Algorithmic Learning in a Random World

Algorithmic Learning in a Random World describes recent theoretical and experimental developments in building computable approximations to Kolmogorov's algorithmic notion of randomness. Based on these approximations, a new set of machine learning algorithms have been developed that can be used to make predictions and to estimate their confidence and credibility in high-dimensional spaces under the usual assumption that the data are independent and identically distributed (assumption of randomness). Another aim of this unique monograph is to outline some limits of predictions: The approach based on algorithmic theory of randomness allows for the proof of impossibility of prediction in certain situations. The book describes how several important machine learning problems, such as density estimation in high-dimensional spaces, cannot be solved if the only assumption is randomness.

《在隨機世界中的演算法學習》描述了近期在建構可計算的近似科爾莫哥洛夫隨機演算法概念方面的理論和實驗發展。基於這些近似，已經開發出一套新的機器學習演算法，可用於進行預測並在高維空間中估計其信心和可信度，前提是數據是獨立且同分佈的（隨機假設）。這本獨特的專著的另一個目標是概述預測的某些限制：基於演算法隨機性理論的方法可以證明在某些情況下無法進行預測。該書描述了如何解決幾個重要的機器學習問題，例如在高維空間中的密度估計，如果唯一的假設是隨機性，則無法解決。

Vladimir Vovk is Professor of Computer Science at Royal Holloway, University of London. His research interests include machine learning and the foundations of probability and statistics. He was one of the founders of prediction with expert advice, an area of machine learning avoiding making any statistical assumptions about the data. Together with Glenn Shafer and with original inspiration from Philip Dawid, he developed game-theoretic foundations for probability and statistics.

Alexander Gammerman is Professor of Computer Science and co-Director of the Centre for Reliable Machine Learning at Royal Holloway, University of London. His research interests lie in machine learning and pattern recognition, where the majority of his research books, papers, and grants can be found. He is a Fellow of the Royal Statistical Society and has held visiting and honorary professorships from several universities in Europe and the USA.

Glenn Shafer is Professor and former Dean of the Rutgers Business School - Newark and New Brunswick. He is best known for his work in the 1970s and 1980s on the Dempster-Shafer theory, an alternative theory of probability that has been applied widely in engineering and artificial intelligence. Glenn is also known for his initiation, with Vladimir Vovk, of the game-theoretic framework for probability. Their first book on the topic was Probability and Finance: It's Only a Game! A new book on the topic, Game-Theoretic Foundations for Probability and Finance, published in 2019 (Wiley).

Vladimir Vovk是倫敦大學皇家霍洛威計算機科學教授。他的研究興趣包括機器學習以及概率和統計的基礎。他是預測與專家建議的創始人之一，這是機器學習的一個領域，避免對數據做出任何統計假設。他與Glenn Shafer以及Philip Dawid的啟發，開發了概率和統計的博弈論基礎。

Alexander Gammerman是倫敦大學皇家霍洛威計算機科學教授，也是可靠機器學習中心的聯合主任。他的研究興趣主要集中在機器學習和模式識別領域，他的研究書籍、論文和研究項目大多集中在這個領域。他是英國皇家統計學會的會士，並曾在歐洲和美國的多所大學擔任訪問和名譽教授。

Glenn Shafer是羅格斯商學院-紐瓦克和新布倫斯維克校區的教授和前院長。他最著名的是在1970年代和1980年代對登普斯特-謝弗理論的研究，這是一種替代的概率理論，在工程和人工智能領域得到了廣泛應用。Glenn還因與Vladimir Vovk共同開創了概率的博弈論框架而聞名。他們關於這一主題的第一本書是《概率與金融：只是一場遊戲！》。2019年出版了一本關於這一主題的新書《概率與金融的博弈論基礎》（Wiley出版）。