arXiv subjects

Isaac Gibbs

Publications and source records attributed to Isaac Gibbs.

10 recordsLinked to original sources

arXiv2026

Locally Adaptive Multi-Objective Learning

We consider the general problem of learning a predictor that satisfies multiple objectives of interest simultaneously, a broad framework that captures a range of specific learning goals including calibration, regret, and multiaccuracy. We work in an online setting where the data distribution can change arbitrarily over time. Existing approaches to this problem aim to minimize the set of objectives over the entire time horizon in a worst-case sense, and in practice they do not necessarily adapt to distribution shifts. Earlier work has aimed to alleviate this problem by incorporating additional objectives that target local guarantees over contiguous subintervals. Empirical evaluation of these proposals is, however, scarce. In this article, we consider an alternative procedure that achieves local adaptivity by replacing one part of the multi-objective learning method with an adaptive online algorithm. Empirical evaluations on datasets from energy forecasting and algorithmic fairness show that our proposed method improves upon existing approaches and achieves unbiased predictions over subgroups, while remaining robust under distribution shift.

cs.LG↗

arXiv2025

Calibrated Multi-Level Quantile Forecasting

We develop an online method that guarantees calibration of quantile forecasts at multiple quantile levels simultaneously. In this work, a sequence of quantile forecasts is said to be calibrated provided that its $\alpha$-level predictions are greater than or equal to the target value at an $\alpha$ fraction of time steps, for each level $\alpha$. Our procedure, called the multi-level quantile tracker (MultiQT), is lightweight and wraps around any point or quantile forecaster to produce adjusted quantile forecasts that are guaranteed to be calibrated, even against adversarial distribution shifts. Critically, it does so while ensuring that the quantiles remain ordered, e.g., the 0.5-level quantile forecast will never be larger than the 0.6-level forecast. Moreover, the method has a no-regret guarantee, implying it will not degrade the performance of the existing forecaster (asymptotically), with respect to the quantile loss. In our experiments, we find that MultiQT significantly improves the calibration of real forecasters in epidemic and energy forecasting problems, while leaving the quantile loss largely unchanged or slightly improved.

stat.ML↗

arXiv2025

Correcting the Coverage Bias of Quantile Regression

We develop a collection of methods for adjusting the predictions of quantile regression to ensure coverage. Our methods are model agnostic and can be used to correct for high-dimensional overfitting bias with only minimal assumptions. Theoretical results show that the estimates we develop are consistent and facilitate accurate calibration in the proportional asymptotic regime where the ratio of the dimension of the data and the sample size converges to a constant. This is further confirmed by experiments on both simulated and real data. A key component of our work is a new connection between the leave-one-out coverage and the fitted values of variables appearing in a dual formulation of the quantile regression problem. This facilitates the use of cross-validation in a variety of settings at significantly reduced computational costs.

stat.ME↗

arXiv2025

Sample-Efficient Omniprediction for Proper Losses

We consider the problem of constructing probabilistic predictions that lead to accurate decisions when employed by downstream users to inform actions. For a single decision maker, designing an optimal predictor is equivalent to minimizing a proper loss function corresponding to the negative utility of that individual. For multiple decision makers, our problem can be viewed as a variant of omniprediction in which the goal is to design a single predictor that simultaneously minimizes multiple losses. Existing algorithms for achieving omniprediction broadly fall into two categories: 1) boosting methods that optimize other auxiliary targets such as multicalibration and obtain omniprediction as a corollary, and 2) adversarial two-player game based approaches that estimate and respond to the ``worst-case" loss in an online fashion. We give lower bounds demonstrating that multicalibration is a strictly more difficult problem than omniprediction and thus the former approach must incur suboptimal sample complexity. For the latter approach, we discuss how these ideas can be used to obtain a sample-efficient algorithm through an online-to-batch conversion. This conversion has the downside of returning a complex, randomized predictor. We improve on this method by designing a more direct, unrandomized algorithm that exploits structural elements of the set of proper losses.

cs.LG↗

arXiv2025

Characterizing the Training-Conditional Coverage of Full Conformal Inference in High Dimensions

We study the coverage properties of full conformal regression in the proportional asymptotic regime where the ratio of the dimension and the sample size converges to a constant. In this setting, existing theory tells us only that full conformal inference is unbiased, in the sense that its average coverage lies at the desired level when marginalized over both the new test point and the training data. Considerably less is known about the behaviour of these methods conditional on the training set. As a result, the exact benefits of full conformal inference over much simpler alternative methods is unclear. This paper investigates the behaviour of full conformal inference and natural uncorrected alternatives for a broad class of $L_2$-regularized linear regression models. We show that in the proportional asymptotic regime the training-conditional coverage of full conformal inference concentrates at the target value. On the other hand, simple alternatives that directly compare test and training residuals realize constant undercoverage bias. While these results demonstrate the necessity of full conformal in correcting for high-dimensional overfitting, we also show that this same methodology is redundant for the related task of tuning the regularization level. In particular, we show that full conformal inference still yields asymptotically valid coverage when the regularization level is selected using only the training set, without consideration of the test point. Simulations show that our asymptotic approximations are accurate in finite samples and can be readily extended to other popular full conformal variants, such as full conformal quantile regression and the LASSO, that do not directly meet our assumptions.

math.ST↗

arXiv2024

Large language model validity via enhanced conformal prediction methods

We develop new conformal inference methods for obtaining validity guarantees on the output of large language models (LLMs). Prior work in conformal language modeling identifies a subset of the text that satisfies a high-probability guarantee of correctness. These methods work by filtering claims from the LLM's original response if a scoring function evaluated on the claim fails to exceed a threshold calibrated via split conformal prediction. Existing methods in this area suffer from two deficiencies. First, the guarantee stated is not conditionally valid. The trustworthiness of the filtering step may vary based on the topic of the response. Second, because the scoring function is imperfect, the filtering step can remove many valuable and accurate claims. We address both of these challenges via two new conformal methods. First, we generalize the conditional conformal procedure of Gibbs et al. (2023) in order to adaptively issue weaker guarantees when they are required to preserve the utility of the output. Second, we show how to systematically improve the quality of the scoring function via a novel algorithm for differentiating through the conditional conformal procedure. We demonstrate the efficacy of our approach on biography and medical question-answering datasets.

stat.ML↗

arXiv2023

Conformal Prediction With Conditional Guarantees

We consider the problem of constructing distribution-free prediction sets with finite-sample conditional guarantees. Prior work has shown that it is impossible to provide exact conditional coverage universally in finite samples. Thus, most popular methods only guarantee marginal coverage over the covariates or are restricted to a limited set of conditional targets, e.g. coverage over a finite set of pre-specified subgroups. This paper bridges this gap by defining a spectrum of problems that interpolate between marginal and conditional validity. We motivate these problems by reformulating conditional coverage as coverage over a class of covariate shifts. When the target class of shifts is finite-dimensional, we show how to simultaneously obtain exact finite-sample coverage over all possible shifts. For example, given a collection of subgroups, our prediction sets guarantee coverage over each group. For more flexible, infinite-dimensional classes where exact coverage is impossible, we provide a procedure for quantifying the coverage errors of our algorithm. Moreover, by tuning interpretable hyperparameters, we allow the practitioner to control the size of these errors across shifts of interest. Our methods can be incorporated into existing split conformal inference pipelines, and thus can be used to quantify the uncertainty of modern black-box algorithms without distributional assumptions.

stat.ME↗

arXiv2022

Conformal Inference for Online Prediction with Arbitrary Distribution Shifts

We consider the problem of forming prediction sets in an online setting where the distribution generating the data is allowed to vary over time. Previous approaches to this problem suffer from over-weighting historical data and thus may fail to quickly react to the underlying dynamics. Here we correct this issue and develop a novel procedure with provably small regret over all local time intervals of a given width. We achieve this by modifying the adaptive conformal inference (ACI) algorithm of Gibbs and Cand\`{e}s (2021) to contain an additional step in which the step-size parameter of ACI's gradient descent update is tuned over time. Crucially, this means that unlike ACI, which requires knowledge of the rate of change of the data-generating mechanism, our new procedure is adaptive to both the size and type of the distribution shift. Our methods are highly flexible and can be used in combination with any baseline predictive algorithm that produces point estimates or estimated quantiles of the target without the need for distributional assumptions. We test our techniques on two real-world datasets aimed at predicting stock market volatility and COVID-19 case counts and find that they are robust and adaptive to real-world distribution shifts.

stat.ME↗

arXiv2021

Adaptive Conformal Inference Under Distribution Shift

We develop methods for forming prediction sets in an online setting where the data generating distribution is allowed to vary over time in an unknown fashion. Our framework builds on ideas from conformal inference to provide a general wrapper that can be combined with any black box method that produces point predictions of the unseen label or estimated quantiles of its distribution. While previous conformal inference methods rely on the assumption that the data points are exchangeable, our adaptive approach provably achieves the desired coverage frequency over long-time intervals irrespective of the true data generating process. We accomplish this by modelling the distribution shift as a learning problem in a single parameter whose optimal value is varying over time and must be continuously re-estimated. We test our method, adaptive conformal inference, on two real world datasets and find that its predictions are robust to visible and significant distribution shifts.

stat.ME↗

arXiv2018

Asymptotic Properties of Random Voronoi Cells with Arbitrary Underlying Density

We consider the Voronoi diagram generated by $n$ i.i.d. $\mathbb{R}^{d}$-valued random variables with an arbitrary underlying probability density function $f$ on $\mathbb{R}^{d}$, and analyse the asymptotic behaviours of certain geometric properties, such as the measure, of the Voronoi cells as $n$ tends to infinity. We adapt the methods used by Devroye et al (2017) to conduct a study of the asymptotic properties of two types of Voronoi cells: 1, Voronoi cells that have a fixed nucleus; 2, Voronoi cells that contain a fixed point. For the first type of Voronoi cells, we show that their geometric properties resemble those in the case when the Voronoi diagram is generated by a homogeneous Poisson point process. For the second type of Voronoi cells, we determine the limiting distribution, which is universal in all choices of $f$, of the rescaled measure of the cells. For both types, we establish the asymptotic independence of measures of disjoint cells.

math.PR↗