As deep learning applications are becoming more and more pervasive in robotics, the question of evaluating the reliability of inferences becomes a central question in the robotics community. This domain, known as predictive uncertainty, has come under the scrutiny of research groups developing Bayesian approaches adapted to deep learning such as Monte Carlo Dropout. Unfortunately, for the time being, the real goal of predictive uncertainty has been swept under the rug. Indeed, these approaches are solely evaluated in terms of raw performance of the network prediction, while the quality of their estimated uncertainty is not assessed. Evaluating such uncertainty prediction quality is especially important in robotics, as actions shall depend on the confidence in perceived information. In this context, the main contribution of this article is to propose a novel metric that is adapted to the evaluation of relative uncertainty assessment and directly applicable to regression with deep neural networks. To experimentally validate this metric, we evaluate it on a toy dataset and then apply it to the task of monocular depth estimation.
Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always intractable, most efforts were made on finding an accurate approximation the true posterior. Even though a decent estimation of the model posterior is obtained, another approximation is required to compute the predictive distribution over the desired output. A common accurate solution is to use Monte Carlo (MC) integration. However, it needs to maintain a large nu…
Imperial College London（帝国理工学院）；King’s College London（伦敦国王学院）；University College London（伦敦大学学院）
MC Dropout is a mainstream "free lunch" method in medical imaging for approximate Bayesian computations (ABC). Its appeal is to solve out-of-the-box the daunting task of ABC and uncertainty quantification in Neural Networks (NNs); to fall within the variational inference (VI) framework; and to propose a highly multimodal, faithful predictive posterior. We question the properties of MC Dropout for approximate inference, as in fact MC Dropout changes the Bayesian model; its predictive posterior assigns $0$ probability to the true model on closed-form benchmarks; the multimodality of its predicti…
We propose \textbf{JAWS}, a series of wrapper methods for distribution-free uncertainty quantification tasks under covariate shift, centered on the core method \textbf{JAW}, the \textbf{JA}ckknife+ \textbf{W}eighted with data-dependent 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 gu…
Deep learning models achieve high predictive accuracy across a broad spectrum of tasks, but rigorously quantifying their predictive uncertainty remains challenging. Usable estimates of predictive uncertainty should (1) cover the true prediction targets with high probability, and (2) discriminate between high- and low-confidence prediction instances. Existing methods for uncertainty quantification are based predominantly on Bayesian neural networks; these may fall short of (1) and (2) -- i.e., Bayesian credible intervals do not guarantee frequentist coverage, and approximate posterior inference…
Manipal Institute of Technology, MAHE（马尼帕尔理工学院，马尼帕尔高等教育学院）
Most machine learning models operate under the assumption that the training, testing and deployment data is independent and identically distributed (i.i.d.). This assumption doesn't generally hold true in a natural setting. Usually, the deployment data is subject to various types of distributional shifts. The magnitude of a model's performance is proportional to this shift in the distribution of the dataset. Thus it becomes necessary to evaluate a model's uncertainty and robustness to distributional shifts to get a realistic estimate of its expected performance on real-world data. Present meth…
The output of predictive models is routinely recalibrated by reconciling low-level predictions with known derived quantities defined at higher levels of aggregation. For example, models predicting turnout probabilities at the individual level in U.S. elections can be adjusted so that their aggregation matches the observed vote totals in each state, thus producing better calibrated predictions. In this research note, we provide theoretical grounding for one of the most commonly used recalibration strategies, known colloquially as the "logit shift." Typically cast as a heuristic optimization pro…
University of São Paulo（圣保罗大学）；Federal University of São Carlos（圣卡洛斯联邦大学）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）
Performance assessment is a key issue in the process of proposing new machine learning/statistical estimators. A possible method to complete such task is by using simulation studies, which can be defined as the procedure of estimating and comparing properties (such as predictive power) of estimators (and other statistics) by averaging over many replications given a true distribution; i.e.: generating a dataset, fitting the estimator, calculating and storing the predictive power, and then repeating the procedure many times and finally averaging over the stored predictive powers. Given that, in …
Predictive analytics is increasingly used to guide decision-making in many applications. However, in practice, we often have limited data on the true predictive task of interest, and must instead rely on more abundant data on a closely-related proxy predictive task. For example, e-commerce platforms use abundant customer click data (proxy) to make product recommendations rather than the relatively sparse customer purchase data (true outcome of interest); alternatively, hospitals often rely on medical risk scores trained on a different patient population (proxy) rather than their own patient po…
Prediction models for clinical outcomes may be developed using a source dataset and additionally applied to new settings. Towards model external validation and model updating in the new setting, one procedure is model modification learning that involves the dual goals of recalibrating overall predictions as well as revising individual feature effects. Modification learning generally requires the collection of an adequate sample of true outcome labels from the new setting, which is frequently an expensive and time-consuming process, as it involves abstraction by human clinical experts. To reduc…
We investigate the performance of a class of particle filters (PFs) that can automatically tune their computational complexity by evaluating online certain predictive statistics which are invariant for a broad class of state-space models. To be specific, we propose a family of block-adaptive PFs based on the methodology of Elvira et al (2017). In this class of algorithms, the number of Monte Carlo samples (known as particles) is adjusted periodically, and we prove that the theoretical error bounds of the PF actually adapt to the updates in the number of particles. The evaluation of the predict…
We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In addition, for the problem to be a well-defined convex program, we must retain the convexity of the feasible set. Consequently, we propose a variational Bayes-based method to approximately compute the posterior predictive integral that ensures tractability and retains the convexity of the feasible set. Under certain regularity conditions, we also show that the solut…
University of Chicago（芝加哥大学）；Toyota Technological Institute at Chicago（芝加哥丰田工业大学）
In this paper, we study a bi-criterion framework for assessing scoring functions in the context of binary classification. The positive and negative predictive values (ppv and npv, respectively) are conditional probabilities of the true label matching a classifier's predicted label. The usual classification error rate is a linear combination of these probabilities, and therefore, concentration inequalities for the error rate do not yield confidence intervals for the two separate predictive values. We study generalization properties of scoring functions with respect to predictive values by deriv…
University of Chicago（芝加哥大学）；University of Toronto（多伦多大学）；Vector Institute（矢量研究所）
While uncertainty estimation is a well-studied topic in deep learning, most such work focuses on marginal uncertainty estimates, i.e. the predictive mean and variance at individual input locations. But it is often more useful to estimate predictive correlations between the function values at different input locations. In this paper, we consider the problem of benchmarking how accurately Bayesian models can estimate predictive correlations. We first consider a downstream task which depends on posterior predictive correlations: transductive active learning (TAL). We find that TAL makes better us…
The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. If the features in reality are dependent this may lead to incorrect explanations. Hence, there have recently been attempts of appropriately modelling/estimating the dependence between the features. Although the proposed methods clearly outperform the traditional approach assuming independence, they have their weaknesses. In this paper we propose two new approaches for modelling the dependence between the features. Both approaches are based on vine c…
University College London（伦敦大学学院）；CNRS, Sorbonne Université（法国国家科学研究中心，索邦大学）；Department of Econometrics and Business Statistics, Monash University（蒙纳士大学计量经济学与商业统计系）
Pathologies of Predictive Diversity in Deep Ensembles
Center for Theoretical Neuroscience（理论神经科学中心）；Department of Neuroscience（神经科学系）；Columbia University（哥伦比亚大学）；Department of Statistics（统计系）；University of British Columbia（不列颠哥伦比亚大学）；Vector Institute（向量研究所）
Imperial College London（帝国理工学院）；Queen Mary University of London（伦敦玛丽女王大学）；University of Cambridge（剑桥大学）
Computational models providing accurate estimates of their uncertainty are crucial for risk management associated with decision making in healthcare contexts. This is especially true since many state-of-the-art systems are trained using the data which has been labelled automatically (self-supervised mode) and tend to overfit. In this work, we investigate the quality of uncertainty estimates from a range of current state-of-the-art predictive models applied to the problem of observation detection in radiology reports. This problem remains understudied for Natural Language Processing in the heal…
Convolutional image classifiers can achieve high predictive accuracy, but quantifying their uncertainty remains an unresolved challenge, hindering their deployment in consequential settings. Existing uncertainty quantification techniques, such as Platt scaling, attempt to calibrate the network's probability estimates, but they do not have formal guarantees. We present an algorithm that modifies any classifier to output a predictive set containing the true label with a user-specified probability, such as 90%. The algorithm is simple and fast like Platt scaling, but provides a formal finite-samp…
