Related papers: Lecture notes on descriptional complexity and rand…
The latest in a series of reports presenting the information-theoretic incompleteness theorems of algorithmic information theory via algorithms written in specially designed versions of LISP. Previously in this LISP code only one-character…
These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author…
These notes provide an introduction to a number of those topics in Classical Mechanics that are useful for field theory.
The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with…
This thesis investigates the quality of randomly collected data by employing a framework built on information-based complexity, a field related to the numerical analysis of abstract problems. The quality or power of gathered information is…
This manuscript is technical memoir about my work at Stanford and Microsoft Research. Included are fundamental concepts central to machine learning and artificial intelligence, applications of these concepts, and stories behind their…
In the first part of this paper, we present a unified framework for analyzing the algorithmic complexity of any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like "input", "size" and…
This chapter examines current developments in linguistic theory and methods, focusing on the increasing integration of computational, cognitive, and evolutionary perspectives. We highlight four major themes shaping contemporary linguistics:…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
Principles for the planning and analysis of observational studies, as suggested by W.G Cochran in 1972, are discussed and compared to additional methodological developments since then.
These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…
These lecture notes were prepared as a basic introduction to the theory of constrained systems which is how the fundamental forces of nature appear in their Hamiltonian formulation. Only a working knowledge of Lagrangian and Hamiltonian…
This manuscript provides a short and practical introduction to the topic of language networks. This text aims at assisting researchers with no practical experience in text and/or network analysis. We provide a practical tutorial on how to…
Algorithmic information theory translates statements about classes of objects into statements about individual objects; it defines individual random sequences, effective Hausdorff dimension of individual points, amount of information in…
I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized.…
Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry, and partly from…