……可测性。部分原因在于‘可测选择’（measurable selection）问题：这可以是一个很深的研究课题，但通常一个相对简单的出路是通过正则条件概率，就像 Leo Breiman 的《Probability》（ISBN 0-89871-296-3，SIAM，费城）里那样。至于 David G. Luenberger 的《Optimization by Vector Space Methods》（John Wiley and Sons, Inc., New York），这大概是对……最容易上手的数学处理了
…measurability. Part of the reason is the issue of 'measurable selection': This can be a deep subject, but often a relatively simple way out is via regular conditional probabilities as in Leo Breiman, 'Probability', ISBN 0-89871-296-3, SIAM, Philadelphia. For David G. Luenberger, 'Optimization by Vector Space Methods', John Wiley and Sons, Inc., New York. this has likely the easiest mathematical treatment of…
……运筹学。Neveu 曾是 M. Loeve 在伯克利的学生。如今机器学习界的红人 L. Breiman 也是，他成名是因为分类与回归树（CART）。Breiman 由 SIAM 出版的《Probability》通常比 Neveu 的更好读。至于随机过程，有几个截然不同的方向可走。鞅理论（Martingale theory）非常优美、令人惊叹、不可思议，伴随着……
…of Operations Research. Neveu was a student of M. Loeve at Berkeley. So was the current darling of machine learning, L. Breiman, because of his Classification and Regression Trees (CART). Breiman's Probability as published by SIAM is generally easier reading than Neveu. For stochastic processes, there are several relatively different directions to go. Martingale theory is gorgeous, astounding, amazing, with…
Hehe ok —- I also love Breiman’s Probability book. It’s really a standout on Ergodic theory. And Breiman et al.’s book on Trees is surprisingly rich, talking about all sorts of stuff besides trees.
…building on top of the axiomatic foundation that you outlined for decades. This is old news. Yup, essentially since Kolmogorov's 1933 paper. The axiomatic approach I gave is just what is used in Breiman's Probability, as published by SIAM. It's a super nicely written book. I have never seen his book on statistics.
……而且我们应该注意到，AI 领域对回归的很大一部分兴趣都建立在 L. Breiman 在分类与回归树（CART）上的工作。如果我没记错的话，Breiman 当时是‘学院派概率学家’；他的教材《Probability》（我的最爱之一，比如讲可测选择那块）完全重度依赖测度论；而他在 CART 上的工作，始于尝试通过来自……的复杂数据来获得拟合与预测模型
…And we should note that much of the AI interest in regression is based on the work of L. Breiman in Classification and Regression Trees (CART). Breiman was, IIRC "an academic probabilist"; his text Probability (one of my favorites, e.g., for measurable selection) was all based heavily on measure theory; and his work on CART started by trying to get fits and predictive models starting with complicated data from…
……《Analysis: A Modern Approach to Advanced Calculus》，不必太当真那些证明，而是看看物理科学和工程如何看待多变量微积分。Neveu 是一本很棒的最后一本概率论教材，但不是好的第一本教材。所以，在 Neveu 之前，快速、不太认真地看看随便什么，包括一些入门统计学教材。另外，Breiman 的《Probability》比 Neveu 好读。……
…Analysis: A Modern Approach to Advanced Calculus,\/} where don't take the proofs very seriously but to see how physical science and engineering look at calculus of several variables. Neveu is a great last probability text but not a good first text. So, before Neveu, look quickly, not very seriously, at whatever, including in some introductory statistics texts. Also, Breiman's Probability is easier to read than Neveu.…
……可测性。部分原因在于‘可测选择’（measurable selection）问题：这可以是一个很深的研究课题，但通常一个相对简单的出路是通过正则条件概率，就像 Leo Breiman 的《Probability》（ISBN 0-89871-296-3，SIAM，费城）里那样。至于 David G. Luenberger 的《Optimization by Vector Space Methods》（John Wiley and Sons, Inc., New York），这大概是对……最容易上手的数学处理了
…measurability. Part of the reason is the issue of 'measurable selection': This can be a deep subject, but often a relatively simple way out is via regular conditional probabilities as in Leo Breiman, 'Probability', ISBN 0-89871-296-3, SIAM, Philadelphia. For David G. Luenberger, 'Optimization by Vector Space Methods', John Wiley and Sons, Inc., New York. this has likely the easiest mathematical treatment of…
……运筹学。Neveu 曾是 M. Loeve 在伯克利的学生。如今机器学习界的红人 L. Breiman 也是，他成名是因为分类与回归树（CART）。Breiman 由 SIAM 出版的《Probability》通常比 Neveu 的更好读。至于随机过程，有几个截然不同的方向可走。鞅理论（Martingale theory）非常优美、令人惊叹、不可思议，伴随着……
…of Operations Research. Neveu was a student of M. Loeve at Berkeley. So was the current darling of machine learning, L. Breiman, because of his Classification and Regression Trees (CART). Breiman's Probability as published by SIAM is generally easier reading than Neveu. For stochastic processes, there are several relatively different directions to go. Martingale theory is gorgeous, astounding, amazing, with…
哈哈好的——我也很喜欢 Breiman 的那本《Probability》。它在遍历理论（Ergodic theory）方面讲得特别出彩。而且 Breiman 等人写的那本关于决策树的书内容丰富得惊人，除了树之外还讲了各种各样的东西。
Hehe ok —- I also love Breiman’s Probability book. It’s really a standout on Ergodic theory. And Breiman et al.’s book on Trees is surprisingly rich, talking about all sorts of stuff besides trees.
……几十年来一直在你概述的公理化基础之上构建。这早就不是新闻了。没错，基本上从柯尔莫哥洛夫 1933 年的论文开始就是这样了。我给出的公理化方法其实就是 SIAM 出版的 Breiman 的《Probability》里用的那套。那本书写得超级棒。我从来没看过他关于统计学的那本书。
…building on top of the axiomatic foundation that you outlined for decades. This is old news. Yup, essentially since Kolmogorov's 1933 paper. The axiomatic approach I gave is just what is used in Breiman's Probability, as published by SIAM. It's a super nicely written book. I have never seen his book on statistics.
……而且我们应该注意到，AI 领域对回归的很大一部分兴趣都建立在 L. Breiman 在分类与回归树（CART）上的工作。如果我没记错的话，Breiman 当时是‘学院派概率学家’；他的教材《Probability》（我的最爱之一，比如讲可测选择那块）完全重度依赖测度论；而他在 CART 上的工作，始于尝试通过来自……的复杂数据来获得拟合与预测模型
…And we should note that much of the AI interest in regression is based on the work of L. Breiman in Classification and Regression Trees (CART). Breiman was, IIRC "an academic probabilist"; his text Probability (one of my favorites, e.g., for measurable selection) was all based heavily on measure theory; and his work on CART started by trying to get fits and predictive models starting with complicated data from…
……《Analysis: A Modern Approach to Advanced Calculus》，不必太当真那些证明，而是看看物理科学和工程如何看待多变量微积分。Neveu 是一本很棒的最后一本概率论教材，但不是好的第一本教材。所以，在 Neveu 之前，快速、不太认真地看看随便什么，包括一些入门统计学教材。另外，Breiman 的《Probability》比 Neveu 好读。……
…Analysis: A Modern Approach to Advanced Calculus,\/} where don't take the proofs very seriously but to see how physical science and engineering look at calculus of several variables. Neveu is a great last probability text but not a good first text. So, before Neveu, look quickly, not very seriously, at whatever, including in some introductory statistics texts. Also, Breiman's Probability is easier to read than Neveu.…