Related papers: Linearity of Data and Linear Probability Space
The lifetimes of subjects which are left-censored lie below a threshold value or a limit of detection. A popular tool used to handle left-censored data is the reversed hazard rate. In this work, we study the properties and develop…
A statistical estimation algorithm of the weight distribution of a linear code is shown, based on using its generator matrix as a compression function on random bit strings.
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
In this paper, I present a completely new type of upper and lower bounds on the right-tail probabilities of continuous random variables with unbounded support and with semi-bounded support from the left. The presented upper and lower…
We derive boundary conditions and estimates based on the energy and entropy analysis of systems of the nonlinear shallow water equations in two spatial dimensions. It is shown that the energy method provides more details, but is fully…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…
The aim of this paper is to show that the concept of probability is best understood by dividing this concept into two different types of probability, namely physical probability and analogical probability. Loosely speaking, a physical…
The analysis of datasets taking the form of simple, undirected graphs continues to gain in importance across a variety of disciplines. Two choices of null model, the logistic-linear model and the implicit log-linear model, have come into…
Initially introduced by Peter Hammer, Logical Analysis of Data is a methodology that aims at computing a logical justification for dividing a group of data in two groups of observations, usually called the positive and negative groups.…
Classification of datasets into two or more distinct classes is an important machine learning task. Many methods are able to classify binary classification tasks with a very high accuracy on test data, but cannot provide any easily…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
An open stochastic system \`a la Jan Willems is a system affected by two qualitatively different kinds of uncertainty: one is probabilistic fluctuation, and the other one is nondeterminism caused by a fundamental lack of information. We…
Many common loss functions such as mean-squared-error, cross-entropy, and reconstruction loss are unnecessarily rigid. Under a probabilistic interpretation, these common losses correspond to distributions with fixed shapes and scales. We…
For any fixed integer $R \geq 2$ we characterise the typical structure of undirected graphs with vertices $1, ..., n$ and maximum degree $R$, as $n$ tends to infinity. The information is used to prove that such graphs satisfy a labelled…
In many data analyses, each measurement may come with a simple yes/no correction; for example, belonging to one of two populations or being contaminated or not. Ignoring such binary effects may bias the results, while accounting for them…
This article shows that any type of binary data can be defined as a collection from codewords of variable length. This feature helps us to define an Injective and surjective function from the suggested codewords to the required codewords.…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
The incorporation of unlabeled data in regression and classification analysis is an increasing focus of the applied statistics and machine learning literatures, with a number of recent examples demonstrating the potential for unlabeled data…
Linear discriminant analysis (LDA) is an important classification tool in statistics and machine learning. This paper investigates the varying coefficient LDA model for dynamic data, with Bayes' discriminant direction being a function of…
When the outcome of interest is semicontinuous and collected longitudinally, efficient testing can be difficult. Daily rainfall data is an excellent example which we use to illustrate the various challenges. Even under the simplest…