Matching High-Dimensional Geometric Quantiles for Test-Time Adaptation of Transformers and Convolutional Networks Alike

Test-time adaptation (TTA) refers to adapting a classifier for the test data when the probability distribution of the test data slightly differs from that of the training data of the model. To the best of our knowledge, most of the existing TTA approaches modify the weights of the classifier relying heavily on the architecture. It is unclear as to how these approaches are extendable to generic architectures. In this article, we propose an architecture-agnostic approach to TTA by adding an adapter network pre-processing the input images suitable to the classifier. This adapter is trained using the proposed quantile loss. Unlike existing approaches, we correct for the distribution shift by matching high-dimensional geometric quantiles. We prove theoretically that under suitable conditions minimizing quantile loss can learn the optimal adapter. We validate our approach on CIFAR10-C, CIFAR100-C and TinyImageNet-C by training both classic convolutional and transformer networks on CIFAR10, CIFAR100 and TinyImageNet datasets.

Radon-Nikodým Derivative: Re-imagining Anomaly Detection from a Measure Theoretic Perspective

Which principle underpins the design of an effective anomaly detection loss function? The answer lies in the concept of \rnthm{} theorem, a fundamental concept in measure theory. The key insight is -- Multiplying the vanilla loss function with the \rnthm{} derivative improves the performance across the board. We refer to this as RN-Loss. This is established using PAC learnability of anomaly detection. We further show that the \rnthm{} derivative offers important insights into unsupervised clustering based anomaly detections as well. We evaluate our algorithm on 96 datasets, including univariate and multivariate data from diverse domains, including healthcare, cybersecurity, and finance. We show that RN-Derivative algorithms outperform state-of-the-art methods on 68\% of Multivariate datasets (based on F-1 scores) and also achieves peak F1-scores on 72\% of time series (Univariate) datasets.