Matteo Sesia

Bat-Sheva Einbinder, Yaniv Romano, Matteo Sesia et al.

Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be overconfident. We begin to address this problem in the context of multi-class classification by developing a novel training algorithm producing models with more dependable uncertainty estimates, without sacrificing predictive power. The idea is to mitigate overconfidence by minimizing a loss function, inspired by advances in conformal inference, that quantifies model uncertainty by carefully leveraging hold-out data. Experiments with synthetic and real data demonstrate this method can lead to smaller conformal prediction sets with higher conditional coverage, after exact calibration with hold-out data, compared to state-of-the-art alternatives.

Meshi Bashari, Amir Epstein, Yaniv Romano et al.

Conformal inference provides a general distribution-free method to rigorously calibrate the output of any machine learning algorithm for novelty detection. While this approach has many strengths, it has the limitation of being randomized, in the sense that it may lead to different results when analyzing twice the same data, and this can hinder the interpretation of any findings. We propose to make conformal inferences more stable by leveraging suitable conformal e-values instead of p-values to quantify statistical significance. This solution allows the evidence gathered from multiple analyses of the same data to be aggregated effectively while provably controlling the false discovery rate. Further, we show that the proposed method can reduce randomness without much loss of power compared to standard conformal inference, 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.

Ziyi Liang, Matteo Sesia, Wenguang Sun

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.

Nitai Fingerhut, Matteo Sesia, Yaniv Romano

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.

Matteo Sesia, Y. X. Rachel Wang, Xin Tong

This paper develops novel conformal prediction methods for classification tasks that can automatically adapt to random label contamination in the calibration sample, leading to more informative prediction sets with stronger coverage guarantees compared to state-of-the-art approaches. This is made possible by a precise 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 of the underlying data distribution or of 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.

Ziyi Liang, Yanfei Zhou, Matteo Sesia

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.

Xinmeng Huang, Shuo Li, Mengxin Yu et al.

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.

Yanfei Zhou, Lars Lindemann, Matteo Sesia

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.

Yiqi Zhao, Xinyi Yu, Matteo Sesia et al.

We propose conformal predictive programming (CPP), a framework to solve chance constrained optimization problems, i.e., optimization problems with constraints that are functions of random variables. CPP utilizes samples from these random variables along with the quantile lemma - central to conformal prediction - to transform the chance constrained optimization problem into a deterministic problem with a quantile reformulation. CPP inherits a priori guarantees on constraint satisfaction from existing sample average approximation approaches for a class of chance constrained optimization problems, and it provides a posteriori guarantees that are of conditional and marginal nature otherwise. The strength of CPP is that it can easily support different variants of conformal prediction which have been (or will be) proposed within the conformal prediction community. To illustrate this, we present robust CPP to deal with distribution shifts in the random variables and Mondrian CPP to deal with class conditional chance constraints. To enable tractable solutions to the quantile reformulation, we present a mixed integer programming method (CPP-MIP) encoding, a bilevel optimization strategy (CPP-Bilevel), and a sampling-and-discarding optimization strategy (CPP-Discarding). We also extend CPP to deal with joint chance constrained optimization (JCCO). In a series of case studies, we show the validity of the aforementioned approaches, empirically compare CPP-MIP, CPP-Bilevel, as well as CPP-Discarding, and illustrate the advantage of CPP as compared to scenario approach.

Matteo Sesia, Vladimir Svetnik

We present a conformal inference method for constructing lower prediction bounds for survival times from right-censored data, extending recent approaches designed for more restrictive type-I censoring scenarios. The proposed method imputes unobserved censoring times using a machine learning model, and then analyzes the imputed data using a survival model calibrated via weighted conformal inference. This approach is theoretically supported by an asymptotic double robustness property. Empirical studies on simulated and real data demonstrate that our method leads to relatively informative predictive inferences and is especially robust in challenging settings where the survival model may be inaccurate.

Yanfei Zhou, Matteo Sesia

This paper introduces a conformal inference method to evaluate uncertainty in classification by generating prediction sets with valid coverage conditional on adaptively chosen features. These features are carefully selected to reflect potential model limitations or biases. This can be useful to find a practical compromise between efficiency -- by providing informative predictions -- and algorithmic fairness -- by ensuring equalized coverage for the most sensitive groups. We demonstrate the validity and effectiveness of this method on simulated and real data sets.

Meshi Bashari, Matteo Sesia, Yaniv Romano

Conformal prediction is a flexible framework for calibrating machine learning predictions, providing distribution-free statistical guarantees. In outlier detection, this calibration relies on a reference set of labeled inlier data to control the type-I error rate. However, obtaining a perfectly labeled inlier reference set is often unrealistic, and a more practical scenario involves access to a contaminated reference set containing a small fraction of outliers. This paper analyzes the impact of such contamination on the validity of conformal methods. We prove that under realistic, non-adversarial settings, calibration on contaminated data yields conservative type-I error control, shedding light on the inherent robustness of conformal methods. This conservativeness, however, typically results in a loss of power. To alleviate this limitation, we propose a novel, active data-cleaning framework that leverages a limited labeling budget and an outlier detection model to selectively annotate data points in the contaminated reference set that are suspected as outliers. By removing only the annotated outliers in this ``suspicious'' subset, we can effectively enhance power while mitigating the risk of inflating the type-I error rate, as supported by our theoretical analysis. Experiments on real datasets validate the conservative behavior of conformal methods under contamination and show that the proposed data-cleaning strategy improves power without sacrificing validity.

Teresa Bortolotti, Y. X. Rachel Wang, Xin Tong et al.

Conformal inference provides a rigorous statistical framework for uncertainty quantification in machine learning, enabling well-calibrated prediction sets with precise coverage guarantees for any classification model. However, its reliance on the idealized assumption of perfect data exchangeability limits its effectiveness in the presence of real-world complications, such as low-quality labels -- a widespread issue in modern large-scale data sets. This work tackles this open problem by introducing an adaptive conformal inference method capable of efficiently handling deviations from exchangeability caused by random label noise, leading to informative prediction sets with tight marginal coverage guarantees even in those challenging scenarios. We validate our method through extensive numerical experiments demonstrating its effectiveness on synthetic and real data sets, including CIFAR-10H and BigEarthNet.

Tianmin Xie, Yanfei Zhou, Ziyi Liang et al.

This paper presents a conformal prediction method for classification in highly imbalanced and open-set settings, where there are many possible classes and not all may be represented in the data. Existing approaches require a finite, known label space and typically involve random sample splitting, which works well when there is a sufficient number of observations from each class. Consequently, they have two limitations: (i) they fail to provide adequate coverage when encountering new labels at test time, and (ii) they may become overly conservative when predicting previously seen labels. To obtain valid prediction sets in the presence of unseen labels, we compute and integrate into our predictions a new family of conformal p-values that can test whether a new data point belongs to a previously unseen class. We study these p-values theoretically, establishing their optimality, and uncover an intriguing connection with the classical Good--Turing estimator for the probability of observing a new species. To make more efficient use of imbalanced data, we also develop a selective sample splitting algorithm that partitions training and calibration data based on label frequency, leading to more informative predictions. Despite breaking exchangeability, this allows maintaining finite-sample guarantees through suitable re-weighting. With both simulated and real data, we demonstrate our method leads to prediction sets with valid coverage even in challenging open-set scenarios with infinite numbers of possible labels, and produces more informative predictions under extreme class imbalance.

Matteo Sesia, Yaniv Romano

This paper develops a conformal method to compute prediction intervals for non-parametric regression that can automatically adapt to skewed data. Leveraging black-box machine learning algorithms to estimate the conditional distribution of the outcome using histograms, it translates their output into the shortest prediction intervals with approximate conditional coverage. The resulting prediction intervals provably have marginal coverage in finite samples, while asymptotically achieving conditional coverage and optimal length if the black-box model is consistent. Numerical experiments with simulated and real data demonstrate improved performance compared to state-of-the-art alternatives, including conformalized quantile regression and other distributional conformal prediction approaches.

Stephen Bates, Emmanuel Candès, Lihua Lei et al.

This paper studies the construction of p-values for nonparametric outlier detection, taking a multiple-testing perspective. The goal is to test whether new independent samples belong to the same distribution as a reference data set or are outliers. We propose a solution based on conformal inference, a broadly applicable framework which yields p-values that are marginally valid but mutually dependent for different test points. We prove these p-values are positively dependent and enable exact false discovery rate control, although in a relatively weak marginal sense. We then introduce a new method to compute p-values that are both valid conditionally on the training data and independent of each other for different test points; this paves the way to stronger type-I error guarantees. Our results depart from classical conformal inference as we leverage concentration inequalities rather than combinatorial arguments to establish our finite-sample guarantees. Furthermore, our techniques also yield a uniform confidence bound for the false positive rate of any outlier detection algorithm, as a function of the threshold applied to its raw statistics. Finally, the relevance of our results is demonstrated by numerical experiments on real and simulated data.

Charmaine Chia, Matteo Sesia, Chi-Sing Ho et al.

Deep neural networks and other sophisticated machine learning models are widely applied to biomedical signal data because they can detect complex patterns and compute accurate predictions. However, the difficulty of interpreting such models is a limitation, especially for applications involving high-stakes decision, including the identification of bacterial infections. In this paper, we consider fast Raman spectroscopy data and demonstrate that a logistic regression model with carefully selected features achieves accuracy comparable to that of neural networks, while being much simpler and more transparent. Our analysis leverages wavelet features with intuitive chemical interpretations, and performs controlled variable selection with knockoffs to ensure the predictors are relevant and non-redundant. Although we focus on a particular data set, the proposed approach is broadly applicable to other types of signal data for which interpretability may be important.

Yaniv Romano, Matteo Sesia, Emmanuel J. Candès

Conformal inference, cross-validation+, and the jackknife+ are hold-out methods that can be combined with virtually any machine learning algorithm to construct prediction sets with guaranteed marginal coverage. In this paper, we develop specialized versions of these techniques for categorical and unordered response labels that, in addition to providing marginal coverage, are also fully adaptive to complex data distributions, in the sense that they perform favorably in terms of approximate conditional coverage compared to alternative methods. The heart of our contribution is a novel conformity score, which we explicitly demonstrate to be powerful and intuitive for classification problems, but whose underlying principle is potentially far more general. Experiments on synthetic and real data demonstrate the practical value of our theoretical guarantees, as well as the statistical advantages of the proposed methods over the existing alternatives.

Matteo Sesia, Emmanuel J. Candès

We compare two recently proposed methods that combine ideas from conformal inference and quantile regression to produce locally adaptive and marginally valid prediction intervals under sample exchangeability (Romano et al., 2019; Kivaranovic et al., 2019). First, we prove that these two approaches are asymptotically efficient in large samples, under some additional assumptions. Then we compare them empirically on simulated and real data. Our results demonstrate that the method in Romano et al. (2019) typically yields tighter prediction intervals in finite samples. Finally, we discuss how to tune these procedures by fixing the relative proportions of observations used for training and conformalization.

Yaniv Romano, Matteo Sesia, Emmanuel J. Candès

This paper introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion measuring the validity of the produced knockoffs is optimized; this criterion is inspired by the popular maximum mean discrepancy in machine learning and can be thought of as measuring the distance to pairwise exchangeability between original and knockoff features. By building upon the existing model-X framework, we thus obtain a flexible and model-free statistical tool to perform controlled variable selection. Extensive numerical experiments and quantitative tests confirm the generality, effectiveness, and power of our deep knockoff machines. Finally, we apply this new method to a real study of mutations linked to changes in drug resistance in the human immunodeficiency virus.