Related papers: Conformal Predictions under Markovian Data
Conformal Prediction (CP) has emerged as a powerful statistical framework for high-stakes classification applications. Instead of predicting a single class, CP generates a prediction set, guaranteed to include the true label with a…
We show that the two-stage minimum description length (MDL) criterion widely used to estimate linear change-point (CP) models corresponds to the marginal likelihood of a Bayesian model with a specific class of prior distributions. This…
Estimating the reliability of individual predictions is key to increase the adoption of computational models and artificial intelligence in preclinical drug discovery, as well as to foster its application to guide decision making in…
I show how to run an N-time-step Markov chain simulation in a circular fashion, so that the state at time 0 follows the state at time N-1 in the same way as states at times t follow those at times t-1 for 0<t<N. This wrap-around of the…
We propose a multi-scale extension of conformal prediction, an approach that constructs prediction sets with finite-sample coverage guarantees under minimal statistical assumptions. Classic conformal prediction relies on a single notion of…
Conformal prediction (CP) generates a set of predictions for a given test sample such that the prediction set almost always contains the true label (e.g., 99.5\% of the time). CP provides comprehensive predictions on possible labels of a…
Digital Twins (DTs) for Water Distribution Networks (WDNs) require accurate state estimation with limited sensors. Uniform sampling often wastes resources across nodes with different uncertainty. We propose an adaptive framework combining…
The reliable deployment of deep learning in medical imaging requires uncertainty quantification that provides rigorous error guarantees while remaining anatomically meaningful. Conformal prediction (CP) is a powerful distribution-free…
Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…
The detection of change-points in heterogeneous sequences is a statistical challenge with applications across a wide variety of fields. In bioinformatics, a vast amount of methodology exists to identify an ideal set of change-points for…
We investigate the complexity of covariance matrix estimation for Gibbs distributions based on dependent samples from a Markov chain. We show that when $\pi$ satisfies a Poincar\'e inequality and the chain possesses a spectral gap, we can…
While split conformal prediction guarantees marginal coverage, approaching the stronger property of conditional coverage is essential for reliable uncertainty quantification. Naive conformal scores, however, suffer from poor conditional…
This paper is concerned with elucidating a relationship between two common coupling methods for the continuous time Markov chain models utilized in the cell biology literature. The couplings considered here are primarily used in a…
Conformal prediction (CP) produces prediction regions with finite-sample, distribution free coverage guarantees, but its interpretation as a quantitative uncertainty tool is often left implicit. We develop a category-theoretic approach that…
Sampling from complex target distributions is a challenging task fundamental to Bayesian inference. Parallel tempering (PT) addresses this problem by constructing a Markov chain on the expanded state space of a sequence of distributions…
This review paper provides an introduction of Markov chains and their convergence rates which is an important and interesting mathematical topic which also has important applications for very widely used Markov chain Monte Carlo (MCMC)…
Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…
We study linear preconditioning in Markov chain Monte Carlo. We consider the class of well-conditioned distributions, for which several mixing time bounds depend on the condition number $\kappa$. First we show that well-conditioned…
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
Conformal prediction can be used to construct prediction sets that cover the true outcome with a desired probability, but can sometimes lead to large prediction sets that are costly in practice. The most useful outcome is a singleton…