Related papers: Probability models characterized by generalized re…
Negative probabilities have long been discussed in connection with the foundations of quantum mechanics. We have recently shown that, if signed measures are allowed on the hidden variables, the class of probability models which can be…
The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…
Statistical and machine learning theory has developed several conditions ensuring that popular estimators such as the Lasso or the Dantzig selector perform well in high-dimensional sparse regression, including the restricted eigenvalue,…
Modeling worlds and actions under uncertainty is one of the central problems in the framework of decision-theoretic planning. The representation must be general enough to capture real-world problems but at the same time it must provide a…
Generalized linear models, such as logistic regression, are widely used to model the association between a treatment and a binary outcome as a function of baseline covariates. However, the coefficients of a logistic regression model…
We give an implementation of a statistical model, which can be successfully applied for compressing of a sequence of binary digits with behavior close to random.
Standard probabilistic models face fundamental challenges such as data scarcity, a large hypothesis space, and poor data transparency. To address these challenges, we propose a novel probabilistic model of data-driven temporal propositional…
In representation theory, the double centraliser property is an important property for a module (bimodule). It plays a fundamental role in many theories. In this paper, we extend this property to complexes in derived categories of finite…
The task of the binary classification problem is to determine which of two distributions has generated a length-$n$ test sequence. The two distributions are unknown; two training sequences of length $N$, one from each distribution, are…
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
In this paper, we introduce a class of generalized tracial approximation ${\rm C^*}$-algebras. Let $\mathcal{P}$ be a class of unital ${\rm C^*}$-algebras which have tracially $\mathcal{Z}$-absorbing (tracial nuclear dimension at most $n$,…
Real-world problems, often couched as machine learning applications, involve quantities of interest that have real-world meaning, independent of any statistical model. To avoid potential model misspecification bias or over-complicating the…
We give several applications of a recent theorem of the second author, which solved a conjecture of the first author with Hay and Neal, concerning contractive approximate identities; and another of Hay from the theory of noncommutative peak…
Power priors are used for incorporating historical data in Bayesian analyses by taking the likelihood of the historical data raised to the power $\alpha$ as the prior distribution for the model parameters. The power parameter $\alpha$ is…
In reverse mathematics, is is possible to have a curious situation where we know that an implication does not reverse, but appear to have no information on on how to weaken the assumption while preserving the conclusion. A main cause of…
In this paper, we introduce some classes of generalized tracial approximation ${\rm C^*}$-algebras. Consider the class of unital ${\rm C^*}$-algebras which are tracially $\mathcal{Z}$-absorbing (or have tracial nuclear dimension at most…
Model memorization has implications for both the generalization capacity of machine learning models and the privacy of their training data. This paper investigates label memorization in binary classification models through two novel passive…
In this article,a three parameter generalisation of inverse lindley distribution is obtained, with the purpose of obtaining a more flexible model relative to the behaviour of hazard rate functions. Various statistical properties such as…
We study the problem of modeling a binary operation that satisfies some algebraic requirements. We first construct a neural network architecture for Abelian group operations and derive a universal approximation property. Then, we extend it…
Forgetting - or variable elimination - is an operation that allows the removal, from a knowledge base, of middle variables no longer deemed relevant. In recent years, many different approaches for forgetting in Answer Set Programming have…