Building Uncertainty Models on Top of Black-Box Predictive APIs

Abstract

With the commoditization of machine learning, more and more off-the-shelf models are available as part of code libraries or cloud services. Typically, data scientists and other users apply these models as "black boxes" within larger projects. In the case of regressing a scalar quantity, such APIs typically offer a predict() function, which outputs the estimated target variable (often referred to aŝ y or, in code, y_hat). However, many real-world problems may require some sort of deviation interval or uncertainty score rather than a single point-wise estimate. In other words, a mechanism is needed with which to answer the question "How confident is the system about that prediction?" Motivated by the lack of this characteristic in most predictive APIs designed for regression purposes, we propose a method that adds an uncertainty score to every black-box prediction. Since the underlying model is not accessible, and therefore standard Bayesian approaches are not applicable, we adopt an empirical approach and fit an uncertainty model using a labelled dataset (x, y) and the outputsŷ of the black box. In order to be able to use any predictive system as a black box and adapt to its complex behaviours, we propose three variants of an uncertainty model based on deep networks. The first adds a heteroscedastic noise component to the black-box output, the second predicts the residuals of the black box, and the third performs quantile regression using deep networks. Experiments using real financial data that contain an inproduction black-box system and two public datasets (energy forecasting and biology responses) illustrate and quantify how uncertainty scores can be added to black-box outputs. INDEX TERMS Aleatoric uncertainty, Deep learning, Neural networks, Regression problems.

Risk-Conditioned Reinforcement Learning: A Generalized Approach for Adapting to Varying Risk Measures

“…However, in this approach, risk measures whose parameter spaces are not shared cannot be addressed simultaneously. In our work, this limitation is addressed by introducing an encoder for risk measures in WV@R. Crossing Quantile Problem: The crossing quantile problem is a significant concern in both statistics (Bondell, Reich, and Wang 2010;Dette and Volgushev 2008) and machine learning areas (Brando et al 2022;Zhou, Wang, and Feng 2020). In the field of statistics, Brando et al (2022) tackled the problem by exploring the numerical integration over a non-negative neural network, similar to UCMNN (Wehenkel and Louppe 2019).…”

Adaptive Conformal Prediction Intervals Using Data-Dependent Weights With Application to Seismic Response Prediction

“…For example, the authors in [23] proposed simultaneous quantile regression as a method of estimating quantiles by minimizing the pinball loss, whereas the target quantile is randomly sampled in every training iteration. The algorithm presented in [24] is designed to predict an arbitrary number of quantiles, which can maintain quantile monotonicity by restricting the partial derivatives of the quantile functions. The use of these approaches may alleviate the problem of quantile-crossing; however, they cannot eliminate it entirely.…”

Can a Single Neuron Learn Predictive Uncertainty?

“…calibration of neural networks using Platt scaling, 52 it was not until recently that such a method is directly used to upgrade any black-box predictive API with an uncertainty score. 53 However, their wrapper is based on deep neural networks and hence is not interpretable. PIM is not a parametric model, but uses a globally interpretable neural network with a single unit.…”