Soham Sarkar

Soham Sarkar, Tanmay Sen, Sayantan Banerjee

Industrial image anomaly detection is a challenging problem owing to extreme class imbalance and the scarcity of labeled defective samples, particularly in few-shot settings. We propose BayPrAnoMeta, a Bayesian generalization of Proto-MAML for few-shot industrial image anomaly detection. Unlike existing Proto-MAML approaches that rely on deterministic class prototypes and distance-based adaptation, BayPrAnoMeta replaces prototypes with task-specific probabilistic normality models and performs inner-loop adaptation via a Bayesian posterior predictive likelihood. We model normal support embeddings with a Normal-Inverse-Wishart (NIW) prior, producing a Student-$t$ predictive distribution that enables uncertainty-aware, heavy-tailed anomaly scoring and is essential for robustness in extreme few-shot settings. We further extend BayPrAnoMeta to a federated meta-learning framework with supervised contrastive regularization for heterogeneous industrial clients and prove convergence to stationary points of the resulting nonconvex objective. Experiments on the MVTec AD benchmark demonstrate consistent and significant AUROC improvements over MAML, Proto-MAML, and PatchCore-based methods in few-shot anomaly detection settings.

Soham Sarkar, Victor M. Panaretos

Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address this problem, we introduce "Covariance Networks" (CovNet) as a modeling and estimation tool. The CovNet model is "universal" - it can be used to approximate any covariance up to desired precision. Moreover, the model can be fitted efficiently to the data and its neural network architecture allows us to employ modern computational tools in the implementation. The CovNet model also admits a closed-form eigendecomposition, which can be computed efficiently, without constructing the covariance itself. This facilitates easy storage and subsequent manipulation of a covariance in the context of the CovNet. We establish consistency of the proposed estimator and derive its rate of convergence. The usefulness of the proposed method is demonstrated by means of an extensive simulation study and an application to resting state fMRI data.

Sarbojit Roy, Soham Sarkar, Subhajit Dutta

In high dimension, low sample size (HDLSS)settings, the simple average distance classifier based on the Euclidean distance performs poorly if differences between the locations get masked by the scale differences. To rectify this issue, modifications to the average distance classifier was proposed by Chan and Hall (2009). However, the existing classifiers cannot discriminate when the populations differ in other aspects than locations and scales. In this article, we propose some simple transformations of the average distance classifier to tackle this issue. The resulting classifiers perform quite well even when the underlying populations have the same location and scale. The high-dimensional behaviour of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated as well as real data sets exhibit the usefulness of the proposed methodology.