Topological Signatures of Adversaries in Multimodal Alignments

Multimodal Machine Learning systems, particularly those aligning text and image data like CLIP/BLIP models, have become increasingly prevalent, yet remain susceptible to adversarial attacks. While substantial research has addressed adversarial robustness in unimodal contexts, defense strategies for multimodal systems are underexplored. This work investigates the topological signatures that arise between image and text embeddings and shows how adversarial attacks disrupt their alignment, introducing distinctive signatures. We specifically leverage persistent homology and introduce two novel Topological-Contrastive losses based on Total Persistence and Multi-scale kernel methods to analyze the topological signatures introduced by adversarial perturbations. We observe a pattern of monotonic changes in the proposed topological losses emerging in a wide range of attacks on image-text alignments, as more adversarial samples are introduced in the data. By designing an algorithm to back-propagate these signatures to input samples, we are able to integrate these signatures into Maximum Mean Discrepancy tests, creating a novel class of tests that leverage topological signatures for better adversarial detection.

On Prediction Feature Assignment in the Heckman Selection Model

Under missing-not-at-random (MNAR) sample selection bias, the performance of a prediction model is often degraded. This paper focuses on one classic instance of MNAR sample selection bias where a subset of samples have non-randomly missing outcomes. The Heckman selection model and its variants have commonly been used to handle this type of sample selection bias. The Heckman model uses two separate equations to model the prediction and selection of samples, where the selection features include all prediction features. When using the Heckman model, the prediction features must be properly chosen from the set of selection features. However, choosing the proper prediction features is a challenging task for the Heckman model. This is especially the case when the number of selection features is large. Existing approaches that use the Heckman model often provide a manually chosen set of prediction features. In this paper, we propose Heckman-FA as a novel data-driven framework for obtaining prediction features for the Heckman model. Heckman-FA first trains an assignment function that determines whether or not a selection feature is assigned as a prediction feature. Using the parameters of the trained function, the framework extracts a suitable set of prediction features based on the goodness-of-fit of the prediction model given the chosen prediction features and the correlation between noise terms of the prediction and selection equations. Experimental results on real-world datasets show that Heckman-FA produces a robust regression model under MNAR sample selection bias.

A Robust Classifier Under Missing-Not-At-Random Sample Selection Bias

The shift between the training and testing distributions is commonly due to sample selection bias, a type of bias caused by non-random sampling of examples to be included in the training set. Although there are many approaches proposed to learn a classifier under sample selection bias, few address the case where a subset of labels in the training set are missing-not-at-random (MNAR) as a result of the selection process. In statistics, Greene's method formulates this type of sample selection with logistic regression as the prediction model. However, we find that simply integrating this method into a robust classification framework is not effective for this bias setting. In this paper, we propose BiasCorr, an algorithm that improves on Greene's method by modifying the original training set in order for a classifier to learn under MNAR sample selection bias. We provide theoretical guarantee for the improvement of BiasCorr over Greene's method by analyzing its bias. Experimental results on real-world datasets demonstrate that BiasCorr produces robust classifiers and can be extended to outperform state-of-the-art classifiers that have been proposed to train under sample selection bias.