Publication Library
Fundamental Theorem of Asset Pricing
Description: Fundamental Theorem of Asset Pricing
Created At: 14 December 2024
Updated At: 14 December 2024
The Probabilistic Method
Description: The Probabilistic Method has recently been developed intensively and became one of the most powerful and widely used tools applied in Combinatorics. One of the major reasons for this rapid development is the important role of randomness in Theoretical ComputerScience, a field which isrecently the source ofmany intriguing combinatorial problems. The interplay between Discrete Mathematics and Computer Science suggests an algorithmic point of view in the study of the Probabilistic Method in Combinatorics and thisis theapproach we triedtoadopt inthisbook. The manuscript thusincludesa discussion of algorithmic techniques together with a study of the classical method as well as the moderntoolsapplied init. The first part ofthe bookcontains a description of the tools applied in probabilistic arguments, including the basic techniques that use expectation and variance, as well as the more recent applications of Martingales and Correlation Inequalities. The second part includes a study of various topics in which probabilistic techniques have been successful. This part contains chapters on discrepancy and random graphs, as well as on several areas in Theoretical Computer Science; Circuit Complexity , Computational Geometry, and Derandomization of randomized algorithms. Scattered between the chapters are gems described under the heading"The Probabilistic Lens". Theseareelegant proofs that are not necessarily related to the chapters after which they appear and can be usually read separately.
Created At: 14 December 2024
Updated At: 14 December 2024
Monte Carlo Statistical Methods
Description: Monte Carlo Statistical Methods
Created At: 14 December 2024
Updated At: 14 December 2024
Causality for Machine Learning
Description: Graphical causal inference as pioneered by Judea Pearl arose from research on artificial intelligence (AI), and for a long time had little connection to the field of machine learning. This article discusses where links have been and should be established, introducing key concepts along the way. It argues that the hard open problems of machine learning and AI are intrinsically related to causality, and explains how the field is beginning to understand them.
Created At: 14 December 2024
Updated At: 14 December 2024
The Next Decade in AI Four Steps Towards Robust Artificial Intelligence
Description: Recent research in artificial intelligence and machine learning has largely emphasized general-purpose learning and ever-larger training sets and more and more compute. In contrast, I propose a hybrid, knowledge-driven, reasoning-based approach, centered around cognitive models, that could provide the substrate for a richer, more robust AI than is currently possible.
Created At: 14 December 2024
Updated At: 14 December 2024