Uncertainty quantification is crucial for building reliable and trustable machine learning systems. We propose to estimate uncertainty in recurrent neural networks (RNNs) via stochastic discrete state transitions over recurrent timesteps. The uncertainty of the model can be quantified by running a prediction several times, each time sampling from the recurrent state transition distribution, leading to potentially different results if the model is uncertain. Alongside uncertainty quantification, our proposed method offers several advantages in different settings. The proposed method can (1) learn deterministic and probabilistic automata from data, (2) learn well-calibrated models on real-world classification tasks, (3) improve the performance of out-of-distribution detection, and (4) control the exploration-exploitation trade-off in reinforcement learning.
Uncertainty in probabilistic classifiers predictions is a key concern when models are used to support human decision making, in broader probabilistic pipelines or when sensitive automatic decisions have to be taken. Studies have shown that most models are not intrinsically well calibrated, meaning that their decision scores are not consistent with posterior probabilities. Hence being able to calibrate these models, or enforce calibration while learning them, has regained interest in recent literature. In this context, properly assessing calibration is paramount to quantify new contributions ta…
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；IIIS, Tsinghua University（清华大学交叉信息研究院）；Tencent（腾讯）
It is often observed that the probabilistic predictions given by a machine learning model can disagree with averaged actual outcomes on specific subsets of data, which is also known as the issue of miscalibration. It is responsible for the unreliability of practical machine learning systems. For example, in online advertising, an ad can receive a click-through rate prediction of 0.1 over some population of users where its actual click rate is 0.15. In such cases, the probabilistic predictions have to be fixed before the system can be deployed. In this paper, we first introduce a new evaluation…
Uppsala University（乌普萨拉大学）；Veoneer Inc.（维宁尔公司）；Linköping University（林雪平大学）
Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their ability to represent uncertainty about predictions. In safety-critical applications, it is pivotal for a model to possess an adequate sense of uncertainty, which for probabilistic classifiers translates into outputting probability distributions that are consistent with the empirical frequencies observed from realized outcomes. A classifier with such a propert…
Compute and memory constraints have historically prevented traffic simulation software users from fully utilizing the predictive models underlying them. When calibrating car-following models, particularly, accommodations have included 1) using sensitivity analysis to limit the number of parameters to be calibrated, and 2) identifying only one set of parameter values using data collected from multiple car-following instances across multiple drivers. Shortcuts are further motivated by insufficient data set sizes, for which a driver may have too few instances to fully account for the variation in…
Uppsala University（乌普萨拉大学）；Linköping University（林雪平大学）
Most supervised machine learning tasks are subject to irreducible prediction errors. Probabilistic predictive models address this limitation by providing probability distributions that represent a belief over plausible targets, rather than point estimates. Such models can be a valuable tool in decision-making under uncertainty, provided that the model output is meaningful and interpretable. Calibrated models guarantee that the probabilistic predictions are neither over- nor under-confident. In the machine learning literature, different measures and statistical tests have been proposed and stud…
New York University（纽约大学）；ICMC-USP（圣保罗大学数学与计算机科学研究所）；Capital One（第一资本金融公司）
Analyzing classification model performance is a crucial task for machine learning practitioners. While practitioners often use count-based metrics derived from confusion matrices, like accuracy, many applications, such as weather prediction, sports betting, or patient risk prediction, rely on a classifier's predicted probabilities rather than predicted labels. In these instances, practitioners are concerned with producing a calibrated model, that is, one which outputs probabilities that reflect those of the true distribution. Model calibration is often analyzed visually, through static reliabi…
Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on non-probabilistic neural networks which by default do not capture this inherent uncertainty. This well-known problem has led to the development of post-hoc calibration procedures, such as Platt scaling (logistic), isotonic and beta calibration, which transforms the scores into well calibrated empirical probabilities. A plausible alternative to the calibration approa…
Uniform convergence of the smooth calibration error and its relationship with functional gradient
The University of Osaka / RIKEN AIP, Japan（大阪大学 / RIKEN AIP，日本）；CFAR and IHPC, Agency for Science, Technology and Research (A*STAR), Singapore（CFAR 和 IHPC，新加坡科技研究局（A*STAR））；College of Computing and Data Science, Nanyang Technological University, Singapore（南洋理工大学计算机与数据科学学院，新加坡）
A probabilistic model is said to be calibrated if its predicted probabilities match the corresponding empirical frequencies. Calibration is important for uncertainty quantification and decision making in safety-critical applications. While calibration of classifiers has been widely studied, we find that calibration is brittle and can be easily lost under minimal covariate shifts. Existing techniques, including domain adaptation ones, primarily focus on prediction accuracy and do not guarantee calibration neither in theory nor in practice. In this work, we formally introduce the problem of cali…
TU Darmstadt（达姆施塔特工业大学）；Centre for Cognitive Science（认知科学中心）；Hessian Center for AI (hessian.AI)（黑森人工智能中心（hessian.AI））
Time series forecasting is a relevant task that is performed in several real-world scenarios such as product sales analysis and prediction of energy demand. Given their accuracy performance, currently, Recurrent Neural Networks (RNNs) are the models of choice for this task. Despite their success in time series forecasting, less attention has been paid to make the RNNs trustworthy. For example, RNNs can not naturally provide an uncertainty measure to their predictions. This could be extremely useful in practice in several cases e.g. to detect when a prediction might be completely wrong due to a…
Google Brain（谷歌大脑）；Google Health（谷歌健康）；Duke University（杜克大学）
In medicine, both ethical and monetary costs of incorrect predictions can be significant, and the complexity of the problems often necessitates increasingly complex models. Recent work has shown that changing just the random seed is enough for otherwise well-tuned deep neural networks to vary in their individual predicted probabilities. In light of this, we investigate the role of model uncertainty methods in the medical domain. Using RNN ensembles and various Bayesian RNNs, we show that population-level metrics, such as AUC-PR, AUC-ROC, log-likelihood, and calibration error, do not capture mo…
We study the problem of making calibrated probabilistic forecasts for a binary sequence generated by an adversarial nature. Following the seminal paper of Foster and Vohra (1998), nature is often modeled as an adaptive adversary who sees all activity of the forecaster except the randomization that the forecaster may deploy. A number of papers have proposed randomized forecasting strategies that achieve an $ε$-calibration error rate of $O(1/\sqrt{T})$, which we prove is tight in general. On the other hand, it is well known that it is not possible to be calibrated without randomization, or if na…
Uppsala University（乌普萨拉大学）；Linköping University（林雪平大学）
In safety-critical applications a probabilistic model is usually required to be calibrated, i.e., to capture the uncertainty of its predictions accurately. In multi-class classification, calibration of the most confident predictions only is often not sufficient. We propose and study calibration measures for multi-class classification that generalize existing measures such as the expected calibration error, the maximum calibration error, and the maximum mean calibration error. We propose and evaluate empirically different consistent and unbiased estimators for a specific class of measures based…
Better Uncertainty Calibration via Proper Scores for Classification and Beyond
German Cancer Research Center (DKFZ)（德国癌症研究中心）；German Cancer Consortium (DKTK)（德国癌症联盟）；Goethe University Frankfurt（法兰克福大学）；Frankfurt Cancer Institute（法兰克福癌症研究所）
In classification applications, we often want probabilistic predictions to reflect confidence or uncertainty. Dropout, a commonly used training technique, has recently been linked to Bayesian inference, yielding an efficient way to quantify uncertainty in neural network models. However, as previously demonstrated, confidence estimates computed with a naive implementation of dropout can be poorly calibrated, particularly when using convolutional networks. In this paper, through the lens of ensemble learning, we associate calibration error with the correlation between the models sampled with dro…
This paper studies theoretically and empirically a method of turning machine-learning algorithms into probabilistic predictors that automatically enjoys a property of validity (perfect calibration) and is computationally efficient. The price to pay for perfect calibration is that these probabilistic predictors produce imprecise (in practice, almost precise for large data sets) probabilities. When these imprecise probabilities are merged into precise probabilities, the resulting predictors, while losing the theoretical property of perfect calibration, are consistently more accurate than the exi…
Probabilistic Conformal Coverage Guarantees in Small-Data Settings
Berkeley Synchrotron Infrared Structural Biology Program（伯克利同步辐射红外结构生物学项目）；Center for Advanced Mathematics in Energy Research Applications（能源研究应用高级数学中心）；Molecular Biophysics and Integrated Bioimaging Division（分子生物物理与整合生物成像部门）
Universitat Politècnica de València（瓦伦西亚理工大学）；Universidad Autónoma de Madrid（马德里自治大学）
Deep Neural Networks (DNNs) have achieved state-of-the-art accuracy performance in many tasks. However, recent works have pointed out that the outputs provided by these models are not well-calibrated, seriously limiting their use in critical decision scenarios. In this work, we propose to use a decoupled Bayesian stage, implemented with a Bayesian Neural Network (BNN), to map the uncalibrated probabilities provided by a DNN to calibrated ones, consistently improving calibration. Our results evidence that incorporating uncertainty provides more reliable probabilistic models, a critical conditio…
University of Bristol（布里斯托大学）；University of Tartu（塔尔图大学）
The task of calibration is to retrospectively adjust the outputs from a machine learning model to provide better probability estimates on the target variable. While calibration has been investigated thoroughly in classification, it has not yet been well-established for regression tasks. This paper considers the problem of calibrating a probabilistic regression model to improve the estimated probability densities over the real-valued targets. We propose to calibrate a regression model through the cumulative probability density, which can be derived from calibrating a multi-class classifier. We …
Amazon（亚马逊）；NEC Laboratories Europe（NEC欧洲实验室）；University of Stuttgart（斯图加特大学）
Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, they are often treated as black-box models and as such it is difficult to understand what exactly they learn as well as how they arrive at a particular prediction. Second, they tend to work poorly on sequences requiring long-term memorization, despite having this capacity in principle. We aim to address both shortcomings with a class of recurrent networks that use a stochastic state transition mechanism between cell applications. This mechanism, which we term state-regulariza…
Renaissance of RNNs in Streaming Clinical Time Series: Compact Recurrence Remains Competitive with Transformers
University of Texas at Dallas（德克萨斯大学达拉斯分校）；Independent Researcher（独立研究者）；Georgia Institute of Technology（佐治亚理工学院）；University of Michigan- Ann Arbor（密歇根大学安娜堡分校）
Bidirectional recurrent neural networks (RNN) are trained to predict both in the positive and negative time directions simultaneously. They have not been used commonly in unsupervised tasks, because a probabilistic interpretation of the model has been difficult. Recently, two different frameworks, GSN and NADE, provide a connection between reconstruction and probabilistic modeling, which makes the interpretation possible. As far as we know, neither GSN or NADE have been studied in the context of time series before. As an example of an unsupervised task, we study the problem of filling in gaps …
The Alan Turing Institute（阿兰·图灵研究所）；Imperial College London（帝国理工学院）
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the calculation of local sensitivities, i.e. derivatives of the loss function with respect to the estimated parameters, which often necessitates several numerical solves of the underlying system of partial or ordinary differential equations. In this paper we present a new probabilistic approach to computing local sensitivities. The proposed method has several advantage…
W. M. Keck Science Department, Claremont McKenna, Scripps, and Pitzer College（克莱蒙特·麦肯纳学院、斯克里普斯学院和皮策学院 W. M. 凯克科学系）；University of California, Davis（加州大学戴维斯分校）
Reservoir computers (RCs) and recurrent neural networks (RNNs) can mimic any finite-state automaton in theory, and some workers demonstrated that this can hold in practice. We test the capability of generalized linear models, RCs, and Long Short-Term Memory (LSTM) RNN architectures to predict the stochastic processes generated by a large suite of probabilistic deterministic finite-state automata (PDFA). PDFAs provide an excellent performance benchmark in that they can be systematically enumerated, the randomness and correlation structure of their generated processes are exactly known, and thei…
Distributional forecasts are important for a wide variety of applications, including forecasting epidemics. Often, forecasts are miscalibrated, or unreliable in assigning uncertainty to future events. We present a recalibration method that can be applied to a black-box forecaster given retrospective forecasts and observations, as well as an extension to make this method more effective in recalibrating epidemic forecasts. This method is guaranteed to improve calibration and log score performance when trained and measured in-sample. We also prove that the increase in expected log score of a reca…
University of Pittsburgh（匹兹堡大学）；Harvard University（哈佛大学）
Discovery of an accurate causal Bayesian network structure from observational data can be useful in many areas of science. Often the discoveries are made under uncertainty, which can be expressed as probabilities. To guide the use of such discoveries, including directing further investigation, it is important that those probabilities be well-calibrated. In this paper, we introduce a novel framework to derive calibrated probabilities of causal relationships from observational data. The framework consists of three components: (1) an approximate method for generating initial probability estimates…
Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. However, they are often overconfident in their predictions, which leads to inaccurate and miscalibrated probabilistic predictions. The problem of overconfidence becomes especially apparent in cases where the test-time data distribution differs from that which was seen during training. We propose a solution to this problem by seeking out regions of feature space where the model is unjustifiably overconfident, and conditionally raising the entropy of those predictions…
Diffusion-Inspired Reconfiguration of Transformers for Uncertainty Calibration
National University of Singapore（新加坡国立大学）；Hanoi University of Science and Technology（河内科学技术大学）；National Institute of Advanced Industrial Science and Technology（国家先进工业科学与技术研究院）；Washington State University（华盛顿州立大学）
In this study, we utilize Gaussian processes, probabilistic neural network, natural gradient boosting, and quantile regression augmented gradient boosting to model lead times of laser manufacturing processes. We introduce probabilistic modelling in the domain and compare the models in terms of different abilities. While providing a comparison between the models in real-life data, our work has many use cases and substantial business value. Our results indicate that all of the models beat the company estimation benchmark that uses domain experience and have good calibration with the empirical fr…
University of Piuttsburgh（匹兹堡大学）；University of Pittsburgh（匹兹堡大学）
Accurate calibration of probabilistic predictive models learned is critical for many practical prediction and decision-making tasks. There are two main categories of methods for building calibrated classifiers. One approach is to develop methods for learning probabilistic models that are well-calibrated, ab initio. The other approach is to use some post-processing methods for transforming the output of a classifier to be well calibrated, as for example histogram binning, Platt scaling, and isotonic regression. One advantage of the post-processing approach is that it can be applied to any exist…
CoCopula: Conformal Calibration and Copula Aggregation for Reliable Renewable Energy Forecasting
NSF Artificial Intelligence Institute for Advances in Optimization（NSF人工智能优化研究所）；H. Milton Stewart School of Industrial and Systems Engineering（H. Milton Stewart工业与系统工程学院）；Georgia Institute of Technology（佐治亚理工学院）
