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11,000 | Lasso type classifiers with a reject option | stat.ML | We consider the problem of binary classification where one can, for a
particular cost, choose not to classify an observation. We present a simple
proof for the oracle inequality for the excess risk of structural risk
minimizers using a lasso type penalty. | statistics |
11,001 | Metric Embedding for Nearest Neighbor Classification | stat.ML | The distance metric plays an important role in nearest neighbor (NN)
classification. Usually the Euclidean distance metric is assumed or a
Mahalanobis distance metric is optimized to improve the NN performance. In this
paper, we study the problem of embedding arbitrary metric spaces into a
Euclidean space with the goal... | statistics |
11,002 | Degenerating families of dendrograms | stat.ML | Dendrograms used in data analysis are ultrametric spaces, hence objects of
nonarchimedean geometry. It is known that there exist $p$-adic representation
of dendrograms. Completed by a point at infinity, they can be viewed as
subtrees of the Bruhat-Tits tree associated to the $p$-adic projective line.
The implications a... | statistics |
11,003 | Families of dendrograms | stat.ML | A conceptual framework for cluster analysis from the viewpoint of p-adic
geometry is introduced by describing the space of all dendrograms for n
datapoints and relating it to the moduli space of p-adic Riemannian spheres
with punctures using a method recently applied by Murtagh (2004b). This method
embeds a dendrogram ... | statistics |
11,004 | Online Learning in Discrete Hidden Markov Models | stat.ML | We present and analyse three online algorithms for learning in discrete
Hidden Markov Models (HMMs) and compare them with the Baldi-Chauvin Algorithm.
Using the Kullback-Leibler divergence as a measure of generalisation error we
draw learning curves in simplified situations. The performance for learning
drifting concep... | statistics |
11,005 | Supervised Machine Learning with a Novel Kernel Density Estimator | stat.ML | In recent years, kernel density estimation has been exploited by computer
scientists to model machine learning problems. The kernel density estimation
based approaches are of interest due to the low time complexity of either O(n)
or O(n*log(n)) for constructing a classifier, where n is the number of sampling
instances.... | statistics |
11,006 | Bayesian Classification and Regression with High Dimensional Features | stat.ML | This thesis responds to the challenges of using a large number, such as
thousands, of features in regression and classification problems.
There are two situations where such high dimensional features arise. One is
when high dimensional measurements are available, for example, gene expression
data produced by microarr... | statistics |
11,007 | Simulated Annealing: Rigorous finite-time guarantees for optimization on continuous domains | stat.ML | Simulated annealing is a popular method for approaching the solution of a
global optimization problem. Existing results on its performance apply to
discrete combinatorial optimization where the optimization variables can assume
only a finite set of possible values. We introduce a new general formulation of
simulated an... | statistics |
11,008 | 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... | statistics |
11,009 | 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. | statistics |
11,010 | 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... | statistics |
11,011 | Variable importance in binary regression trees and forests | stat.ML | We characterize and study variable importance (VIMP) and pairwise variable
associations in binary regression trees. A key component involves the node mean
squared error for a quantity we refer to as a maximal subtree. The theory
naturally extends from single trees to ensembles of trees and applies to
methods like rando... | statistics |
11,012 | Pac-Bayesian Supervised Classification: The Thermodynamics of Statistical Learning | stat.ML | This monograph deals with adaptive supervised classification, using tools
borrowed from statistical mechanics and information theory, stemming from the
PACBayesian approach pioneered by David McAllester and applied to a conception
of statistical learning theory forged by Vladimir Vapnik. Using convex analysis
on the se... | statistics |
11,013 | Classification Constrained Dimensionality Reduction | stat.ML | Dimensionality reduction is a topic of recent interest. In this paper, we
present the classification constrained dimensionality reduction (CCDR)
algorithm to account for label information. The algorithm can account for
multiple classes as well as the semi-supervised setting. We present an
out-of-sample expressions for ... | statistics |
11,014 | 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... | statistics |
11,015 | Testing for Homogeneity with Kernel Fisher Discriminant Analysis | stat.ML | We propose to investigate test statistics for testing homogeneity in
reproducing kernel Hilbert spaces. Asymptotic null distributions under null
hypothesis are derived, and consistency against fixed and local alternatives is
assessed. Finally, experimental evidence of the performance of the proposed
approach on both ar... | statistics |
11,016 | On the underestimation of model uncertainty by Bayesian K-nearest neighbors | stat.ML | When using the K-nearest neighbors method, one often ignores uncertainty in
the choice of K. To account for such uncertainty, Holmes and Adams (2002)
proposed a Bayesian framework for K-nearest neighbors (KNN). Their Bayesian KNN
(BKNN) approach uses a pseudo-likelihood function, and standard Markov chain
Monte Carlo (... | statistics |
11,017 | Information Preserving Component Analysis: Data Projections for Flow Cytometry Analysis | stat.ML | Flow cytometry is often used to characterize the malignant cells in leukemia
and lymphoma patients, traced to the level of the individual cell. Typically,
flow cytometric data analysis is performed through a series of 2-dimensional
projections onto the axes of the data set. Through the years, clinicians have
determined... | statistics |
11,018 | Random projection trees for vector quantization | stat.ML | A simple and computationally efficient scheme for tree-structured vector
quantization is presented. Unlike previous methods, its quantization error
depends only on the intrinsic dimension of the data distribution, rather than
the apparent dimension of the space in which the data happen to lie. | statistics |
11,019 | Manifold Learning: The Price of Normalization | stat.ML | We analyze the performance of a class of manifold-learning algorithms that
find their output by minimizing a quadratic form under some normalization
constraints. This class consists of Locally Linear Embedding (LLE), Laplacian
Eigenmap, Local Tangent Space Alignment (LTSA), Hessian Eigenmaps (HLLE), and
Diffusion maps.... | statistics |
11,020 | Local Procrustes for Manifold Embedding: A Measure of Embedding Quality and Embedding Algorithms | stat.ML | We present the Procrustes measure, a novel measure based on Procrustes
rotation that enables quantitative comparison of the output of manifold-based
embedding algorithms (such as LLE (Roweis and Saul, 2000) and Isomap (Tenenbaum
et al, 2000)). The measure also serves as a natural tool when choosing
dimension-reduction ... | statistics |
11,021 | Supervised functional classification: A theoretical remark and some comparisons | stat.ML | The problem of supervised classification (or discrimination) with functional
data is considered, with a special interest on the popular k-nearest neighbors
(k-NN) classifier. First, relying on a recent result by Cerou and Guyader
(2006), we prove the consistency of the k-NN classifier for functional data
whose distribu... | statistics |
11,022 | High-dimensional additive modeling | stat.ML | We propose a new sparsity-smoothness penalty for high-dimensional generalized
additive models. The combination of sparsity and smoothness is crucial for
mathematical theory as well as performance for finite-sample data. We present a
computationally efficient algorithm, with provable numerical convergence
properties, fo... | statistics |
11,023 | LLE with low-dimensional neighborhood representation | stat.ML | The local linear embedding algorithm (LLE) is a non-linear dimension-reducing
technique, widely used due to its computational simplicity and intuitive
approach. LLE first linearly reconstructs each input point from its nearest
neighbors and then preserves these neighborhood relations in the
low-dimensional embedding. W... | statistics |
11,024 | Persistent Clustering and a Theorem of J. Kleinberg | stat.ML | We construct a framework for studying clustering algorithms, which includes
two key ideas: persistence and functoriality. The first encodes the idea that
the output of a clustering scheme should carry a multiresolution structure, the
second the idea that one should be able to compare the results of clustering
algorithm... | statistics |
11,025 | Decomposable Principal Component Analysis | stat.ML | We consider principal component analysis (PCA) in decomposable Gaussian
graphical models. We exploit the prior information in these models in order to
distribute its computation. For this purpose, we reformulate the problem in the
sparse inverse covariance (concentration) domain and solve the global
eigenvalue problem ... | statistics |
11,026 | 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... | statistics |
11,027 | 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... | statistics |
11,028 | 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... | statistics |
11,029 | Improved Estimation of High-dimensional Ising Models | stat.ML | We consider the problem of jointly estimating the parameters as well as the
structure of binary valued Markov Random Fields, in contrast to earlier work
that focus on one of the two problems. We formulate the problem as a
maximization of $\ell_1$-regularized surrogate likelihood that allows us to
find a sparse solution... | statistics |
11,030 | Kernel Regression by Mode Calculation of the Conditional Probability Distribution | stat.ML | The most direct way to express arbitrary dependencies in datasets is to
estimate the joint distribution and to apply afterwards the argmax-function to
obtain the mode of the corresponding conditional distribution. This method is
in practice difficult, because it requires a global optimization of a
complicated function,... | statistics |
11,031 | Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks | stat.ML | We present a procedure for effective estimation of entropy and mutual
information from small-sample data, and apply it to the problem of inferring
high-dimensional gene association networks. Specifically, we develop a
James-Stein-type shrinkage estimator, resulting in a procedure that is highly
efficient statistically ... | statistics |
11,032 | Random Forests: some methodological insights | stat.ML | This paper examines from an experimental perspective random forests, the
increasingly used statistical method for classification and regression problems
introduced by Leo Breiman in 2001. It first aims at confirming, known but
sparse, advice for using random forests and at proposing some complementary
remarks for both ... | statistics |
11,033 | An information-theoretic derivation of min-cut based clustering | stat.ML | Min-cut clustering, based on minimizing one of two heuristic cost-functions
proposed by Shi and Malik, has spawned tremendous research, both analytic and
algorithmic, in the graph partitioning and image segmentation communities over
the last decade. It is however unclear if these heuristics can be derived from
a more g... | statistics |
11,034 | 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... | statistics |
11,035 | 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... | statistics |
11,036 | On the Geometry of Discrete Exponential Families with Application to Exponential Random Graph Models | stat.ML | There has been an explosion of interest in statistical models for analyzing
network data, and considerable interest in the class of exponential random
graph (ERG) models, especially in connection with difficulties in computing
maximum likelihood estimates. The issues associated with these difficulties
relate to the bro... | statistics |
11,037 | Reconstruction of Epsilon-Machines in Predictive Frameworks and Decisional States | stat.ML | This article introduces both a new algorithm for reconstructing
epsilon-machines from data, as well as the decisional states. These are defined
as the internal states of a system that lead to the same decision, based on a
user-provided utility or pay-off function. The utility function encodes some a
priori knowledge ex... | statistics |
11,038 | Lanczos Approximations for the Speedup of Kernel Partial Least Squares Regression | stat.ML | The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is
quadratic in the number of examples. However, the necessity of obtaining
sensitivity measures as degrees of freedom for model selection or confidence
intervals for more detailed analysis requires cubic runtime, and thus
constitutes a computationa... | statistics |
11,039 | Escaping the curse of dimensionality with a tree-based regressor | stat.ML | We present the first tree-based regressor whose convergence rate depends only
on the intrinsic dimension of the data, namely its Assouad dimension. The
regressor uses the RPtree partitioning procedure, a simple randomized variant
of k-d trees. | statistics |
11,040 | 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 ... | statistics |
11,041 | Finding Exogenous Variables in Data with Many More Variables than Observations | stat.ML | Many statistical methods have been proposed to estimate causal models in
classical situations with fewer variables than observations (p<n, p: the number
of variables and n: the number of observations). However, modern datasets
including gene expression data need high-dimensional causal modeling in
challenging situation... | statistics |
11,042 | Structured Variable Selection with Sparsity-Inducing Norms | stat.ML | We consider the empirical risk minimization problem for linear supervised
learning, with regularization by structured sparsity-inducing norms. These are
defined as sums of Euclidean norms on certain subsets of variables, extending
the usual $\ell_1$-norm and the group $\ell_1$-norm by allowing the subsets to
overlap. T... | statistics |
11,043 | Supplementary material for Markov equivalence for ancestral graphs | stat.ML | We prove that the criterion for Markov equivalence provided by Zhao et al.
(2005) may involve a set of features of a graph that is exponential in the
number of vertices. | statistics |
11,044 | A more robust boosting algorithm | stat.ML | We present a new boosting algorithm, motivated by the large margins theory
for boosting. We give experimental evidence that the new algorithm is
significantly more robust against label noise than existing boosting algorithm. | statistics |
11,045 | 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... | statistics |
11,046 | 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... | statistics |
11,047 | 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... | statistics |
11,048 | 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... | statistics |
11,049 | 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 ... | statistics |
11,050 | 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... | statistics |
11,051 | 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... | statistics |
11,052 | Mean-Field Theory of Meta-Learning | stat.ML | We discuss here the mean-field theory for a cellular automata model of
meta-learning. The meta-learning is the process of combining outcomes of
individual learning procedures in order to determine the final decision with
higher accuracy than any single learning method. Our method is constructed from
an ensemble of inte... | statistics |
11,053 | How the initialization affects the stability of the k-means algorithm | stat.ML | We investigate the role of the initialization for the stability of the
k-means clustering algorithm. As opposed to other papers, we consider the
actual k-means algorithm and do not ignore its property of getting stuck in
local optima. We are interested in the actual clustering, not only in the costs
of the solution. We... | statistics |
11,054 | Classification by Set Cover: The Prototype Vector Machine | stat.ML | We introduce a new nearest-prototype classifier, the prototype vector machine
(PVM). It arises from a combinatorial optimization problem which we cast as a
variant of the set cover problem. We propose two algorithms for approximating
its solution. The PVM selects a relatively small number of representative
points which... | statistics |
11,055 | Convex Multiview Fisher Discriminant Analysis | stat.ML | Section 1.3 was incorrect, and 2.1 will be removed from further submissions.
A rewritten version will be posted in the future. | statistics |
11,056 | Relative Expected Improvement in Kriging Based Optimization | stat.ML | We propose an extension of the concept of Expected Improvement criterion
commonly used in Kriging based optimization. We extend it for more complex
Kriging models, e.g. models using derivatives. The target field of application
are CFD problems, where objective function are extremely expensive to evaluate,
but the theor... | statistics |
11,057 | Learning Bayesian Networks with the bnlearn R Package | stat.ML | bnlearn is an R package which includes several algorithms for learning the
structure of Bayesian networks with either discrete or continuous variables.
Both constraint-based and score-based algorithms are implemented, and can use
the functionality provided by the snow package to improve their performance via
parallel c... | statistics |
11,058 | 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... | statistics |
11,059 | 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... | statistics |
11,060 | 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... | statistics |
11,061 | 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 ... | statistics |
11,062 | 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... | statistics |
11,063 | 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)... | statistics |
11,064 | Expectation Propagation on the Maximum of Correlated Normal Variables | stat.ML | Many inference problems involving questions of optimality ask for the maximum
or the minimum of a finite set of unknown quantities. This technical report
derives the first two posterior moments of the maximum of two correlated
Gaussian variables and the first two posterior moments of the two generating
variables (corre... | statistics |
11,065 | Functional learning through kernels | stat.ML | This paper reviews the functional aspects of statistical learning theory. The
main point under consideration is the nature of the hypothesis set when no
prior information is available but data. Within this framework we first discuss
about the hypothesis set: it is a vectorial space, it is a set of pointwise
defined fun... | statistics |
11,066 | Sparsification and feature selection by compressive linear regression | stat.ML | The Minimum Description Length (MDL) principle states that the optimal model
for a given data set is that which compresses it best. Due to practial
limitations the model can be restricted to a class such as linear regression
models, which we address in this study. As in other formulations such as the
LASSO and forward ... | statistics |
11,067 | Distinguishing Cause and Effect via Second Order Exponential Models | stat.ML | We propose a method to infer causal structures containing both discrete and
continuous variables. The idea is to select causal hypotheses for which the
conditional density of every variable, given its causes, becomes smooth. We
define a family of smooth densities and conditional densities by second order
exponential mo... | statistics |
11,068 | Causal Inference on Discrete Data using Additive Noise Models | stat.ML | Inferring the causal structure of a set of random variables from a finite
sample of the joint distribution is an important problem in science. Recently,
methods using additive noise models have been suggested to approach the case of
continuous variables. In many situations, however, the variables of interest
are discre... | statistics |
11,069 | How slow is slow? SFA detects signals that are slower than the driving force | stat.ML | Slow feature analysis (SFA) is a method for extracting slowly varying driving
forces from quickly varying nonstationary time series. We show here that it is
possible for SFA to detect a component which is even slower than the driving
force itself (e.g. the envelope of a modulated sine wave). It is shown that it
depends... | statistics |
11,070 | Sparse Convolved Multiple Output Gaussian Processes | stat.ML | Recently there has been an increasing interest in methods that deal with
multiple outputs. This has been motivated partly by frameworks like multitask
learning, multisensor networks or structured output data. From a Gaussian
processes perspective, the problem reduces to specifying an appropriate
covariance function tha... | statistics |
11,071 | Positive Definite Kernels in Machine Learning | stat.ML | This survey is an introduction to positive definite kernels and the set of
methods they have inspired in the machine learning literature, namely kernel
methods. We first discuss some properties of positive definite kernels as well
as reproducing kernel Hibert spaces, the natural extension of the set of
functions $\{k(x... | statistics |
11,072 | Under-determined reverberant audio source separation using a full-rank spatial covariance model | stat.ML | This article addresses the modeling of reverberant recording environments in
the context of under-determined convolutive blind source separation. We model
the contribution of each source to all mixture channels in the time-frequency
domain as a zero-mean Gaussian random variable whose covariance encodes the
spatial cha... | statistics |
11,073 | Hyper-sparse optimal aggregation | stat.ML | In this paper, we consider the problem of "hyper-sparse aggregation". Namely,
given a dictionary $F = \{f_1, ..., f_M \}$ of functions, we look for an
optimal aggregation algorithm that writes $\tilde f = \sum_{j=1}^M \theta_j
f_j$ with as many zero coefficients $\theta_j$ as possible. This problem is of
particular int... | statistics |
11,074 | Multi-Way, Multi-View Learning | stat.ML | We extend multi-way, multivariate ANOVA-type analysis to cases where one
covariate is the view, with features of each view coming from different,
high-dimensional domains. The different views are assumed to be connected by
having paired samples; this is a common setup in recent bioinformatics
experiments, of which we a... | statistics |
11,075 | Variational Inducing Kernels for Sparse Convolved Multiple Output Gaussian Processes | stat.ML | Interest in multioutput kernel methods is increasing, whether under the guise
of multitask learning, multisensor networks or structured output data. From the
Gaussian process perspective a multioutput Mercer kernel is a covariance
function over correlated output functions. One way of constructing such kernels
is based ... | statistics |
11,076 | Composite Binary Losses | stat.ML | We study losses for binary classification and class probability estimation
and extend the understanding of them from margin losses to general composite
losses which are the composition of a proper loss with a link function. We
characterise when margin losses can be proper composite losses, explicitly show
how to determ... | statistics |
11,077 | A Geometric Proof of Calibration | stat.ML | We provide yet another proof of the existence of calibrated forecasters; it
has two merits. First, it is valid for an arbitrary finite number of outcomes.
Second, it is short and simple and it follows from a direct application of
Blackwell's approachability theorem to carefully chosen vector-valued payoff
function and ... | statistics |
11,078 | Learning the Structure of Deep Sparse Graphical Models | stat.ML | Deep belief networks are a powerful way to model complex probability
distributions. However, learning the structure of a belief network,
particularly one with hidden units, is difficult. The Indian buffet process has
been used as a nonparametric Bayesian prior on the directed structure of a
belief network with a single... | statistics |
11,079 | Forest Density Estimation | stat.ML | We study graph estimation and density estimation in high dimensions, using a
family of density estimators based on forest structured undirected graphical
models. For density estimation, we do not assume the true distribution
corresponds to a forest; rather, we form kernel density estimates of the
bivariate and univaria... | statistics |
11,080 | Probabilistic Recovery of Multiple Subspaces in Point Clouds by Geometric lp Minimization | stat.ML | We assume data independently sampled from a mixture distribution on the unit
ball of the D-dimensional Euclidean space with K+1 components: the first
component is a uniform distribution on that ball representing outliers and the
other K components are uniform distributions along K d-dimensional linear
subspaces restric... | statistics |
11,081 | Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast with Algebraic Optimal Step Size | stat.ML | Independent component analysis (ICA) aims at decomposing an observed random
vector into statistically independent variables. Deflation-based
implementations, such as the popular one-unit FastICA algorithm and its
variants, extract the independent components one after another. A novel method
for deflationary ICA, referr... | statistics |
11,082 | Security Analysis of Online Centroid Anomaly Detection | stat.ML | Security issues are crucial in a number of machine learning applications,
especially in scenarios dealing with human activity rather than natural
phenomena (e.g., information ranking, spam detection, malware detection, etc.).
It is to be expected in such cases that learning algorithms will have to deal
with manipulated... | statistics |
11,083 | Supervised Topic Models | stat.ML | We introduce supervised latent Dirichlet allocation (sLDA), a statistical
model of labelled documents. The model accommodates a variety of response
types. We derive an approximate maximum-likelihood procedure for parameter
estimation, which relies on variational methods to handle intractable posterior
expectations. Pre... | statistics |
11,084 | Optimal Allocation Strategies for the Dark Pool Problem | stat.ML | We study the problem of allocating stocks to dark pools. We propose and
analyze an optimal approach for allocations, if continuous-valued allocations
are allowed. We also propose a modification for the case when only
integer-valued allocations are possible. We extend the previous work on this
problem to adversarial sce... | statistics |
11,085 | Linear Time Feature Selection for Regularized Least-Squares | stat.ML | We propose a novel algorithm for greedy forward feature selection for
regularized least-squares (RLS) regression and classification, also known as
the least-squares support vector machine or ridge regression. The algorithm,
which we call greedy RLS, starts from the empty feature set, and on each
iteration adds the feat... | statistics |
11,086 | On the Schoenberg Transformations in Data Analysis: Theory and Illustrations | stat.ML | The class of Schoenberg transformations, embedding Euclidean distances into
higher dimensional Euclidean spaces, is presented, and derived from theorems on
positive definite and conditionally negative definite matrices. Original
results on the arc lengths, angles and curvature of the transformations are
proposed, and v... | statistics |
11,087 | Visualization of Manifold-Valued Elements by Multidimensional Scaling | stat.ML | The present contribution suggests the use of a multidimensional scaling (MDS)
algorithm as a visualization tool for manifold-valued elements. A visualization
tool of this kind is useful in signal processing and machine learning whenever
learning/adaptation algorithms insist on high-dimensional parameter manifolds. | statistics |
11,088 | Strong Consistency of Prototype Based Clustering in Probabilistic Space | stat.ML | In this paper we formulate in general terms an approach to prove strong
consistency of the Empirical Risk Minimisation inductive principle applied to
the prototype or distance based clustering. This approach was motivated by the
Divisive Information-Theoretic Feature Clustering model in probabilistic space
with Kullbac... | statistics |
11,089 | Sparse Linear Identifiable Multivariate Modeling | stat.ML | In this paper we consider sparse and identifiable linear latent variable
(factor) and linear Bayesian network models for parsimonious analysis of
multivariate data. We propose a computationally efficient method for joint
parameter and model inference, and model comparison. It consists of a fully
Bayesian hierarchy for ... | statistics |
11,090 | Training linear ranking SVMs in linearithmic time using red-black trees | stat.ML | We introduce an efficient method for training the linear ranking support
vector machine. The method combines cutting plane optimization with red-black
tree based approach to subgradient calculations, and has O(m*s+m*log(m)) time
complexity, where m is the number of training examples, and s the average
number of non-zer... | statistics |
11,091 | Improving the Johnson-Lindenstrauss Lemma | stat.ML | The Johnson-Lindenstrauss Lemma allows for the projection of $n$ points in
$p-$dimensional Euclidean space onto a $k-$dimensional Euclidean space, with $k
\ge \frac{24\ln \emph{n}}{3\epsilon^2-2\epsilon^3}$, so that the pairwise
distances are preserved within a factor of $1\pm\epsilon$. Here, working
directly with the ... | statistics |
11,092 | Refinements of Universal Approximation Results for Deep Belief Networks and Restricted Boltzmann Machines | stat.ML | We improve recently published results about resources of Restricted Boltzmann
Machines (RBM) and Deep Belief Networks (DBN) required to make them Universal
Approximators. We show that any distribution p on the set of binary vectors of
length n can be arbitrarily well approximated by an RBM with k-1 hidden units,
where ... | statistics |
11,093 | Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models | stat.ML | A challenging problem in estimating high-dimensional graphical models is to
choose the regularization parameter in a data-dependent way. The standard
techniques include $K$-fold cross-validation ($K$-CV), Akaike information
criterion (AIC), and Bayesian information criterion (BIC). Though these methods
work well for lo... | statistics |
11,094 | Gaussian Mixture Modeling with Gaussian Process Latent Variable Models | stat.ML | Density modeling is notoriously difficult for high dimensional data. One
approach to the problem is to search for a lower dimensional manifold which
captures the main characteristics of the data. Recently, the Gaussian Process
Latent Variable Model (GPLVM) has successfully been used to find low
dimensional manifolds in... | statistics |
11,095 | Euclidean Distances, soft and spectral Clustering on Weighted Graphs | stat.ML | We define a class of Euclidean distances on weighted graphs, enabling to
perform thermodynamic soft graph clustering. The class can be constructed form
the "raw coordinates" encountered in spectral clustering, and can be extended
by means of higher-dimensional embeddings (Schoenberg transformations).
Geographical flow ... | statistics |
11,096 | Clustering Stability: An Overview | stat.ML | A popular method for selecting the number of clusters is based on stability
arguments: one chooses the number of clusters such that the corresponding
clustering results are "most stable". In recent years, a series of papers has
analyzed the behavior of this method from a theoretical point of view. However,
the results ... | statistics |
11,097 | Directional Statistics on Permutations | stat.ML | Distributions over permutations arise in applications ranging from
multi-object tracking to ranking of instances. The difficulty of dealing with
these distributions is caused by the size of their domain, which is factorial
in the number of considered entities ($n!$). It makes the direct definition of
a multinomial dist... | statistics |
11,098 | Reduced Rank Vector Generalized Linear Models for Feature Extraction | stat.ML | Supervised linear feature extraction can be achieved by fitting a reduced
rank multivariate model. This paper studies rank penalized and rank constrained
vector generalized linear models. From the perspective of thresholding rules,
we build a framework for fitting singular value penalized models and use it for
feature ... | statistics |
11,099 | Support Vector Machines for Additive Models: Consistency and Robustness | stat.ML | Support vector machines (SVMs) are special kernel based methods and belong to
the most successful learning methods since more than a decade. SVMs can
informally be described as a kind of regularized M-estimators for functions and
have demonstrated their usefulness in many complicated real-life problems.
During the last... | statistics |
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