Related papers: Resolution Limits for the Noisy Non-Adaptive 20 Qu…
A channel coding achievability bound expressed in terms of the ratio between two Neyman-Pearson $\beta$ functions is proposed. This bound is the dual of a converse bound established earlier by Polyanskiy and Verd\'{u} (2014). The new bound…
Adapting to a priori unknown noise level is a very important but challenging problem in sequential decision-making as efficient exploration typically requires knowledge of the noise level, which is often loosely specified. We report…
The two-way capacities of quantum channels determine the ultimate entanglement and secret-key distribution rates achievable by two distant parties that are connected by a noisy transmission line, in absence of quantum repeaters. Since…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
In this paper, we consider the group testing problem with adaptive test designs and noisy outcomes. We propose a computationally efficient four-stage procedure with components including random binning, identification of bins containing…
In quantum computation, amplitude estimation is a fundamental subroutine that is utilized in various quantum algorithms. A general important task of such estimation problems is to characterize the estimation lower bound, which is referred…
This paper shows new general nonasymptotic achievability and converse bounds and performs their dispersion analysis for the lossy compression problem in which the compressor observes the source through a noisy channel. While this problem is…
A Chernoff-type distribution is a nonnormal distribution defined by the slope at zero of the greatest convex minorant of a two-sided Brownian motion with a polynomial drift. While a Chernoff-type distribution is known to appear as the…
This paper is devoted to the problem of determining the concentration bounds that are achievable in non-parametric regression. We consider the setting where features are supported on a bounded subset of $\mathbb{R}^d$, the regression…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
Motivated by the application of point-to-point communication networks and biological storage, we investigate new achievability bounds for noisy permutation channels with strictly positive and full-rank square matrices. Our new bounds use…
We study the maximum achievable differential entropy at the output of a system assigning to each input X the sum X+N, with N a given noise with probability law absolutely continuous with respect to the Lebesgue measure and where the input…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
Consider a target moving at a constant velocity on a unit-circumference circle, starting at an arbitrary location. To acquire the target, any region of the circle can be probed to obtain a noisy measurement of the target's presence, where…
The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of…
Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the…
We consider the problem of 20 questions with noise for multiple players under the minimum entropy criterion in the setting of stochastic search, with application to target localization. Each player yields a noisy response to a binary query…
Calibration is nowadays one of the most important processes involved in the extraction of valuable data from measurements. The current availability of an optimum data cube measured from a heterogeneous set of instruments and surveys relies…
The noisy permutation channel is a useful abstraction introduced by Makur for point-to-point communication networks and biological storage. While the asymptotic capacity results exist for this model, the characterization of the second-order…
We derive new bounds on achievable precision in the most general adaptive quantum metrological scenarios. The bounds are proven to be asymptotically saturable and equivalent to the known parallel scheme bounds in the limit of large number…