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Title: Confidence Calibration in Deep Neural Networks through Stochastic Inferences

Paper content:
We propose a generic framework to calibrate accuracy and confidence (score) of a prediction through stochastic inferences in deep neural networks.
We first analyze relation between variation of multiple model parameters for a single example inference and variance of the corresponding prediction scores by Bayesian modeling of stochastic regularization.
Our empirical observation shows that accuracy and score of a prediction are highly correlated with variance of multiple stochastic inferences given by stochastic depth or dropout.
Motivated by these facts, we design a novel variance-weighted confidence-integrated loss function that is composed of two cross-entropy loss terms with respect to ground-truth and uniform distribution, which are balanced by variance of stochastic prediction scores.
The proposed loss function enables us to learn deep neural networks that predict confidence calibrated scores using a single inference.
Our algorithm presents outstanding confidence calibration performance and improves classification accuracy with two popular stochastic regularization techniques---stochastic depth and dropout---in multiple models and datasets; it alleviates overconfidence issue in deep neural networks significantly by training networks to achieve prediction accuracy proportional to confidence of prediction.
Deep neural networks have achieved remarkable performance in various tasks, but have critical limitations in reliability of their predictions.
One example is that inference results are often overly confident even for unseen or tricky examples; the maximum scores of individual predictions are very high even for out-of-distribution examples and consequently distort interpretation about the predictions.
Since many practical applications including autonomous driving, medical diagnosis, and machine inspection require accurate uncertainty estimation as well as high prediction accuracy for each inference, such an overconfidence issue makes deep neural networks inappropriate to be deployed for real-world problems in spite of their impressive accuracy.Regularization is a common technique in training deep neural networks to avoid overfitting problems and improve generalization accuracy BID18 ; BID6 ; BID7 .
However, their objectives are not directly related to generating score distributions aligned with uncertainty of individual predictions.
In other words, existing deep neural networks are inherently poor at calibrating prediction accuracy and confidence.Our goal is to learn deep neural networks that are able to estimate accuracy and uncertainty of each prediction at the same time.
Hence, we propose a generic framework to calibrate prediction score (confidence) with accuracy in deep neural networks.
Our algorithm starts with an observation that variance of prediction scores measured from multiple stochastic inferences is highly correlated with accuracy and confidence of the prediction based on the average score, where we employ stochastic regularization techniques such as stochastic depth or dropout to obtain multiple stochastic inference results.
We also interpret stochastic regularization as a Bayesian model, which shows relation between stochastic modeling and stochastic inferences of deep neural networks.
By exploiting these properties, we design a loss function to enable deep neural network to predict confidence-calibrated scores based only on a single prediction, without stochastic inferences.
Our contribution is summarized below:• We provide a generic framework to estimate uncertainty of a prediction based on stochastic inferences in deep neural networks, which is motivated by empirical observation and theoretical analysis.•
We design a variance-weighted confidence-integrated loss function in a principled way without hyper-parameters, which enables deep neural networks to produce confidencecalibrated predictions even without stochastic inferences.•
The proposed framework presents outstanding performance to reduce overconfidence issue and estimate accurate uncertainty in various architectures and datasets.The rest of the paper is organized as follows. We
first discuss prior research related to our algorithm, and describe theoretical background for Bayesian interpretation of our approach in Section 2 and 3, respectively. Section
4 presents our confidence calibration algorithm through stochastic inferences, and Section 5 illustrates experimental results.
We presented a generic framework for uncertainty estimation of a prediction in deep neural networks by calibrating accuracy and score based on stochastic inferences.
Based on Bayesian interpretation of stochastic regularization and our empirical observation results, we claim that variation of multiple stochastic inferences for a single example is a crucial factor to estimate uncertainty of the average prediction.
Motivated by this fact, we design the variance-weighted confidence-integrated loss to learn confidence-calibrated networks and enable uncertainty to be estimated by a single prediction.
The proposed algorithm is also useful to understand existing confidence calibration methods in a unified way, and we compared our algorithm with other variations within our framework to analyze their characteristics.

assistant: text: We propose a framework to learn confidence-calibrated networks by designing a novel loss function that incorporates predictive uncertainty estimated through stochastic inferences.