Related papers: Lowness, randomness, and computable analysis

Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them…

The blog focusses on algorithmic randomness and its connections to quantum information theory, group theory and its connections to logic, and computability analogs of cardinal characteristics.

We characterize some major algorithmic randomness notions via differentiability of effective functions. (1) As the main result we show that a real number z in [0,1] is computably random if and only if each nondecreasing computable function…

Data generated in the fields of science, technology, business and in many other fields of research are increasing in an exponential rate. The way to extract knowledge from a huge set of data is a challenging task. This paper aims to propose…

Individuals have an intuitive perception of what makes a good coincidence. Though the sensitivity to coincidences has often been presented as resulting from an erroneous assessment of probability, it appears to be a genuine competence,…

These notes survey and explore an emerging method, which we call the low-degree method, for predicting and understanding statistical-versus-computational tradeoffs in high-dimensional inference problems. In short, the method posits that a…

This work starts from definition of randomness, the results of algorithmic randomness are analyzed from the perspective of application. Then, the source and nature of randomness is explored, and the relationship between infinity and…

We survey the Kolmogorov's approach to the notion of randomness through the Kolmogorov complexity theory. The original motivation of Kolmogorov was to give up a quantitative definition of information. In this theory, an object is randomness…

Fair Machine Learning endeavors to prevent unfairness arising in the context of machine learning applications embedded in society. Despite the variety of definitions of fairness and proposed "fair algorithms", there remain unresolved…

The theory of random real numbers is exceedingly well-developed, and fascinating from many points of view. It is also quite challenging mathematically. The present notes are intended as no more than a gateway to the larger theory. They…

The 2012 logic blog has focussed on the following: Randomness and computable analysis/ergodic theory; Systematizing algorithmic randomness notions; Traceability; Higher randomness; Calibrating the complexity of equivalence relations from…

Randomness is fundamental in quantum theory, with many philosophical and practical implications. In this paper we discuss the concept of algorithmic randomness, which provides a quantitative method to assess the Borel normality of a given…

Initially introduced by Peter Hammer, Logical Analysis of Data is a methodology that aims at computing a logical justification for dividing a group of data in two groups of observations, usually called the positive and negative groups.…

Algorithmic fairness is a new interdisciplinary field of study focused on how to measure whether a process, or algorithm, may unintentionally produce unfair outcomes, as well as whether or how the potential unfairness of such processes can…

Depth of an object concerns a tradeoff between computation time and excess of program length over the shortest program length required to obtain the object. It gives an unconditional lower bound on the computation time from a given program…

Some notions from algorithmic randomness are extended to measures and to quantum states. There is a lot on group theory and its relation to logic. This includes some new results on oligomorphic groups. There's also metric spaces and Scott…

The effective teaching and learning of statistics persist as a challenge in K-12 education and has clear impacts in developing competence and confidence of students in entering STEM fields especially in today's digital age of data science.…

We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these…

We discuss recent work for causal inference and predictive robustness in a unifying way. The key idea relies on a notion of probabilistic invariance or stability: it opens up new insights for formulating causality as a certain risk…

This paper studies the notion of computational entropy. Using techniques from convex optimization, we investigate the following problems: (a) Can we derandomize the computational entropy? More precisely, for the computational entropy, what…