相关论文: On the impossibility of discovering a formula for …
In the present work we use maximum entropy methods to derive several theorems in probabilistic number theory, including a version of the Hardy-Ramanujan Theorem. We also provide a theoretical argument explaining the experimental…
We develop conjectures and theorems expressing the idea that the prime sequence exhibits computational irreducibility in the transition from one prime to its successor. Informally, given a prime pp p, no general algorithm can compute the…
The coding theorem for Kolmogorov complexity states that any string sampled from a computable distribution has a description length close to its information content. A coding theorem for resource-bounded Kolmogorov complexity is the key to…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
We study practical approximations to Kolmogorov prefix complexity (K) using IMP2, a high-level programming language. Our focus is on investigating the interpreter optimality for this language as the reference machine for the Coding Theorem…
Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…
We consider the problem of inferring the probability distribution associated with a language, given data consisting of an infinite sequence of elements of the languge. We do this under two assumptions on the algorithms concerned: (i) like a…
Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and…
We summarize our recent findings, where we proposed a framework for learning a Kolmogorov model, for a collection of binary random variables. More specifically, we derive conditions that link outcomes of specific random variables, and…
In [1, 2], we have explored the theoretical aspects of feature extraction optimization processes for solving largescale problems and overcoming machine learning limitations. Majority of optimization algorithms that have been introduced in…
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information'. We discuss the extent to which Kolmogorov's and Shannon's…
Within the setting of rare event modelling, the method of level sets allows us to define an equivalence relation over rare events with distinct rates of entropy production. This method allows us to clarify the relation between the empirical…
Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
This paper develops fundamental limits of deep neural network learning by characterizing what is possible if no constraints are imposed on the learning algorithm and on the amount of training data. Concretely, we consider Kolmogorov-optimal…
Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief…
Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one…
Randomness and regularities in Finance are usually treated in probabilistic terms. In this paper, we develop a completely different approach in using a non-probabilistic framework based on the algorithmic information theory initially…
Given the widespread use of lossless compression algorithms to approximate algorithmic (Kolmogorov-Chaitin) complexity, and that lossless compression algorithms fall short at characterizing patterns other than statistical ones not different…