Cosmic shear estimation is an essential scientific goal for large galaxy
surveys. It refers to the coherent distortion of distant galaxy images due to
weak gravitational lensing along the line of sight. It can be used as a tracer
of the matter distribution in the Universe. The unbiased estimation of the
local value of the cosmic shear can be obtained via Bayesian analysis which
relies on robust estimation of the galaxies ellipticity (shape) posterior
distribution. This is not a simple problem as, among other things, the images
may be corrupted with strong background noise. For current and coming surveys,
another central issue in galaxy shape determination is the treatment of
statistically dominant overlapping (blended) objects. We propose a Bayesian
Convolutional Neural Network based on Monte-Carlo Dropout to reliably estimate
the ellipticity of galaxies and the corresponding measurement uncertainties. We
show that while a convolutional network can be trained to correctly estimate
well calibrated aleatoric uncertainty, -- the uncertainty due to the presence
of noise in the images -- it is unable to generate a trustworthy ellipticity
distribution when exposed to previously unseen data (i.e. here, blended
scenes). By introducing a Bayesian Neural Network, we show how to reliably
estimate the posterior predictive distribution of ellipticities along with
robust estimation of epistemic uncertainties. Experiments also show that
epistemic uncertainty can detect inconsistent predictions due to unknown
blended scenes.

该研究提出了一种基于蒙特卡洛 dropout 的贝叶斯卷积神经网络，用于可靠地估计星系的椭圆度和相应的测量不确定性，并展示了如何可靠地估计其后验预测分布以及鲁棒的估计认识的不确定性。

用贝叶斯卷积神经网络进行鲁棒性星系椭偏率回归

A Bayesian Convolutional Neural Network for Robust Galaxy Ellipticity  Regression

Artificial Neural Networks are connectionist systems that perform a given
task by learning on examples without having prior knowledge about the task.
This is done by finding an optimal point estimate for the weights in every
node. Generally, the network using point estimates as weights perform well with
large datasets, but they fail to express uncertainty in regions with little or
no data, leading to overconfident decisions.
In this paper, Bayesian Convolutional Neural Network (BayesCNN) using
Variational Inference is proposed, that introduces probability distribution
over the weights. Furthermore, the proposed BayesCNN architecture is applied to
tasks like Image Classification, Image Super-Resolution and Generative
Adversarial Networks. The results are compared to point-estimates based
architectures on MNIST, CIFAR-10 and CIFAR-100 datasets for Image
CLassification task, on BSD300 dataset for Image Super Resolution task and on
CIFAR10 dataset again for Generative Adversarial Network task.
BayesCNN is based on Bayes by Backprop which derives a variational
approximation to the true posterior. We, therefore, introduce the idea of
applying two convolutional operations, one for the mean and one for the
variance. Our proposed method not only achieves performances equivalent to
frequentist inference in identical architectures but also incorporate a
measurement for uncertainties and regularisation. It further eliminates the use
of dropout in the model. Moreover, we predict how certain the model prediction
is based on the epistemic and aleatoric uncertainties and empirically show how
the uncertainty can decrease, allowing the decisions made by the network to
become more deterministic as the training accuracy increases. Finally, we
propose ways to prune the Bayesian architecture and to make it more
computational and time effective.

本文提出了基于贝叶斯卷积神经网络的变分推断方法，通过引入欠拟合和过拟合的概率分布来解决神经网络普遍存在的预测不确定性问题，并在图像分类等任务上进行了实验测试。

贝叶斯卷积神经网络与变分推断的全面指南

A Comprehensive guide to Bayesian Convolutional Neural Network with  Variational Inference

Motivated by the problem of computer-aided detection (CAD) of pulmonary
nodules, we introduce methods to propagate and fuse uncertainty information in
a multi-stage Bayesian convolutional neural network (CNN) architecture. The
question we seek to answer is "can we take advantage of the model uncertainty
provided by one deep learning model to improve the performance of the
subsequent deep learning models and ultimately of the overall performance in a
multi-stage Bayesian deep learning architecture?". Our experiments show that
propagating uncertainty through the pipeline enables us to improve the overall
performance in terms of both final prediction accuracy and model confidence.

该研究针对计算机辅助肺结节检测问题，介绍了一种多阶段贝叶斯卷积神经网络架构中传播和融合不确定性信息的方法，并通过实验验证了通过传播不确定性信息可以提高模型预测准确性和置信度的效果。

应用于肺结节检测的多级贝叶斯卷积神经网络中的不确定性传播

Propagating Uncertainty in Multi-Stage Bayesian Convolutional Neural  Networks with Application to Pulmonary Nodule Detection

We present a robust and real-time monocular six degree of freedom visual
relocalization system. We use a Bayesian convolutional neural network to
regress the 6-DOF camera pose from a single RGB image. It is trained in an
end-to-end manner with no need of additional engineering or graph optimisation.
The algorithm can operate indoors and outdoors in real time, taking under 6ms
to compute. It obtains approximately 2m and 6 degrees accuracy for very large
scale outdoor scenes and 0.5m and 10 degrees accuracy indoors. Using a Bayesian
convolutional neural network implementation we obtain an estimate of the
model's relocalization uncertainty and improve state of the art localization
accuracy on a large scale outdoor dataset. We leverage the uncertainty measure
to estimate metric relocalization error and to detect the presence or absence
of the scene in the input image. We show that the model's uncertainty is caused
by images being dissimilar to the training dataset in either pose or
appearance.

使用贝叶斯卷积神经网络实现六自由度视觉重定位系统，并利用其不确定性测量提高室内和户外场景的定位精度，实现实时处理。