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In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large…
This work examines adaptive distributed learning strategies designed to operate under communication constraints. We consider a network of agents that must solve an online optimization problem from continual observation of streaming data.…
We consider the exact channel synthesis problem. This problem concerns the determination of the minimum amount of information required to create exact correlation remotely when there is a certain rate of randomness shared by two terminals.…
We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…
Communication complexity is the amount of communication needed to compute a function when the function inputs are distributed over multiple parties. In its simplest form, one-way communication complexity, Alice and Bob compute a function…
Approximate Bayesian computation (ABC) performs statistical inference for otherwise intractable probability models by accepting parameter proposals when corresponding simulated datasets are sufficiently close to the observations. Producing…
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
Entropy Estimation is an important problem with many applications in cryptography, statistic,machine learning. Although the estimators optimal with respect to the sample complexity have beenrecently developed, there are still some…
We consider the following communication task in the multi-party setting, which involves a joint random variable $XYZMN$ with the property that $M$ is independent of $YZN$ conditioned on $X$ and $N$ is independent of $XZM$ conditioned on…
The broadcast channel (BC) with one common and two private messages with leakage constraints is studied, where leakage rate refers to the normalized mutual information between a message and a channel symbol string. Each private message is…
We consider the closest lattice point problem in a distributed network setting and study the communication cost and the error probability for computing an approximate nearest lattice point, using the nearest-plane algorithm, due to Babai.…
In the Max-Cut problem in the streaming model, an algorithm is given the edges of an unknown graph $G = (V,E)$ in some fixed order, and its goal is to approximate the size of the largest cut in $G$. Improving upon an earlier result of…
In open systems, i.e. systems operating in an environment that they cannot control and with components that may join or leave, behaviors can arise as side effects of intensive components interaction. Finding ways to understand and design…
A strong direct product theorem states that, in order to solve k instances of a problem, if we provide less than k times the resource required to compute one instance, then the probability of overall success is exponentially small in k. In…
Distributed computing models typically assume reliable communication between processors. While such assumptions often hold for engineered networks, e.g., due to underlying error correction protocols, their relevance to biological systems,…
The study of the fundamental limits of covert communications, where a transmitter Alice wants to send information to a desired recipient Bob without detection of that transmission by an attentive and capable warden Willie, has emerged…
We show a dichotomy result for $p$-pass streaming algorithms for all CSPs and for up to polynomially many passes. More precisely, we prove that for any arity parameter $k$, finite alphabet $\Sigma$, collection $\mathcal{F}$ of $k$-ary…
We study the problem of reaching agreement in a synchronous distributed system by $n$ autonomous parties, when the communication links from/to faulty parties can omit messages. The faulty parties are selected and controlled by an adaptive,…
Channel simulation is to simulate a noisy channel using noiseless channels with unlimited shared randomness. This can be interpreted as the reverse problem to Shannon's noisy coding theorem. In contrast to previous works, our approach…
Given a redundant dictionary $\Phi$, represented by an $M \times N$ matrix ($\Phi \in \mathbb{R}^{M \times N}$) and a target signal $y \in \mathbb{R}^M$, the \emph{sparse approximation problem} asks to find an approximate representation of…