The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

In the last years, Artificial Intelligence (AI) has achieved a notable momentum that may deliver the best of expectations over many application sectors across the field. For this to occur, the entire community stands in front of the barrier of explainability, an inherent problem of AI techniques brought by sub-symbolism (e.g. ensembles or Deep Neural Networks) that were not present in the last hype of AI. Paradigms underlying this problem fall within the so-called eXplainable AI (XAI) field, which is acknowledged as a crucial feature for the practical deployment of AI models. This overview examines the existing literature in the field of XAI, including a prospect toward what is yet to be reached. We summarize previous efforts to define explainability in Machine Learning, establishing a novel definition that covers prior conceptual propositions with a major focus on the audience for which explainability is sought. We then propose and discuss about a taxonomy of recent contributions related to the explainability of different Machine Learning models, including those aimed at Deep Learning methods for which a second taxonomy is built. This literature analysis serves as the background for a series of challenges faced by XAI, such as the crossroads between data fusion and explainability. Our prospects lead toward the concept of Responsible Artificial Intelligence, namely, a methodology for the large-scale implementation of AI methods in real organizations with fairness, model explainability and accountability at its core. Our ultimate goal is to provide newcomers to XAI with a reference material in order to stimulate future research advances, but also to encourage experts and professionals from other disciplines to embrace the benefits of AI in their activity sectors, without any prior bias for its lack of interpretability.

Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI.

Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science approaches. Motivated by the explosive growth in FL research, this paper discusses recent advances and presents an extensive collection of open problems and challenges.

Advances and Open Problems in Federated Learning

In recent years, deep neural networks have been successful in both industry and academia, especially for computer vision tasks. The great success of deep learning is mainly due to its scalability to encode large-scale data and to maneuver billions of model parameters. However, it is a challenge to deploy these cumbersome deep models on devices with limited resources, e.g., mobile phones and embedded devices, not only because of the high computational complexity but also the large storage requirements. To this end, a variety of model compression and acceleration techniques have been developed. As a representative type of model compression and acceleration, knowledge distillation effectively learns a small student model from a large teacher model. It has received rapid increasing attention from the community. This paper provides a comprehensive survey of knowledge distillation from the perspectives of knowledge categories, training schemes, teacher-student architecture, distillation algorithms, performance comparison and applications. Furthermore, challenges in knowledge distillation are briefly reviewed and comments on future research are discussed and forwarded.

Knowledge Distillation: A Survey

我的台灣, 看見心靈的故鄉 =2009林磐聳藝術與設計展

. We introduce extension-based proofs, a class of impossibility proofs that includes valency arguments. They are modelled as an interaction between a prover and a protocol. Using proofs based on combinatorial topology, it has been shown that it is impossible to deterministically solve k -set agreement among n > k ≥ 2 processes or approximate agreement on a cycle of length 4 among n > 2 processes in a wait-free manner in asynchronous models where processes communicate using objects that can be constructed from shared registers. However, it was unknown whether proofs based on simpler techniques were possible. We show that these impossibility results cannot be obtained by extension-based proofs in the iterated snapshot model and, hence, extension-based proofs are limited in power.

Why extension-based

As this is the rst column I am editing, I would like to sincerely thank Jennifer Welch for inviting me as editor, and for being extremely helpful with the transition. I will do my best to maintain the very high standard set for the column by her, and by the previous editors. Following custom, the December issue is devoted to a review of some notable events related to distributed computing which occurred during the year. First, congratulations to Alessandro Panconesi and Aravind Srinivasan for being awarded the 2019 Edsger W. Dijkstra Prize in Distributed Computing for their paper \Randomized Distributed Edge Coloring via an Extension of the Cherno Hoe ding Bounds," which appeared in the SIAM Journal on Computing in 1997. The prize is jointly sponsored by ACM and EATCS, and is given alternately at PODC1 and DISC2; this year it was awarded at DISC.

Distributed Computing Column 76: Annual Review 2019

We study a distributed multi-armed bandit setting among a population of $n$ memory-constrained nodes in the gossip model: at each round, every node locally adopts one of $m$ arms, observes a reward drawn from the arm's (adversarially chosen) distribution, and then communicates with a randomly sampled neighbor, exchanging information to determine its policy in the next round. We introduce and analyze several families of dynamics for this task that are decentralized: each node's decision is entirely local and depends only on its most recently obtained reward and that of the neighbor it sampled. We show a connection between the global evolution of these decentralized dynamics with a certain class of"zero-sum"multiplicative weight update algorithms, and we develop a general framework for analyzing the population-level regret of these natural protocols. Using this framework, we derive sublinear regret bounds under a wide range of parameter regimes (i.e., the size of the population and number of arms) for both the stationary reward setting (where the mean of each arm's distribution is fixed over time) and the adversarial reward setting (where means can vary over time). Further, we show that these protocols can approximately optimize convex functions over the simplex when the reward distributions are generated from a stochastic gradient oracle.

Decentralized Learning Dynamics in the Gossip Model

In this paper, we show that distributed systems are vul- nerable to routing attacks and propose an architecture to obviate this vulnerability. A somewhat surprising finding is that even a small-scale routing attack can completely dis- rupt the operation of a state-machine replication service. The architecture that we propose is based on the following simple ideas: (1) Circumvent the adversary if possible and (2) if it is not possible, relax the application semantics.

https://www.net.t-labs.tu-berlin.de/papers/ATAK-RAVTCSSPT-10.pdf

Routing Attacks as a Viable Threat: Can Software Systems Protect Themselves?

Renaming is a classic distributed coordination task in which a set of processes must pick distinct identiers from a small namespace. In this paper, we consider the time complexity of this problem when the namespace is linear in the number of participants, a variant known as loose renaming. We give a non-adaptive algorithm with O(log logn) (individual) step complexity, where n is a known upper bound on contention, and an adaptive algorithm with step complexity O((log logk) 2 ), where k is the actual contention in the execution. We also present a variant of the adaptive algorithm which requires O(k log logk) total process steps. All upper bounds hold with high probability against a strong adaptive adversary. We complement the algorithms with an (log log n) expected time lower bound on the complexity of randomized renaming using test-and-set operations and linear space. The result is based on a new coupling technique, and is the rst to apply to non-adaptive randomized renaming. Since our algorithms use O(n) test-and-set objects, our results provide matching bounds on the cost of loose renaming in this setting.

Dan Alistarh

Papers

Why extension-based

Distributed Computing Column 76: Annual Review 2019

Decentralized Learning Dynamics in the Gossip Model

Routing Attacks as a Viable Threat: Can Software Systems Protect Themselves?

Randomized Loose Renaming in O(loglogn) Time (Extended Abstract)