Related papers: Universal Codes as a Basis for Nonparametric Testi…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
Two objects are independent if they do not affect each other. Independence is well-understood in classical information theory, but less in algorithmic information theory. Working in the framework of algorithmic information theory, the paper…
We propose a flexible and robust nonparametric framework for testing spatial dependence in two- and three-dimensional random fields. Our approach involves converting spatial data into one-dimensional time series using space-filling Hilbert…
An important problem in time series analysis is the discrimination between non-stationarity and longrange dependence. Most of the literature considers the problem of testing specific parametric hypotheses of non-stationarity (such as a…
We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypotheses testing in a framework of classical mathematical statistics. The methods for identity testing and…
In this paper, we propose {\em distributed network compression via memory}. We consider two spatially separated sources with correlated unknown source parameters. We wish to study the universal compression of a sequence of length $n$ from…
To render a sequence testable, namely capable of identifying and detecting errors, it is necessary to apply a transformation that increases its length by introducing statistical dependence among symbols, as commonly exemplified by the…
Let $X_1,X_2,..., X_n,...$ be a stochastic process with independent values whose distribution $P_\theta$ depends on an unknown parameter $\theta$, $\theta\in\Theta$, where $\Theta$ is an open subset of the real line. The problem of testing…
We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the…
We are concerned with semilinear parabolic equations, with a time-dependent source term of the form $h(t)u^q$ with $q>1$, posed on an infinite graph. We assume that the bottom of the $L^2$-spectrum of the Laplacian on the graph, denoted by…
We propose a nonparametric test of spatial independence for data observed on irregular, non-lattice point clouds $\mathcal{V}_{n}\subset\mathbb{R}^{2}$. For each location $v\in\mathcal{V}_{n}$, we encode the local spatial configuration…
Noiseless coding theorem for finite stationary memoryless information sources is proved by using induction on the number of source symbols and the inequality of geometric and harmonic means.
Many empirical time series are genuinely symbolic: examples range from link activation patterns in network science, DNA coding or firing patterns in neuroscience to cryptography or combinatorics on words. In some other contexts, the…
The problem of prediction consists in forecasting the conditional distribution of the next outcome given the past. Assume that the source generating the data is such that there is a stationary ergodic predictor whose error converges to zero…
In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
We propose a novel statistical test to assess the mutual independence of multidimensional random vectors. Our approach is based on the $L_1$-distance between the joint density function and the product of the marginal densities associated…
For each uniformity $k \geq 3$, we construct $k$-uniform linear hypergraphs $G$ with arbitrarily large maximum degree $\Delta$ whose independence polynomial $Z_G$ has a root $\lambda$ with $\lvert\lambda\rvert = O\left(\frac{\log…
Identifying patterns of relations among the units of a complex system from measurements of their activities in time is a fundamental problem with many practical applications. Here, we introduce a method that detects dependencies of any…
We describe a family of conservative statistical tests for independence of two autocorrelated time series. The series may take values in any sets, and one of them must be stationary. A user-specified function quantifying the association of…