Anomaly Detection (AD) in images is a fundamental computer vision problem and
refers to identifying images and image substructures that deviate significantly
from the norm. Popular AD algorithms commonly try to learn a model of normality
from scratch using task specific datasets, but are limited to semi-supervised
approaches employing mostly normal data due to the inaccessibility of anomalies
on a large scale combined with the ambiguous nature of anomaly appearance.
We follow an alternative approach and demonstrate that deep feature
representations learned by discriminative models on large natural image
datasets are well suited to describe normality and detect even subtle anomalies
in a transfer learning setting. Our model of normality is established by
fitting a multivariate Gaussian (MVG) to deep feature representations of
classification networks trained on ImageNet using normal data only. By
subsequently applying the Mahalanobis distance as the anomaly score we
outperform the current state of the art on the public MVTec AD dataset,
achieving an AUROC value of $95.8 \pm 1.2$ (mean $\pm$ SEM) over all 15
classes. We further investigate why the learned representations are
discriminative to the AD task using Principal Component Analysis. We find that
the principal components containing little variance in normal data are the ones
crucial for discriminating between normal and anomalous instances. This gives a
possible explanation to the often sub-par performance of AD approaches trained
from scratch using normal data only. By selectively fitting a MVG to these most
relevant components only, we are able to further reduce model complexity while
retaining AD performance. We also investigate setting the working point by
selecting acceptable False Positive Rate thresholds based on the MVG
assumption.
Code available at this https URL

本研究提出了一种使用深度学习和多元高斯模型相结合的方法来进行图像中的异常检测，该方法通过预先训练大规模图像数据集上的分类器来建立正常图像的模型，使用马氏距离作为异常得分，可以在 MVTec AD 数据集上获得 95.8±1.2 的 AUROC 值，并探究了该方法在图像中异常检测中的可行性和影响因素。

预训练深度特征中正常数据分布的建模用于异常检测

Modeling the Distribution of Normal Data in Pre-Trained Deep Features  for Anomaly Detection

A graph neural network transforms features in each vertex's neighborhood into
a vector representation of the vertex. Afterward, each vertex's representation
is used independently for predicting its label. This standard pipeline
implicitly assumes that vertex labels are conditionally independent given their
neighborhood features. However, this is a strong assumption, and we show that
it is far from true on many real-world graph datasets. Focusing on regression
tasks, we find that this conditional independence assumption severely limits
predictive power. This should not be that surprising, given that traditional
graph-based semi-supervised learning methods such as label propagation work in
the opposite fashion by explicitly modeling the correlation in predicted
outcomes.
Here, we address this problem with an interpretable and efficient framework
that can improve any graph neural network architecture simply by exploiting
correlation structure in the regression residuals. In particular, we model the
joint distribution of residuals on vertices with a parameterized multivariate
Gaussian, and estimate the parameters by maximizing the marginal likelihood of
the observed labels. Our framework achieves substantially higher accuracy than
competing baselines, and the learned parameters can be interpreted as the
strength of correlation among connected vertices. Furthermore, we develop
linear time algorithms for low-variance, unbiased model parameter estimates,
allowing us to scale to large networks. We also provide a basic version of our
method that makes stronger assumptions on correlation structure but is painless
to implement, often leading to great practical performance with minimal
overhead.

通过建模回归残差之间的相关性，提出一种简单、高效且可解释性强的框架，可以显著提高图神经网络的预测能力，并可扩展到大规模网络。

图神经网络回归中的残差相关性

Residual Correlation in Graph Neural Network Regression

We present novel, computationally efficient, and differentially private
algorithms for two fundamental high-dimensional learning problems: learning a
multivariate Gaussian and learning a product distribution over the Boolean
hypercube in total variation distance. The sample complexity of our algorithms
nearly matches the sample complexity of the optimal non-private learners for
these tasks in a wide range of parameters, showing that privacy comes
essentially for free for these problems. In particular, in contrast to previous
approaches, our algorithm for learning Gaussians does not require strong a
priori bounds on the range of the parameters. Our algorithms introduce a novel
technical approach to reducing the sensitivity of the estimation procedure that
we call recursive private preconditioning.

本文介绍了用于两种基本高维学习问题的新型、计算有效和差分隐私算法：学习多元高斯分布和在布尔超立方体上学习乘积分布。我们的算法的样本复杂度几乎与这些任务的最优非隐私学习器的样本复杂度相匹配，表明隐私在这些问题上是几乎免费的。