Publications de Jonathan Mark Scarlett

Phase Transitions in Group Testing

The group testing problem consists of determining a sparse subset of a set of items that are ``defective'' based on a set of possibly noisy tests, and arises in areas such as medical testing, fault detection, communication protocols, pattern matching, and ...

2016

Learning-Based Compressive Subsampling

Volkan Cevher, Jonathan Mark Scarlett, Ilija Bogunovic, Yen-Huan Li, Luca Baldassarre, Baran Gözcü

The problem of recovering a structured signal

\mathbf{x} \in \mathbb{C}^p

from a set of dimensionality-reduced linear measurements

\mathbf{b} = \mathbf {A}\mathbf {x}

arises in a variety of applications, such as medical imaging, spectroscopy, Fourier o ...

Ieee-Inst Electrical Electronics Engineers Inc2016

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

Volkan Cevher, Jonathan Mark Scarlett

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 ...

2016

On the Difficulty of Selecting Ising Models with Approximate Recovery

Volkan Cevher, Jonathan Mark Scarlett

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 ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Converse Bounds for Noisy Group Testing with Arbitrary Measurement Matrices

Volkan Cevher, Jonathan Mark Scarlett

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 ...

Ieee2016

Partial Recovery Bounds for the Sparse Stochastic Block Model

Volkan Cevher, Jonathan Mark Scarlett

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 ...

Ieee2016

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

Jonathan Mark Scarlett

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 ...

Institute of Electrical and Electronics Engineers2015

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

Volkan Cevher, Jonathan Mark Scarlett, Yen-Huan Li

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 ...

2015

Active Learning of Self-concordant like Multi-index Functions

Volkan Cevher, Jonathan Mark Scarlett, Ilija Bogunovic

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 ...

2015

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

Jonathan Mark Scarlett, Albert Guillén i Fàbregas

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 ...

Ieee-Inst Electrical Electronics Engineers Inc2015

Jonathan Mark Scarlett

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Phase Transitions in Group Testing

Learning-Based Compressive Subsampling

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

On the Difficulty of Selecting Ising Models with Approximate Recovery

Converse Bounds for Noisy Group Testing with Arbitrary Measurement Matrices

Partial Recovery Bounds for the Sparse Stochastic Block Model

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

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

Active Learning of Self-concordant like Multi-index Functions

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

Converse Bounds for Noisy Group Testing with Arbitrary Measurement Matrices

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

Phase Transitions in Group Testing

Partial Recovery Bounds for the Sparse Stochastic Block Model

Active Learning of Self-concordant like Multi-index Functions

Learning-Based Compressive Subsampling

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

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

On the Difficulty of Selecting Ising Models with Approximate Recovery

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