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The AGI Landscape

$\Omega$

is going to push the boundary of artificial general intelligence.$\mathbf{\Omega} = \underset{\theta}{\arg\max}\ \mathcal{AGI}(\theta)$

Concepts

Frameworks

- Out-of-sample extension of graph adjacency spectral embedding: consider the problem of obtaining an out-of-sample extension for the adjacency spectral embedding, a procedure for embedding the vertices of a graph into Euclidean space.
- Measuring and avoiding side effects using relative reachability: introduces a general definition of side effects, based on relative reachability of states compared to a default state, that avoids these undesirable incentives.

Nov

Books

Probability

**P. Billingsley**Probability and Measure (3rd Edition). Chapters 1-30 contain a more careful and detailed treatment of some of the topics of this semester, in particular the measure-theory background. Recommended for students who have not done measure theory.**R. Leadbetter et al**A Basic Course in Measure and Probability: Theory for Applications is a new book giving a careful treatment of the measure-theory background.

There are many other books at roughly the same ``first year graduate" level. Here are my personal comments on some.

**R. Bhattacharya and E. C. Waymire**A Basic Course in Probability Theory is another well-written account, mostly on the 205A topics.**K.L. Chung**A Course in Probability Theory covers many of the topics of 205A: more leisurely than Durrett and more focused than Billingsley.**D. Williams**Probability with Martingales has a uniquely enthusiastic style; concise treatment emphasizes usefulness of martingales.**Y.S. Chow and H. Teicher**Probability Theory: Independence, Interchangeability, Martingales . Uninspired exposition, but has useful variations on technical topics such as inequalities for sums and for martingales.**R.M. Dudley**Real Analysis and Probability. Best account of the functional analysis and metric space background relevant for research in theoretical probability.**B. Fristedt and L. Gray**A Modern Approach to Probability Theory. 700 pages allow coverage of broad range of topics in probability and stochastic processes.**O. Kallenberg**Foundations of Modern Probability. Quoting an amazon.com reviewer: ``.... a compendium of all the relevant results of probability ..... similar in breadth and depth to Loeve's classical text of the mid 70's. It is not suited as a textbook, as it lacks the many examples that are needed to absorb the theory at a first pass. It works best as a reference book or a "second pass" textbook."**John B. Walsh**Knowing the Odds: An Introduction to Probability. New in 2012. Looks very nice -- concise treatment with quite challenging exercises developing part of theory.**George Roussas**An Introduction to Measure-Theoretic Probability. Recent treatment of classical content.**Santosh Venkatesh**The Theory of Probability: Explorations and Applications. Unique new book, intertwining a broad range of undergraduate and graduate-level topics for an applied audience.**I. Florescu**Probability and Stochastic Processes. Very clearly written, and with 550 pages gives a broad coverage of topics including intro to SDEs.- Jim Pitman has his very useful lecture notes linked to the Durrett text; these notes cover more ground than my course will! Also some lecture notes by Amir Dembo for the Stanford courses equivalent to our 205AB.

Reference

- 1.The
`Books`

: https://www.stat.berkeley.edu/~aldous/205B/index.html, by Professor David Aldous from UC Berkeley.

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Outline

Concepts

Frameworks

Important Papers

Books

Probability

Reference