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21,702 | 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... | computer science |
21,703 | 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... | computer science |
21,704 | 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... | computer science |
21,705 | 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... | computer science |
21,706 | 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 ... | computer science |
21,707 | 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... | computer science |
21,708 | 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... | computer science |
21,709 | 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... | computer science |
21,710 | Asymptotic Normality of Support Vector Machine Variants and Other
Regularized Kernel Methods | stat.ML | In nonparametric classification and regression problems, regularized kernel
methods, in particular support vector machines, attract much attention in
theoretical and in applied statistics. In an abstract sense, regularized kernel
methods (simply called SVMs here) can be seen as regularized M-estimators for a
parameter ... | computer science |
21,711 | Regularizers for Structured Sparsity | stat.ML | We study the problem of learning a sparse linear regression vector under
additional conditions on the structure of its sparsity pattern. This problem is
relevant in machine learning, statistics and signal processing. It is well
known that a linear regression can benefit from knowledge that the underlying
regression vec... | computer science |
21,712 | A bagging SVM to learn from positive and unlabeled examples | stat.ML | We consider the problem of learning a binary classifier from a training set
of positive and unlabeled examples, both in the inductive and in the
transductive setting. This problem, often referred to as \emph{PU learning},
differs from the standard supervised classification problem by the lack of
negative examples in th... | computer science |
21,713 | Online Multiple Kernel Learning for Structured Prediction | stat.ML | Despite the recent progress towards efficient multiple kernel learning (MKL),
the structured output case remains an open research front. Current approaches
involve repeatedly solving a batch learning problem, which makes them
inadequate for large scale scenarios. We propose a new family of online
proximal algorithms fo... | computer science |
21,714 | Exact block-wise optimization in group lasso and sparse group lasso for
linear regression | stat.ML | The group lasso is a penalized regression method, used in regression problems
where the covariates are partitioned into groups to promote sparsity at the
group level. Existing methods for finding the group lasso estimator either use
gradient projection methods to update the entire coefficient vector
simultaneously at e... | computer science |
21,715 | Maximum Likelihood Joint Tracking and Association in a Strong Clutter
without Combinatorial Complexity | stat.ML | We have developed an efficient algorithm for the maximum likelihood joint
tracking and association problem in a strong clutter for GMTI data. By using an
iterative procedure of the dynamic logic process "from vague-to-crisp," the new
tracker overcomes combinatorial complexity of tracking in highly-cluttered
scenarios a... | computer science |
21,716 | f-divergence estimation and two-sample homogeneity test under
semiparametric density-ratio models | stat.ML | A density ratio is defined by the ratio of two probability densities. We
study the inference problem of density ratios and apply a semi-parametric
density-ratio estimator to the two-sample homogeneity test. In the proposed
test procedure, the f-divergence between two probability densities is estimated
using a density-r... | computer science |
21,717 | Bistatic SAR ATR | stat.ML | With the present revival of interest in bistatic radar systems, research in
that area has gained momentum. Given some of the strategic advantages for a
bistatic configuration, and tech- nological advances in the past few years,
large-scale implementation of the bistatic systems is a scope for the near
future. If the bi... | computer science |
21,718 | Generation of SAR Image for Real-life Objects using General Purpose EM
Simulators | stat.ML | In the applications related to airborne radars, simulation has always played
an important role. This is mainly because of the two fold reason of the
unavailability of desired data and the difficulty associated with the
collection of data under controlled environment. A simple example will be
regarding the collection of... | computer science |
21,719 | Autoregressive Kernels For Time Series | stat.ML | We propose in this work a new family of kernels for variable-length time
series. Our work builds upon the vector autoregressive (VAR) model for
multivariate stochastic processes: given a multivariate time series x, we
consider the likelihood function p_{\theta}(x) of different parameters \theta
in the VAR model as feat... | computer science |
21,720 | DirectLiNGAM: A direct method for learning a linear non-Gaussian
structural equation model | stat.ML | Structural equation models and Bayesian networks have been widely used to
analyze causal relations between continuous variables. In such frameworks,
linear acyclic models are typically used to model the data-generating process
of variables. Recently, it was shown that use of non-Gaussianity identifies the
full structur... | computer science |
21,721 | An Analysis of the Convergence of Graph Laplacians | stat.ML | Existing approaches to analyzing the asymptotics of graph Laplacians
typically assume a well-behaved kernel function with smoothness assumptions. We
remove the smoothness assumption and generalize the analysis of graph
Laplacians to include previously unstudied graphs including kNN graphs. We also
introduce a kernel-fr... | computer science |
21,722 | Robust Nonparametric Regression via Sparsity Control with Application to
Load Curve Data Cleansing | stat.ML | Nonparametric methods are widely applicable to statistical inference
problems, since they rely on a few modeling assumptions. In this context, the
fresh look advocated here permeates benefits from variable selection and
compressive sampling, to robustify nonparametric regression against outliers -
that is, data markedl... | computer science |
21,723 | Unified Treatment of Hidden Markov Switching Models | stat.ML | Many real-world problems encountered in several disciplines deal with the
modeling of time-series containing different underlying dynamical regimes, for
which probabilistic approaches are very often employed. In this paper we
describe several such approaches in the common framework of graphical models.
We give a unifie... | computer science |
21,724 | Joint estimation of linear non-Gaussian acyclic models | stat.ML | A linear non-Gaussian structural equation model called LiNGAM is an
identifiable model for exploratory causal analysis. Previous methods estimate a
causal ordering of variables and their connection strengths based on a single
dataset. However, in many application domains, data are obtained under
different conditions, t... | computer science |
21,725 | Robust PCA and subspace tracking from incomplete observations using
L0-surrogates | stat.ML | Many applications in data analysis rely on the decomposition of a data matrix
into a low-rank and a sparse component. Existing methods that tackle this task
use the nuclear norm and L1-cost functions as convex relaxations of the rank
constraint and the sparsity measure, respectively, or employ thresholding
techniques. ... | computer science |
21,726 | Improved Graph Clustering | stat.ML | Graph clustering involves the task of dividing nodes into clusters, so that
the edge density is higher within clusters as opposed to across clusters. A
natural, classic and popular statistical setting for evaluating solutions to
this problem is the stochastic block model, also referred to as the planted
partition model... | computer science |
21,727 | Adaptive Stratified Sampling for Monte-Carlo integration of
Differentiable functions | stat.ML | We consider the problem of adaptive stratified sampling for Monte Carlo
integration of a differentiable function given a finite number of evaluations
to the function. We construct a sampling scheme that samples more often in
regions where the function oscillates more, while allocating the samples such
that they are wel... | computer science |
21,728 | Multi-Stage Multi-Task Feature Learning | stat.ML | Multi-task sparse feature learning aims to improve the generalization
performance by exploiting the shared features among tasks. It has been
successfully applied to many applications including computer vision and
biomedical informatics. Most of the existing multi-task sparse feature learning
algorithms are formulated a... | computer science |
21,729 | Graph Estimation From Multi-attribute Data | stat.ML | Many real world network problems often concern multivariate nodal attributes
such as image, textual, and multi-view feature vectors on nodes, rather than
simple univariate nodal attributes. The existing graph estimation methods built
on Gaussian graphical models and covariance selection algorithms can not handle
such d... | computer science |
21,730 | Anomaly Detection in Time Series of Graphs using Fusion of Graph
Invariants | stat.ML | Given a time series of graphs G(t) = (V, E(t)), t = 1, 2, ..., where the
fixed vertex set V represents "actors" and an edge between vertex u and vertex
v at time t (uv \in E(t)) represents the existence of a communications event
between actors u and v during the tth time period, we wish to detect anomalies
and/or chang... | computer science |
21,731 | Adaptive Reconfiguration Moves for Dirichlet Mixtures | stat.ML | Bayesian mixture models are widely applied for unsupervised learning and
exploratory data analysis. Markov chain Monte Carlo based on Gibbs sampling and
split-merge moves are widely used for inference in these models. However, both
methods are restricted to limited types of transitions and suffer from torpid
mixing and... | computer science |
21,732 | Causal Inference through a Witness Protection Program | stat.ML | One of the most fundamental problems in causal inference is the estimation of
a causal effect when variables are confounded. This is difficult in an
observational study, because one has no direct evidence that all confounders
have been adjusted for. We introduce a novel approach for estimating causal
effects that explo... | computer science |
21,733 | Maximum margin classifier working in a set of strings | stat.ML | Numbers and numerical vectors account for a large portion of data. However,
recently the amount of string data generated has increased dramatically.
Consequently, classifying string data is a common problem in many fields. The
most widely used approach to this problem is to convert strings into numerical
vectors using ... | computer science |
21,734 | Linear Dimensionality Reduction: Survey, Insights, and Generalizations | stat.ML | Linear dimensionality reduction methods are a cornerstone of analyzing high
dimensional data, due to their simple geometric interpretations and typically
attractive computational properties. These methods capture many data features
of interest, such as covariance, dynamical structure, correlation between data
sets, inp... | computer science |
21,735 | Consistent procedures for cluster tree estimation and pruning | stat.ML | For a density $f$ on ${\mathbb R}^d$, a {\it high-density cluster} is any
connected component of $\{x: f(x) \geq \lambda\}$, for some $\lambda > 0$. The
set of all high-density clusters forms a hierarchy called the {\it cluster
tree} of $f$. We present two procedures for estimating the cluster tree given
samples from $... | computer science |
21,736 | Compressed Gaussian Process | stat.ML | Nonparametric regression for massive numbers of samples (n) and features (p)
is an increasingly important problem. In big n settings, a common strategy is
to partition the feature space, and then separately apply simple models to each
partition set. We propose an alternative approach, which avoids such
partitioning and... | computer science |
21,737 | Nonparametric Independence Testing for Small Sample Sizes | stat.ML | This paper deals with the problem of nonparametric independence testing, a
fundamental decision-theoretic problem that asks if two arbitrary (possibly
multivariate) random variables $X,Y$ are independent or not, a question that
comes up in many fields like causality and neuroscience. While quantities like
correlation o... | computer science |
21,738 | Provable Tensor Factorization with Missing Data | stat.ML | We study the problem of low-rank tensor factorization in the presence of
missing data. We ask the following question: how many sampled entries do we
need, to efficiently and exactly reconstruct a tensor with a low-rank
orthogonal decomposition? We propose a novel alternating minimization based
method which iteratively ... | computer science |
21,739 | Algebraic-Combinatorial Methods for Low-Rank Matrix Completion with
Application to Athletic Performance Prediction | stat.ML | This paper presents novel algorithms which exploit the intrinsic algebraic
and combinatorial structure of the matrix completion task for estimating
missing en- tries in the general low rank setting. For positive data, we
achieve results out- performing the state of the art nuclear norm, both in
accuracy and computation... | computer science |
21,740 | Distributed Parameter Estimation in Probabilistic Graphical Models | stat.ML | This paper presents foundational theoretical results on distributed parameter
estimation for undirected probabilistic graphical models. It introduces a
general condition on composite likelihood decompositions of these models which
guarantees the global consistency of distributed estimators, provided the local
estimator... | computer science |
21,741 | Generalization and Robustness of Batched Weighted Average Algorithm with
V-geometrically Ergodic Markov Data | stat.ML | We analyze the generalization and robustness of the batched weighted average
algorithm for V-geometrically ergodic Markov data. This algorithm is a good
alternative to the empirical risk minimization algorithm when the latter
suffers from overfitting or when optimizing the empirical risk is hard. For the
generalization... | computer science |
21,742 | Fast and Robust Least Squares Estimation in Corrupted Linear Models | stat.ML | Subsampling methods have been recently proposed to speed up least squares
estimation in large scale settings. However, these algorithms are typically not
robust to outliers or corruptions in the observed covariates.
The concept of influence that was developed for regression diagnostics can be
used to detect such corr... | computer science |
21,743 | LOCO: Distributing Ridge Regression with Random Projections | stat.ML | We propose LOCO, an algorithm for large-scale ridge regression which
distributes the features across workers on a cluster. Important dependencies
between variables are preserved using structured random projections which are
cheap to compute and must only be communicated once. We show that LOCO obtains
a solution which ... | computer science |
21,744 | Dimensionality reduction for time series data | stat.ML | Despite the fact that they do not consider the temporal nature of data,
classic dimensionality reduction techniques, such as PCA, are widely applied to
time series data. In this paper, we introduce a factor decomposition specific
for time series that builds upon the Bayesian multivariate autoregressive model
and hence ... | computer science |
21,745 | Spectral Methods meet EM: A Provably Optimal Algorithm for Crowdsourcing | stat.ML | Crowdsourcing is a popular paradigm for effectively collecting labels at low
cost. The Dawid-Skene estimator has been widely used for inferring the true
labels from the noisy labels provided by non-expert crowdsourcing workers.
However, since the estimator maximizes a non-convex log-likelihood function, it
is hard to t... | computer science |
21,746 | DFacTo: Distributed Factorization of Tensors | stat.ML | We present a technique for significantly speeding up Alternating Least
Squares (ALS) and Gradient Descent (GD), two widely used algorithms for tensor
factorization. By exploiting properties of the Khatri-Rao product, we show how
to efficiently address a computationally challenging sub-step of both
algorithms. Our algor... | computer science |
21,747 | A Statistical Perspective on Randomized Sketching for Ordinary
Least-Squares | stat.ML | We consider statistical as well as algorithmic aspects of solving large-scale
least-squares (LS) problems using randomized sketching algorithms. For a LS
problem with input data $(X, Y) \in \mathbb{R}^{n \times p} \times
\mathbb{R}^n$, sketching algorithms use a sketching matrix, $S\in\mathbb{R}^{r
\times n}$ with $r \... | computer science |
21,748 | Automatic Dimension Selection for a Non-negative Factorization Approach
to Clustering Multiple Random Graphs | stat.ML | We consider a problem of grouping multiple graphs into several clusters using
singular value thesholding and non-negative factorization. We derive a model
selection information criterion to estimate the number of clusters. We
demonstrate our approach using "Swimmer data set" as well as simulated data
set, and compare i... | computer science |
21,749 | Techniques for clustering interaction data as a collection of graphs | stat.ML | A natural approach to analyze interaction data of form
"what-connects-to-what-when" is to create a time-series (or rather a sequence)
of graphs through temporal discretization (bandwidth selection) and spatial
discretization (vertex contraction). Such discretization together with
non-negative factorization techniques c... | computer science |
21,750 | A Fuzzy Clustering Algorithm for the Mode Seeking Framework | stat.ML | In this paper, we propose a new fuzzy clustering algorithm based on the
mode-seeking framework. Given a dataset in $\mathbb{R}^d$, we define regions of
high density that we call cluster cores. We then consider a random walk on a
neighborhood graph built on top of our data points which is designed to be
attracted by hig... | computer science |
21,751 | Proximal Quasi-Newton for Computationally Intensive L1-regularized
M-estimators | stat.ML | We consider the class of optimization problems arising from computationally
intensive L1-regularized M-estimators, where the function or gradient values
are very expensive to compute. A particular instance of interest is the
L1-regularized MLE for learning Conditional Random Fields (CRFs), which are a
popular class of ... | computer science |
21,752 | Direct Density-Derivative Estimation and Its Application in
KL-Divergence Approximation | stat.ML | Estimation of density derivatives is a versatile tool in statistical data
analysis. A naive approach is to first estimate the density and then compute
its derivative. However, such a two-step approach does not work well because a
good density estimator does not necessarily mean a good density-derivative
estimator. In t... | computer science |
21,753 | Variable Selection in High Dimensions with Random Designs and Orthogonal
Matching Pursuit | stat.ML | The performance of Orthogonal Matching Pursuit (OMP) for variable selection
is analyzed for random designs. When contrasted with the deterministic case,
since the performance is here measured after averaging over the distribution of
the design matrix, one can have far less stringent sparsity constraints on the
coeffici... | computer science |
21,754 | Learning Nonlinear Functions Using Regularized Greedy Forest | stat.ML | We consider the problem of learning a forest of nonlinear decision rules with
general loss functions. The standard methods employ boosted decision trees such
as Adaboost for exponential loss and Friedman's gradient boosting for general
loss. In contrast to these traditional boosting algorithms that treat a tree
learner... | computer science |
21,755 | Nominal Association Vector and Matrix | stat.ML | When response variables are nominal and populations are cross-classified with
respect to multiple polytomies, questions often arise about the degree of
association of the responses with explanatory variables. When populations are
known, we introduce a nominal association vector and matrix to evaluate the
dependence of ... | computer science |
21,756 | Mixtures of conditional Gaussian scale mixtures applied to multiscale
image representations | stat.ML | We present a probabilistic model for natural images which is based on
Gaussian scale mixtures and a simple multiscale representation. In contrast to
the dominant approach to modeling whole images focusing on Markov random
fields, we formulate our model in terms of a directed graphical model. We show
that it is able to ... | computer science |
21,757 | Comparing Probabilistic Models for Melodic Sequences | stat.ML | Modelling the real world complexity of music is a challenge for machine
learning. We address the task of modeling melodic sequences from the same music
genre. We perform a comparative analysis of two probabilistic models; a
Dirichlet Variable Length Markov Model (Dirichlet-VMM) and a Time Convolutional
Restricted Boltz... | computer science |
21,758 | Graph Prediction in a Low-Rank and Autoregressive Setting | stat.ML | We study the problem of prediction for evolving graph data. We formulate the
problem as the minimization of a convex objective encouraging sparsity and
low-rank of the solution, that reflect natural graph properties. The convex
formulation allows to obtain oracle inequalities and efficient solvers. We
provide empirical... | computer science |
21,759 | Asymptotic Accuracy of Bayes Estimation for Latent Variables with
Redundancy | stat.ML | Hierarchical parametric models consisting of observable and latent variables
are widely used for unsupervised learning tasks. For example, a mixture model
is a representative hierarchical model for clustering. From the statistical
point of view, the models can be regular or singular due to the distribution of
data. In ... | computer science |
21,760 | Scaling of Model Approximation Errors and Expected Entropy Distances | stat.ML | We compute the expected value of the Kullback-Leibler divergence to various
fundamental statistical models with respect to canonical priors on the
probability simplex. We obtain closed formulas for the expected model
approximation errors, depending on the dimension of the models and the
cardinalities of their sample sp... | computer science |
21,761 | Nested Expectation Propagation for Gaussian Process Classification with
a Multinomial Probit Likelihood | stat.ML | We consider probabilistic multinomial probit classification using Gaussian
process (GP) priors. The challenges with the multiclass GP classification are
the integration over the non-Gaussian posterior distribution, and the increase
of the number of unknown latent variables as the number of target classes
grows. Expecta... | computer science |
21,762 | Models of Disease Spectra | stat.ML | Case vs control comparisons have been the classical approach to the study of
neurological diseases. However, most patients will not fall cleanly into either
group. Instead, clinicians will typically find patients that cannot be
classified as having clearly progressed into the disease state. For those
subjects, very lit... | computer science |
21,763 | Group Iterative Spectrum Thresholding for Super-Resolution Sparse
Spectral Selection | stat.ML | Recently, sparsity-based algorithms are proposed for super-resolution
spectrum estimation. However, to achieve adequately high resolution in
real-world signal analysis, the dictionary atoms have to be close to each other
in frequency, thereby resulting in a coherent design. The popular convex
compressed sensing methods... | computer science |
21,764 | Predictive Correlation Screening: Application to Two-stage Predictor
Design in High Dimension | stat.ML | We introduce a new approach to variable selection, called Predictive
Correlation Screening, for predictor design. Predictive Correlation Screening
(PCS) implements false positive control on the selected variables, is well
suited to small sample sizes, and is scalable to high dimensions. We establish
asymptotic bounds f... | computer science |
21,765 | Visualizing and Interacting with Concept Hierarchies | stat.ML | Concept Hierarchies and Formal Concept Analysis are theoretically well
grounded and largely experimented methods. They rely on line diagrams called
Galois lattices for visualizing and analysing object-attribute sets. Galois
lattices are visually seducing and conceptually rich for experts. However they
present important... | computer science |
21,766 | Refinement revisited with connections to Bayes error, conditional
entropy and calibrated classifiers | stat.ML | The concept of refinement from probability elicitation is considered for
proper scoring rules. Taking directions from the axioms of probability,
refinement is further clarified using a Hilbert space interpretation and
reformulated into the underlying data distribution setting where connections to
maximal marginal diver... | computer science |
21,767 | Toward Optimal Stratification for Stratified Monte-Carlo Integration | stat.ML | We consider the problem of adaptive stratified sampling for Monte Carlo
integration of a noisy function, given a finite budget n of noisy evaluations
to the function. We tackle in this paper the problem of adapting to the
function at the same time the number of samples into each stratum and the
partition itself. More p... | computer science |
21,768 | A dependent partition-valued process for multitask clustering and time
evolving network modelling | stat.ML | The fundamental aim of clustering algorithms is to partition data points. We
consider tasks where the discovered partition is allowed to vary with some
covariate such as space or time. One approach would be to use
fragmentation-coagulation processes, but these, being Markov processes, are
restricted to linear or tree s... | computer science |
21,769 | Expectation Propagation for Neural Networks with Sparsity-promoting
Priors | stat.ML | We propose a novel approach for nonlinear regression using a two-layer neural
network (NN) model structure with sparsity-favoring hierarchical priors on the
network weights. We present an expectation propagation (EP) approach for
approximate integration over the posterior distribution of the weights, the
hierarchical s... | computer science |
21,770 | ParceLiNGAM: A causal ordering method robust against latent confounders | stat.ML | We consider learning 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 |
21,771 | Some Options for L1-Subspace Signal Processing | stat.ML | We describe ways to define and calculate $L_1$-norm signal subspaces which
are less sensitive to outlying data than $L_2$-calculated subspaces. We focus
on the computation of the $L_1$ maximum-projection principal component of a
data matrix containing N signal samples of dimension D and conclude that the
general proble... | computer science |
21,772 | Noisy Sparse Subspace Clustering | stat.ML | This paper considers the problem of subspace clustering under noise.
Specifically, we study the behavior of Sparse Subspace Clustering (SSC) when
either adversarial or random noise is added to the unlabelled input data
points, which are assumed to be in a union of low-dimensional subspaces. We
show that a modified vers... | computer science |
21,773 | Spectral Clustering with Imbalanced Data | stat.ML | Spectral clustering is sensitive to how graphs are constructed from data
particularly when proximal and imbalanced clusters are present. We show that
Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to
imbalanced data since they tend to emphasize cut sizes over cut values. We
propose a graph partit... | computer science |
21,774 | Sparse and Functional Principal Components Analysis | stat.ML | Regularized principal components analysis, especially Sparse PCA and
Functional PCA, has become widely used for dimension reduction in
high-dimensional settings. Many examples of massive data, however, may benefit
from estimating both sparse AND functional factors. These include neuroimaging
data where there are discre... | computer science |
21,775 | Local Support Vector Machines:Formulation and Analysis | stat.ML | We provide a formulation for Local Support Vector Machines (LSVMs) that
generalizes previous formulations, and brings out the explicit connections to
local polynomial learning used in nonparametric estimation literature. We
investigate the simplest type of LSVMs called Local Linear Support Vector
Machines (LLSVMs). For... | computer science |
21,776 | Predictive PAC Learning and Process Decompositions | stat.ML | We informally call a stochastic process learnable if it admits a
generalization error approaching zero in probability for any concept class with
finite VC-dimension (IID processes are the simplest example). A mixture of
learnable processes need not be learnable itself, and certainly its
generalization error need not de... | computer science |
21,777 | Ellipsoidal Rounding for Nonnegative Matrix Factorization Under Noisy
Separability | stat.ML | We present a numerical algorithm for nonnegative matrix factorization (NMF)
problems under noisy separability. An NMF problem under separability can be
stated as one of finding all vertices of the convex hull of data points. The
research interest of this paper is to find the vectors as close to the vertices
as possible... | computer science |
21,778 | Stratified Graphical Models - Context-Specific Independence in Graphical
Models | stat.ML | Theory of graphical models has matured over more than three decades to
provide the backbone for several classes of models that are used in a myriad of
applications such as genetic mapping of diseases, credit risk evaluation,
reliability and computer security, etc. Despite of their generic applicability
and wide adoptan... | computer science |
21,779 | Causal Discovery with Continuous Additive Noise Models | stat.ML | We consider the problem of learning causal directed acyclic graphs from an
observational joint distribution. One can use these graphs to predict the
outcome of interventional experiments, from which data are often not available.
We show that if the observational distribution follows a structural equation
model with an ... | computer science |
21,780 | MPBART - Multinomial Probit Bayesian Additive Regression Trees | stat.ML | This article proposes Multinomial Probit Bayesian Additive Regression Trees
(MPBART) as a multinomial probit extension of BART - Bayesian Additive
Regression Trees (Chipman et al (2010)). MPBART is flexible to allow inclusion
of predictors that describe the observed units as well as the available choice
alternatives. T... | computer science |
21,781 | A Linear-Time Particle Gibbs Sampler for Infinite Hidden Markov Models | stat.ML | Infinite Hidden Markov Models (iHMM's) are an attractive, nonparametric
generalization of the classical Hidden Markov Model which can automatically
infer the number of hidden states in the system. However, due to the
infinite-dimensional nature of transition dynamics performing inference in the
iHMM is difficult. In th... | computer science |
21,782 | On the Feasibility of Distributed Kernel Regression for Big Data | stat.ML | In modern scientific research, massive datasets with huge numbers of
observations are frequently encountered. To facilitate the computational
process, a divide-and-conquer scheme is often used for the analysis of big
data. In such a strategy, a full dataset is first split into several manageable
segments; the final out... | computer science |
21,783 | Consistency of Spectral Hypergraph Partitioning under Planted Partition
Model | stat.ML | Hypergraph partitioning lies at the heart of a number of problems in machine
learning and network sciences. Many algorithms for hypergraph partitioning have
been proposed that extend standard approaches for graph partitioning to the
case of hypergraphs. However, theoretical aspects of such methods have seldom
received ... | computer science |
21,784 | Bayesian Optimization for Synthetic Gene Design | stat.ML | We address the problem of synthetic gene design using Bayesian optimization.
The main issue when designing a gene is that the design space is defined in
terms of long strings of characters of different lengths, which renders the
optimization intractable. We propose a three-step approach to deal with this
issue. First, ... | computer science |
21,785 | Dense Distributions from Sparse Samples: Improved Gibbs Sampling
Parameter Estimators for LDA | stat.ML | We introduce a novel approach for estimating Latent Dirichlet Allocation
(LDA) parameters from collapsed Gibbs samples (CGS), by leveraging the full
conditional distributions over the latent variable assignments to efficiently
average over multiple samples, for little more computational cost than drawing
a single addit... | computer science |
21,786 | Relations Between Adjacency and Modularity Graph Partitioning | stat.ML | In this paper the exact linear relation between the leading eigenvector of
the unnormalized modularity matrix and the eigenvectors of the adjacency matrix
is developed. Based on this analysis a method to approximate the leading
eigenvector of the modularity matrix is given, and the relative error of the
approximation i... | computer science |
21,787 | Bootstrapped Adaptive Threshold Selection for Statistical Model
Selection and Estimation | stat.ML | A central goal of neuroscience is to understand how activity in the nervous
system is related to features of the external world, or to features of the
nervous system itself. A common approach is to model neural responses as a
weighted combination of external features, or vice versa. The structure of the
model weights c... | computer science |
21,788 | Local identifiability of $l_1$-minimization dictionary learning: a
sufficient and almost necessary condition | stat.ML | We study the theoretical properties of learning a dictionary from $N$ signals
$\mathbf x_i\in \mathbb R^K$ for $i=1,...,N$ via $l_1$-minimization. We assume
that $\mathbf x_i$'s are $i.i.d.$ random linear combinations of the $K$ columns
from a complete (i.e., square and invertible) reference dictionary $\mathbf D_0
\in... | computer science |
21,789 | Harmonic Exponential Families on Manifolds | stat.ML | In a range of fields including the geosciences, molecular biology, robotics
and computer vision, one encounters problems that involve random variables on
manifolds. Currently, there is a lack of flexible probabilistic models on
manifolds that are fast and easy to train. We define an extremely flexible
class of exponent... | computer science |
21,790 | Towards Faster Rates and Oracle Property for Low-Rank Matrix Estimation | stat.ML | We present a unified framework for low-rank matrix estimation with nonconvex
penalties. We first prove that the proposed estimator attains a faster
statistical rate than the traditional low-rank matrix estimator with nuclear
norm penalty. Moreover, we rigorously show that under a certain condition on
the magnitude of t... | computer science |
21,791 | Vector-Space Markov Random Fields via Exponential Families | stat.ML | We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of
undirected graphical models where each variable can belong to an arbitrary
vector space. VS-MRFs generalize a recent line of work on scalar-valued,
uni-parameter exponential family and mixed graphical models, thereby greatly
broadening the class o... | computer science |
21,792 | Statistical and Algorithmic Perspectives on Randomized Sketching for
Ordinary Least-Squares -- ICML | stat.ML | We consider statistical and algorithmic aspects of solving large-scale
least-squares (LS) problems using randomized sketching algorithms. Prior
results show that, from an \emph{algorithmic perspective}, when using sketching
matrices constructed from random projections and leverage-score sampling, if
the number of sampl... | computer science |
21,793 | Stochastic Annealing for Variational Inference | stat.ML | We empirically evaluate a stochastic annealing strategy for Bayesian
posterior optimization with variational inference. Variational inference is a
deterministic approach to approximate posterior inference in Bayesian models in
which a typically non-convex objective function is locally optimized over the
parameters of t... | computer science |
21,794 | Automatic Relevance Determination For Deep Generative Models | stat.ML | A recurring problem when building probabilistic latent variable models is
regularization and model selection, for instance, the choice of the
dimensionality of the latent space. In the context of belief networks with
latent variables, this problem has been adressed with Automatic Relevance
Determination (ARD) employing... | computer science |
21,795 | Batch Bayesian Optimization via Local Penalization | stat.ML | The popularity of Bayesian optimization methods for efficient exploration of
parameter spaces has lead to a series of papers applying Gaussian processes as
surrogates in the optimization of functions. However, most proposed approaches
only allow the exploration of the parameter space to occur sequentially. Often,
it is... | computer science |
21,796 | A Dynamic Bayesian Network Model for Inventory Level Estimation in
Retail Marketing | stat.ML | Many retailers today employ inventory management systems based on Re-Order
Point Policies, most of which rely on the assumption that all decreases in
product inventory levels result from product sales. Unfortunately, it usually
happens that small but random quantities of the product get lost, stolen or
broken without r... | computer science |
21,797 | Nonparametric Detection of Geometric Structures over Networks | stat.ML | Nonparametric detection of existence of an anomalous structure over a network
is investigated. Nodes corresponding to the anomalous structure (if one exists)
receive samples generated by a distribution q, which is different from a
distribution p generating samples for other nodes. If an anomalous structure
does not exi... | computer science |
21,798 | Manifold unwrapping using density ridges | stat.ML | Research on manifold learning within a density ridge estimation framework has
shown great potential in recent work for both estimation and de-noising of
manifolds, building on the intuitive and well-defined notion of principal
curves and surfaces. However, the problem of unwrapping or unfolding manifolds
has received r... | computer science |
21,799 | Monitoring Chinese Population Migration in Consecutive Weekly Basis from
Intra-city scale to Inter-province scale by Didi's Bigdata | stat.ML | Population migration is valuable information which leads to proper decision
in urban-planning strategy, massive investment, and many other fields. For
instance, inter-city migration is a posterior evidence to see if the
government's constrain of population works, and inter-community immigration
might be a prior evidenc... | computer science |
21,800 | An Adaptive Resample-Move Algorithm for Estimating Normalizing Constants | stat.ML | The estimation of normalizing constants is a fundamental step in
probabilistic model comparison. Sequential Monte Carlo methods may be used for
this task and have the advantage of being inherently parallelizable. However,
the standard choice of using a fixed number of particles at each iteration is
suboptimal because s... | computer science |
21,801 | A Unified Framework for Sparse Non-Negative Least Squares using
Multiplicative Updates and the Non-Negative Matrix Factorization Problem | stat.ML | We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS
occurs naturally in a wide variety of applications where an unknown,
non-negative quantity must be recovered from linear measurements. We present a
unified framework for S-NNLS based on a rectified power exponential scale
mixture prior on the spars... | computer science |
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