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Seismic datasets contain valuable information that originate from areas of interest in the subsurface; such seismic reflections are however inevitably contaminated by other events created by waves reverberating in the overburden.…
We study generalization properties of random features (RF) regression in high dimensions optimized by stochastic gradient descent (SGD) in under-/over-parameterized regime. In this work, we derive precise non-asymptotic error bounds of RF…
This paper considers a general data-fitting problem over a networked system, in which many computing nodes are connected by an undirected graph. This kind of problem can find many real-world applications and has been studied extensively in…
Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the…
Deep Neural Network (DNN) based super-resolution algorithms have greatly improved the quality of the generated images. However, these algorithms often yield significant artifacts when dealing with real-world super-resolution problems due to…
Noise fundamentally limits the performance and predictive capabilities of classical and quantum dynamical systems by degrading stability and obscuring intrinsic dynamical characteristics. Characterizing such noise accurately is essential…
Dynamical decoupling (DD) is a promising technique for mitigating errors in near-term quantum devices. However, its effectiveness depends on both hardware characteristics and algorithm implementation details. This paper explores the…
One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A…
Many contemporary signal processing, machine learning and wireless communication applications can be formulated as nonconvex nonsmooth optimization problems. Often there is a lack of efficient algorithms for these problems, especially when…
As the key advancement of the convolutional neural networks (CNNs), depthwise separable convolutions (DSCs) are becoming one of the most popular techniques to reduce the computations and parameters size of CNNs meanwhile maintaining the…
While there exists a rich array of matrix column subset selection problem (CSSP) algorithms for use with interpolative and CUR-type decompositions, their use can often become prohibitive as the size of the input matrix increases. In an…
The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…
Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…
Deep learning networks are typically trained by Stochastic Gradient Descent (SGD) methods that iteratively improve the model parameters by estimating a gradient on a very small fraction of the training data. A major roadblock faced when…
GS2 is an initial value gyrokinetic simulation code developed to study low-frequency turbulence in magnetized plasma. It is parallelised using MPI with the simulation domain decomposed across tasks. The optimal domain decomposition is…
The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. In this…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
We study the relationship between disturbance decoupling (DD) and H2 optimal control for linear time-invariant (LTI) systems, revealing a fundamental gap between DD subspace constraints and semi-definite program (SDP)-based H2 minimization.…
Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…
The precision, stability, and performance of lightweight high-strength steel structures in heavy machinery is affected by their highly nonlinear dynamics. This, in turn, makes control more difficult, simulation more computationally…