Related papers: Scalable Machine Learning Algorithms using Path Si…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

Understanding large-scale patterns in student course enrollment is a problem of great interest to university administrators and educational researchers. Yet important decisions are often made without a good quantitative framework of the…

Large neural networks trained on large datasets have become the dominant paradigm in machine learning. These systems rely on maximum likelihood point estimates of their parameters, precluding them from expressing model uncertainty. This may…

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

Obtaining accurate information about future traffic flows of all links in a traffic network is of great importance for traffic management and control applications. This research studies two particular problems in traffic forecasting: (1)…

In this paper, we introduce the branched signature model, motivated by the branched rough path framework of [Gubinelli, Journal of Differential Equations, 248(4), 2010], which generalizes the classical geometric rough path. We establish a…

Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…

Inference and prediction of routes have become of interest over the past decade owing to a dramatic increase in package delivery and ride-sharing services. Given the underlying combinatorial structure and the incorporation of probabilities,…

The signature is a canonical representation of a multidimensional path over an interval. However, it treats all historical information uniformly, offering no intrinsic mechanism for contextualising the relevance of the past. To address…

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

Temporal graph learning is pivotal for deciphering dynamic systems, where the core challenge lies in explicitly modeling the underlying evolving patterns that govern network transformation. However, prevailing methods are predominantly…

In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…

Reliable molecular property prediction is essential for various scientific endeavors and industrial applications, such as drug discovery. However, the data scarcity, combined with the highly non-linear causal relationships between…

Complex structures are typical in machine learning. Tailoring learning algorithms for every structure requires an effort that may be saved by defining a generic learning procedure adaptive to any complex structure. In this paper, we propose…

Large Language Models (LLMs) face significant limitations when applied to large-scale graphs, struggling with context constraints and inflexible reasoning. We present GraphChain, a framework that enables LLMs to analyze complex graphs…

Large scale pretrained models have revolutionized Natural Language Processing (NLP) and Computer Vision (CV), showcasing remarkable cross domain generalization abilities. However, in graph learning, models are typically trained on…

Graph neural networks (GNNs) have shown great potential in learning on graphs, but they are known to perform sub-optimally on link prediction tasks. Existing GNNs are primarily designed to learn node-wise representations and usually fail to…

High dimensional piecewise stationary graphical models represent a versatile class for modelling time varying networks arising in diverse application areas, including biology, economics, and social sciences. There has been recent work in…

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…