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Register a new userBeyond Marginal Uncertainty: How Accurately can Bayesian Regression Models Estimate Posterior Predictive Correlations?
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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 use of models uncertainty estimates than ordinary active learning, and recommend this as a benchmark for evaluating Bayesian models. Since TAL is too expensive and indirect to guide development of algorithms, we introduce two metrics which more directly evaluate the predictive correlations and which can be computed efficiently: meta-correlations (i.e. the correlations between the models correlation estimates and the true values), and cross-normalized likelihoods (XLL). We validate these metrics by demonstrating their consistency with TAL performance and obtain insights about the relative performance of current Bayesian neural net and Gaussian process models.
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Bayesian Dark Knowledge is a method for compressing the posterior predictive distribution of a neural network model into a more compact form. Specifically, the method attempts to compress a Monte Carlo approximation to the parameter posterior into a single network representing the posterior predictive distribution. Further, the authors show that this approach is successful in the classification setting using a student network whose architecture matches that of a single network in the teacher ensemble. In this work, we examine the robustness of Bayesian Dark Knowledge to higher levels of posterior uncertainty. We show that using a student network that matches the teacher architecture may fail to yield acceptable performance. We study an approach to close the resulting performance gap by increasing student model capacity.
High-risk domains require reliable confidence estimates from predictive models. Deep latent variable models provide these, but suffer from the rigid variational distributions used for tractable inference, which err on the side of overconfidence. We propose Stochastic Quantized Activation Distributions (SQUAD), which imposes a flexible yet tractable distribution over discretized latent variables. The proposed method is scalable, self-normalizing and sample efficient. We demonstrate that the model fully utilizes the flexible distribution, learns interesting non-linearities, and provides predictive uncertainty of competitive quality.
Generating high quality uncertainty estimates for sequential regression, particularly deep recurrent networks, remains a challenging and open problem. Existing approaches often make restrictive assumptions (such as stationarity) yet still perform poorly in practice, particularly in presence of real world non-stationary signals and drift. This paper describes a flexible method that can generate symmetric and asymmetric uncertainty estimates, makes no assumptions about stationarity, and outperforms competitive baselines on both drift and non drift scenarios. This work helps make sequential regression more effective and practical for use in real-world applications, and is a powerful new addition to the modeling toolbox for sequential uncertainty quantification in general.
Predictive uncertainty estimation is an essential next step for the reliable deployment of deep object detectors in safety-critical tasks. In this work, we focus on estimating predictive distributions for bounding box regression output with variance networks. We show that in the context of object detection, training variance networks with negative log likelihood (NLL) can lead to high entropy predictive distributions regardless of the correctness of the output mean. We propose to use the energy score as a non-local proper scoring rule and find that when used for training, the energy score leads to better calibrated and lower entropy predictive distributions than NLL. We also address the widespread use of non-proper scoring metrics for evaluating predictive distributions from deep object detectors by proposing an alternate evaluation approach founded on proper scoring rules. Using the proposed evaluation tools, we show that although variance networks can be used to produce high quality predictive distributions, ad-hoc approaches used by seminal object detectors for choosing regression targets during training do not provide wide enough data support for reliable variance learning. We hope that our work helps shift evaluation in probabilistic object detection to better align with predictive uncertainty evaluation in other machine learning domains. Code for all models, evaluation, and datasets is available at: https://github.com/asharakeh/probdet.git.
Modern machine learning methods including deep learning have achieved great success in predictive accuracy for supervised learning tasks, but may still fall short in giving useful estimates of their predictive {em uncertainty}. Quantifying uncertainty is especially critical in real-world settings, which often involve input distributions that are shifted from the training distribution due to a variety of factors including sample bias and non-stationarity. In such settings, well calibrated uncertainty estimates convey information about when a models output should (or should not) be trusted. Many probabilistic deep learning methods, including Bayesian-and non-Bayesian methods, have been proposed in the literature for quantifying predictive uncertainty, but to our knowledge there has not previously been a rigorous large-scale empirical comparison of these methods under dataset shift. We present a large-scale benchmark of existing state-of-the-art methods on classification problems and investigate the effect of dataset shift on accuracy and calibration. We find that traditional post-hoc calibration does indeed fall short, as do several other previous methods. However, some methods that marginalize over models give surprisingly strong results across a broad spectrum of tasks.
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