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Register a new userCalibration of Neural Networks using Splines
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Added by
Thalaiyasingam Ajanthan
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Calibrating neural networks is of utmost importance when employing them in safety-critical applications where the downstream decision making depends on the predicted probabilities. Measuring calibration error amounts to comparing two empirical distributions. In this work, we introduce a binning-free calibration measure inspired by the classical Kolmogorov-Smirnov (KS) statistical test in which the main idea is to compare the respective cumulative probability distributions. From this, by approximating the empirical cumulative distribution using a differentiable function via splines, we obtain a recalibration function, which maps the network outputs to actual (calibrated) class assignment probabilities. The spine-fitting is performed using a held-out calibration set and the obtained recalibration function is evaluated on an unseen test set. We tested our method against existing calibration approaches on various image classification datasets and our spline-based recalibration approach consistently outperforms existing methods on KS error as well as other commonly used calibration measures.
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Calibration of neural networks is a critical aspect to consider when incorporating machine learning models in real-world decision-making systems where the confidence of decisions are equally important as the decisions themselves. In recent years, there is a surge of research on neural network calibration and the majority of the works can be categorized into post-hoc calibration methods, defined as methods that learn an additional function to calibrate an already trained base network. In this work, we intend to understand the post-hoc calibration methods from a theoretical point of view. Especially, it is known that minimizing Negative Log-Likelihood (NLL) will lead to a calibrated network on the training set if the global optimum is attained (Bishop, 1994). Nevertheless, it is not clear learning an additional function in a post-hoc manner would lead to calibration in the theoretical sense. To this end, we prove that even though the base network ($f$) does not lead to the global optimum of NLL, by adding additional layers ($g$) and minimizing NLL by optimizing the parameters of $g$ one can obtain a calibrated network $g circ f$. This not only provides a less stringent condition to obtain a calibrated network but also provides a theoretical justification of post-hoc calibration methods. Our experiments on various image classification benchmarks confirm the theory.
Accurate estimation of predictive uncertainty (model calibration) is essential for the safe application of neural networks. Many instances of miscalibration in modern neural networks have been reported, suggesting a trend that newer, more accurate models produce poorly calibrated predictions. Here, we revisit this question for recent state-of-the-art image classification models. We systematically relate model calibration and accuracy, and find that the most recent models, notably those not using convolutions, are among the best calibrated. Trends observed in prior model generations, such as decay of calibration with distribution shift or model size, are less pronounced in recent architectures. We also show that model size and amount of pretraining do not fully explain these differences, suggesting that architecture is a major determinant of calibration properties.
Miscalibration - a mismatch between a models confidence and its correctness - of Deep Neural Networks (DNNs) makes their predictions hard to rely on. Ideally, we want networks to be accurate, calibrated and confident. We show that, as opposed to the standard cross-entropy loss, focal loss [Lin et. al., 2017] allows us to learn models that are already very well calibrated. When combined with temperature scaling, whilst preserving accuracy, it yields state-of-the-art calibrated models. We provide a thorough analysis of the factors causing miscalibration, and use the insights we glean from this to justify the empirically excellent performance of focal loss. To facilitate the use of focal loss in practice, we also provide a principled approach to automatically select the hyperparameter involved in the loss function. We perform extensive experiments on a variety of computer vision and NLP datasets, and with a wide variety of network architectures, and show that our approach achieves state-of-the-art calibration without compromising on accuracy in almost all cases. Code is available at https://github.com/torrvision/focal_calibration.
We draw a formal connection between using synthetic training data to optimize neural network parameters and approximate, Bayesian, model-based reasoning. In particular, training a neural network using synthetic data can be viewed as learning a proposal distribution generator for approximate inference in the synthetic-data generative model. We demonstrate this connection in a recognition task where we develop a novel Captcha-breaking architecture and train it using synthetic data, demonstrating both state-of-the-art performance and a way of computing task-specific posterior uncertainty. Using a neural network trained this way, we also demonstrate successful breaking of real-world Captchas currently used by Facebook and Wikipedia. Reasoning from these empirical results and drawing connections with Bayesian modeling, we discuss the robustness of synthetic data results and suggest important considerations for ensuring good neural network generalization when training with synthetic data.
Nested networks or slimmable networks are neural networks whose architectures can be adjusted instantly during testing time, e.g., based on computational constraints. Recent studies have focused on a nested dropout layer, which is able to order the nodes of a layer by importance during training, thus generating a nested set of sub-networks that are optimal for different configurations of resources. However, the dropout rate is fixed as a hyper-parameter over different layers during the whole training process. Therefore, when nodes are removed, the performance decays in a human-specified trajectory rather than in a trajectory learned from data. Another drawback is the generated sub-networks are deterministic networks without well-calibrated uncertainty. To address these two problems, we develop a Bayesian approach to nested neural networks. We propose a variational ordering unit that draws samples for nested dropout at a low cost, from a proposed Downhill distribution, which provides useful gradients to the parameters of nested dropout. Based on this approach, we design a Bayesian nested neural network that learns the order knowledge of the node distributions. In experiments, we show that the proposed approach outperforms the nested network in terms of accuracy, calibration, and out-of-domain detection in classification tasks. It also outperforms the related approach on uncertainty-critical tasks in computer vision.
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