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The dominant theme of this thesis is the construction of matrix representations of finite solvable groups using a suitable system of generators. For a finite solvable group $G$ of order $N = p_{1}p_{2}\dots p_{n}$, where $p_{i}$'s are…
Data simulation is fundamental for machine learning and causal inference, as it allows exploration of scenarios and assessment of methods in settings with full control of ground truth. Directed acyclic graphs (DAGs) are well established for…
Foundation models are increasingly developed in computational pathology (CPath) given their promise in facilitating many downstream tasks. While recent studies have evaluated task performance across models, less is known about the structure…
Over the last decade, a number of Computational Imaging (CI) systems have been proposed for tasks such as motion deblurring, defocus deblurring and multispectral imaging. These techniques increase the amount of light reaching the sensor via…
The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…
Covariate adjustment is a widely used approach to estimate total causal effects from observational data. Several graphical criteria have been developed in recent years to identify valid covariates for adjustment from graphical causal…
Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities.…
We develop terminology and methods for working with maximally oriented partially directed acyclic graphs (maximal PDAGs). Maximal PDAGs arise from imposing restrictions on a Markov equivalence class of directed acyclic graphs, or…
Gradient-based methods are a prototypical family of explainability techniques, especially for image-based models. Nonetheless, they have several shortcomings in that they (1) require white-box access to models, (2) are vulnerable to…
Automated segmentation is a fundamental medical image analysis task, which enjoys significant advances due to the advent of deep learning. While foundation models have been useful in natural language processing and some vision tasks for…
Deploying Retrieval-Augmented Generation (RAG) on edge devices is in high demand, but is hindered by the latency of massive data movement and computation on traditional architectures. Compute-in-Memory (CiM) architectures address this…
Recent advancements in biomedical image analysis have been significantly driven by the Segment Anything Model (SAM). This transformative technology, originally developed for general-purpose computer vision, has found rapid application in…
Let $\mathcal{C}$ be a class of finite groups closed for subgroups, quotients groups and extensions. Let $\Gamma$ be a finite simplicial graph and $G = G_{\Gamma}$ be the corresponding pro-$\mathcal C$ RAAG. We show that if $N$ is a…
Beneath the uncertain primitive visual features of face images are the primitive intrinsic structural patterns (PISP) essential for characterizing a sample face discriminative attributes. It is on this basis that this paper presents a…
Recent work on causal abstraction, in particular graphical approaches focusing on causal structure between clusters of variables, aims to summarize a high-dimensional causal structure in terms of a low-dimensional one. Existing methods for…
Computing many useful properties of Boolean formulas, such as their weighted or unweighted model count, is intractable on general representations. It can become tractable when formulas are expressed in a special form, such as the decision…
This paper considers the problem of estimating the structure of multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP…
Directed acyclic graph (DAG) learning is a central task in structure discovery and causal inference. Although the field has witnessed remarkable advances over the past few years, it remains statistically and computationally challenging to…
We present a new class of graded irreducible representations of a Leavitt path algebra. This class is new in the sense that its representation space is not isomorphic to any of the existing simple Chen modules. The corresponding graded…
EEG foundation models are typically pretrained on narrow-source clinical archives and evaluated on benchmarks from the same ecosystem, leaving unclear whether representations encode neural physiology or recording-distribution artifacts. We…