Related papers: Statistical complexity as a criterion for the usef…
Although numerous algorithms have been proposed to solve the categorical data clustering problem, how to access the statistical significance of a set of categorical clusters remains unaddressed. To fulfill this void, we employ the…
Machine-learning techniques have become fundamental in high-energy physics and, for new physics searches, it is crucial to know their performance in terms of experimental sensitivity, understood as the statistical significance of the…
This paper introduces a Bayesian framework to detect multiple signals embedded in noisy observations from a sensor array. For various states of knowledge on the communication channel and the noise at the receiving sensors, a marginalization…
It is shown that a well-known theory of random stationary processes contain contradictions. Integral representations of correlation functions and random stationary processes are investigated further. The new method of struggle with…
The development of modern information technologies permits to collect and to analyze huge amounts of statistical data in different spheres of life. The main problem is not to only to collect but to process all relevant information. The…
The independence clustering problem is considered in the following formulation: given a set $S$ of random variables, it is required to find the finest partitioning $\{U_1,\dots,U_k\}$ of $S$ into clusters such that the clusters…
In this paper, multiplexing of discrete chaotic signals in the presence of noise is investigated. Existing methods are based on chaotic synchronization which is susceptible to noise and parameter mismatch. Furthermore, these methods fail…
In a bivariate setting, we consider the problem of detecting a sparse contamination or mixture component, where the effect manifests itself as a positive dependence between the variables, which are otherwise independent in the main…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
We propose an approach to rapidly find the upper limit of separability between datasets that is directly applicable to HEP classification problems. The most common HEP classification task is to use $n$ values (variables) for an object…
In this work a robust clustering algorithm for stationary time series is proposed. The algorithm is based on the use of estimated spectral densities, which are considered as functional data, as the basic characteristic of stationary time…
We consider the quickest change detection problem where both the parameters of pre- and post- change distributions are unknown, which prevents the use of classical simple hypothesis testing. Without additional assumptions, optimal solutions…
Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…
A common problem in data analysis is that the functional form, as well as the parameter values, of the underlying model which should describe a dataset is not known a priori. In these cases some extra uncertainty must be assigned to the…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
Identifying the number $K$ of clusters in a dataset is one of the most difficult problems in clustering analysis. A choice of $K$ that correctly characterizes the features of the data is essential for building meaningful clusters. In this…
In many modern statistical problems, the limited available data must be used both to develop the hypotheses to test, and to test these hypotheses-that is, both for exploratory and confirmatory data analysis. Reusing the same dataset for…
Feature selection is an important but challenging task in causal inference for obtaining unbiased estimates of causal quantities. Properly selected features in causal inference not only significantly reduce the time required to implement a…
This work proposes a new loss function targeting classification problems, utilizing a source of information overlooked by cross entropy loss. First, we derive a series of the tightest upper and lower bounds for the probability of a random…
Finding the most probable explanation for observed variables in a Bayesian network is a notoriously intractable problem, particularly if there are hidden variables in the network. In this paper we examine the complexity of a related…