Conformal Drug Property Prediction with Density Estimation under Covariate Shift

In drug discovery, it is vital to confirm the predictions of pharmaceutical properties from computational models using costly wet-lab experiments. Hence, obtaining reliable uncertainty estimates is crucial for prioritizing drug molecules for subsequent experimental validation. Conformal Prediction (CP) is a promising tool for creating such prediction sets for molecular properties with a coverage guarantee. However, the exchangeability assumption of CP is often challenged with covariate shift in drug discovery tasks: Most datasets contain limited labeled data, which may not be representative of the vast chemical space from which molecules are drawn. To address this limitation, we propose a method called CoDrug that employs an energy-based model leveraging both training data and unlabelled data, and Kernel Density Estimation (KDE) to assess the densities of a molecule set. The estimated densities are then used to weigh the molecule samples while building prediction sets and rectifying for distribution shift. In extensive experiments involving realistic distribution drifts in various small-molecule drug discovery tasks, we demonstrate the ability of CoDrug to provide valid prediction sets and its utility in addressing the distribution shift arising from de novo drug design models. On average, using CoDrug can reduce the coverage gap by over 35% when compared to conformal prediction sets not adjusted for covariate shift.Comment: Accepted at NeurIPS 202

Bayesian Optimization with Conformal Prediction Sets

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e. objective function queries) with maximal expected utility with respect to the posterior distribution of a Bayesian model, which quantifies reducible, epistemic uncertainty about query outcomes. In practice, subjectively implausible outcomes can occur regularly for two reasons: 1) model misspecification and 2) covariate shift. Conformal prediction is an uncertainty quantification method with coverage guarantees even for misspecified models and a simple mechanism to correct for covariate shift. We propose conformal Bayesian optimization, which directs queries towards regions of search space where the model predictions have guaranteed validity, and investigate its behavior on a suite of black-box optimization tasks and tabular ranking tasks. In many cases we find that query coverage can be significantly improved without harming sample-efficiency.Comment: For code, see https://www.github.com/samuelstanton/conformal-bayesopt.gi

Not all distributional shifts are equal: Fine-grained robust conformal inference

We introduce a fine-grained framework for uncertainty quantification of predictive models under distributional shifts. This framework distinguishes the shift in covariate distributions from that in the conditional relationship between the outcome ($Y$) and the covariates ($X$). We propose to reweight the training samples to adjust for an identifiable covariate shift while protecting against worst-case conditional distribution shift bounded in an $f$-divergence ball. Based on ideas from conformal inference and distributionally robust learning, we present an algorithm that outputs (approximately) valid and efficient prediction intervals in the presence of distributional shifts. As a use case, we apply the framework to sensitivity analysis of individual treatment effects with hidden confounding. The proposed methods are evaluated in simulation studies and three real data applications, demonstrating superior robustness and efficiency compared with existing benchmarks.Comment: 25 pages, 5 figure

Conformal Prediction: a Unified Review of Theory and New Challenges

In this work we provide a review of basic ideas and novel developments about Conformal Prediction -- an innovative distribution-free, non-parametric forecasting method, based on minimal assumptions -- that is able to yield in a very straightforward way predictions sets that are valid in a statistical sense also in in the finite sample case. The in-depth discussion provided in the paper covers the theoretical underpinnings of Conformal Prediction, and then proceeds to list the more advanced developments and adaptations of the original idea.Comment: arXiv admin note: text overlap with arXiv:0706.3188, arXiv:1604.04173, arXiv:1709.06233, arXiv:1203.5422 by other author

Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach

We propose a model-free framework for sensitivity analysis of individual treatment effects (ITEs), building upon ideas from conformal inference. For any unit, our procedure reports the $\Gamma$-value, a number which quantifies the minimum strength of confounding needed to explain away the evidence for ITE. Our approach rests on the reliable predictive inference of counterfactuals and ITEs in situations where the training data is confounded. Under the marginal sensitivity model of Tan (2006), we characterize the shift between the distribution of the observations and that of the counterfactuals. We first develop a general method for predictive inference of test samples from a shifted distribution; we then leverage this to construct covariate-dependent prediction sets for counterfactuals. No matter the value of the shift, these prediction sets (resp. approximately) achieve marginal coverage if the propensity score is known exactly (resp. estimated). We describe a distinct procedure also attaining coverage, however, conditional on the training data. In the latter case, we prove a sharpness result showing that for certain classes of prediction problems, the prediction intervals cannot possibly be tightened. We verify the validity and performance of the new methods via simulation studies and apply them to analyze real datasets

JAWS: Predictive Inference Under Covariate Shift

We propose \textbf{JAWS}, a series of wrapper methods for distribution-free uncertainty quantification tasks under covariate shift, centered on our core method \textbf{JAW}, the \textbf{JA}ckknife+ \textbf{W}eighted with likelihood-ratio weights. JAWS also includes computationally efficient \textbf{A}pproximations of JAW using higher-order influence functions: \textbf{JAWA}. Theoretically, we show that JAW relaxes the jackknife+'s assumption of data exchangeability to achieve the same finite-sample coverage guarantee even under covariate shift. JAWA further approaches the JAW guarantee in the limit of either the sample size or the influence function order under mild assumptions. Moreover, we propose a general approach to repurposing any distribution-free uncertainty quantification method and its guarantees to the task of risk assessment: a task that generates the estimated probability that the true label lies within a user-specified interval. We then propose \textbf{JAW-R} and \textbf{JAWA-R} as the repurposed versions of proposed methods for \textbf{R}isk assessment. Practically, JAWS outperform the state-of-the-art predictive inference baselines in a variety of biased real world data sets for both interval-generation and risk-assessment auditing tasks

Group-Weighted Conformal Prediction

Conformal prediction (CP) is a method for constructing a prediction interval around the output of a fitted model, whose validity does not rely on the model being correct--the CP interval offers a coverage guarantee that is distribution-free, but relies on the training data being drawn from the same distribution as the test data. A recent variant, weighted conformal prediction (WCP), reweights the method to allow for covariate shift between the training and test distributions. However, WCP requires knowledge of the nature of the covariate shift-specifically,the likelihood ratio between the test and training covariate distributions. In practice, since this likelihood ratio is estimated rather than known exactly, the coverage guarantee may degrade due to the estimation error. In this paper, we consider a special scenario where observations belong to a finite number of groups, and these groups determine the covariate shift between the training and test distributions-for instance, this may arise if the training set is collected via stratified sampling. Our results demonstrate that in this special case, the predictive coverage guarantees of WCP can be drastically improved beyond the bounds given by existing estimation error bounds

Test-time Recalibration of Conformal Predictors Under Distribution Shift Based on Unlabeled Examples

Modern image classifiers achieve high predictive accuracy, but the predictions typically come without reliable uncertainty estimates. Conformal prediction algorithms provide uncertainty estimates by predicting a set of classes based on the probability estimates of the classifier (for example, the softmax scores). To provide such sets, conformal prediction algorithms often rely on estimating a cutoff threshold for the probability estimates, and this threshold is chosen based on a calibration set. Conformal prediction methods guarantee reliability only when the calibration set is from the same distribution as the test set. Therefore, the methods need to be recalibrated for new distributions. However, in practice, labeled data from new distributions is rarely available, making calibration infeasible. In this work, we consider the problem of predicting the cutoff threshold for a new distribution based on unlabeled examples only. While it is impossible in general to guarantee reliability when calibrating based on unlabeled examples, we show that our method provides excellent uncertainty estimates under natural distribution shifts, and provably works for a specific model of a distribution shift