Related papers: Predictive Sets
Let $\mathcal{I}$ be an analytic P-ideal [respectively, a summable ideal] on the positive integers and let $(x_n)$ be a sequence taking values in a metric space $X$. First, it is shown that the set of ideal limit points of $(x_n)$ is an…
In this paper, we study a part of approximation theory that presents the conditions under which a closed set in a normed linear space is proximinal or Chebyshev.
Recent research demonstrate that prediction of time series by predictive recurrent neural networks based on the noisy input generates a smooth anticipated trajectory. We examine influence of the noise component in both the training data…
Conformal Prediction (CP) quantifies network uncertainty by building a small prediction set with a pre-defined probability that the correct class is within this set. In this study we tackle the problem of CP calibration based on a…
This paper addresses the task of set prediction using deep feed-forward neural networks. A set is a collection of elements which is invariant under permutation and the size of a set is not fixed in advance. Many real-world problems, such as…
This two-part paper presents a new approach to predictive analysis for social processes. Part I identifies a class of social processes, called positive externality processes, which are both important and difficult to predict, and introduces…
Conformal prediction is an uncertainty quantification method that constructs a prediction set for a previously unseen datum, ensuring the true label is included with a predetermined coverage probability. Adaptive conformal prediction has…
We study monitorable sets from a topological standpoint. In particular, we use descriptive set theory to describe the complexity of the family of monitorable sets in a countable space $X$. When $X$ is second countable, we observe that the…
We prove that if a Bessel sequence in a Hilbert space, that is indexed by a countably infinite group in an invariant manner, can be partitioned into finitely many Riesz basic sequences, then each of the sets in the partition can be chosen…
A discrete subset $S$ of a topological group $G$ is called a {\it suitable set} for $G$ if $S\cup \{e\}$ is closed in $G$ and the subgroup generated by $S$ is dense in $G$, where $e$ is the identity element of $G$. In this paper, the…
In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not…
A generalization of numeration system in which the set N of the natural numbers is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. Here we show that if P belonging to Q[x]…
Predictions in the form of sets of probability distributions, so-called credal sets, provide a suitable means to represent a learner's epistemic uncertainty. In this paper, we propose a theoretically grounded approach to credal prediction…
Decision support systems based on prediction sets have proven to be effective at helping human experts solve classification tasks. Rather than providing single-label predictions, these systems provide sets of label predictions constructed…
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…
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…
In principle, all the natural systems such as biological, ecological and economical systems are structure-variable systems (in which some environment parameters are not fixed). In this Letter we show that data sequences from many…
We say that $S\subset\mathbb Z$ is a set of $k$-recurrence if for every measure preserving transformation $T$ of a probability measure space $(X,\mu)$ and every $A\subseteq X$ with $\mu(A)>0$, there is an $n\in S$ such that $\mu(A\cap…
A new general procedure for a priori selection of more predictable events from a time series of observed variable is proposed. The procedure is applicable to time series which contains different types of events that feature significantly…
Gaussian processes provide a flexible framework for spatial prediction, but their computational cost limits applicability to large-scale data with large sample size $n$. Predictive processes (PPs), a popular low-rank approximation, mitigate…