3,758 research outputs found
UMSL Bulletin 2023-2024
The 2023-2024 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1088/thumbnail.jp
Machine learning in solar physics
The application of machine learning in solar physics has the potential to
greatly enhance our understanding of the complex processes that take place in
the atmosphere of the Sun. By using techniques such as deep learning, we are
now in the position to analyze large amounts of data from solar observations
and identify patterns and trends that may not have been apparent using
traditional methods. This can help us improve our understanding of explosive
events like solar flares, which can have a strong effect on the Earth
environment. Predicting hazardous events on Earth becomes crucial for our
technological society. Machine learning can also improve our understanding of
the inner workings of the sun itself by allowing us to go deeper into the data
and to propose more complex models to explain them. Additionally, the use of
machine learning can help to automate the analysis of solar data, reducing the
need for manual labor and increasing the efficiency of research in this field.Comment: 100 pages, 13 figures, 286 references, accepted for publication as a
Living Review in Solar Physics (LRSP
The Geometric Median and Applications to Robust Mean Estimation
This paper is devoted to the statistical and numerical properties of the
geometric median, and its applications to the problem of robust mean estimation
via the median of means principle. Our main theoretical results include (a) an
upper bound for the distance between the mean and the median for general
absolutely continuous distributions in R^d, and examples of specific classes of
distributions for which these bounds do not depend on the ambient dimension
; (b) exponential deviation inequalities for the distance between the sample
and the population versions of the geometric median, which again depend only on
the trace-type quantities and not on the ambient dimension. As a corollary, we
deduce improved bounds for the (geometric) median of means estimator that hold
for large classes of heavy-tailed distributions. Finally, we address the error
of numerical approximation, which is an important practical aspect of any
statistical estimation procedure. We demonstrate that the objective function
minimized by the geometric median satisfies a "local quadratic growth"
condition that allows one to translate suboptimality bounds for the objective
function to the corresponding bounds for the numerical approximation to the
median itself. As a corollary, we propose a simple stopping rule (applicable to
any optimization method) which yields explicit error guarantees. We conclude
with the numerical experiments including the application to estimation of mean
values of log-returns for S&P 500 data.Comment: 28 pages, 2 figure
Beam scanning by liquid-crystal biasing in a modified SIW structure
A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium
Compressed and distributed least-squares regression: convergence rates with applications to Federated Learning
In this paper, we investigate the impact of compression on stochastic
gradient algorithms for machine learning, a technique widely used in
distributed and federated learning. We underline differences in terms of
convergence rates between several unbiased compression operators, that all
satisfy the same condition on their variance, thus going beyond the classical
worst-case analysis. To do so, we focus on the case of least-squares regression
(LSR) and analyze a general stochastic approximation algorithm for minimizing
quadratic functions relying on a random field. We consider weak assumptions on
the random field, tailored to the analysis (specifically, expected H\"older
regularity), and on the noise covariance, enabling the analysis of various
randomizing mechanisms, including compression. We then extend our results to
the case of federated learning.
More formally, we highlight the impact on the convergence of the covariance
of the additive noise induced by the algorithm.
We demonstrate despite the non-regularity of the stochastic field, that the
limit variance term scales with (where is the Hessian of the optimization problem and the
number of iterations) generalizing the rate for the vanilla LSR case where it
is (Bach and Moulines,
2013). Then, we analyze the dependency of on the
compression strategy and ultimately its impact on convergence, first in the
centralized case, then in two heterogeneous FL frameworks
Algorithmic Behaviours of Adagrad in Underdetermined Linear Regression
With the high use of over-parameterized data in deep learning, the choice of optimizer in training plays a big role in a model’s ability to generalize well due to the existence of solution selection bias. We consider the popular adaptive gradient method: Adagrad, and aim to study its convergence and algorithmic biases in the underdetermined linear regression regime. First we prove that Adagrad converges in this problem regime. Subsequently, we empirically find that when using sufficiently small step sizes, Adagrad promotes diffuse solutions, in the sense of uniformity among the coordinates of the solution. Additionally, when compared to gradient descent, we see empirically and show theoretically that Adagrad’s solution, under the same conditions, exhibits greater diffusion compared to the solution obtained through gradient descent. This behaviour is unexpected as conventional data science encourages the utilization of optimizers that attain sparser solutions. This preference arises due to some inherent advantages such as helping to prevent overfitting, and reducing the dimensionality of the data. However, we show that in the application of interpolation, diffuse solutions yield beneficial results when compared to solutions with localization; Namely, we experimentally observe the success of diffuse solutions when interpolating a line via the weighted sum of spike-like functions. The thesis concludes with some suggestions to possible extensions of the content in future work
Tradition and Innovation in Construction Project Management
This book is a reprint of the Special Issue 'Tradition and Innovation in Construction Project Management' that was published in the journal Buildings
Modeling and Simulation in Engineering
The Special Issue Modeling and Simulation in Engineering, belonging to the section Engineering Mathematics of the Journal Mathematics, publishes original research papers dealing with advanced simulation and modeling techniques. The present book, “Modeling and Simulation in Engineering I, 2022”, contains 14 papers accepted after peer review by recognized specialists in the field. The papers address different topics occurring in engineering, such as ferrofluid transport in magnetic fields, non-fractal signal analysis, fractional derivatives, applications of swarm algorithms and evolutionary algorithms (genetic algorithms), inverse methods for inverse problems, numerical analysis of heat and mass transfer, numerical solutions for fractional differential equations, Kriging modelling, theory of the modelling methodology, and artificial neural networks for fault diagnosis in electric circuits. It is hoped that the papers selected for this issue will attract a significant audience in the scientific community and will further stimulate research involving modelling and simulation in mathematical physics and in engineering
Sparse Plus Low Rank Matrix Decomposition: A Discrete Optimization Approach
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the
problem of decomposing a corrupted data matrix into a sparse matrix of
perturbations plus a low-rank matrix containing the ground truth. SLR is a
fundamental problem in Operations Research and Machine Learning which arises in
various applications, including data compression, latent semantic indexing,
collaborative filtering, and medical imaging. We introduce a novel formulation
for SLR that directly models its underlying discreteness. For this formulation,
we develop an alternating minimization heuristic that computes high-quality
solutions and a novel semidefinite relaxation that provides meaningful bounds
for the solutions returned by our heuristic. We also develop a custom
branch-and-bound algorithm that leverages our heuristic and convex relaxations
to solve small instances of SLR to certifiable (near) optimality. Given an
input -by- matrix, our heuristic scales to solve instances where
in minutes, our relaxation scales to instances where in
hours, and our branch-and-bound algorithm scales to instances where in
minutes. Our numerical results demonstrate that our approach outperforms
existing state-of-the-art approaches in terms of rank, sparsity, and
mean-square error while maintaining a comparable runtime
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