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Register a new userPrediction Intervals: Split Normal Mixture from Quality-Driven Deep Ensembles
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Prediction intervals are a machine- and human-interpretable way to represent predictive uncertainty in a regression analysis. In this paper, we present a method for generating prediction intervals along with point estimates from an ensemble of neural networks. We propose a multi-objective loss function fusing quality measures related to prediction intervals and point estimates, and a penalty function, which enforces semantic integrity of the results and stabilizes the training process of the neural networks. The ensembled prediction intervals are aggregated as a split normal mixture accounting for possible multimodality and asymmetricity of the posterior predictive distribution, and resulting in prediction intervals that capture aleatoric and epistemic uncertainty. Our results show that both our quality-driven loss function and our aggregation method contribute to well-calibrated prediction intervals and point estimates.
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Ongoing developments in neural network models are continually advancing the state of the art in terms of system accuracy. However, the predicted labels should not be regarded as the only core output; also important is a well-calibrated estimate of the prediction uncertainty. Such estimates and their calibration are critical in many practical applications. Despite their obvious aforementioned advantage in relation to accuracy, contemporary neural networks can, generally, be regarded as poorly calibrated and as such do not produce reliable output probability estimates. Further, while post-processing calibration solutions can be found in the relevant literature, these tend to be for systems performing classification. In this regard, we herein present two novel methods for acquiring calibrated predictions intervals for neural network regressors: empirical calibration and temperature scaling. In experiments using different regression tasks from the audio and computer vision domains, we find that both our proposed methods are indeed capable of producing calibrated prediction intervals for neural network regressors with any desired confidence level, a finding that is consistent across all datasets and neural network architectures we experimented with. In addition, we derive an additional practical recommendation for producing more accurate calibrated prediction intervals. We release the source code implementing our proposed methods for computing calibrated predicted intervals. The code for computing calibrated predicted intervals is publicly available.
This paper presents new deviation inequalities that are valid uniformly in time under adaptive sampling in a multi-armed bandit model. The deviations are measured using the Kullback-Leibler divergence in a given one-dimensional exponential family, and may take into account several arms at a time. They are obtained by constructing for each arm a mixture martingale based on a hierarchical prior, and by multiplying those martingales. Our deviation inequalities allow us to analyze stopping rules based on generalized likelihood ratios for a large class of sequential identification problems, and to construct tight confidence intervals for some functions of the means of the arms.
Deep Learning methods are known to suffer from calibration issues: they typically produce over-confident estimates. These problems are exacerbated in the low data regime. Although the calibration of probabilistic models is well studied, calibrating extremely over-parametrized models in the low-data regime presents unique challenges. We show that deep-ensembles do not necessarily lead to improved calibration properties. In fact, we show that standard ensembling methods, when used in conjunction with modern techniques such as mixup regularization, can lead to less calibrated models. In this text, we examine the interplay between three of the most simple and commonly used approaches to leverage deep learning when data is scarce: data-augmentation, ensembling, and post-processing calibration methods. We demonstrate that, although standard ensembling techniques certainly help to boost accuracy, the calibration of deep-ensembles relies on subtle trade-offs. Our main finding is that calibration methods such as temperature scaling need to be slightly tweaked when used with deep-ensembles and, crucially, need to be executed after the averaging process. Our simulations indicate that, in the low data regime, this simple strategy can halve the Expected Calibration Error (ECE) on a range of benchmark classification problems when compared to standard deep-ensembles.
We introduce a novel Deep Reinforcement Learning (DRL) algorithm called Deep Quality-Value (DQV) Learning. DQV uses temporal-difference learning to train a Value neural network and uses this network for training a second Quality-value network that learns to estimate state-action values. We first test DQVs update rules with Multilayer Perceptrons as function approximators on two classic RL problems, and then extend DQV with the use of Deep Convolutional Neural Networks, `Experience Replay and `Target Neural Networks for tackling four games of the Atari Arcade Learning environment. Our results show that DQV learns significantly faster and better than Deep Q-Learning and Double Deep Q-Learning, suggesting that our algorithm can potentially be a better performing synchronous temporal difference algorithm than what is currently present in DRL.
Auto-annotation by ensemble of models is an efficient method of learning on unlabeled data. Wrong or inaccurate annotations generated by the ensemble may lead to performance degradation of the trained model. To deal with this problem we propose filtering the auto-labeled data using a trained model that predicts the quality of the annotation from the degree of consensus between ensemble models. Using semantic segmentation as an example, we show the advantage of the proposed auto-annotation filtering over training on data contaminated with inaccurate labels. Moreover, our experimental results show that in the case of semantic segmentation, the performance of a state-of-the-art model can be achieved by training it with only a fraction (30$%$) of the original manually labeled data set, and replacing the rest with the auto-annotated, quality filtered labels.
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