Related papers: Algorithmic information and simplicity in statisti…
Recently, there has been a growing literature exploring the generalization of quantum algorithms, such that different quantum algorithms are special examples of a more fundamental structure. In this short paper, we provide a general…
The main purpose of this paper is to show that we can exploit the difference ($l_1$-norm and $l_2$-norm) in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficiencies. It…
In this work, conditional entropy is used to quantify the information loss induced by passing a continuous random variable through a memoryless nonlinear input-output system. We derive an expression for the information loss depending on the…
We observe an infinite sequence of independent identically distributed random variables $X_1,X_2,\ldots$ drawn from an unknown distribution $p$ over $[n]$, and our goal is to estimate the entropy $H(p)=-\mathbb{E}[\log p(X)]$ within an…
The vast majority of optimization and online learning algorithms today require some prior information about the data (often in the form of bounds on gradients or on the optimal parameter value). When this information is not available, these…
Mutual information has been successfully adopted in filter feature-selection methods to assess both the relevancy of a subset of features in predicting the target variable and the redundancy with respect to other variables. However,…
We propose a probabilistic Hoare logic aHL based on the union bound, a tool from basic probability theory. While the union bound is simple, it is an extremely common tool for analyzing randomized algorithms. In formal verification terms,…
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…
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…
This paper presents the computational methods of information cohomology applied to genetic expression in and in the companion paper and proposes its interpretations in terms of statistical physics and machine learning. In order to further…
It is always possible to decide, with one-sided error, whether two quantum states are the same under a specific unitary transformation. However we show here that it is {\em impossible} to do so if the transformation is anti-linear and…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
An outlier is a datapoint that is set apart from a sample population. The outlier theorem in algorithmic information theory states that given a computable sampling method, outliers must appear. We present a simple proof to the outlier…
The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of…
Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively…
We apply recent ideas about complexity and randomness to the philosophy of laws and chances. We develop two ways to use algorithmic randomness to characterize probabilistic laws of nature. The first, a generative chance* law, employs a…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
We describe a statistical method to avoid biased estimation of the content of different particle species. We consider the case when the particle identification information strongly depends on some kinematical variables, whose distributions…
Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only…
The particle filter is a popular Bayesian filtering algorithm for use in cases where the state-space model is nonlinear and/or the random terms (initial state or noises) are non-Gaussian distributed. We study the behavior of the error in…