Unnamed: 0 int64 0 41k | title stringlengths 4 274 | category stringlengths 5 18 | summary stringlengths 22 3.66k | theme stringclasses 8
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14,202 | Reservoir computing approaches for representation and classification of
multivariate time series | cs.NE | Classification of multivariate time series (MTS) has been tackled with a
large variety of methodologies and applied to a wide range of scenarios. Among
the existing approaches, reservoir computing (RC) techniques, which implement a
fixed and high-dimensional recurrent network to process sequential data, are
computation... | computer science |
14,203 | Mixed membership stochastic blockmodels | stat.ME | Observations consisting of measurements on relationships for pairs of objects
arise in many settings, such as protein interaction and gene regulatory
networks, collections of author-recipient email, and social networks. Analyzing
such data with probabilisic models can be delicate because the simple
exchangeability assu... | computer science |
14,204 | On Universal Prediction and Bayesian Confirmation | math.ST | The Bayesian framework is a well-studied and successful framework for
inductive reasoning, which includes hypothesis testing and confirmation,
parameter estimation, sequence prediction, classification, and regression. But
standard statistical guidelines for choosing the model class and prior are not
always available or... | computer science |
14,205 | Catching Up Faster by Switching Sooner: A Prequential Solution to the
AIC-BIC Dilemma | math.ST | Bayesian model averaging, model selection and its approximations such as BIC
are generally statistically consistent, but sometimes achieve slower rates og
convergence than other methods such as AIC and leave-one-out cross-validation.
On the other hand, these other methods can br inconsistent. We identify the
"catch-up ... | computer science |
14,206 | Active Learning for Hidden Attributes in Networks | stat.ML | In many networks, vertices have hidden attributes, or types, that are
correlated with the networks topology. If the topology is known but these
attributes are not, and if learning the attributes is costly, we need a method
for choosing which vertex to query in order to learn as much as possible about
the attributes of ... | computer science |
14,207 | Information Theoretic Limits on Learning Stochastic Differential
Equations | cs.IT | Consider the problem of learning the drift coefficient of a stochastic
differential equation from a sample path. In this paper, we assume that the
drift is parametrized by a high dimensional vector. We address the question of
how long the system needs to be observed in order to learn this vector of
parameters. We prove... | computer science |
14,208 | One Permutation Hashing for Efficient Search and Learning | cs.LG | Recently, the method of b-bit minwise hashing has been applied to large-scale
linear learning and sublinear time near-neighbor search. The major drawback of
minwise hashing is the expensive preprocessing cost, as the method requires
applying (e.g.,) k=200 to 500 permutations on the data. The testing time can
also be ex... | computer science |
14,209 | Robust subspace clustering | cs.LG | Subspace clustering refers to the task of finding a multi-subspace
representation that best fits a collection of points taken from a
high-dimensional space. This paper introduces an algorithm inspired by sparse
subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern
Recognition, CVPR (2009) 2790-27... | computer science |
14,210 | Robust High Dimensional Sparse Regression and Matching Pursuit | stat.ML | We consider high dimensional sparse regression, and develop strategies able
to deal with arbitrary -- possibly, severe or coordinated -- errors in the
covariance matrix $X$. These may come from corrupted data, persistent
experimental errors, or malicious respondents in surveys/recommender systems,
etc. Such non-stochas... | computer science |
14,211 | Sparse Signal Processing with Linear and Nonlinear Observations: A
Unified Shannon-Theoretic Approach | cs.IT | We derive fundamental sample complexity bounds for recovering sparse and
structured signals for linear and nonlinear observation models including sparse
regression, group testing, multivariate regression and problems with missing
features. In general, sparse signal processing problems can be characterized in
terms of t... | computer science |
14,212 | Precisely Verifying the Null Space Conditions in Compressed Sensing: A
Sandwiching Algorithm | cs.IT | In this paper, we propose new efficient algorithms to verify the null space
condition in compressed sensing (CS). Given an $(n-m) \times n$ ($m>0$) CS
matrix $A$ and a positive $k$, we are interested in computing $\displaystyle
\alpha_k = \max_{\{z: Az=0,z\neq 0\}}\max_{\{K: |K|\leq k\}}$ ${\|z_K
\|_{1}}{\|z\|_{1}}$, w... | computer science |
14,213 | Rare-Allele Detection Using Compressed Se(que)nsing | cs.IT | Detection of rare variants by resequencing is important for the
identification of individuals carrying disease variants. Rapid sequencing by
new technologies enables low-cost resequencing of target regions, although it
is still prohibitive to test more than a few individuals. In order to improve
cost trade-offs, it has... | computer science |
14,214 | Discrete MDL Predicts in Total Variation | math.PR | The Minimum Description Length (MDL) principle selects the model that has the
shortest code for data plus model. We show that for a countable class of
models, MDL predictions are close to the true distribution in a strong sense.
The result is completely general. No independence, ergodicity, stationarity,
identifiabilit... | computer science |
14,215 | From Small-World Networks to Comparison-Based Search | cs.LG | The problem of content search through comparisons has recently received
considerable attention. In short, a user searching for a target object
navigates through a database in the following manner: the user is asked to
select the object most similar to her target from a small list of objects. A
new object list is then p... | computer science |
14,216 | Predicting protein contact map using evolutionary and physical
constraints by integer programming (extended version) | cs.CE | Motivation. Protein contact map describes the pairwise spatial and functional
relationship of residues in a protein and contains key information for protein
3D structure prediction. Although studied extensively, it remains very
challenging to predict contact map using only sequence information. Most
existing methods pr... | computer science |
14,217 | When are Overcomplete Topic Models Identifiable? Uniqueness of Tensor
Tucker Decompositions with Structured Sparsity | cs.LG | Overcomplete latent representations have been very popular for unsupervised
feature learning in recent years. In this paper, we specify which overcomplete
models can be identified given observable moments of a certain order. We
consider probabilistic admixture or topic models in the overcomplete regime,
where the numbe... | computer science |
14,218 | On the Decreasing Power of Kernel and Distance based Nonparametric
Hypothesis Tests in High Dimensions | stat.ML | This paper is about two related decision theoretic problems, nonparametric
two-sample testing and independence testing. There is a belief that two
recently proposed solutions, based on kernels and distances between pairs of
points, behave well in high-dimensional settings. We identify different sources
of misconception... | computer science |
14,219 | Active Learning for Node Classification in Assortative and
Disassortative Networks | cs.IT | In many real-world networks, nodes have class labels, attributes, or
variables that affect the network's topology. If the topology of the network is
known but the labels of the nodes are hidden, we would like to select a small
subset of nodes such that, if we knew their labels, we could accurately predict
the labels of... | computer science |
14,220 | Risk estimation for matrix recovery with spectral regularization | math.OC | In this paper, we develop an approach to recursively estimate the quadratic
risk for matrix recovery problems regularized with spectral functions. Toward
this end, in the spirit of the SURE theory, a key step is to compute the (weak)
derivative and divergence of a solution with respect to the observations. As
such a so... | computer science |
14,221 | Pseudo-likelihood methods for community detection in large sparse
networks | cs.SI | Many algorithms have been proposed for fitting network models with
communities, but most of them do not scale well to large networks, and often
fail on sparse networks. Here we propose a new fast pseudo-likelihood method
for fitting the stochastic block model for networks, as well as a variant that
allows for an arbitr... | computer science |
14,222 | State estimation under non-Gaussian Levy noise: A modified Kalman
filtering method | math.DS | The Kalman filter is extensively used for state estimation for linear systems
under Gaussian noise. When non-Gaussian L\'evy noise is present, the
conventional Kalman filter may fail to be effective due to the fact that the
non-Gaussian L\'evy noise may have infinite variance. A modified Kalman filter
for linear system... | computer science |
14,223 | Subspace Clustering via Thresholding and Spectral Clustering | cs.IT | We consider the problem of clustering a set of high-dimensional data points
into sets of low-dimensional linear subspaces. The number of subspaces, their
dimensions, and their orientations are unknown. We propose a simple and
low-complexity clustering algorithm based on thresholding the correlations
between the data po... | computer science |
14,224 | Network Detection Theory and Performance | cs.SI | Network detection is an important capability in many areas of applied
research in which data can be represented as a graph of entities and
relationships. Oftentimes the object of interest is a relatively small subgraph
in an enormous, potentially uninteresting background. This aspect characterizes
network detection as ... | computer science |
14,225 | Bayesian Structural Inference for Hidden Processes | stat.ML | We introduce a Bayesian approach to discovering patterns in structurally
complex processes. The proposed method of Bayesian Structural Inference (BSI)
relies on a set of candidate unifilar HMM (uHMM) topologies for inference of
process structure from a data series. We employ a recently developed exact
enumeration of to... | computer science |
14,226 | Equitability, interval estimation, and statistical power | math.ST | For analysis of a high-dimensional dataset, a common approach is to test a
null hypothesis of statistical independence on all variable pairs using a
non-parametric measure of dependence. However, because this approach attempts
to identify any non-trivial relationship no matter how weak, it often
identifies too many rel... | computer science |
14,227 | Measuring dependence powerfully and equitably | stat.ME | Given a high-dimensional data set we often wish to find the strongest
relationships within it. A common strategy is to evaluate a measure of
dependence on every variable pair and retain the highest-scoring pairs for
follow-up. This strategy works well if the statistic used is equitable [Reshef
et al. 2015a], i.e., if, ... | computer science |
14,228 | An Empirical Study of Leading Measures of Dependence | stat.ME | In exploratory data analysis, we are often interested in identifying
promising pairwise associations for further analysis while filtering out
weaker, less interesting ones. This can be accomplished by computing a measure
of dependence on all variable pairs and examining the highest-scoring pairs,
provided the measure o... | computer science |
14,229 | Should we really use post-hoc tests based on mean-ranks? | cs.LG | The statistical comparison of multiple algorithms over multiple data sets is
fundamental in machine learning. This is typically carried out by the Friedman
test. When the Friedman test rejects the null hypothesis, multiple comparisons
are carried out to establish which are the significant differences among
algorithms. ... | computer science |
14,230 | On the tightness of an SDP relaxation of k-means | cs.IT | Recently, Awasthi et al. introduced an SDP relaxation of the $k$-means
problem in $\mathbb R^m$. In this work, we consider a random model for the data
points in which $k$ balls of unit radius are deterministically distributed
throughout $\mathbb R^m$, and then in each ball, $n$ points are drawn according
to a common ro... | computer science |
14,231 | Solving Random Quadratic Systems of Equations Is Nearly as Easy as
Solving Linear Systems | cs.IT | We consider the fundamental problem of solving quadratic systems of equations
in $n$ variables, where $y_i = |\langle \boldsymbol{a}_i, \boldsymbol{x}
\rangle|^2$, $i = 1, \ldots, m$ and $\boldsymbol{x} \in \mathbb{R}^n$ is
unknown. We propose a novel method, which starting with an initial guess
computed by means of a ... | computer science |
14,232 | Low-Rank Matrix Recovery from Row-and-Column Affine Measurements | cs.LG | We propose and study a row-and-column affine measurement scheme for low-rank
matrix recovery. Each measurement is a linear combination of elements in one
row or one column of a matrix $X$. This setting arises naturally in
applications from different domains. However, current algorithms developed for
standard matrix rec... | computer science |
14,233 | On the Computational Complexity of High-Dimensional Bayesian Variable
Selection | math.ST | We study the computational complexity of Markov chain Monte Carlo (MCMC)
methods for high-dimensional Bayesian linear regression under sparsity
constraints. We first show that a Bayesian approach can achieve
variable-selection consistency under relatively mild conditions on the design
matrix. We then demonstrate that t... | computer science |
14,234 | Online Nonnegative Matrix Factorization with Outliers | stat.ML | We propose a unified and systematic framework for performing online
nonnegative matrix factorization in the presence of outliers. Our framework is
particularly suited to large-scale data. We propose two solvers based on
projected gradient descent and the alternating direction method of multipliers.
We prove that the se... | computer science |
14,235 | Robust Estimators in High Dimensions without the Computational
Intractability | cs.DS | We study high-dimensional distribution learning in an agnostic setting where
an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the
samples. Such questions have a rich history spanning statistics, machine
learning and theoretical computer science. Even in the most basic settings, the
only known... | computer science |
14,236 | Fully scalable online-preprocessing algorithm for short oligonucleotide
microarray atlases | cs.CE | Accumulation of standardized data collections is opening up novel
opportunities for holistic characterization of genome function. The limited
scalability of current preprocessing techniques has, however, formed a
bottleneck for full utilization of contemporary microarray collections. While
short oligonucleotide arrays ... | computer science |
14,237 | Exact Sparse Recovery with L0 Projections | stat.ML | Many applications concern sparse signals, for example, detecting anomalies
from the differences between consecutive images taken by surveillance cameras.
This paper focuses on the problem of recovering a K-sparse signal x in N
dimensions. In the mainstream framework of compressed sensing (CS), the vector
x is recovered... | computer science |
14,238 | A consistent clustering-based approach to estimating the number of
change-points in highly dependent time-series | stat.ML | The problem of change-point estimation is considered under a general
framework where the data are generated by unknown stationary ergodic process
distributions. In this context, the consistent estimation of the number of
change-points is provably impossible. However, it is shown that a consistent
clustering method may ... | computer science |
14,239 | Model Selection for High-Dimensional Regression under the Generalized
Irrepresentability Condition | math.ST | In the high-dimensional regression model a response variable is linearly
related to $p$ covariates, but the sample size $n$ is smaller than $p$. We
assume that only a small subset of covariates is `active' (i.e., the
corresponding coefficients are non-zero), and consider the model-selection
problem of identifying the a... | computer science |
14,240 | Noisy Subspace Clustering via Thresholding | cs.IT | We consider the problem of clustering noisy high-dimensional data points into
a union of low-dimensional subspaces and a set of outliers. The number of
subspaces, their dimensions, and their orientations are unknown. A
probabilistic performance analysis of the thresholding-based subspace
clustering (TSC) algorithm intr... | computer science |
14,241 | On model selection consistency of regularized M-estimators | math.ST | Regularized M-estimators are used in diverse areas of science and engineering
to fit high-dimensional models with some low-dimensional structure. Usually the
low-dimensional structure is encoded by the presence of the (unknown)
parameters in some low-dimensional model subspace. In such settings, it is
desirable for est... | computer science |
14,242 | Computing Entropy Rate Of Symbol Sources & A Distribution-free Limit
Theorem | cs.IT | Entropy rate of sequential data-streams naturally quantifies the complexity
of the generative process. Thus entropy rate fluctuations could be used as a
tool to recognize dynamical perturbations in signal sources, and could
potentially be carried out without explicit background noise characterization.
However, state of... | computer science |
14,243 | Dual-to-kernel learning with ideals | stat.ML | In this paper, we propose a theory which unifies kernel learning and symbolic
algebraic methods. We show that both worlds are inherently dual to each other,
and we use this duality to combine the structure-awareness of algebraic methods
with the efficiency and generality of kernels. The main idea lies in relating
polyn... | computer science |
14,244 | Phase transitions and sample complexity in Bayes-optimal matrix
factorization | cs.NA | We analyse the matrix factorization problem. Given a noisy measurement of a
product of two matrices, the problem is to estimate back the original matrices.
It arises in many applications such as dictionary learning, blind matrix
calibration, sparse principal component analysis, blind source separation, low
rank matrix ... | computer science |
14,245 | Probabilistic Interpretation of Linear Solvers | math.OC | This manuscript proposes a probabilistic framework for algorithms that
iteratively solve unconstrained linear problems $Bx = b$ with positive definite
$B$ for $x$. The goal is to replace the point estimates returned by existing
methods with a Gaussian posterior belief over the elements of the inverse of
$B$, which can ... | computer science |
14,246 | Matroid Regression | math.ST | We propose an algebraic combinatorial method for solving large sparse linear
systems of equations locally - that is, a method which can compute single
evaluations of the signal without computing the whole signal. The method scales
only in the sparsity of the system and not in its size, and allows to provide
error estim... | computer science |
14,247 | On the Impossibility of Learning the Missing Mass | stat.ML | This paper shows that one cannot learn the probability of rare events without
imposing further structural assumptions. The event of interest is that of
obtaining an outcome outside the coverage of an i.i.d. sample from a discrete
distribution. The probability of this event is referred to as the "missing
mass". The impo... | computer science |
14,248 | Decentralized learning for wireless communications and networking | math.OC | This chapter deals with decentralized learning algorithms for in-network
processing of graph-valued data. A generic learning problem is formulated and
recast into a separable form, which is iteratively minimized using the
alternating-direction method of multipliers (ADMM) so as to gain the desired
degree of paralleliza... | computer science |
14,249 | Square Hellinger Subadditivity for Bayesian Networks and its
Applications to Identity Testing | cs.LG | We show that the square Hellinger distance between two Bayesian networks on
the same directed graph, $G$, is subadditive with respect to the neighborhoods
of $G$. Namely, if $P$ and $Q$ are the probability distributions defined by two
Bayesian networks on the same DAG, our inequality states that the square
Hellinger di... | computer science |
14,250 | Gradient Coding | stat.ML | We propose a novel coding theoretic framework for mitigating stragglers in
distributed learning. We show how carefully replicating data blocks and coding
across gradients can provide tolerance to failures and stragglers for
Synchronous Gradient Descent. We implement our schemes in python (using MPI) to
run on Amazon EC... | computer science |
14,251 | A geometric analysis of subspace clustering with outliers | cs.IT | This paper considers the problem of clustering a collection of unlabeled data
points assumed to lie near a union of lower-dimensional planes. As is common in
computer vision or unsupervised learning applications, we do not know in
advance how many subspaces there are nor do we have any information about their
dimension... | computer science |
14,252 | Exact and Stable Covariance Estimation from Quadratic Sampling via
Convex Programming | cs.IT | Statistical inference and information processing of high-dimensional data
often require efficient and accurate estimation of their second-order
statistics. With rapidly changing data, limited processing power and storage at
the acquisition devices, it is desirable to extract the covariance structure
from a single pass ... | computer science |
14,253 | Hypothesis Testing for Automated Community Detection in Networks | stat.ML | Community detection in networks is a key exploratory tool with applications
in a diverse set of areas, ranging from finding communities in social and
biological networks to identifying link farms in the World Wide Web. The
problem of finding communities or clusters in a network has received much
attention from statisti... | computer science |
14,254 | Bayesian Discovery of Threat Networks | cs.SI | A novel unified Bayesian framework for network detection is developed, under
which a detection algorithm is derived based on random walks on graphs. The
algorithm detects threat networks using partial observations of their activity,
and is proved to be optimum in the Neyman-Pearson sense. The algorithm is
defined by a ... | computer science |
14,255 | Rapid and deterministic estimation of probability densities using
scale-free field theories | cs.LG | The question of how best to estimate a continuous probability density from
finite data is an intriguing open problem at the interface of statistics and
physics. Previous work has argued that this problem can be addressed in a
natural way using methods from statistical field theory. Here I describe new
results that allo... | computer science |
14,256 | Probabilistic Group Testing under Sum Observations: A Parallelizable
2-Approximation for Entropy Loss | cs.IT | We consider the problem of group testing with sum observations and noiseless
answers, in which we aim to locate multiple objects by querying the number of
objects in each of a sequence of chosen sets. We study a probabilistic setting
with entropy loss, in which we assume a joint Bayesian prior density on the
locations ... | computer science |
14,257 | Scalable Parallel Factorizations of SDD Matrices and Efficient Sampling
for Gaussian Graphical Models | cs.DS | Motivated by a sampling problem basic to computational statistical inference,
we develop a nearly optimal algorithm for a fundamental problem in spectral
graph theory and numerical analysis. Given an $n\times n$ SDDM matrix ${\bf
\mathbf{M}}$, and a constant $-1 \leq p \leq 1$, our algorithm gives efficient
access to a... | computer science |
14,258 | Fast Exact Matrix Completion with Finite Samples | cs.NA | Matrix completion is the problem of recovering a low rank matrix by observing
a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14]
have proposed fast non-convex optimization based iterative algorithms to solve
this problem. However, the sample complexity in all these results is
sub-optimal in it... | computer science |
14,259 | Error Rate Bounds and Iterative Weighted Majority Voting for
Crowdsourcing | stat.ML | Crowdsourcing has become an effective and popular tool for human-powered
computation to label large datasets. Since the workers can be unreliable, it is
common in crowdsourcing to assign multiple workers to one task, and to
aggregate the labels in order to obtain results of high quality. In this paper,
we provide finit... | computer science |
14,260 | Sequential Sensing with Model Mismatch | stat.ML | We characterize the performance of sequential information guided sensing,
Info-Greedy Sensing, when there is a mismatch between the true signal model and
the assumed model, which may be a sample estimate. In particular, we consider a
setup where the signal is low-rank Gaussian and the measurements are taken in
the dire... | computer science |
14,261 | Information Recovery from Pairwise Measurements | cs.IT | This paper is concerned with jointly recovering $n$ node-variables $\left\{
x_{i}\right\}_{1\leq i\leq n}$ from a collection of pairwise difference
measurements. Imagine we acquire a few observations taking the form of
$x_{i}-x_{j}$; the observation pattern is represented by a measurement graph
$\mathcal{G}$ with an ed... | computer science |
14,262 | Testing Closeness With Unequal Sized Samples | cs.LG | We consider the problem of closeness testing for two discrete distributions
in the practically relevant setting of \emph{unequal} sized samples drawn from
each of them. Specifically, given a target error parameter $\varepsilon > 0$,
$m_1$ independent draws from an unknown distribution $p,$ and $m_2$ draws from
an unkno... | computer science |
14,263 | Spectral MLE: Top-$K$ Rank Aggregation from Pairwise Comparisons | cs.LG | This paper explores the preference-based top-$K$ rank aggregation problem.
Suppose that a collection of items is repeatedly compared in pairs, and one
wishes to recover a consistent ordering that emphasizes the top-$K$ ranked
items, based on partially revealed preferences. We focus on the
Bradley-Terry-Luce (BTL) model... | computer science |
14,264 | Optimal change point detection in Gaussian processes | math.ST | We study the problem of detecting a change in the mean of one-dimensional
Gaussian process data. This problem is investigated in the setting of
increasing domain (customarily employed in time series analysis) and in the
setting of fixed domain (typically arising in spatial data analysis). We
propose a detection method ... | computer science |
14,265 | Completing Low-Rank Matrices with Corrupted Samples from Few
Coefficients in General Basis | cs.IT | Subspace recovery from corrupted and missing data is crucial for various
applications in signal processing and information theory. To complete missing
values and detect column corruptions, existing robust Matrix Completion (MC)
methods mostly concentrate on recovering a low-rank matrix from few corrupted
coefficients w... | computer science |
14,266 | Sum-of-Squares Lower Bounds for Sparse PCA | cs.LG | This paper establishes a statistical versus computational trade-off for
solving a basic high-dimensional machine learning problem via a basic convex
relaxation method. Specifically, we consider the {\em Sparse Principal
Component Analysis} (Sparse PCA) problem, and the family of {\em
Sum-of-Squares} (SoS, aka Lasserre/... | computer science |
14,267 | Estimating an Activity Driven Hidden Markov Model | stat.ML | We define a Hidden Markov Model (HMM) in which each hidden state has
time-dependent $\textit{activity levels}$ that drive transitions and emissions,
and show how to estimate its parameters. Our construction is motivated by the
problem of inferring human mobility on sub-daily time scales from, for example,
mobile phone ... | computer science |
14,268 | Dropping Convexity for Faster Semi-definite Optimization | stat.ML | We study the minimization of a convex function $f(X)$ over the set of
$n\times n$ positive semi-definite matrices, but when the problem is recast as
$\min_U g(U) := f(UU^\top)$, with $U \in \mathbb{R}^{n \times r}$ and $r \leq
n$. We study the performance of gradient descent on $g$---which we refer to as
Factored Gradi... | computer science |
14,269 | How Robust are Reconstruction Thresholds for Community Detection? | cs.DS | The stochastic block model is one of the oldest and most ubiquitous models
for studying clustering and community detection. In an exciting sequence of
developments, motivated by deep but non-rigorous ideas from statistical
physics, Decelle et al. conjectured a sharp threshold for when community
detection is possible in... | computer science |
14,270 | Sparse Recovery via Partial Regularization: Models, Theory and
Algorithms | math.OC | In the context of sparse recovery, it is known that most of existing
regularizers such as $\ell_1$ suffer from some bias incurred by some leading
entries (in magnitude) of the associated vector. To neutralize this bias, we
propose a class of models with partial regularizers for recovering a sparse
solution of a linear ... | computer science |
14,271 | Infomax strategies for an optimal balance between exploration and
exploitation | cs.LG | Proper balance between exploitation and exploration is what makes good
decisions, which achieve high rewards like payoff or evolutionary fitness. The
Infomax principle postulates that maximization of information directs the
function of diverse systems, from living systems to artificial neural networks.
While specific a... | computer science |
14,272 | Recommender systems inspired by the structure of quantum theory | cs.LG | Physicists use quantum models to describe the behavior of physical systems.
Quantum models owe their success to their interpretability, to their relation
to probabilistic models (quantization of classical models) and to their high
predictive power. Beyond physics, these properties are valuable in general data
science. ... | computer science |
14,273 | Minimax Lower Bounds for Linear Independence Testing | stat.ML | Linear independence testing is a fundamental information-theoretic and
statistical problem that can be posed as follows: given $n$ points
$\{(X_i,Y_i)\}^n_{i=1}$ from a $p+q$ dimensional multivariate distribution
where $X_i \in \mathbb{R}^p$ and $Y_i \in\mathbb{R}^q$, determine whether $a^T
X$ and $b^T Y$ are uncorrela... | computer science |
14,274 | Kernels for sequentially ordered data | stat.ML | We present a novel framework for kernel learning with sequential data of any
kind, such as time series, sequences of graphs, or strings. Our approach is
based on signature features which can be seen as an ordered variant of sample
(cross-)moments; it allows to obtain a "sequentialized" version of any static
kernel. The... | computer science |
14,275 | Active Learning Algorithms for Graphical Model Selection | stat.ML | The problem of learning the structure of a high dimensional graphical model
from data has received considerable attention in recent years. In many
applications such as sensor networks and proteomics it is often expensive to
obtain samples from all the variables involved simultaneously. For instance,
this might involve ... | computer science |
14,276 | Clustering subgaussian mixtures by semidefinite programming | stat.ML | We introduce a model-free relax-and-round algorithm for k-means clustering
based on a semidefinite relaxation due to Peng and Wei. The algorithm
interprets the SDP output as a denoised version of the original data and then
rounds this output to a hard clustering. We provide a generic method for
proving performance guar... | computer science |
14,277 | High-Dimensional $L_2$Boosting: Rate of Convergence | stat.ML | Boosting is one of the most significant developments in machine learning.
This paper studies the rate of convergence of $L_2$Boosting, which is tailored
for regression, in a high-dimensional setting. Moreover, we introduce so-called
\textquotedblleft post-Boosting\textquotedblright. This is a post-selection
estimator w... | computer science |
14,278 | Online Rules for Control of False Discovery Rate and False Discovery
Exceedance | math.ST | Multiple hypothesis testing is a core problem in statistical inference and
arises in almost every scientific field. Given a set of null hypotheses
$\mathcal{H}(n) = (H_1,\dotsc, H_n)$, Benjamini and Hochberg introduced the
false discovery rate (FDR), which is the expected proportion of false positives
among rejected nu... | computer science |
14,279 | Interaction Screening: Efficient and Sample-Optimal Learning of Ising
Models | cs.LG | We consider the problem of learning the underlying graph of an unknown Ising
model on p spins from a collection of i.i.d. samples generated from the model.
We suggest a new estimator that is computationally efficient and requires a
number of samples that is near-optimal with respect to previously established
informatio... | computer science |
14,280 | Communication-Efficient Distributed Statistical Inference | stat.ML | We present a Communication-efficient Surrogate Likelihood (CSL) framework for
solving distributed statistical inference problems. CSL provides a
communication-efficient surrogate to the global likelihood that can be used for
low-dimensional estimation, high-dimensional regularized estimation and
Bayesian inference. For... | computer science |
14,281 | Fast Algorithms for Robust PCA via Gradient Descent | cs.IT | We consider the problem of Robust PCA in the fully and partially observed
settings. Without corruptions, this is the well-known matrix completion
problem. From a statistical standpoint this problem has been recently
well-studied, and conditions on when recovery is possible (how many
observations do we need, how many co... | computer science |
14,282 | Randomized block proximal damped Newton method for composite
self-concordant minimization | math.OC | In this paper we consider the composite self-concordant (CSC) minimization
problem, which minimizes the sum of a self-concordant function $f$ and a
(possibly nonsmooth) proper closed convex function $g$. The CSC minimization is
the cornerstone of the path-following interior point methods for solving a
broad class of co... | computer science |
14,283 | Solving a Mixture of Many Random Linear Equations by Tensor
Decomposition and Alternating Minimization | cs.LG | We consider the problem of solving mixed random linear equations with $k$
components. This is the noiseless setting of mixed linear regression. The goal
is to estimate multiple linear models from mixed samples in the case where the
labels (which sample corresponds to which model) are not observed. We give a
tractable a... | computer science |
14,284 | Non-square matrix sensing without spurious local minima via the
Burer-Monteiro approach | stat.ML | We consider the non-square matrix sensing problem, under restricted isometry
property (RIP) assumptions. We focus on the non-convex formulation, where any
rank-$r$ matrix $X \in \mathbb{R}^{m \times n}$ is represented as $UV^\top$,
where $U \in \mathbb{R}^{m \times r}$ and $V \in \mathbb{R}^{n \times r}$. In
this paper... | computer science |
14,285 | Finite-sample and asymptotic analysis of generalization ability with an
application to penalized regression | stat.ML | In this paper, we study the performance of extremum estimators from the
perspective of generalization ability (GA): the ability of a model to predict
outcomes in new samples from the same population. By adapting the classical
concentration inequalities, we derive upper bounds on the empirical
out-of-sample prediction e... | computer science |
14,286 | Randomized Independent Component Analysis | stat.ML | Independent component analysis (ICA) is a method for recovering statistically
independent signals from observations of unknown linear combinations of the
sources. Some of the most accurate ICA decomposition methods require searching
for the inverse transformation which minimizes different approximations of the
Mutual I... | computer science |
14,287 | Phase Retrieval Meets Statistical Learning Theory: A Flexible Convex
Relaxation | cs.IT | We propose a flexible convex relaxation for the phase retrieval problem that
operates in the natural domain of the signal. Therefore, we avoid the
prohibitive computational cost associated with "lifting" and semidefinite
programming (SDP) in methods such as PhaseLift and compete with recently
developed non-convex techn... | computer science |
14,288 | BET on Independence | math.ST | We study the problem of nonparametric dependence detection. Many existing
methods suffer severe power loss due to non-uniform consistency, which we
illustrate with a paradox. To avoid such power loss, we approach the
nonparametric test of independence through the new framework of binary
expansion statistics (BEStat) an... | computer science |
14,289 | Solving Equations of Random Convex Functions via Anchored Regression | cs.LG | We consider the question of estimating a solution to a system of equations
that involve convex nonlinearities, a problem that is common in machine
learning and signal processing. Because of these nonlinearities, conventional
estimators based on empirical risk minimization generally involve solving a
non-convex optimiza... | computer science |
14,290 | Bayesian Boolean Matrix Factorisation | stat.ML | Boolean matrix factorisation aims to decompose a binary data matrix into an
approximate Boolean product of two low rank, binary matrices: one containing
meaningful patterns, the other quantifying how the observations can be
expressed as a combination of these patterns. We introduce the OrMachine, a
probabilistic genera... | computer science |
14,291 | Structured signal recovery from quadratic measurements: Breaking sample
complexity barriers via nonconvex optimization | cs.LG | This paper concerns the problem of recovering an unknown but structured
signal $x \in R^n$ from $m$ quadratic measurements of the form
$y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting
where the number of measurements is significantly smaller than the dimension of
the signal ($m<<n$). We for... | computer science |
14,292 | Exact tensor completion with sum-of-squares | cs.LG | We obtain the first polynomial-time algorithm for exact tensor completion
that improves over the bound implied by reduction to matrix completion. The
algorithm recovers an unknown 3-tensor with $r$ incoherent, orthogonal
components in $\mathbb R^n$ from $r\cdot \tilde O(n^{1.5})$ randomly observed
entries of the tensor... | computer science |
14,293 | Markov Chain Lifting and Distributed ADMM | stat.ML | The time to converge to the steady state of a finite Markov chain can be
greatly reduced by a lifting operation, which creates a new Markov chain on an
expanded state space. For a class of quadratic objectives, we show an analogous
behavior where a distributed ADMM algorithm can be seen as a lifting of
Gradient Descent... | computer science |
14,294 | Robustly Learning a Gaussian: Getting Optimal Error, Efficiently | cs.DS | We study the fundamental problem of learning the parameters of a
high-dimensional Gaussian in the presence of noise -- where an
$\varepsilon$-fraction of our samples were chosen by an adversary. We give
robust estimators that achieve estimation error $O(\varepsilon)$ in the total
variation distance, which is optimal up... | computer science |
14,295 | On the Gap Between Strict-Saddles and True Convexity: An Omega(log d)
Lower Bound for Eigenvector Approximation | cs.LG | We prove a \emph{query complexity} lower bound on rank-one principal
component analysis (PCA). We consider an oracle model where, given a symmetric
matrix $M \in \mathbb{R}^{d \times d}$, an algorithm is allowed to make $T$
\emph{exact} queries of the form $w^{(i)} = Mv^{(i)}$ for $i \in
\{1,\dots,T\}$, where $v^{(i)}$... | computer science |
14,296 | A Flexible Framework for Hypothesis Testing in High-dimensions | math.ST | Hypothesis testing in the linear regression model is a fundamental
statistical problem. We consider linear regression in the high-dimensional
regime where the number of parameters exceeds the number of samples ($p> n$)
and assume that the high-dimensional parameters vector is $s_0$ sparse. We
develop a general and flex... | computer science |
14,297 | Hypothesis Testing For Densities and High-Dimensional Multinomials:
Sharp Local Minimax Rates | math.ST | We consider the goodness-of-fit testing problem of distinguishing whether the
data are drawn from a specified distribution, versus a composite alternative
separated from the null in the total variation metric. In the discrete case, we
consider goodness-of-fit testing when the null distribution has a possibly
growing or... | computer science |
14,298 | Generalization Properties of Doubly Stochastic Learning Algorithms | stat.ML | Doubly stochastic learning algorithms are scalable kernel methods that
perform very well in practice. However, their generalization properties are not
well understood and their analysis is challenging since the corresponding
learning sequence may not be in the hypothesis space induced by the kernel. In
this paper, we p... | computer science |
14,299 | Spectral Method and Regularized MLE Are Both Optimal for Top-$K$ Ranking | stat.ML | This paper is concerned with the problem of top-$K$ ranking from pairwise
comparisons. Given a collection of $n$ items and a few pairwise binary
comparisons across them, one wishes to identify the set of $K$ items that
receive the highest ranks. To tackle this problem, we adopt the logistic
parametric model---the Bradl... | computer science |
14,300 | Universal Function Approximation by Deep Neural Nets with Bounded Width
and ReLU Activations | stat.ML | This article concerns the expressive power of depth in neural nets with ReLU
activations and bounded width. We are particularly interested in the following
questions: what is the minimal width $w_{\text{min}}(d)$ so that ReLU nets of
width $w_{\text{min}}(d)$ (and arbitrary depth) can approximate any continuous
functio... | computer science |
14,301 | Hypotheses testing on infinite random graphs | cs.LG | Drawing on some recent results that provide the formalism necessary to
definite stationarity for infinite random graphs, this paper initiates the
study of statistical and learning questions pertaining to these objects.
Specifically, a criterion for the existence of a consistent test for complex
hypotheses is presented,... | computer science |
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