In this paper, we study an emerging class of neural networks, the Morphological Neural networks, from some modern perspectives. Our approach utilizes ideas from tropical geometry and mathematical morphology. First, we state the training of a binary morphol ...
Inverse reconstruction from images is a central problem in many scientific and engineering disciplines. Recent progress on differentiable rendering has led to methods that can efficiently differentiate the full process of image formation with respect to mi ...
In this dissertation, we propose gradient-based methods for characterizing model behaviour for the purposes of knowledge transfer and post-hoc model interpretation. Broadly, gradients capture the variation of some output feature of the model upon unit vari ...
Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available wor ...
Stochastic gradient descent (SGD) and randomized coordinate descent (RCD) are two of the workhorses for training modern automated decision systems. Intriguingly, convergence properties of these methods are not well-established as we move away from the spec ...
We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...
We give an information-theoretic interpretation of Canonical Correlation Analysis (CCA) via (relaxed) Wyner's common information. CCA permits to extract from two high-dimensional data sets low-dimensional descriptions (features) that capture the commonalit ...
In developed countries, the management of existing civil infrastructure is challenging due to evolving functional requirements, aging and climate change. Due to conservative approaches in construction design and practice, infrastructure often has hidden re ...
In the era of big data, new transportation-related concepts and methodologies need to be proposed for understanding how congestion propagates. pNEUMA, a unique dataset that was acquired during a first-of-its-kind experiment with a swarm of drones over a de ...
