相关论文: Strong converses for group testing in the finite b…
The weak converse coding theorems have been proved for the quantum source and channel. The results give the lower bound for capacity of source and the upper bound for capacity of channel. The monotonicity of mutual quantum information have…
In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate $R$ is above channel capacity $C$, the error probability of decoding goes to one as the block length $n$ of code…
In this work we prove non-trivial impossibility results for perhaps the simplest non-linear estimation problem, that of {\it Group Testing} (GT), via the recently developed Madiman-Tetali inequalities. Group Testing concerns itself with…
In this paper we consider the problem of a multi-agent system achieving a formation in the presence of misbehaving or adversarial agents. We introduce a novel continuous time resilient controller to guarantee that normally behaving agents…
In this paper, we study the problem of non-adaptive group testing, in which one seeks to identify which items are defective given a set of suitably-designed tests whose outcomes indicate whether or not at least one defective item was…
We study the group testing problem where the goal is to identify a set of k infected individuals carrying a rare disease within a population of size n, based on the outcomes of pooled tests which return positive whenever there is at least…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
We determine the exact error and strong converse exponents of shared randomness-assisted channel simulation in worst case total-variation distance. Namely, we find that these exponents can be written as simple optimizations over the R\'enyi…
We continue the study of statistical/computational tradeoffs in learning robust classifiers, following the recent work of Bubeck, Lee, Price and Razenshteyn who showed examples of classification tasks where (a) an efficient robust…
We consider the extent to which we can learn from a completely randomized experiment whether all individuals have treatment effects that are weakly of the same sign, a condition we call monotonicity. From a classical sampling perspective,…
Recent diffusion large language models (dLLMs) have demonstrated both effectiveness and efficiency in reasoning via a block-based semi-autoregressive generation paradigm. Despite their progress, the fixed-size block generations remain a…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
We derive several efficiently computable converse bounds for quantum communication over quantum channels in both the one-shot and asymptotic regime. First, we derive one-shot semidefinite programming (SDP) converse bounds on the amount of…
The group testing problem consists of determining a small set of defective items from a larger set of items based on tests on groups of items, and is relevant in applications such as medical testing, communication protocols, pattern…
Many natural notions of additive and multiplicative largeness arise from results in Ramsey theory. In this paper, we explain the relationships between these notions for subsets of $\mathbb{N}$ and in more general ring-theoretic structures.…
In 2017, Polyanskiy [1] showed that the trade-off between power and bandwidth efficiency for massive Gaussian random access is governed by two fundamentally different regimes: low power and high power. For both regimes, tight performance…
In this article, we study the long-time behavior of a finite-volume discretization for a nonlinear kinetic reaction model involving two interacting species. Building upon the seminal work of [Favre, Pirner, Schmeiser, ARMA, 2023], we extend…
We focus on designing error-correcting codes for the symmetric Gaussian broadcast channel with feedback. Feedback not only expands the capacity region of the broadcast channel but also enhances transmission reliability. In this work, we…
We prove anti-concentration bounds for the inner product of two independent random vectors. For example, we show that if $A,B$ are subsets of the cube $\{\pm 1\}^n$ with $|A| \cdot |B| \geq 2^{1.01 n}$, and $X \in A$ and $Y \in B$ are…