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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 |
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