Related papers: Inference under Information Constraints I: Lower B…
We study channel resolvability for the discrete memoryless multiple-access channel with cribbing, i.e., the characterization of the amount of randomness required at the inputs to approximately produce a chosen i.i.d. output distribution…
We provide a unified method for constructing explicit distributions which are difficult for restricted models of computation to generate. Our constructions are based on a new notion of robust extractors, which are extractors that remain…
Provable lower bounds are presented for the information rate I(X; X+S+N) where X is the symbol drawn independently and uniformly from a finite-size alphabet, S is a discrete-valued random variable (RV) and N is a Gaussian RV. It is well…
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…
Data are often accommodated on centralized storage servers. This is the case, for instance, in remote sensing and astronomy, where projects produce several petabytes of data every year. While machine learning models are often trained on…
Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…
Consider a distributed detection problem in which the underlying distributions of the observations are unknown; instead of these distributions, noisy versions of empirically observed statistics are available to the fusion center. These…
Models which include domain constraints occur in myriad contexts such as econometrics, genomics, and environmetrics, though simulating from constrained distributions can be computationally expensive. In particular, repeated sampling from…
A privacy-constrained information extraction problem is considered where for a pair of correlated discrete random variables $(X,Y)$ governed by a given joint distribution, an agent observes $Y$ and wants to convey to a potentially public…
In this paper, an interference network with arbitrary number of transmitters and receivers is studied, where each transmitter is equipped with a finite size cache. We obtain an information-theoretic lower bound on both the peak normalized…
We consider the processing of statistical samples $X\sim P_\theta$ by a channel $p(y|x)$, and characterize how the statistical information from the samples for estimating the parameter $\theta\in\mathbb{R}^d$ can scale with the mutual…
The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one…
This paper presents tight upper and lower bounds for minimum number of samples (copies of a quantum state) required to attain a prescribed accuracy (measured by error variance) for scalar parameters estimation using unbiased estimators…
Private inference refers to a two-party setting in which one has a model (e.g., a linear classifier), the other has data, and the model is to be applied over the data while safeguarding the privacy of both parties. In particular, models in…
Distribution-preserving integrated sensing and communication with secure reconstruction is investigated in this paper. In addition to the distortion constraint, we impose another constraint on the distance between the reconstructed sequence…
We derive a tight lower bound on equivocation (conditional entropy), or equivalently a tight upper bound on mutual information between a signal variable and channel outputs. The bound is in terms of the joint distribution of the signals and…
The $K$-receiver degraded broadcast channel with secrecy outside a bounded range is studied, in which a transmitter sends $K$ messages to $K$ receivers, and the channel quality gradually degrades from receiver $K$ to receiver 1. Each…
The capacity of the Gaussian cognitive interference channel, a variation of the classical two-user interference channel where one of the transmitters (referred to as cognitive) has knowledge of both messages, is known in several parameter…
The limit distribution of the nonparametric maximum likelihood estimator for interval censored data with more than one observation time per unobservable observation, is still unknown in general. For the so-called separated case, where one…
Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…