Related papers: Algorithmic information theory and martingales
Given a finite sequence of events and a well-defined notion of events being interesting, the Odds-theorem (Bruss (2000)) gives an online strategy to stop on the last interesting event. It is optimal for independent events. Here we study…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
We study randomness beyond $\Pi^1_1$-randomness and its Martin-L\"of type variant, introduced in \cite{MR2340241} and further studied in \cite{Continuous-higher-randomness}. The class given by the infinite time Turing machines (\ITTM s),…
Ordered pivotal sampling is one of the simplest algorithm to perform without-replacement unequal probability sampling. It has found uses in the context of longitudinal surveys and spatial sampling, and enables in particular a good spatial…
There exists a theory of a single general-purpose learning algorithm which could explain the principles of its operation. This theory assumes that the brain has some initial rough architecture, a small library of simple innate circuits…
We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense…
Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…
The progress of machine learning over the past decade is undeniable. In retrospect, it is both remarkable and unsettling that this progress was achievable with little to no rigorous theory to guide experimentation. Despite this fact,…
In this paper we develop the elements of the theory of algorithmic randomness in continuous-time Markov chains (CTMCs). Our main contribution is a rigorous, useful notion of what it means for an individual trajectory of a CTMC to be random.…
Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a…
Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and…
I will survey some matters of relevance to a philosophical discussion of information, taking into account developments in algorithmic information theory (AIT). I will propose that meaning is deep in the sense of Bennett's logical depth, and…
Kobayashi introduced a uniform notion of compressibility of infinite binary sequences in terms of relative Turing computations with sub-identity use of the oracle. Kobayashi compressibility has remained a relatively obscure notion, with the…
When a variety of anomalous features motivate flagging different samples as outliers, Algorithmic Information Theory (AIT) offers a principled way to unify them in terms of a sample's randomness deficiency. Subject to the algorithmic Markov…
Since genetic algorithm was proposed by John Holland (Holland J. H., 1975) in the early 1970s, the study of evolutionary algorithm has emerged as a popular research field (Civicioglu & Besdok, 2013). Researchers from various scientific and…
When Kurt Goedel layed the foundations of theoretical computer science in 1931, he also introduced essential concepts of the theory of Artificial Intelligence (AI). Although much of subsequent AI research has focused on heuristics, which…
This paper introduces time into information theory, gives a more accurate definition of information, and unifies the information in cognition and Shannon information theory. Specially, we consider time as a measure of information, giving a…
In this paper, we will expound upon the concepts proffered in [1], where we proposed an information theoretic approach to intelligence in the computational sense. We will examine data and meme aggregation, and study the effect of limited…
We introduce scalable algorithms for online learning of neural network parameters and Bayesian sequential decision making. Unlike classical Bayesian neural networks, which induce predictive uncertainty through a posterior over model…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…