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Time series forecasting is an important application in various domains such as energy management, traffic planning, financial markets, meteorology, and medicine. However, real-time series data often present intricate temporal variability…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
Hierarchical forecasting is a key problem in many practical multivariate forecasting applications - the goal is to simultaneously predict a large number of correlated time series that are arranged in a pre-specified aggregation hierarchy.…
Conformal prediction is a statistically rigorous method for quantifying uncertainty in models by having them output sets of predictions, with larger sets indicating more uncertainty. However, prediction sets are not inherently actionable;…
Conventional time-series forecasting methods typically aim to minimize overall prediction error, without accounting for the varying importance of different forecast ranges in downstream applications. We propose a training methodology that…
Functional time series have become an integral part of both functional data and time series analysis. Important contributions to methodology, theory and application for the prediction of future trajectories and the estimation of functional…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…
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…
Time series forecasting using historical data has been an interesting and challenging topic, especially when the data is corrupted by missing values. In many industrial problem, it is important to learn the inference function between the…
Distribution-free prediction sets play a pivotal role in uncertainty quantification for complex statistical models. Their validity hinges on reliable calibration data, which may not be readily available as real-world environments often…
This article develops flexible methodology to study the association between scalar outcomes and functional predictors observed over time, at many instances, in longitudinal studies. We propose a parsimonious modeling framework to study…
The zero-shot capabilities of foundation models (FMs) for time series forecasting offer promising potentials in conformal prediction, as most of the available data can be allocated to calibration. This study compares the performance of Time…
Conformal Prediction provides distribution-free prediction intervals with guaranteed coverage, but its reliance on a single global calibration threshold obscures the sources of uncertainty at the instance level. In particular, it conflates…
Operational forecasting centers are investing in decadal (1-10 year) forecast systems to support long-term decision making for a more climate-resilient society. One method that has previously been employed is the Dynamic Mode Decomposition…
Several uncertainty estimation methods have been recently proposed for machine translation evaluation. While these methods can provide a useful indication of when not to trust model predictions, we show in this paper that the majority of…
We introduce Longitudinal Predictive Conformal Inference (LPCI), a novel distribution-free conformal prediction algorithm for longitudinal data. Current conformal prediction approaches for time series data predominantly focus on the…
Conformal prediction, which makes no distributional assumptions about the data, has emerged as a powerful and reliable approach to uncertainty quantification in practical applications. The nonconformity measure used in conformal prediction…
Conformal predictive systems are sets of predictive distributions with theoretical out-of-sample calibration guarantees. The calibration guarantees are typically that the set of predictions contains a forecast distribution whose prediction…