Estimating Uncertainty Online Against an Adversary

Assessing uncertainty is an important step towards ensuring the safety and reliability of machine learning systems. Existing uncertainty estimation techniques may fail when their modeling assumptions are not met, e.g. when the data distribution differs from the one seen at training time. Here, we propose techniques that assess a classification algorithm's uncertainty via calibrated probabilities (i.e. probabilities that match empirical outcome frequencies in the long run) and which are guaranteed to be reliable (i.e. accurate and calibrated) on out-of-distribution input, including input generated by an adversary. This represents an extension of classical online learning that handles uncertainty in addition to guaranteeing accuracy under adversarial assumptions. We establish formal guarantees for our methods, and we validate them on two real-world problems: question answering and medical diagnosis from genomic data

Calibrated Propensity Scores for Causal Effect Estimation

Propensity scores are commonly used to balance observed covariates while estimating treatment effects. Estimates obtained through propensity score weighing can be biased when the propensity score model cannot learn the true treatment assignment mechanism. We argue that the probabilistic output of a learned propensity score model should be calibrated, i.e. a predictive treatment probability of 90% should correspond to 90% of individuals being assigned the treatment group. We propose simple recalibration techniques to ensure this property. We investigate the theoretical properties of a calibrated propensity score model and its role in unbiased treatment effect estimation. We demonstrate improved causal effect estimation with calibrated propensity scores in several tasks including high-dimensional genome-wide association studies, where we also show reduced computational requirements when calibration is applied to simpler propensity score models.Comment: 23 pages, 3 figure

Adversarial Calibrated Regression for Online Decision Making

Accurately estimating uncertainty is an essential component of decision-making and forecasting in machine learning. However, existing uncertainty estimation methods may fail when data no longer follows the distribution seen during training. Here, we introduce online uncertainty estimation algorithms that are guaranteed to be reliable on arbitrary streams of data points, including data chosen by an adversary. Specifically, our algorithms perform post-hoc recalibration of a black-box regression model and produce outputs that are provably calibrated -- i.e., an 80% confidence interval will contain the true outcome 80% of the time -- and that have low regret relative to the learning objective of the base model. We apply our algorithms in the context of Bayesian optimization, an online model-based decision-making task in which the data distribution shifts over time, and observe accelerated convergence to improved optima. Our results suggest that robust uncertainty quantification has the potential to improve online decision-making.Comment: arXiv admin note: text overlap with arXiv:1607.0359

Calibrated Uncertainty Estimation Improves Bayesian Optimization

Bayesian optimization is a sequential procedure for obtaining the global optimum of black-box functions without knowing a priori their true form. Good uncertainty estimates over the shape of the objective function are essential in guiding the optimization process. However, these estimates can be inaccurate if the true objective function violates assumptions made by its model (e.g., Gaussianity). This paper studies which uncertainties are needed in Bayesian optimization models and argues that ideal uncertainties should be calibrated -- i.e., an 80% predictive interval should contain the true outcome 80% of the time. We propose a simple algorithm for enforcing this property and show that it enables Bayesian optimization to arrive at the global optimum in fewer steps. We provide theoretical insights into the role of calibrated uncertainties and demonstrate the improved performance of our method on standard benchmark functions and hyperparameter optimization tasks