Related papers: Sequential inductive prediction intervals
The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all…
We develop the concept of exponential stochastic inequality (ESI), a novel notation that simultaneously captures high-probability and in-expectation statements. It is especially well suited to succinctly state, prove, and reason about…
PAC-Bayes bounds have been proposed to get risk estimates based on a training sample. In this paper the PAC-Bayes approach is combined with stability of the hypothesis learned by a Hilbert space valued algorithm. The PAC-Bayes setting is…
We present a novel and easy-to-use method for calibrating error-rate based confidence intervals to evidence-based support intervals. Support intervals are obtained from inverting Bayes factors based on a parameter estimate and its standard…
In an attempt to provide an answer to the increasing criticism against p-values and to bridge the gap between statistical inference and prediction modelling, we introduce the probability of improved prediction (PIP). In general, the PIP is…
The sequential analysis of series often requires nonparametric procedures, where the most powerful ones frequently use rank transformations. Re-ranking the data sequence after each new observation can become too intensive computationally.…
The present paper is about estimation and prediction in high-dimensional additive models under a sparsity assumption ($p\gg n$ paradigm). A PAC-Bayesian strategy is investigated, delivering oracle inequalities in probability. The…
Conformal predictors are machine learning algorithms that output prediction sets that have a guarantee of marginal validity for finite samples with minimal distributional assumptions. This is a property that makes conformal predictors…
A reliable representation of uncertainty is essential for the application of modern machine learning methods in safety-critical settings. In this regard, the use of credal sets (i.e., convex sets of probability distributions) has recently…
We present new estimators for the statistical analysis of the dependence of the mean gap time length between consecutive recurrent events, on a set of explanatory random variables and in the presence of right censoring. The dependence is…
We introduce a method which enables a recurrent dynamics model to be temporally abstract. Our approach, which we call Adaptive Skip Intervals (ASI), is based on the observation that in many sequential prediction tasks, the exact time at…
Prediction models are used amongst others to inform medical decisions on interventions. Typically, individuals with high risks of adverse outcomes are advised to undergo an intervention while those at low risk are advised to refrain from…
Existing conformal prediction algorithms estimate prediction intervals at target confidence levels to characterize the performance of a regression model on new test samples. However, considering an autonomous system consisting of multiple…
We construct long-term prediction intervals for time-aggregated future values of univariate economic time series. We propose computational adjustments of the existing methods to improve coverage probability under a small sample constraint.…
Widely used methods and software for group sequential tests of a null hypothesis of no treatment difference that allow for early stopping of a clinical trial depend primarily on the fact that sequentially-computed test statistics have the…
Probabilistic programming is the idea of writing models from statistics and machine learning using program notations and reasoning about these models using generic inference engines. Recently its combination with deep learning has been…
In this paper we present a novel model checking approach to finite-time safety verification of black-box continuous-time dynamical systems within the framework of probably approximately correct (PAC) learning. The black-box dynamical…
We develop a general framework for constructing distribution-free prediction intervals for time series. Theoretically, we establish explicit bounds on conditional and marginal coverage gaps of estimated prediction intervals, which…
This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…