Related papers: A Note on Absolutely Continuous Processes
Conformal prediction is a framework for uncertainty quantification that constructs prediction sets for previously unseen data, guaranteeing coverage of the true label with a specified probability. However, the efficiency of these prediction…
Process Outcome Prediction entails predicting a discrete property of an unfinished process instance from its partial trace. High-capacity outcome predictors discovered with ensemble and deep learning methods have been shown to achieve top…
We examine the feasibility of predicting and subsequently managing the future evolution of a Complex Adaptive System. Our archetypal system mimics a competitive population of mechanical, biological, informational or human objects. We show…
Almost every biological, economic and social system is a complex adaptive system (CAS). Mathematical and computer models are relevant to CAS. Some approaches to modeling CAS are given. Applications in vaccination and the immune system are…
This paper develops some extensions to the work of [1] which studied the continuous-time adaptive output tracking control schemes with the reference output signal generated from an unknown reference model system. The presented extensions…
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
Conformal prediction is a general method that converts almost any point predictor to a prediction set. The resulting set keeps good statistical properties of the original estimator under standard assumptions, and guarantees valid average…
In this paper, we study the purely discontinuous Girsanov transforms which were discussed in Chen and Song \cite{CS2} and Song \cite{S3}. We show that the transition density of any purely discontinuous Girsanov transform of a…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step towards extracting essential physical knowledge from complex systems, by addressing the challenging…
In many practical settings one can sequentially and adaptively guide the collection of future data, based on information extracted from data collected previously. These sequential data collection procedures are known by different names,…
A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…
Conformal prediction is a model-agnostic approach to generating prediction sets that cover the true class with a high probability. Although its prediction set size is expected to capture aleatoric uncertainty, there is a lack of evidence…
We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory…
In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by…
Continuous adaptation to variable environments is crucial for the survival of living organisms. Here, we analyze how adaptation, forecasting, and resource mobilization towards a target state, termed actionability, interact to determine…
Conformal Inference (CI) is a popular approach for generating finite sample prediction intervals based on the output of any point prediction method when data are exchangeable. Adaptive Conformal Inference (ACI) algorithms extend CI to the…
The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that…
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…