We study the problem of distributed information bottleneck, in which multiple encoders separately compress their observations in a manner such that, collectively, the compressed signals preserve as much information as possible about another signal. The model generalizes Tishby's centralized information bottleneck method to the setting of multiple distributed encoders. We establish single-letter characterizations of the information-rate region of this problem for both i) a class of discrete memoryless sources and ii) memoryless vector Gaussian sources. Furthermore, assuming a sum constraint on rate or complexity, for both models we develop Blahut-Arimoto type iterative algorithms that allow to compute optimal information-rate trade-offs, by iterating over a set of self-consistent equations.
This paper considers the distributed information bottleneck (D-IB) problem for a primitive Gaussian diamond channel with two relays and Rayleigh fading. Due to the bottleneck constraint, it is impossible for the relays to inform the destination node of the perfect channel state information (CSI) in each realization. To evaluate the bottleneck rate, we provide an upper bound by assuming that the destination node knows the CSI and the relays can cooperate with each other, and also three achievable schemes with simple symbol-by-symbol relay processing and compression. Numerical results show that …
We study a distributed learning problem in which Alice sends a compressed distillation of a set of training data to Bob, who uses the distilled version to best solve an associated learning problem. We formalize this as a rate-distortion problem in which the training set is the source and Bob's cross-entropy loss is the distortion measure. We consider this problem for unsupervised learning for batch and sequential data. In the batch data, this problem is equivalent to the information bottleneck (IB), and we show that reduced-complexity versions of standard IB methods solve the associated rate-d…
We prove rigorously a source coding theorem that can probably be considered folklore, a generalization to arbitrary alphabets of a problem motivated by the Information Bottleneck method. For general random variables $(Y, X)$, we show essentially that for some $n \in \mathbb{N}$, a function $f$ with rate limit $\log|f| \le nR$ and $I(Y^n; f(X^n)) \ge nS$ exists if and only if there is a random variable $U$ such that the Markov chain $Y - X - U$ holds, $I(U; X) \le R$ and $I(U; Y) \ge S$. The proof relies on the well established discrete case and showcases a technique for lifting discrete coding…
University of Pennsylvania（宾夕法尼亚大学）；The Santa Fe Institute（圣塔菲研究所）
The fruits of science are relationships made comprehensible, often by way of approximation. While deep learning is an extremely powerful way to find relationships in data, its use in science has been hindered by the difficulty of understanding the learned relationships. The Information Bottleneck (IB) is an information theoretic framework for understanding a relationship between an input and an output in terms of a trade-off between the fidelity and complexity of approximations to the relationship. Here we show that a crucial modification -- distributing bottlenecks across multiple components …
Distributed Information Bottleneck Theory for Multi-Modal Task-Aware Semantic Communication
School of Electronic Information and Communications, Huazhong University of Science and Technology（电子信息与通信学院，华中科技大学）；Peng Cheng Laboratory（鹏城实验室）；Pazhou Laboratory (Huangpu)（琶洲实验室（黄埔））；School of Mechanical Engineering and Electronic Information, China University of Geosciences（机械工程与电子信息学院，中国地质大学）；State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications（网络与交换技术国家重点实验室，北京邮电大学）
We consider a distributed caching device-to-device (D2D) network in which a user's file of interest is cached as several portions in the storage of other devices in the network. Assuming that the user needs to obtain all these file portions, the portions cached farther away naturally become the performance bottleneck. This is due to the fact that dominant interferers may be closer to the receiver than the serving device. Using a simple stochastic geometry model, we concretely demonstrate that this bottleneck can be loosened if the users are mobile. Gains obtained from mobility are quantified i…
Large-scale distributed computing systems face two major bottlenecks that limit their scalability: straggler delay caused by the variability of computation times at different worker nodes and communication bottlenecks caused by shuffling data across many nodes in the network. Recently, it has been shown that codes can provide significant gains in overcoming these bottlenecks. In particular, optimal coding schemes for minimizing latency in distributed computation of linear functions and mitigating the effect of stragglers was proposed for a wired network, where the workers can simultaneously tr…
This paper proposes a distributed alternating mixed discrete-continuous (DAMDC) algorithm to approach the oracle algorithm based on the diffusion strategy for parameter and spectrum estimation over sensor networks. A least mean squares (LMS) type algorithm that obtains the oracle matrix adaptively is developed and compared with the existing sparsity-aware and conventional algorithms. The proposed algorithm exhibits improved performance in terms of mean square deviation and power spectrum estimation accuracy. Numerical results show that the DAMDC algorithm achieves excellent performance.
Santa Fe Institute（圣塔菲研究所）；Massachusetts Institute of Technology（麻省理工学院）；Complexity Science Hub（复杂性科学中心）；Arizona State University（亚利桑那州立大学）
Information bottleneck (IB) is a technique for extracting information in one random variable $X$ that is relevant for predicting another random variable $Y$. IB works by encoding $X$ in a compressed "bottleneck" random variable $M$ from which $Y$ can be accurately decoded. However, finding the optimal bottleneck variable involves a difficult optimization problem, which until recently has been considered for only two limited cases: discrete $X$ and $Y$ with small state spaces, and continuous $X$ and $Y$ with a Gaussian joint distribution (in which case optimal encoding and decoding maps are lin…
A distributed binary hypothesis testing (HT) problem involving two parties, one referred to as the observer and the other as the detector is studied. The observer observes a discrete memoryless source (DMS) and communicates its observations to the detector over a discrete memoryless channel (DMC). The detector observes another DMS correlated with that at the observer, and performs a binary HT on the joint distribution of the two DMS's using its own observed data and the information received from the observer. The trade-off between the type I error probability and the type II error-exponent of …
Harvard University（哈佛大学）；University of Chicago（芝加哥大学）；Massachusetts Institute of Technology（麻省理工学院）
Given a pair of random variables $(X,Y)\sim P_{XY}$ and two convex functions $f_1$ and $f_2$, we introduce two bottleneck functionals as the lower and upper boundaries of the two-dimensional convex set that consists of the pairs $\left(I_{f_1}(W; X), I_{f_2}(W; Y)\right)$, where $I_f$ denotes $f$-information and $W$ varies over the set of all discrete random variables satisfying the Markov condition $W \to X \to Y$. Applying Witsenhausen and Wyner's approach, we provide an algorithm for computing boundaries of this set for $f_1$, $f_2$, and discrete $P_{XY}$. In the binary symmetric case, we f…
Due to the low per-antenna SNR and high signaling overhead, channel estimation is a major bottleneck in Massive MIMO systems. Spatial constraints can improve estimation performance by exploiting sparsity. Solutions exist for far field - beam domain channel estimation based on angle of arrival estimation. However, there is no equivalent solution for near field and distributed MIMO spatial channel estimation. We present a solution- source domain channel estimation- that is based on source location estimation. We extend this to employ a "Channel Database" incorporating information about the physi…
Ozyegin University（厄兹耶金大学）；Imperial College London（帝国理工学院）
Distributed learning, particularly variants of distributed stochastic gradient descent (DSGD), are widely employed to speed up training by leveraging computational resources of several workers. However, in practise, communication delay becomes a bottleneck due to the significant amount of information that needs to be exchanged between the workers and the parameter server. One of the most efficient strategies to mitigate the communication bottleneck is top-K sparsification. However, top-K sparsification requires additional communication load to represent the sparsity pattern, and the mismatch b…
This tutorial paper focuses on the variants of the bottleneck problem taking an information theoretic perspective and discusses practical methods to solve it, as well as its connection to coding and learning aspects. The intimate connections of this setting to remote source-coding under logarithmic loss distortion measure, information combining, common reconstruction, the Wyner-Ahlswede-Korner problem, the efficiency of investment information, as well as, generalization, variational inference, representation learning, autoencoders, and others are highlighted. We discuss its extension to the di…
Sharif University of Technology（谢里夫理工大学）；Technical University of Munich（慕尼黑工业大学）；Universite Paris-Est（巴黎东部大学）
The Information Bottleneck method is a learning technique that seeks a right balance between accuracy and generalization capability through a suitable tradeoff between compression complexity, measured by minimum description length, and distortion evaluated under logarithmic loss measure. In this paper, we study a variation of the problem, called scalable information bottleneck, where the encoder outputs multiple descriptions of the observation with increasingly richer features. The problem at hand is motivated by some application scenarios that require varying levels of accuracy depending on t…
We consider the problem of secure distributed matrix computation (SDMC), where a \textit{user} queries a function of data matrices generated at distributed \textit{source} nodes. We assume the availability of $N$ honest but curious computation servers, which are connected to the sources, the user, and each other through orthogonal and reliable communication links. Our goal is to minimize the amount of data that must be transmitted from the sources to the servers, called the \textit{upload cost}, while guaranteeing that no $T$ colluding servers can learn any information about the source matrice…
