In-Network Learning: Distributed Training and Inference in Networks

It is widely perceived that leveraging the success of modern machine learning techniques to mobile devices and wireless networks has the potential of enabling important new services. This, however, poses significant challenges, essentially due to that both data and processing power are highly distributed in a wireless network. In this paper, we develop a learning algorithm and an architecture that make use of multiple data streams and processing units, not only during the training phase but also during the inference phase. In particular, the analysis reveals how inference propagates and fuses across a network. We study the design criterion of our proposed method and its bandwidth requirements. Also, we discuss implementation aspects using neural networks in typical wireless radio access; and provide experiments that illustrate benefits over state-of-the-art techniques.Comment: Submitted to the IEEE Journal on Selected Areas in Communications (JSAC) Series on Machine Learning for Communications and Networks. arXiv admin note: substantial text overlap with arXiv:2104.1492

Bottleneck Problems: Information and Estimation-Theoretic View

Information bottleneck (IB) and privacy funnel (PF) are two closely related optimization problems which have found applications in machine learning, design of privacy algorithms, capacity problems (e.g., Mrs. Gerber's Lemma), strong data processing inequalities, among others. In this work, we first investigate the functional properties of IB and PF through a unified theoretical framework. We then connect them to three information-theoretic coding problems, namely hypothesis testing against independence, noisy source coding and dependence dilution. Leveraging these connections, we prove a new cardinality bound for the auxiliary variable in IB, making its computation more tractable for discrete random variables. In the second part, we introduce a general family of optimization problems, termed as \textit{bottleneck problems}, by replacing mutual information in IB and PF with other notions of mutual information, namely $f$-information and Arimoto's mutual information. We then argue that, unlike IB and PF, these problems lead to easily interpretable guarantee in a variety of inference tasks with statistical constraints on accuracy and privacy. Although the underlying optimization problems are non-convex, we develop a technique to evaluate bottleneck problems in closed form by equivalently expressing them in terms of lower convex or upper concave envelope of certain functions. By applying this technique to binary case, we derive closed form expressions for several bottleneck problems

Distributed Information Bottleneck Method for Discrete and Gaussian Sources

Submitted to the 2018 International Zurich Seminar on Information and Communication (IZS)International audienceWe 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

Distributed Information Bottleneck Method for Discrete and Gaussian Sources

Submitted to the 2018 International Zurich Seminar on Information and Communication (IZS)International audienceWe 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