Calibration: Respice, Adspice, Prospice

“Those who claim for themselves to judge the truth are bound to possess a criterion of truth.” JEL Code: C18, C53, D89calibration, prediction

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

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

Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation

There is increasing consensus in the hydrologic literature that an appropriate framework for streamflow forecasting and simulation should include explicit recognition of forcing and parameter and model structural error. This paper presents a novel Markov chain Monte Carlo (MCMC) sampler, entitled differential evolution adaptive Metropolis (DREAM), that is especially designed to efficiently estimate the posterior probability density function of hydrologic model parameters in complex, high-dimensional sampling problems. This MCMC scheme adaptively updates the scale and orientation of the proposal distribution during sampling and maintains detailed balance and ergodicity. It is then demonstrated how DREAM can be used to analyze forcing data error during watershed model calibration using a five-parameter rainfall-runoff model with streamflow data from two different catchments. Explicit treatment of precipitation error during hydrologic model calibration not only results in prediction uncertainty bounds that are more appropriate but also significantly alters the posterior distribution of the watershed model parameters. This has significant implications for regionalization studies. The approach also provides important new ways to estimate areal average watershed precipitation, information that is of utmost importance for testing hydrologic theory, diagnosing structural errors in models, and appropriately benchmarking rainfall measurement devices