Probabilistic reasoning and machine learning

概率推理和机器学习

• 批准号: RGPIN-2020-05070
• 负责人: Panangaden, Prakash
• 金额: $ 4.66万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=750375
• 关键词: Probabilistic; reasoning; machine; learning

Machine learning has had many spectacular successes recently which have sparked interest in understanding the reasons for, and the limitations of, these achievements.  I have worked on probabilistic systems for the past 25 years originally with a view to working on formal verification of such systems.  In the last 15 years I have been more and more in contact with machine learning colleagues with whom I have increasingly collaborated on research on theoretical topics.  My research proposal focuses on: (i) metric-based tools for reasoning about reinforcement learning algorithms, (ii) new logical structures that will make reasoning more modular, (iii) theoretical results about quantitative logics and (iv) automata learning.  There have been a number of developments in my research in the last five years that are relevant to the subject of my proposal.  These are: (1) the development of quantitative equational logic which allows one to combine algebras and metrics and which gives new insights into concepts like the Wasserstein metric which emerge in a canonical way, (2) the development of bisimulation concepts for continuous-time systems like diffusion processes, (3) semantics for higher-order probabilistic programming languages which are playing an important role in Bayesian inference, (4) the use of metrics between probability distributions and coupling arguments to reason about convergence of stochastic approximation algorithms, and (5) the the development of a notion of approximate minimization of weighted automata.  I have begun work on all the areas mentioned above.  In (i) we have obtained promising results showing that a variety of different convergence arguments are amenable to our technique and we are working to extend it to new examples.  In (iii) we have shown that the Wasserstein metric emerges as the "free algebra" of a certain equational theory that we have defined.  This gives it universal properties that may turn out to be useful in computing it.  Under topic (ii) We have developed a new type of semantics for a stochastic lambda-calculus based on Boolean-valued sets.  Much remains to be done to link this to languages used in practice.  We have also developed Stone-type dualities for Markov processes which give completeness theorems for modal logics for reasoning about Markov processes.  Topic (iv) is a new venture for me.  The work we have already done gives some powerful new tools to simplify complicated automata.  We are hoping to apply such ideas to automata learning.  In traditional automata learning one learns exactly the right deterministic automaton.  We are hoping to approximately learn a probabilistic automaton.  Ideas from metrics and bisimulation will certainly be useful here since our metrics measure behavioural similarity of automata.  It will be particularly interesting to use this in conjunction with the extraction of automata from recurrent neural nets; a topic which is gaining currency.

机器学习最近取得了许多惊人的成功，这引发了人们对理解机器学习的原因和局限性的兴趣，这些成就。在过去的25年里，我一直致力于概率系统的研究，最初的目的是研究此类系统的形式化验证。在过去的15年里，我越来越多地与机器学习的同事接触，我与他们的合作越来越多。在理论课题的研究。我的研究计划集中在：（i）用于推理强化学习算法的基于度量的工具，（ii）使推理更加模块化的新逻辑结构，（iii）关于数量逻辑的理论结果;（iv）自动机学习。在过去的五年里，我的研究取得了许多进展，这些进展与我的建议主题有关。这些措施包括：（1）定量方程逻辑的发展，它允许人们将联合收割机代数和度量结合起来，并为以规范方式出现的Wasserstein度量等概念提供了新的见解，（2）扩散过程等连续时间系统的互模拟概念的发展，（3）在贝叶斯推理中发挥重要作用的高阶概率编程语言的语义，（4）利用概率分布和耦合参数之间的度量来推理随机逼近算法的收敛性，（5）发展了加权自动机的近似最小化的概念。我已经开始了上述所有领域的工作。在（i）中，我们已经得到了有希望的结果表明，各种不同的收敛参数是服从我们的技术，我们正在努力将其扩展到新的例子。我们证明了Wasserstein度量是作为我们定义的某个方程理论的“自由代数”出现的。这赋予了它可能在计算它时有用的普遍性质。在主题（ii）中，我们开发了一种新的基于布尔-值集。还有很多工作要做，以联系这在实践中使用的语言。我们还开发了石型对偶马尔可夫过程，给出完整性定理的模态逻辑推理马尔可夫过程。主题（四）对我来说是一个新的尝试。我们已经完成的工作提供了一些强大的新工具来简化复杂的自动机。我们希望将这些想法应用于自动机学习。在传统的自动机学习中，人们可以精确地学习正确的确定性自动机。我们希望近似地学习概率自动机。度量和互模拟的想法在这里肯定会有用因为我们的指标测量自动机的行为相似性。将其与从递归神经网络中提取自动机结合使用将特别有趣;这是一个越来越流行的话题。