Related papers: The Capacity of Adaptive Group Testing
In this paper, we introduce a variation of the group testing problem where each test is specified by an ordered subset of items and returns the first defective item in the specified order or returns null if there are no defectives. We refer…
The basic goal of threshold group testing is to identify up to $d$ defective items among a population of $n$ items, where $d$ is usually much smaller than $n$. The outcome of a test on a subset of items is positive if the subset has at…
Recent outer bounds on the capacity region of Gaussian interference channels are generalized to $m$-user channels with $m>2$ and asymmetric powers and crosstalk coefficients. The bounds are again shown to give the sum-rate capacity for…
This paper studies an $n$-dimensional additive Gaussian noise channel with a peak-power-constrained input. It is well known that, in this case, when $n=1$ the capacity-achieving input distribution is discrete with finitely many mass points,…
We compute Shannon capacity of nonlinear channels with regenerative elements. Conditions are found under which capacity of such nonlinear channels is higher than the Shannon capacity of the classical linear additive white Gaussian noise…
We develop several analytical lower bounds on the capacity of binary insertion and deletion channels by considering independent uniformly distributed (i.u.d.) inputs and computing lower bounds on the mutual information between the input and…
As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this paper, we obtain a lower bound on the redundancy required for $\epsilon$-accurate…
We study the excess capacity of deep networks in the context of supervised classification. That is, given a capacity measure of the underlying hypothesis class - in our case, empirical Rademacher complexity - to what extent can we (a…
We present an efficient technique, which allows to train classification networks which are verifiably robust against norm-bounded adversarial attacks. This framework is built upon the work of Gowal et al., who applies the interval…
Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…
We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel that has a fixed and limited number of messages and is subject to exogenous noise. We provide an upper bound on…
We revisit the problem of computing with noisy information considered in Feige et al. 1994, which includes computing the OR function from noisy queries, and computing the MAX, SEARCH and SORT functions from noisy pairwise comparisons. For…
Collective intelligence, which aggregates the shared information from large crowds, is often negatively impacted by unreliable information sources with the low quality data. This becomes a barrier to the effective use of collective…
This paper characterizes the capacity of a class of modulo additive noise relay channels, in which the relay observes a corrupted version of the noise and has a separate channel to the destination. The capacity is shown to be strictly below…
A novel technique to optimize the input distribution and compute a lower bound for the capacity of the nonlinear optical fiber channel is proposed. The technique improves previous bounds obtained with the additive white Gaussian noise…
In this work, we consider the sparsity-constrained community-based group testing problem, where the population follows a community structure. In particular, the community consists of $F$ families, each with $M$ members. A number $k_f$ out…
We consider finite-sample inference for a single regression coefficient in the fixed-design linear model $Y = Z\beta + bX + \varepsilon$, where $\varepsilon\in\mathbb{R}^n$ may exhibit complex dependence or heterogeneity. We develop a group…
In group testing, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether at least one defective item is present. This problem is relevant in areas such as medical…
This paper derives upper and lower bounds on the capacity of the multiple-input single-output free-space optical intensity channel with signal-independent additive Gaussian noise subject to both an average-intensity and a peak-intensity…
Consider a Gaussian relay network where a number of sources communicate to a destination with the help of several layers of relays. Recent work has shown that a compress-and-forward based strategy at the relays can achieve the capacity of…