FedMM: Saddle Point Optimization for Federated Adversarial Domain Adaptation

Federated adversary domain adaptation is a unique distributed minimax training task due to the prevalence of label imbalance among clients, with each client only seeing a subset of the classes of labels required to train a global model. To tackle this problem, we propose a distributed minimax optimizer referred to as FedMM, designed specifically for the federated adversary domain adaptation problem. It works well even in the extreme case where each client has different label classes and some clients only have unsupervised tasks. We prove that FedMM ensures convergence to a stationary point with domain-shifted unsupervised data. On a variety of benchmark datasets, extensive experiments show that FedMM consistently achieves either significant communication savings or significant accuracy improvements over federated optimizers based on the gradient descent ascent (GDA) algorithm. When training from scratch, for example, it outperforms other GDA based federated average methods by around $20\%$ in accuracy over the same communication rounds; and it consistently outperforms when training from pre-trained models with an accuracy improvement from $5.4\%$ to $9\%$ for different networks.

Towards Medical Knowmetrics: Representing and Computing Medical Knowledge using Semantic Predications as the Knowledge Unit and the Uncertainty as the Knowledge Context

In China, Prof. Hongzhou Zhao and Zeyuan Liu are the pioneers of the concept "knowledge unit" and "knowmetrics" for measuring knowledge. However, the definition of "computable knowledge object" remains controversial so far in different fields. For example, it is defined as 1) quantitative scientific concept in natural science and engineering, 2) knowledge point in the field of education research, and 3) semantic predications, i.e., Subject-Predicate-Object (SPO) triples in biomedical fields. The Semantic MEDLINE Database (SemMedDB), a high-quality public repository of SPO triples extracted from medical literature, provides a basic data infrastructure for measuring medical knowledge. In general, the study of extracting SPO triples as computable knowledge unit from unstructured scientific text has been overwhelmingly focusing on scientific knowledge per se. Since the SPO triples would be possibly extracted from hypothetical, speculative statements or even conflicting and contradictory assertions, the knowledge status (i.e., the uncertainty), which serves as an integral and critical part of scientific knowledge has been largely overlooked. This article aims to put forward a framework for Medical Knowmetrics using the SPO triples as the knowledge unit and the uncertainty as the knowledge context. The lung cancer publications dataset is used to validate the proposed framework. The uncertainty of medical knowledge and how its status evolves over time indirectly reflect the strength of competing knowledge claims, and the probability of certainty for a given SPO triple. We try to discuss the new insights using the uncertainty-centric approaches to detect research fronts, and identify knowledge claims with high certainty level, in order to improve the efficacy of knowledge-driven decision support.

Variational Optimization for the Submodular Maximum Coverage Problem

We examine the \emph{submodular maximum coverage problem} (SMCP), which is related to a wide range of applications. We provide the first variational approximation for this problem based on the Nemhauser divergence, and show that it can be solved efficiently using variational optimization. The algorithm alternates between two steps: (1) an E step that estimates a variational parameter to maximize a parameterized \emph{modular} lower bound; and (2) an M step that updates the solution by solving the local approximate problem. We provide theoretical analysis on the performance of the proposed approach and its curvature-dependent approximate factor, and empirically evaluate it on a number of public data sets and several application tasks.

Topology Adaptive Graph Convolutional Networks

Spectral graph convolutional neural networks (CNNs) require approximation to the convolution to alleviate the computational complexity, resulting in performance loss. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network defined in the vertex domain. We provide a systematic way to design a set of fixed-size learnable filters to perform convolutions on graphs. The topologies of these filters are adaptive to the topology of the graph when they scan the graph to perform convolution. The TAGCN not only inherits the properties of convolutions in CNN for grid-structured data, but it is also consistent with convolution as defined in graph signal processing. Since no approximation to the convolution is needed, TAGCN exhibits better performance than existing spectral CNNs on a number of data sets and is also computationally simpler than other recent methods.

Convergence Analysis of Distributed Inference with Vector-Valued Gaussian Belief Propagation

This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean vector, and message passing between neighbors. Under broad conditions, it is shown that the message information matrix converges to a unique positive definite limit matrix for arbitrary positive semidefinite initialization, and it approaches an arbitrarily small neighborhood of this limit matrix at a doubly exponential rate. A necessary and sufficient convergence condition for the belief mean vector to converge to the optimal centralized estimator is provided under the assumption that the message information matrix is initialized as a positive semidefinite matrix. Further, it is shown that Gaussian BP always converges when the underlying factor graph is given by the union of a forest and a single loop. The proposed convergence condition in the setup of distributed linear Gaussian models is shown to be strictly weaker than other existing convergence conditions and requirements, including the Gaussian Markov random field based walk-summability condition, and applicable to a large class of scenarios.

Convergence analysis of belief propagation for pairwise linear Gaussian models

Gaussian belief propagation (BP) has been widely used for distributed inference in large-scale networks such as the smart grid, sensor networks, and social networks, where local measurements/observations are scattered over a wide geographical area. One particular case is when two neighboring agents share a common observation. For example, to estimate voltage in the direct current (DC) power flow model, the current measurement over a power line is proportional to the voltage difference between two neighboring buses. When applying the Gaussian BP algorithm to this type of problem, the convergence condition remains an open issue. In this paper, we analyze the convergence properties of Gaussian BP for this pairwise linear Gaussian model. We show analytically that the updating information matrix converges at a geometric rate to a unique positive definite matrix with arbitrary positive semidefinite initial value and further provide the necessary and sufficient convergence condition for the belief mean vector to the optimal estimate.

Convergence analysis of the information matrix in Gaussian belief propagation

Gaussian belief propagation (BP) has been widely used for distributed estimation in large-scale networks such as the smart grid, communication networks, and social networks, where local measurements/observations are scattered over a wide geographical area. However, the convergence of Gaus- sian BP is still an open issue. In this paper, we consider the convergence of Gaussian BP, focusing in particular on the convergence of the information matrix. We show analytically that the exchanged message information matrix converges for arbitrary positive semidefinite initial value, and its dis- tance to the unique positive definite limit matrix decreases exponentially fast.