Related papers: Predictive Sets
Echo-state networks are simple models of discrete dynamical systems driven by a time series. By selecting network parameters such that the dynamics of the network is contractive, characterized by a negative maximal Lyapunov exponent, the…
A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the order-type of the natural numbers -- we call such a linear extension a…
The aim of this article is to employ the Lazy Set algorithm as an example for a mathematical framework for proving the linearizability of distributed systems. The proof in this approach is divided into two stages of lower and higher…
Although a recent shift has been made in the field of predictive process monitoring to use models from the explainable artificial intelligence field, the evaluation still occurs mainly through performance-based metrics, thus not accounting…
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…
We show that if $X$ is an $m$-dimensional definable set in $\mathbb{R}^\text{pow}_\text{an}$, the structure of real subanalytic sets with real power maps added, then for any positive integer r there exists a $C^r$-parameterization of X…
The predictive performance of any inferential model is critical to its practical success, but quantifying predictive performance is a subtle statistical problem. In this paper I show how the natural structure of any inferential problem…
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update…
In the field of machine learning, regression problems are pivotal due to their ability to predict continuous outcomes. Traditional error metrics like mean squared error, mean absolute error, and coefficient of determination measure model…
Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been…
We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of…
A stochastically continuous process $\xi(t)$, $t\geq0$, is said to be time-stable if the sum of $n$ i.i.d. copies of $\xi$ equals in distribution to the time-scaled stochastic process $\xi(nt)$, $t\geq0$. The paper advances the…
Conformal Prediction (CP) controls the prediction uncertainty of classification systems by producing a small prediction set, ensuring a predetermined probability that the true class lies within this set. This is commonly done by defining a…
We investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed…
The paper presents sufficient conditions of predictability for continuous time processes in deterministic setting. We found that processes with exponential decay on energy for higher frequencies are predictable in some weak sense on some…
We describe the norming sets for the space of global holomorphic sections to a $k$-power of a positive holomorphic line bundle on a compact complex manifold $X$. We characterize in metric terms the sequence of measurable subsets…
A set is called recurrent if its minimal automaton is strongly connected and birecurrent if it is recurrent as well as its reversal. We prove a series of results concerning birecurrent sets. It is already known that any birecurrent set is…
We consider prediction theory for stationary stochastic processes in continuous time. We discuss prediction using the whole (infinite) past, and using only a finite section of the past. The solutions to both these classical problems have…
We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can…