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Unsupervised data representation and visualization using tools from topology is an active and growing field of Topological Data Analysis (TDA) and data science. Its most prominent line of work is based on the so-called Mapper graph, which…

The problem of complex data analysis is a central topic of modern statistical science and learning systems and is becoming of broader interest with the increasing prevalence of high-dimensional data. The challenge is to develop statistical…

This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors…

Almost all statistical and machine learning methods in analyzing brain networks rely on distances and loss functions, which are mostly Euclidean or matrix norms. The Euclidean or matrix distances may fail to capture underlying subtle…

We introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate…

We introduce Deep Linear Discriminant Analysis (DeepLDA) which learns linearly separable latent representations in an end-to-end fashion. Classic LDA extracts features which preserve class separability and is used for dimensionality…

In this paper, we develop a Topological Approximate Dynamic Programming (TADP) method for planningin stochastic systems modeled as Markov Decision Processesto maximize the probability of satisfying high-level systemspecifications expressed…

Recent advances in unsupervised domain adaptation (UDA) show that transferable prototypical learning presents a powerful means for class conditional alignment, which encourages the closeness of cross-domain class centroids. However, the…

Streaming Linear Discriminant Analysis (LDA) while proven in Class-incremental Learning deployments at the edge with limited classes (upto 1000), has not been proven for deployment in extreme classification scenarios. In this paper, we…

Data augmentation (DA) is indispensable in modern machine learning and deep neural networks. The basic idea of DA is to construct new training data to improve the model's generalization by adding slightly disturbed versions of existing data…

Traditional machine learning assumes that training and test sets are derived from the same distribution; however, this assumption does not always hold in practical applications. This distribution disparity can lead to severe performance…

Domain Adaptation (DA), the process of effectively adapting task models learned on one domain, the source, to other related but distinct domains, the targets, with no or minimal retraining, is typically accomplished using the process of…

Topological Data Analysis (TDA) is a field that leverages tools and ideas from algebraic topology to provide robust methods for analysing geometric and topological aspects of data. One of the principal tools of TDA, persistent homology,…

Training data attribution (TDA) methods aim to identify which training examples influence a model's predictions on specific test data most. By quantifying these influences, TDA supports critical applications such as data debugging,…

The attention mechanism is an important reason for the success of transformers. It relies on computing pairwise relations between tokens. To reduce the high computational cost of standard quadratic attention, linear attention has been…

Higher-order data with high dimensionality is of immense importance in many areas of machine learning, computer vision, and video analytics. Multidimensional arrays (commonly referred to as tensors) are used for arranging higher-order data…

Precision mental health requires treatment decisions that account for heterogeneous symptoms reflecting multiple clinical domains. However, existing methods for estimating individualized treatment effects (ITE) rely on a single summary…

Multimodal models have demonstrated powerful capabilities in complex tasks requiring multimodal alignment, including zero-shot classification and cross-modal retrieval. However, existing models typically rely on millions of paired…

Unsupervised domain adaptation (UDA) adapts a model trained on one domain (called source) to a novel domain (called target) using only unlabeled data. Due to its high annotation cost, researchers have developed many UDA methods for semantic…

In this work we define a metric structure to compare functions defined on different merge trees. The metric introduced possesses some stability properties, which we illustrate within a standard topological data analysis (TDA) framework, and…