Model-based Sketching and Recovery with Expanders

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In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

Transformer models such as GPT generate human-like language and are predictive of human brain responses to language. Here, using functional-MRI-measured brain responses to 1,000 diverse sentences, we first show that a GPT-based encoding model can predict t ...

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

\gamma

and momentum parameter

\beta

that allows u ...

Speech recognition-based applications upon the advancements in artificial intelligence play an essential role to transform most aspects of modern life. However, speech recognition in real-life conditions (e.g., in the presence of overlapping speech, varyin ...

In this paper, we investigate the impact of stochasticity and large stepsizes on the implicit regularisation of gradient descent (GD) and stochastic gradient descent (SGD) over diagonal linear networks. We prove the convergence of GD and SGD with macroscop ...

This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex relationships between ...

By the addition of entropic regularization, multimarginal optimal transport problems can be trans-formed into tensor scaling problems, which can be solved numerically using the multimarginal Sinkhorn algorithm. The main computational bottleneck of this alg ...

Synaptic plasticity underlies our ability to learn and adapt to the constantly changing environment. The phenomenon of synapses changing their efficacy in an activity-dependent manner is often studied in small groups of neurons in vitro or indirectly throu ...

End-to-end learning methods like deep neural networks have been the driving force in the remarkable progress of machine learning in recent years. However, despite their success, the deployment process of such networks in safety-critical use cases, such as ...

Fast and accurate transmission line outage detection can help the central control unit to respond rapidly to better maintain the security and reliability of power systems. It is especially critical in the situation of multiple line outages which is more li ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

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We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

One of the most basic graph problems, All-Pairs Shortest Paths (APSP) is known to be solvable in n^{3-o(1)} time, and it is widely open whether it has an O(n^{3-ε}) time algorithm for ε > 0. To better understand APSP, one often strives to obtain subcubic t ...

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In this article, we are interested in adaptive and distributed estimation of graph filters from streaming data. We formulate this problem as a consensus estimation problem over graphs, which can be addressed with diffusion LMS strategies. Most popular grap ...

The goal of this thesis is to study continuous-domain inverse problems for the reconstruction of sparse signals and to develop efficient algorithms to solve such problems computationally. The task is to recover a signal of interest as a continuous function ...

Model-based Sketching and Recovery with Expanders

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