Uncertainty in Language Models: Assessment through Rank-Calibration

Language Models (LMs) have shown promising performance in natural language generation. However, as LMs often generate incorrect or hallucinated responses, it is crucial to correctly quantify their uncertainty in responding to given inputs. In addition to verbalized confidence elicited via prompting, many uncertainty measures ($e.g.$, semantic entropy and affinity-graph-based measures) have been proposed. However, these measures can differ greatly, and it is unclear how to compare them, partly because they take values over different ranges ($e.g.$, $[0,\infty)$ or $[0,1]$). In this work, we address this issue by developing a novel and practical framework, termed $Rank$-$Calibration$, to assess uncertainty and confidence measures for LMs. Our key tenet is that higher uncertainty (or lower confidence) should imply lower generation quality, on average. Rank-calibration quantifies deviations from this ideal relationship in a principled manner, without requiring ad hoc binary thresholding of the correctness score ($e.g.$, ROUGE or METEOR). The broad applicability and the granular interpretability of our methods are demonstrated empirically.

Conformalized Adaptive Forecasting of Heterogeneous Trajectories

This paper presents a new conformal method for generating simultaneous forecasting bands guaranteed to cover the entire path of a new random trajectory with sufficiently high probability. Prompted by the need for dependable uncertainty estimates in motion planning applications where the behavior of diverse objects may be more or less unpredictable, we blend different techniques from online conformal prediction of single and multiple time series, as well as ideas for addressing heteroscedasticity in regression. This solution is both principled, providing precise finite-sample guarantees, and effective, often leading to more informative predictions than prior methods.

Frequency and cardinality recovery from sketched data: a novel approach bridging Bayesian and frequentist views

We study how to recover the frequency of a symbol in a large discrete data set, using only a compressed representation, or sketch, of those data obtained via random hashing. This is a classical problem in computer science, with various algorithms available, such as the count-min sketch. However, these algorithms often assume that the data are fixed, leading to overly conservative and potentially inaccurate estimates when dealing with randomly sampled data. In this paper, we consider the sketched data as a random sample from an unknown distribution, and then we introduce novel estimators that improve upon existing approaches. Our method combines Bayesian nonparametric and classical (frequentist) perspectives, addressing their unique limitations to provide a principled and practical solution. Additionally, we extend our method to address the related but distinct problem of cardinality recovery, which consists of estimating the total number of distinct objects in the data set. We validate our method on synthetic and real data, comparing its performance to state-of-the-art alternatives.

Adaptive conformal classification with noisy labels

This paper develops novel conformal prediction methods for classification tasks that can automatically adapt to random label contamination in the calibration sample, enabling more informative prediction sets with stronger coverage guarantees compared to state-of-the-art approaches. This is made possible by a precise theoretical characterization of the effective coverage inflation (or deflation) suffered by standard conformal inferences in the presence of label contamination, which is then made actionable through new calibration algorithms. Our solution is flexible and can leverage different modeling assumptions about the label contamination process, while requiring no knowledge about the data distribution or the inner workings of the machine-learning classifier. The advantages of the proposed methods are demonstrated through extensive simulations and an application to object classification with the CIFAR-10H image data set.

Derandomized Novelty Detection with FDR Control via Conformal E-values

Conformal prediction and other randomized model-free inference techniques are gaining increasing attention as general solutions to rigorously calibrate the output of any machine learning algorithm for novelty detection. This paper contributes to the field by developing a novel method for mitigating their algorithmic randomness, leading to an even more interpretable and reliable framework for powerful novelty detection under false discovery rate control. The idea is to leverage suitable conformal e-values instead of p-values to quantify the significance of each finding, which allows the evidence gathered from multiple mutually dependent analyses of the same data to be seamlessly aggregated. Further, the proposed method can reduce randomness without much loss of power, partly thanks to an innovative way of weighting conformal e-values based on additional side information carefully extracted from the same data. Simulations with synthetic and real data confirm this solution can be effective at eliminating random noise in the inferences obtained with state-of-the-art alternative techniques, sometimes also leading to higher power.

Conformal inference is (almost) free for neural networks trained with early stopping

Early stopping based on hold-out data is a popular regularization technique designed to mitigate overfitting and increase the predictive accuracy of neural networks. Models trained with early stopping often provide relatively accurate predictions, but they generally still lack precise statistical guarantees unless they are further calibrated using independent hold-out data. This paper addresses the above limitation with conformalized early stopping: a novel method that combines early stopping with conformal calibration while efficiently recycling the same hold-out data. This leads to models that are both accurate and able to provide exact predictive inferences without multiple data splits nor overly conservative adjustments. Practical implementations are developed for different learning tasks -- outlier detection, multi-class classification, regression -- and their competitive performance is demonstrated on real data.

Conformal Frequency Estimation with Sketched Data under Relaxed Exchangeability

A flexible method is developed to construct a confidence interval for the frequency of a queried object in a very large data set, based on a much smaller sketch of the data. The approach requires no knowledge of the data distribution or of the details of the sketching algorithm; instead, it constructs provably valid frequentist confidence intervals for random queries using a conformal inference approach. After achieving marginal coverage for random queries under the assumption of data exchangeability, the proposed method is extended to provide stronger inferences accounting for possibly heterogeneous frequencies of different random queries, redundant queries, and distribution shifts. While the presented methods are broadly applicable, this paper focuses on use cases involving the count-min sketch algorithm and a non-linear variation thereof, to facilitate comparison to prior work. In particular, the developed methods are compared empirically to frequentist and Bayesian alternatives, through simulations and experiments with data sets of SARS-CoV-2 DNA sequences and classic English literature.

Bayesian nonparametric estimation of coverage probabilities and distinct counts from sketched data

The estimation of coverage probabilities, and in particular of the missing mass, is a classical statistical problem with applications in numerous scientific fields. In this paper, we study this problem in relation to randomized data compression, or sketching. This is a novel but practically relevant perspective, and it refers to situations in which coverage probabilities must be estimated based on a compressed and imperfect summary, or sketch, of the true data, because neither the full data nor the empirical frequencies of distinct symbols can be observed directly. Our contribution is a Bayesian nonparametric methodology to estimate coverage probabilities from data sketched through random hashing, which also solves the challenging problems of recovering the numbers of distinct counts in the true data and of distinct counts with a specified empirical frequency of interest. The proposed Bayesian estimators are shown to be easily applicable to large-scale analyses in combination with a Dirichlet process prior, although they involve some open computational challenges under the more general Pitman-Yor process prior. The empirical effectiveness of our methodology is demonstrated through numerical experiments and applications to real data sets of Covid DNA sequences, classic English literature, and IP addresses.

Integrative conformal p-values for powerful out-of-distribution testing with labeled outliers

This paper develops novel conformal methods to test whether a new observation was sampled from the same distribution as a reference set. Blending inductive and transductive conformal inference in an innovative way, the described methods can re-weight standard conformal p-values based on dependent side information from known out-of-distribution data in a principled way, and can automatically take advantage of the most powerful model from any collection of one-class and binary classifiers. The solution can be implemented either through sample splitting or via a novel transductive cross-validation+ scheme which may also be useful in other applications of conformal inference, due to tighter guarantees compared to existing cross-validation approaches. After studying false discovery rate control and power within a multiple testing framework with several possible outliers, the proposed solution is shown to outperform standard conformal p-values through simulations as well as applications to image recognition and tabular data.

Coordinated Double Machine Learning

Double machine learning is a statistical method for leveraging complex black-box models to construct approximately unbiased treatment effect estimates given observational data with high-dimensional covariates, under the assumption of a partially linear model. The idea is to first fit on a subset of the samples two non-linear predictive models, one for the continuous outcome of interest and one for the observed treatment, and then to estimate a linear coefficient for the treatment using the remaining samples through a simple orthogonalized regression. While this methodology is flexible and can accommodate arbitrary predictive models, typically trained independently of one another, this paper argues that a carefully coordinated learning algorithm for deep neural networks may reduce the estimation bias. The improved empirical performance of the proposed method is demonstrated through numerical experiments on both simulated and real data.