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13,102 | On the Difficulty of Selecting Ising Models with Approximate Recovery | cs.IT | In this paper, we consider the problem of estimating the underlying graph
associated with an Ising model given a number of independent and identically
distributed samples. We adopt an \emph{approximate recovery} criterion that
allows for a number of missed edges or incorrectly-included edges, in contrast
with the widel... | computer science |
13,103 | Adversarial Top-$K$ Ranking | cs.IR | We study the top-$K$ ranking problem where the goal is to recover the set of
top-$K$ ranked items out of a large collection of items based on partially
revealed preferences. We consider an adversarial crowdsourced setting where
there are two population sets, and pairwise comparison samples drawn from one
of the populat... | computer science |
13,104 | Anomaly Detection in Clutter using Spectrally Enhanced Ladar | cs.LG | Discrete return (DR) Laser Detection and Ranging (Ladar) systems provide a
series of echoes that reflect from objects in a scene. These can be first, last
or multi-echo returns. In contrast, Full-Waveform (FW)-Ladar systems measure
the intensity of light reflected from objects continuously over a period of
time. In a c... | computer science |
13,105 | Online optimization and regret guarantees for non-additive long-term
constraints | stat.ML | We consider online optimization in the 1-lookahead setting, where the
objective does not decompose additively over the rounds of the online game. The
resulting formulation enables us to deal with non-stationary and/or long-term
constraints , which arise, for example, in online display advertising problems.
We propose a... | computer science |
13,106 | Top-$K$ Ranking from Pairwise Comparisons: When Spectral Ranking is
Optimal | cs.LG | We explore the top-$K$ rank aggregation problem. Suppose a collection of
items is compared in pairs repeatedly, and we aim to recover a consistent
ordering that focuses on the top-$K$ ranked items based on partially revealed
preference information. We investigate the Bradley-Terry-Luce model in which
one ranks items ac... | computer science |
13,107 | Trading-off variance and complexity in stochastic gradient descent | stat.ML | Stochastic gradient descent is the method of choice for large-scale machine
learning problems, by virtue of its light complexity per iteration. However, it
lags behind its non-stochastic counterparts with respect to the convergence
rate, due to high variance introduced by the stochastic updates. The popular
Stochastic ... | computer science |
13,108 | Algorithms for Learning Sparse Additive Models with Interactions in High
Dimensions | cs.LG | A function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a Sparse Additive
Model (SPAM), if it is of the form $f(\mathbf{x}) = \sum_{l \in
\mathcal{S}}\phi_{l}(x_l)$ where $\mathcal{S} \subset [d]$, $|\mathcal{S}| \ll
d$. Assuming $\phi$'s, $\mathcal{S}$ to be unknown, there exists extensive work
for estimating $f$ from ... | computer science |
13,109 | A Bayesian Approach to Policy Recognition and State Representation
Learning | stat.ML | Learning from demonstration (LfD) is the process of building behavioral
models of a task from demonstrations provided by an expert. These models can be
used e.g. for system control by generalizing the expert demonstrations to
previously unencountered situations. Most LfD methods, however, make strong
assumptions about ... | computer science |
13,110 | Competitive analysis of the top-K ranking problem | cs.DS | Motivated by applications in recommender systems, web search, social choice
and crowdsourcing, we consider the problem of identifying the set of top $K$
items from noisy pairwise comparisons. In our setting, we are non-actively
given $r$ pairwise comparisons between each pair of $n$ items, where each
comparison has noi... | computer science |
13,111 | Fast Randomized Semi-Supervised Clustering | cs.LG | We consider the problem of clustering partially labeled data from a minimal
number of randomly chosen pairwise comparisons between the items. We introduce
an efficient local algorithm based on a power iteration of the non-backtracking
operator and study its performance on a simple model. For the case of two
clusters, w... | computer science |
13,112 | A note on the expected minimum error probability in equientropic
channels | cs.IT | While the channel capacity reflects a theoretical upper bound on the
achievable information transmission rate in the limit of infinitely many bits,
it does not characterise the information transfer of a given encoding routine
with finitely many bits. In this note, we characterise the quality of a code
(i. e. a given en... | computer science |
13,113 | Average-case Hardness of RIP Certification | cs.LG | The restricted isometry property (RIP) for design matrices gives guarantees
for optimal recovery in sparse linear models. It is of high interest in
compressed sensing and statistical learning. This property is particularly
important for computationally efficient recovery methods. As a consequence,
even though it is in ... | computer science |
13,114 | CYCLADES: Conflict-free Asynchronous Machine Learning | stat.ML | We present CYCLADES, a general framework for parallelizing stochastic
optimization algorithms in a shared memory setting. CYCLADES is asynchronous
during shared model updates, and requires no memory locking mechanisms, similar
to HOGWILD!-type algorithms. Unlike HOGWILD!, CYCLADES introduces no conflicts
during the par... | computer science |
13,115 | Learning Power Spectrum Maps from Quantized Power Measurements | cs.IT | Power spectral density (PSD) maps providing the distribution of RF power
across space and frequency are constructed using power measurements collected
by a network of low-cost sensors. By introducing linear compression and
quantization to a small number of bits, sensor measurements can be communicated
to the fusion cen... | computer science |
13,116 | Inferring Sparsity: Compressed Sensing using Generalized Restricted
Boltzmann Machines | cs.IT | In this work, we consider compressed sensing reconstruction from $M$
measurements of $K$-sparse structured signals which do not possess a writable
correlation model. Assuming that a generative statistical model, such as a
Boltzmann machine, can be trained in an unsupervised manner on example signals,
we demonstrate how... | computer science |
13,117 | Lower Bounds on Active Learning for Graphical Model Selection | cs.IT | We consider the problem of estimating the underlying graph associated with a
Markov random field, with the added twist that the decoding algorithm can
iteratively choose which subsets of nodes to sample based on the previous
samples, resulting in an active learning setting. Considering both Ising and
Gaussian models, w... | computer science |
13,118 | LazySVD: Even Faster SVD Decomposition Yet Without Agonizing Pain | cs.NA | We study $k$-SVD that is to obtain the first $k$ singular vectors of a matrix
$A$. Recently, a few breakthroughs have been discovered on $k$-SVD: Musco and
Musco [1] proved the first gap-free convergence result using the block Krylov
method, Shamir [2] discovered the first variance-reduction stochastic method,
and Bhoj... | computer science |
13,119 | First Efficient Convergence for Streaming k-PCA: a Global, Gap-Free, and
Near-Optimal Rate | math.OC | We study streaming principal component analysis (PCA), that is to find, in
$O(dk)$ space, the top $k$ eigenvectors of a $d\times d$ hidden matrix $\bf
\Sigma$ with online vectors drawn from covariance matrix $\bf \Sigma$.
We provide $\textit{global}$ convergence for Oja's algorithm which is
popularly used in practice... | computer science |
13,120 | Faster Principal Component Regression and Stable Matrix Chebyshev
Approximation | stat.ML | We solve principal component regression (PCR), up to a multiplicative
accuracy $1+\gamma$, by reducing the problem to $\tilde{O}(\gamma^{-1})$
black-box calls of ridge regression. Therefore, our algorithm does not require
any explicit construction of the top principal components, and is suitable for
large-scale PCR ins... | computer science |
13,121 | Global analysis of Expectation Maximization for mixtures of two
Gaussians | math.ST | Expectation Maximization (EM) is among the most popular algorithms for
estimating parameters of statistical models. However, EM, which is an iterative
algorithm based on the maximum likelihood principle, is generally only
guaranteed to find stationary points of the likelihood objective, and these
points may be far from... | computer science |
13,122 | A Tutorial on Distributed (Non-Bayesian) Learning: Problem, Algorithms
and Results | math.OC | We overview some results on distributed learning with focus on a family of
recently proposed algorithms known as non-Bayesian social learning. We consider
different approaches to the distributed learning problem and its algorithmic
solutions for the case of finitely many hypotheses. The original centralized
problem is ... | computer science |
13,123 | Linear Hypothesis Testing in Dense High-Dimensional Linear Models | stat.ME | We propose a methodology for testing linear hypothesis in high-dimensional
linear models. The proposed test does not impose any restriction on the size of
the model, i.e. model sparsity or the loading vector representing the
hypothesis. Providing asymptotically valid methods for testing general linear
functions of the ... | computer science |
13,124 | Single Pass PCA of Matrix Products | stat.ML | In this paper we present a new algorithm for computing a low rank
approximation of the product $A^TB$ by taking only a single pass of the two
matrices $A$ and $B$. The straightforward way to do this is to (a) first sketch
$A$ and $B$ individually, and then (b) find the top components using PCA on the
sketch. Our algori... | computer science |
13,125 | Cross: Efficient Low-rank Tensor Completion | stat.ME | The completion of tensors, or high-order arrays, attracts significant
attention in recent research. Current literature on tensor completion primarily
focuses on recovery from a set of uniformly randomly measured entries, and the
required number of measurements to achieve recovery is not guaranteed to be
optimal. In add... | computer science |
13,126 | Learning an Astronomical Catalog of the Visible Universe through
Scalable Bayesian Inference | cs.DC | Celeste is a procedure for inferring astronomical catalogs that attains
state-of-the-art scientific results. To date, Celeste has been scaled to at
most hundreds of megabytes of astronomical images: Bayesian posterior inference
is notoriously demanding computationally. In this paper, we report on a
scalable, parallel v... | computer science |
13,127 | Efficient Policy Learning | math.ST | We consider the problem of using observational data to learn treatment
assignment policies that satisfy certain constraints specified by a
practitioner, such as budget, fairness, or functional form constraints. This
problem has previously been studied in economics, statistics, and computer
science, and several regret-c... | computer science |
13,128 | Approximations of the Restless Bandit Problem | math.ST | The multi-armed restless bandit problem is studied in the case where the
pay-offs are not necessarily independent over time nor across the arms. Even
though this version of the problem provides a more realistic model for most
real-world applications, it cannot be optimally solved in practice since it is
known to be PSP... | computer science |
13,129 | Scalable and Distributed Clustering via Lightweight Coresets | stat.ML | Coresets are compact representations of data sets such that models trained on
a coreset are provably competitive with models trained on the full data set. As
such, they have been successfully used to scale up clustering models to massive
data sets. While existing approaches generally only allow for multiplicative
appro... | computer science |
13,130 | Distributed Bayesian Matrix Factorization with Limited Communication | stat.ML | Bayesian matrix factorization (BMF) is a powerful tool for producing low-rank
representations of matrices and for predicting missing values and their
confidence intervals. Scaling up the posterior inference for massive-scale
matrices is challenging and requires distributing both data and computation
over many workers, ... | computer science |
13,131 | Being Robust (in High Dimensions) Can Be Practical | cs.LG | Robust estimation is much more challenging in high dimensions than it is in
one dimension: Most techniques either lead to intractable optimization problems
or estimators that can tolerate only a tiny fraction of errors. Recent work in
theoretical computer science has shown that, in appropriate distributional
models, it... | computer science |
13,132 | Exact MAP Inference by Avoiding Fractional Vertices | stat.ML | Given a graphical model, one essential problem is MAP inference, that is,
finding the most likely configuration of states according to the model.
Although this problem is NP-hard, large instances can be solved in practice. A
major open question is to explain why this is true. We give a natural condition
under which we ... | computer science |
13,133 | Leveraging Sparsity for Efficient Submodular Data Summarization | stat.ML | The facility location problem is widely used for summarizing large datasets
and has additional applications in sensor placement, image retrieval, and
clustering. One difficulty of this problem is that submodular optimization
algorithms require the calculation of pairwise benefits for all items in the
dataset. This is i... | computer science |
13,134 | Tensor SVD: Statistical and Computational Limits | math.ST | In this paper, we propose a general framework for tensor singular value
decomposition (tensor SVD), which focuses on the methodology and theory for
extracting the hidden low-rank structure from high-dimensional tensor data.
Comprehensive results are developed on both the statistical and computational
limits for tensor ... | computer science |
13,135 | Riemannian stochastic quasi-Newton algorithm with variance reduction and
its convergence analysis | cs.LG | Stochastic variance reduction algorithms have recently become popular for
minimizing the average of a large, but finite number of loss functions. The
present paper proposes a Riemannian stochastic quasi-Newton algorithm with
variance reduction (R-SQN-VR). The key challenges of averaging, adding, and
subtracting multipl... | computer science |
13,136 | Characterization of Deterministic and Probabilistic Sampling Patterns
for Finite Completability of Low Tensor-Train Rank Tensor | cs.LG | In this paper, we analyze the fundamental conditions for low-rank tensor
completion given the separation or tensor-train (TT) rank, i.e., ranks of
unfoldings. We exploit the algebraic structure of the TT decomposition to
obtain the deterministic necessary and sufficient conditions on the locations
of the samples to ens... | computer science |
13,137 | The Informativeness of $k$-Means and Dimensionality Reduction for
Learning Mixture Models | stat.ML | The learning of mixture models can be viewed as a clustering problem. Indeed,
given data samples independently generated from a mixture of distributions, we
often would like to find the correct target clustering of the samples according
to which component distribution they were generated from. For a clustering
problem,... | computer science |
13,138 | Distributed Learning for Cooperative Inference | math.OC | We study the problem of cooperative inference where a group of agents
interact over a network and seek to estimate a joint parameter that best
explains a set of observations. Agents do not know the network topology or the
observations of other agents. We explore a variational interpretation of the
Bayesian posterior de... | computer science |
13,139 | Group Importance Sampling for Particle Filtering and MCMC | stat.CO | Importance Sampling (IS) is a well-known Monte Carlo technique that
approximates integrals involving a posterior distribution by means of weighted
samples. In this work, we study the assignation of a single weighted sample
which compresses the information contained in a population of weighted samples.
Part of the theor... | computer science |
13,140 | Energy Propagation in Deep Convolutional Neural Networks | cs.IT | Many practical machine learning tasks employ very deep convolutional neural
networks. Such large depths pose formidable computational challenges in
training and operating the network. It is therefore important to understand how
fast the energy contained in the propagated signals (a.k.a. feature maps)
decays across laye... | computer science |
13,141 | A decentralized proximal-gradient method with network independent
step-sizes and separated convergence rates | math.OC | This paper considers the problem of decentralized optimization with a
composite objective containing smooth and non-smooth terms. To solve the
problem, a proximal-gradient scheme is studied. Specifically, the smooth and
nonsmooth terms are dealt with by gradient update and proximal update,
respectively. The studied alg... | computer science |
13,142 | Accelerating Stochastic Gradient Descent | stat.ML | There is widespread sentiment that it is not possible to effectively utilize
fast gradient methods (e.g. Nesterov's acceleration, conjugate gradient, heavy
ball) for the purposes of stochastic optimization due to their instability and
error accumulation, a notion made precise in d'Aspremont 2008 and Devolder,
Glineur, ... | computer science |
13,143 | Geometry and Dynamics for Markov Chain Monte Carlo | stat.CO | Markov Chain Monte Carlo methods have revolutionised mathematical computation
and enabled statistical inference within many previously intractable models. In
this context, Hamiltonian dynamics have been proposed as an efficient way of
building chains which can explore probability densities efficiently. The method
emerg... | computer science |
13,144 | Learning ReLUs via Gradient Descent | cs.LG | In this paper we study the problem of learning Rectified Linear Units (ReLUs)
which are functions of the form $max(0,<w,x>)$ with $w$ denoting the weight
vector. We study this problem in the high-dimensional regime where the number
of observations are fewer than the dimension of the weight vector. We assume
that the we... | computer science |
13,145 | Learning Feature Nonlinearities with Non-Convex Regularized Binned
Regression | cs.LG | For various applications, the relations between the dependent and independent
variables are highly nonlinear. Consequently, for large scale complex problems,
neural networks and regression trees are commonly preferred over linear models
such as Lasso. This work proposes learning the feature nonlinearities by
binning fe... | computer science |
13,146 | Personalized and Private Peer-to-Peer Machine Learning | cs.LG | The rise of connected personal devices together with privacy concerns call
for machine learning algorithms capable of leveraging the data of a large
number of agents to learn personalized models under strong privacy
requirements. In this paper, we introduce an efficient algorithm to address the
above problem in a fully... | computer science |
13,147 | Learning Whenever Learning is Possible: Universal Learning under General
Stochastic Processes | stat.ML | This work initiates a general study of learning and generalization without
the i.i.d. assumption, starting from first principles. While the standard
approach to statistical learning theory is based on assumptions chosen largely
for their convenience (e.g., i.i.d. or stationary ergodic), in this work we are
interested i... | computer science |
13,148 | On the Optimization Landscape of Tensor Decompositions | cs.LG | Non-convex optimization with local search heuristics has been widely used in
machine learning, achieving many state-of-art results. It becomes increasingly
important to understand why they can work for these NP-hard problems on typical
data. The landscape of many objective functions in learning has been
conjectured to ... | computer science |
13,149 | Clustering with Noisy Queries | stat.ML | In this paper, we initiate a rigorous theoretical study of clustering with
noisy queries (or a faulty oracle). Given a set of $n$ elements, our goal is to
recover the true clustering by asking minimum number of pairwise queries to an
oracle. Oracle can answer queries of the form : "do elements $u$ and $v$ belong
to the... | computer science |
13,150 | Query Complexity of Clustering with Side Information | stat.ML | Suppose, we are given a set of $n$ elements to be clustered into $k$
(unknown) clusters, and an oracle/expert labeler that can interactively answer
pair-wise queries of the form, "do two elements $u$ and $v$ belong to the same
cluster?". The goal is to recover the optimum clustering by asking the minimum
number of quer... | computer science |
13,151 | Accelerated Stochastic Power Iteration | math.OC | Principal component analysis (PCA) is one of the most powerful tools in
machine learning. The simplest method for PCA, the power iteration, requires
$\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a
matrix with eigen-gap $\Delta$. Lanczos, a significantly more complex method,
achieves an a... | computer science |
13,152 | Subdeterminant Maximization via Nonconvex Relaxations and
Anti-concentration | cs.DS | Several fundamental problems that arise in optimization and computer science
can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a
constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that
maximizes the squared volume of the simplex spanned by the vectors in $S$. A
motivatin... | computer science |
13,153 | Theoretical insights into the optimization landscape of
over-parameterized shallow neural networks | cs.LG | In this paper we study the problem of learning a shallow artificial neural
network that best fits a training data set. We study this problem in the
over-parameterized regime where the number of observations are fewer than the
number of parameters in the model. We show that with quadratic activations the
optimization la... | computer science |
13,154 | Differentially Private Identity and Closeness Testing of Discrete
Distributions | cs.LG | We investigate the problems of identity and closeness testing over a discrete
population from random samples. Our goal is to develop efficient testers while
guaranteeing Differential Privacy to the individuals of the population. We
describe an approach that yields sample-efficient differentially private
testers for the... | computer science |
13,155 | Comparison of Decision Tree Based Classification Strategies to Detect
External Chemical Stimuli from Raw and Filtered Plant Electrical Response | cs.LG | Plants monitor their surrounding environment and control their physiological
functions by producing an electrical response. We recorded electrical signals
from different plants by exposing them to Sodium Chloride (NaCl), Ozone (O3)
and Sulfuric Acid (H2SO4) under laboratory conditions. After applying
pre-processing tec... | computer science |
13,156 | Belief Propagation, Bethe Approximation and Polynomials | cs.LG | Factor graphs are important models for succinctly representing probability
distributions in machine learning, coding theory, and statistical physics.
Several computational problems, such as computing marginals and partition
functions, arise naturally when working with factor graphs. Belief propagation
is a widely deplo... | computer science |
13,157 | Fixed effects testing in high-dimensional linear mixed models | stat.ME | Many scientific and engineering challenges -- ranging from pharmacokinetic
drug dosage allocation and personalized medicine to marketing mix (4Ps)
recommendations -- require an understanding of the unobserved heterogeneity in
order to develop the best decision making-processes. In this paper, we develop
a hypothesis te... | computer science |
13,158 | Mixing time estimation in reversible Markov chains from a single sample
path | math.ST | The spectral gap $\gamma$ of a finite, ergodic, and reversible Markov chain
is an important parameter measuring the asymptotic rate of convergence. In
applications, the transition matrix $P$ may be unknown, yet one sample of the
chain up to a fixed time $n$ may be observed. We consider here the problem of
estimating $\... | computer science |
13,159 | Conditional Generative Adversarial Networks for Speech Enhancement and
Noise-Robust Speaker Verification | eess.AS | Improving speech system performance in noisy environments remains a
challenging task, and speech enhancement (SE) is one of the effective
techniques to solve the problem. Motivated by the promising results of
generative adversarial networks (GANs) in a variety of image processing tasks,
we explore the potential of cond... | computer science |
13,160 | Rates of Convergence of Spectral Methods for Graphon Estimation | stat.ML | This paper studies the problem of estimating the grahpon model - the
underlying generating mechanism of a network. Graphon estimation arises in many
applications such as predicting missing links in networks and learning user
preferences in recommender systems. The graphon model deals with a random graph
of $n$ vertices... | computer science |
13,161 | DAGGER: A sequential algorithm for FDR control on DAGs | stat.ME | We propose a top-down algorithm for multiple testing on directed acyclic
graphs (DAGs), where nodes represent hypotheses and edges specify a partial
ordering in which hypotheses must be tested. The procedure is guaranteed to
reject a sub-DAG with bounded false discovery rate (FDR) while satisfying the
logical constrain... | computer science |
13,162 | Bayesian estimation from few samples: community detection and related
problems | cs.DS | We propose an efficient meta-algorithm for Bayesian estimation problems that
is based on low-degree polynomials, semidefinite programming, and tensor
decomposition. The algorithm is inspired by recent lower bound constructions
for sum-of-squares and related to the method of moments. Our focus is on sample
complexity bo... | computer science |
13,163 | Online control of the false discovery rate with decaying memory | stat.ME | In the online multiple testing problem, p-values corresponding to different
null hypotheses are observed one by one, and the decision of whether or not to
reject the current hypothesis must be made immediately, after which the next
p-value is observed. Alpha-investing algorithms to control the false discovery
rate (FDR... | computer science |
13,164 | Forecasting Across Time Series Databases using Long Short-Term Memory
Networks on Groups of Similar Series | cs.LG | With the advent of Big Data, nowadays in many applications databases
containing large quantities of similar time series are available. Forecasting
time series in these domains with traditional univariate forecasting procedures
leaves great potentials for producing accurate forecasts untapped. Recurrent
neural networks,... | computer science |
13,165 | An introduction to Topological Data Analysis: fundamental and practical
aspects for data scientists | math.ST | Topological Data Analysis (tda) is a recent and fast growing eld providing a
set of new topological and geometric tools to infer relevant features for
possibly complex data. This paper is a brief introduction, through a few
selected topics, to basic fundamental and practical aspects of tda for non
experts. 1 Introducti... | computer science |
13,166 | Convergence diagnostics for stochastic gradient descent with constant
step size | stat.ML | Many iterative procedures in stochastic optimization exhibit a transient
phase followed by a stationary phase. During the transient phase the procedure
converges towards a region of interest, and during the stationary phase the
procedure oscillates in that region, commonly around a single point. In this
paper, we devel... | computer science |
13,167 | Stability and Generalization of Learning Algorithms that Converge to
Global Optima | stat.ML | We establish novel generalization bounds for learning algorithms that
converge to global minima. We do so by deriving black-box stability results
that only depend on the convergence of a learning algorithm and the geometry
around the minimizers of the loss function. The results are shown for nonconvex
loss functions sa... | computer science |
13,168 | Contextual Regression: An Accurate and Conveniently Interpretable
Nonlinear Model for Mining Discovery from Scientific Data | cs.LG | Machine learning algorithms such as linear regression, SVM and neural network
have played an increasingly important role in the process of scientific
discovery. However, none of them is both interpretable and accurate on
nonlinear datasets. Here we present contextual regression, a method that joins
these two desirable ... | computer science |
13,169 | Implicit Causal Models for Genome-wide Association Studies | stat.ML | Progress in probabilistic generative models has accelerated, developing
richer models with neural architectures, implicit densities, and with scalable
algorithms for their Bayesian inference. However, there has been limited
progress in models that capture causal relationships, for example, how
individual genetic factor... | computer science |
13,170 | Orthogonal Machine Learning: Power and Limitations | cs.LG | Double machine learning provides $\sqrt{n}$-consistent estimates of
parameters of interest even when high-dimensional or nonparametric nuisance
parameters are estimated at an $n^{-1/4}$ rate. The key is to employ
Neyman-orthogonal moment equations which are first-order insensitive to
perturbations in the nuisance param... | computer science |
13,171 | Medoids in almost linear time via multi-armed bandits | stat.ML | Computing the medoid of a large number of points in high-dimensional space is
an increasingly common operation in many data science problems. We present an
algorithm Med-dit which uses O(n log n) distance evaluations to compute the
medoid with high probability. Med-dit is based on a connection with the
multi-armed band... | computer science |
13,172 | Simultaneous Block-Sparse Signal Recovery Using Pattern-Coupled Sparse
Bayesian Learning | cs.LG | In this paper, we consider the block-sparse signals recovery problem in the
context of multiple measurement vectors (MMV) with common row sparsity
patterns. We develop a new method for recovery of common row sparsity MMV
signals, where a pattern-coupled hierarchical Gaussian prior model is
introduced to characterize bo... | computer science |
13,173 | Convex Optimization with Nonconvex Oracles | cs.DS | In machine learning and optimization, one often wants to minimize a convex
objective function $F$ but can only evaluate a noisy approximation $\hat{F}$ to
it. Even though $F$ is convex, the noise may render $\hat{F}$ nonconvex, making
the task of minimizing $F$ intractable in general. As a consequence, several
works in... | computer science |
13,174 | Crafting Adversarial Examples For Speech Paralinguistics Applications | cs.LG | Computational paralinguistic analysis is increasingly being used in a wide
range of applications, including security-sensitive applications such as
speaker verification, deceptive speech detection, and medical diagnosis. While
state-of-the-art machine learning techniques, such as deep neural networks, can
provide robus... | computer science |
13,175 | Straggler Mitigation in Distributed Optimization Through Data Encoding | stat.ML | Slow running or straggler tasks can significantly reduce computation speed in
distributed computation. Recently, coding-theory-inspired approaches have been
applied to mitigate the effect of straggling, through embedding redundancy in
certain linear computational steps of the optimization algorithm, thus
completing the... | computer science |
13,176 | Predictive Independence Testing, Predictive Conditional Independence
Testing, and Predictive Graphical Modelling | stat.ML | Testing (conditional) independence of multivariate random variables is a task
central to statistical inference and modelling in general - though
unfortunately one for which to date there does not exist a practicable
workflow. State-of-art workflows suffer from the need for heuristic or
subjective manual choices, high c... | computer science |
13,177 | Scaling Limit: Exact and Tractable Analysis of Online Learning
Algorithms with Applications to Regularized Regression and PCA | cs.LG | We present a framework for analyzing the exact dynamics of a class of online
learning algorithms in the high-dimensional scaling limit. Our results are
applied to two concrete examples: online regularized linear regression and
principal component analysis. As the ambient dimension tends to infinity, and
with proper tim... | computer science |
13,178 | Riemann-Theta Boltzmann Machine | stat.ML | A general Boltzmann machine with continuous visible and discrete integer
valued hidden states is introduced. Under mild assumptions about the connection
matrices, the probability density function of the visible units can be solved
for analytically, yielding a novel parametric density function involving a
ratio of Riema... | computer science |
13,179 | IHT dies hard: Provable accelerated Iterative Hard Thresholding | math.OC | We study --both in theory and practice-- the use of momentum motions in
classic iterative hard thresholding (IHT) methods. By simply modifying plain
IHT, we investigate its convergence behavior on convex optimization criteria
with non-convex constraints, under standard assumptions. In diverse scenaria,
we observe that ... | computer science |
13,180 | Momentum and Stochastic Momentum for Stochastic Gradient, Newton,
Proximal Point and Subspace Descent Methods | math.OC | In this paper we study several classes of stochastic optimization algorithms
enriched with heavy ball momentum. Among the methods studied are: stochastic
gradient descent, stochastic Newton, stochastic proximal point and stochastic
dual subspace ascent. This is the first time momentum variants of several of
these metho... | computer science |
13,181 | Probabilistic supervised learning | stat.ML | Predictive modelling and supervised learning are central to modern data
science. With predictions from an ever-expanding number of supervised black-box
strategies - e.g., kernel methods, random forests, deep learning aka neural
networks - being employed as a basis for decision making processes, it is
crucial to underst... | computer science |
13,182 | Which Neural Net Architectures Give Rise To Exploding and Vanishing
Gradients? | stat.ML | We give a rigorous analysis of the statistical behavior of gradients in
randomly initialized feed-forward networks with ReLU activations. Our results
show that a fully connected depth $d$ ReLU net with hidden layer widths $n_j$
will have exploding and vanishing gradients if and only if $\sum_{j=1}^{d-1}
1/n_j$ is large... | computer science |
13,183 | Estimating the Number of Connected Components in a Graph via Subgraph
Sampling | math.ST | Learning properties of large graphs from samples has been an important
problem in statistical network analysis since the early work of Goodman
\cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated
by Frank \cite{Frank1978} of estimating the number of connected components in a
large graph based ... | computer science |
13,184 | Learning Compact Neural Networks with Regularization | cs.LG | We study the impact of regularization for learning neural networks. Our goal
is speeding up training, improving generalization performance, and training
compact models that are cost efficient. Our results apply to weight-sharing
(e.g.~convolutional), sparsity (i.e.~pruning), and low-rank constraints among
others. We fi... | computer science |
13,185 | Communication-Computation Efficient Gradient Coding | stat.ML | This paper develops coding techniques to reduce the running time of
distributed learning tasks. It characterizes the fundamental tradeoff to
compute gradients (and more generally vector summations) in terms of three
parameters: computation load, straggler tolerance and communication cost. It
further gives an explicit c... | computer science |
13,186 | Learning to Gather without Communication | cs.DC | A standard belief on emerging collective behavior is that it emerges from
simple individual rules. Most of the mathematical research on such collective
behavior starts from imperative individual rules, like always go to the center.
But how could an (optimal) individual rule emerge during a short period within
the group... | computer science |
13,187 | Sampling as optimization in the space of measures: The Langevin dynamics
as a composite optimization problem | math.OC | We study sampling as optimization in the space of measures. We focus on
gradient flow-based optimization with the Langevin dynamics as a case study. We
investigate the source of the bias of the unadjusted Langevin algorithm (ULA)
in discrete time, and consider how to remove or reduce the bias. We point out
the difficul... | computer science |
13,188 | Proportional Volume Sampling and Approximation Algorithms for A-Optimal
Design | cs.DS | We study the $A$-optimal design problem where we are given vectors
$v_1,\ldots,v_n\in\mathbb{R}^d$, an integer $k\geq d$, and the goal is to
select a set $S$ of $k$ vectors that minimizes the trace of $(\sum_{i\in
S}v_iv_i^\top)^{-1}$. Traditionally, the problem is an instance of optimal
design of experiments in statis... | computer science |
13,189 | An efficient $k$-means-type algorithm for clustering datasets with
incomplete records | stat.ML | The $k$-means algorithm is the most popular nonparametric clustering method
in use, but cannot generally be applied to data sets with missing observations.
The usual practice with such data sets is to either impute the values under an
assumption of a missing-at-random mechanism or to ignore the incomplete
records, and ... | computer science |
13,190 | Harnessing Structures in Big Data via Guaranteed Low-Rank Matrix
Estimation | stat.ML | Low-rank modeling plays a pivotal role in signal processing and machine
learning, with applications ranging from collaborative filtering, video
surveillance, medical imaging, to dimensionality reduction and adaptive
filtering. Many modern high-dimensional data and interactions thereof can be
modeled as lying approximat... | computer science |
13,191 | Dimensionally Tight Running Time Bounds for Second-Order Hamiltonian
Monte Carlo | cs.DS | Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from a
given high-dimensional distribution in Statistics and Machine learning. HMC is
known to run very efficiently in practice and its second-order variant was
conjectured to run in $d^{1/4}$ steps in 1988. Here we show that this
conjecture is true wh... | computer science |
13,192 | Random perturbation and matrix sparsification and completion | stat.ML | We discuss general perturbation inequalities when the perturbation is random.
As applications, we obtain several new results concerning two important
problems: matrix sparsification and matrix completion. | computer science |
13,193 | Learning to Recognize Musical Genre from Audio | cs.SD | We here summarize our experience running a challenge with open data for
musical genre recognition. Those notes motivate the task and the challenge
design, show some statistics about the submissions, and present the results. | computer science |
13,194 | Aggregating Strategies for Long-term Forecasting | cs.LG | The article is devoted to investigating the application of aggregating
algorithms to the problem of the long-term forecasting. We examine the classic
aggregating algorithms based on the exponential reweighing. For the general
Vovk's aggregating algorithm we provide its generalization for the long-term
forecasting. For ... | computer science |
13,195 | Numerical Integration on Graphs: where to sample and how to weigh | math.ST | Let $G=(V,E,w)$ be a finite, connected graph with weighted edges. We are
interested in the problem of finding a subset $W \subset V$ of vertices and
weights $a_w$ such that $$ \frac{1}{|V|}\sum_{v \in V}^{}{f(v)} \sim \sum_{w
\in W}{a_w f(w)}$$ for functions $f:V \rightarrow \mathbb{R}$ that are `smooth'
with respect t... | computer science |
13,196 | Entropy estimation of symbol sequences | cs.CL | We discuss algorithms for estimating the Shannon entropy h of finite symbol
sequences with long range correlations. In particular, we consider algorithms
which estimate h from the code lengths produced by some compression algorithm.
Our interest is in describing their convergence with sequence length, assuming
no limit... | computer science |
13,197 | Statistical methods for tissue array images - algorithmic scoring and
co-training | stat.ME | Recent advances in tissue microarray technology have allowed
immunohistochemistry to become a powerful medium-to-high throughput analysis
tool, particularly for the validation of diagnostic and prognostic biomarkers.
However, as study size grows, the manual evaluation of these assays becomes a
prohibitive limitation; i... | computer science |
13,198 | Getting Feasible Variable Estimates From Infeasible Ones: MRF Local
Polytope Study | cs.NA | This paper proposes a method for construction of approximate feasible primal
solutions from dual ones for large-scale optimization problems possessing
certain separability properties. Whereas infeasible primal estimates can
typically be produced from (sub-)gradients of the dual function, it is often
not easy to project... | computer science |
13,199 | Quantum Energy Regression using Scattering Transforms | cs.LG | We present a novel approach to the regression of quantum mechanical energies
based on a scattering transform of an intermediate electron density
representation. A scattering transform is a deep convolution network computed
with a cascade of multiscale wavelet transforms. It possesses appropriate
invariant and stability... | computer science |
13,200 | The Ordered Weighted $\ell_1$ Norm: Atomic Formulation, Projections, and
Algorithms | cs.DS | The ordered weighted $\ell_1$ norm (OWL) was recently proposed, with two
different motivations: its good statistical properties as a sparsity promoting
regularizer; the fact that it generalizes the so-called {\it octagonal
shrinkage and clustering algorithm for regression} (OSCAR), which has the
ability to cluster/grou... | computer science |
13,201 | Meta learning of bounds on the Bayes classifier error | cs.LG | Meta learning uses information from base learners (e.g. classifiers or
estimators) as well as information about the learning problem to improve upon
the performance of a single base learner. For example, the Bayes error rate of
a given feature space, if known, can be used to aid in choosing a classifier,
as well as in ... | computer science |
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