to estimate the missing data. Genetic algorithm is implemented for network optimization and estimating the missing data. Missing data is treated as Missing At Random mechanism by implementing maximum likelihood algorithm. The network performance is determined by calculating the...
computer science
21,693
Prediction with Restricted Resources and Finite Automata
stat.ML
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite automata. We generate a set of biased sequences by applying a finite state auto...
computer science
21,694
The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs
stat.ML
Recent methods for estimating sparse undirected graphs for real-valued data in high dimensional problems rely heavily on the assumption of normality. We show how to use a semiparametric Gaussian copula--or "nonparanormal"--for high dimensional inference. Just as additive models extend linear models by replacing linear ...
computer science
21,695
Forest Garrote
stat.ML
Variable selection for high-dimensional linear models has received a lot of attention lately, mostly in the context of l1-regularization. Part of the attraction is the variable selection effect: parsimonious models are obtained, which are very suitable for interpretation. In terms of predictive power, however, these re...
computer science
21,696
The Feature Importance Ranking Measure
stat.ML
Most accurate predictions are typically obtained by learning machines with complex feature spaces (as e.g. induced by kernels). Unfortunately, such decision rules are hardly accessible to humans and cannot easily be used to gain insights about the application domain. Therefore, one often resorts to linear models in com...
computer science
21,697
KNIFE: Kernel Iterative Feature Extraction
stat.ML
Selecting important features in non-linear or kernel spaces is a difficult challenge in both classification and regression problems. When many of the features are irrelevant, kernel methods such as the support vector machine and kernel ridge regression can sometimes perform poorly. We propose weighting the features wit...
computer science
21,698
Bayesian Agglomerative Clustering with Coalescents
stat.ML
We introduce a new Bayesian model for hierarchical clustering based on a prior over trees called Kingman's coalescent. We develop novel greedy and sequential Monte Carlo inferences which operate in a bottom-up agglomerative fashion. We show experimentally the superiority of our algorithms over others, and demonstrate o...
computer science
21,699
Visualizing Topics with Multi-Word Expressions
stat.ML
We describe a new method for visualizing topics, the distributions over terms that are automatically extracted from large text corpora using latent variable models. Our method finds significant $n$-grams related to a topic, which are then used to help understand and interpret the underlying distribution. Compared with ...
computer science
21,700
Sparsistent Estimation of Time-Varying Discrete Markov Random Fields
stat.ML
Network models have been popular for modeling and representing complex relationships and dependencies between observed variables. When data comes from a dynamic stochastic process, a single static network model cannot adequately capture transient dependencies, such as, gene regulatory dependencies throughout a developm...
computer science
21,701
Empirical Bernstein Bounds and Sample Variance Penalization
stat.ML
We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the sample size n. The bounds lead us to consider sample variance penalization, a nov...
computer science