Related papers: Algorithmic statistics: normal objects and univers…
This paper is motivated by a conjecture that BPP can be characterized in terms of polynomial-time nonadaptive reductions to the set of Kolmogorov-random strings. In this paper we show that an approach laid out in [Allender et al] to settle…
A knowledge system S describing a part of real world does in general not contain complete information. Reasoning with incomplete information is prone to errors since any belief derived from S may be false in the present state of the world.…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
The combined universal probability M(D) of strings x in sets D is close to max_{x \in D} M({x}): their ~ logs differ by at most D's information j = I(D:H) about the halting sequence H. Thus if all x have complexity K(x) > k, D carries > i…
Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical?…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…
Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modelling transportation networks, social circles, and the human brain. A…
In [She82], it is shown that four basic functional properties are enough to characterize plain Kolmogorov complexity, hence obtaining an axiomatic characterization of this notion. In this paper, we try to extend this work, both by looking…
We present a fully automatic method for music classification, based only on compression of strings that represent the music pieces. The method uses no background knowledge about music whatsoever: it is completely general and can, without…
Multivariate goodness-of-fit and two-sample tests are important components of many nuclear and particle physics analyses. While a variety of powerful methods are available if the dimensionality of the feature space is small, such tests…
Economic choices are often stochastic: the same person may make a different choice when facing the same alternatives repeatedly. Standard models assume that the degree of randomness reflects the size of utility differences, but choice…
We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given $n$ i.i.d. samples from the distribution…
We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…
In several different settings, one comes across situations in which the objects of study are locally consistent but globally inconsistent. Earlier work about probability distributions by Vorob'ev (1962) and about database relations by…
We provide tight upper and lower bounds on the expected minimum Kolmogorov complexity of binary classifiers that are consistent with labeled samples. The expected size is not more than complexity of the target concept plus the conditional…
The posterior predictive $p$-value (ppp) is widely used in Bayesian model evaluation. However, due to double use of the data, the ppp may not be a valid $p$-value even in large samples: The asymptotic null distribution of the ppp can be…
Classification models are very sensitive to data uncertainty, and finding robust classifiers that are less sensitive to data uncertainty has raised great interest in the machine learning literature. This paper aims to construct robust…
The probability distribution P from which the history of our universe is sampled represents a theory of everything or TOE. We assume P is formally describable. Since most (uncountably many) distributions are not, this imposes a strong…
We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…
The clustering objects has become one of themes in many studies, and do not few researchers use the similarity to cluster the instances automatically. However, few research consider using Kommogorov Complexity to get information about…