Jonathan Mark Scarlett

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The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings, such as compressive sensing, subset selection in regression, and gro ...

In this paper, we study the {\em pooled data} problem of identifying the labels associated with a large collection of items, based on a sequence of pooled tests revealing the counts of each label within the pool. In the noiseless setting, we identify an ex ...

The problem of approximately computing the

k

dominant Fourier coefficients of a vector

X

quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT has resulted in ...

We present a new algorithm, truncated variance reduction (TruVaR), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a set ...

In this paper, we consider the problem of sequentially optimizing a black-box function

f

based on noisy samples and bandit feedback. We assume that

f

is smooth in the sense of having a bounded norm in some reproducing kernel Hilbert space (RKHS), yield ...

The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of tests, and is relevant in applications such as medical testing, communication protocols, pattern matching, and more. In this pa ...

This paper studies the second-order coding rates for memoryless channels with a state sequence known non-causally at the encoder. In the case of finite alphabets, an achievability result is obtained using constant-composition random coding, and by using a ...

In the area of magnetic resonance imaging (MRI), an extensive range of non-linear reconstruction algorithms have been proposed that can be used with general Fourier subsampling patterns. However, the design of these subsampling patterns has typically been ...

Linear sketching is a powerful tool for the problem of sparse signal recovery, having numerous applications such as compressive sensing, data stream computing, graph sketching, and routing. Motivated by applications where the \emph{positions} of the non-ze ...

This paper studies the second-order asymptotics of the Gaussian multiple-access channel with degraded message sets. For a fixed average error probability epsilon is an element of (0, 1) and an arbitrary point on the boundary of the capacity region, we char ...

We study the problem of actively learning a multi-index function of the form f (x) = g_0 (A_0 x) from its point evaluations, where A_0 ∈ R_{k×d} with k ≪ d. We build on the assumptions and techniques of an existing approach based on low-rank matrix recover ...

We consider the model selection consistency or sparsistency of a broad set of

\ell_1

-regularized

M

-estimators for linear and non-linear statistical models in a unified fashion. For this purpose, we propose the local structured smoothness condition (LSS ...

This paper studies the second-order asymptotics of coding rates for the discrete memoryless multiple-access channel (MAC) with a fixed target error probability. Using constant-composition random coding, coded time-sharing, and a variant of Hoeffding's comb ...

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 approximate recovery criterion that allows for a number of missed edges ...

We consider the group testing problem, in which one seeks to identify a subset of defective items within a larger set of items based on a number of noisy tests. While matching achievability and converse bounds are known in several cases of interest for i.i ...

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 ...

We study the problem of maximizing a monotone submodular function subject to a cardinality constraint

k

, with the added twist that a number of items

\tau

from the returned set may be removed. We focus on the worst-case setting considered in Orlin et al ...

Information theory plays an indispensable role in the development of algorithm-independent impossibility results, both for communication problems and for seemingly distinct areas such as statistics and machine learning. While numerous information-theoretic ...

In this paper, we study the information-theoretic limits of community detection in the symmetric two-community stochastic block model, with intra-community and inter-community edge probabilities

\frac{a}{n}

and

\frac{b}{n}

respectively. We consider the ...

In this paper, we consider the problem of Gaussian process (GP) optimization with an added robustness requirement: The returned point may be perturbed by an adversary, and we require the function value to remain as high as possible even after this perturba ...

Jonathan Mark Scarlett

Chat with Graph Search

Limits on Support Recovery With Probabilistic Models: An Information-Theoretic Framework

Phase Transitions in the Pooled Data Problem

An Adaptive Sublinear-Time Block Sparse Fourier Transform

Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation

Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization

Near-Optimal Noisy Group Testing via Separate Decoding of Items

On the Dispersions of the Gel'fand-Pinsker Channel and Dirty Paper Coding

Learning-Based Compressive MRI

Limits on Sparse Support Recovery via Linear Sketching with Random Expander Matrices

Second-order asymptotics for the Gaussian MAC with degraded message sets

Active Learning of Self-concordant like Multi-index Functions

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Second-Order Rate Region of Constant-Composition Codes for the Multiple-Access Channel

On the Difficulty of Selecting Ising Models with Approximate Recovery

Converse Bounds for Noisy Group Testing with Arbitrary Measurement Matrices

Lower Bounds on Active Learning for Graphical Model Selection

Robust Submodular Maximization: A Non-Uniform Partitioning Approach

An Introductory Guide to Fano's Inequality with Applications in Statistical Estimation

Partial Recovery Bounds for the Sparse Stochastic Block Model

Adversarially Robust Optimization with Gaussian Processes