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Frequency-Resolved Optical Gating Recovery via Smoothing Gradient

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arXiv 2019年

作者： Pinilla, Samuel Bendory, Tamir Eldar, Yonina C. Arguello, Henry Department of Electrical Engineering Universidad Industrial de Santander BucaramangaSantander680002 Colombia Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Weizmann Institute of Science Rehovot7610001 Israel Department of Computer Science Universidad Industrial de Santander BucaramangaSantander680002 Colombia

Frequency-resolved optical gating (FROG) is a popular technique for complete characterization of ultrashort laser pulses. The acquired data in FROG, called FROG trace, is the Fourier magnitude of the product of the unknown pulse with a time-shifted version of itself, for several different shifts. To estimate the pulse from the FROG trace, we propose an algorithm that minimizes a smoothed non-convex least-squares objective function. The method consists of two steps. First, we approximate the pulse by an iterative spectral algorithm. Then, the attained initialization is refined based upon a sequence of block stochastic gradient iterations. The algorithm is theoretically simple, numerically scalable, and easy-to-implement. Empirically, our approach outperforms the state-of-the-art when the FROG trace is incomplete, that is, when only few shifts are recorded. Simulations also suggest that the proposed algorithm exhibits similar computational cost compared to a state-of-the-art technique for both complete and incomplete data. In addition, we prove that in the vicinity of the true solution, the algorithm converges to a critical point. A Matlab implementation is publicly available at https://***/samuelpinilla/FROG. Copyright © 2019, The Authors. All rights reserved.

关键词： Ultrashort pulses

Geometry-based data generation

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arXiv 2018年

作者： Lindenbaum, Ofir Stanley, Jay S. Wolf, Guy Krishnaswamy, Smita Department of Genetics Yale University New HavenCT United States Applied Mathematics Program Yale University New HavenCT United States Computational Biology & Bioinformatics Program Yale University New HavenCT United States Department of Computer Science Yale University New HavenCT United States

We propose a new type of generative model of high-dimensional data that learns a manifold geometry of the data, rather than density, and can generate points evenly along this manifold. This is in contrast to existing generative models that represent data density, and are strongly affected by noise and other artifacts of data collection. We demonstrate how this approach corrects sampling biases and artifacts, and improves several downstream data analysis tasks such as clustering and classification. Finally, we demonstrate that this approach is especially useful in biology where, despite the advent of single-cell technologies, rare subpopulations and gene-interaction relationships are affected by biased sampling. We show that SUGAR can generate hypothetical populations and reveal intrinsic patterns and mutual-information relationships between genes on a single cell dataset of hematopoiesis. Copyright © 2018, The Authors. All rights reserved.

关键词： Clustering algorithms

Crouzeix’s Conjecture and Related Problems

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arXiv 2020年

作者： Bickel, Kelly Gorkin, Pamela Greenbaum, Anne Ransford, Thomas Schwenninger, Felix Wegert, Elias Department of Mathematics Bucknell University LewisburgPA17837 United States Department of Mathematics Bucknell University LewisburgPA17837 United States Department of Applied Mathematics University of Washington Département de mathématiques et de statistique Université Laval QuébecQCG1V 0A6 Canada Department of Mathematics Universität Hamburg Department of Applied Mathematics University of Twente Netherlands Department of Mathematics and Computer Science Technische Universität Bergakademie Freiberg Division of Mathematical Sciences National Science Foundation United States NSERC and the Canada Research Chairs program

In this paper, we establish several results related to Crouzeixs conjecture. We show that the conjecture holds for contractions with eigenvalues that are sufficiently well-separated. This separation is measured by the so-called separation constant, which is defined in terms of the pseudohyperbolic metric. Moreover, we study general properties of related extremal functions and associated vectors. Throughout, compressions of the shift serve as illustrating examples which also allow for refined *** Codes 47A25, 47A12, 15A60, 47A20, 30J10 Copyright © 2020, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Bayesian Formulations for Graph Spectral Denoising

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arXiv 2023年

作者： Leone, Sam Sun, Xingzhi Perlmutter, Michael Krishnaswamy, Smita Program for Applied Mathematics Yale University United States Department of Computer Science Yale University United States Department of Mathematics Boise State University United States Department of Genetics Yale School of Medicine United States Wu Tsai Institute Yale University United States FAIR Meta AI United States Computational Biology and Bioinformatics Program Yale University United States

Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is very high-dimensional, but its structure can be captured via an affinity graph. This allows us to utilize ideas from graph signal processing. In particular, we present algorithms for the cases where the signal is perturbed by Gaussian noise, dropout, and uniformly distributed noise. The signals are assumed to follow a prior distribution defined in the frequency domain which favors signals which are smooth across the edges of the graph. By pairing this prior distribution with our three models of noise generation, we propose Maximum A Posteriori (M.A.P.) estimates of the true signal in the presence of noisy data and provide algorithms for computing the M.A.P. Finally, we demonstrate the algorithms' ability to effectively restore signals from white noise on image data and from severe dropout in single-cell RNA sequence data. © 2023, CC BY.

关键词： Frequency domain analysis

Unbiased Estimation Using a Class of Diffusion Processes

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SSRN

SSRN 2022年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (Rd,B(Rd)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}t∈[0,1] on Rd, d ∈ N0. This latter process is constructed such that, starting at X0 = 0, one has X1 ∼ π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10, 15] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(Ε2), for arbitrary Ε > 0, the associated cost is O(Ε−5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(Ε2), the associated cost is, with high probability, O(Ε−2|log(Ε)|2+δ), for any δ > 0. We implement our method on several examples including Bayesian inverse problems. © 2022, The Authors. All rights reserved.

关键词： Diffusion

Sequential Markov Chain Monte Carlo for Lagrangian Data Assimilation with Applications to Unknown Data Locations

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arXiv 2023年

We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is high-dimensional, but the model for the signal yields longer-range time dependencies through the observation locations. Motivated by this model we revisit a lesser-known and provably convergent computational methodology from [4, 11, 28] that uses sequential Markov Chain Monte Carlo (MCMC) chains. We extend this methodology for data filtering problems with unknown observation locations. We benchmark our algorithms on Linear Gaussian state space models against competing ensemble methods and demonstrate a significant improvement in both execution speed and accuracy. Finally, we implement a realistic case study on a high-dimensional rotating shallow water model (of about 104 - 105 dimensions) with real and synthetic data. The data is provided by the National Oceanic and Atmospheric Administration (NOAA) and contains observations from ocean drifters in a domain of the Atlantic Ocean restricted to the longitude and latitude intervals [-51◦,-41◦], [17◦,27◦] *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2023, CC BY.

关键词： Location

The Smart Analysis of Performing Scalable Inference for Big Data Analytics

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The Smart Analysis of Performing Scalable Inference for Big ...

2023 International Conference on Power Energy, Environment and Intelligent Control, PEEIC 2023

作者： Bhandarkar, Vishakha D. Rongali, Aruna Sri Shamout, Mohamed Dawood Pund, Sachin Nama, Gigih Forda Patil, Shrishailappa Yeshwantrao Chavan College of Engineering Applied Mathematics and Humanities India University of the Cumberlands Graduate Doctoral Information Technology Information Technology Emphasis/Information Technology United States College of Business Administration University of Sharjah Department of Management Sharjah United Arab Emirates Shri Ramdeobaba College of Engineering and Management Department of Industrial Engineering Maharashtra Nagpur India Doctoral Program of Environtmental Science University of Lampung Department of Informatics Bandar Lampung Indonesia Vishwakarma Institute of Technology Computer Engineering Pune India

ISBN: (纸本)9798350357769

This paper examines the reproducibility of massive information analytics under particular factors. The paper proposes the 'performing Scalable Inference' technique to cope with scalability troubles and to exploit current big statistics platforms for efficient computing and statistics garage of the statistics. In particular, the paper describes how to perform leak-free, parallelizable visible analytics over massive datasets using present extensive records analytics frameworks such as Apache Flink. This method presents an automated manner to execute analytics that preserves reproducibility and the ability to make adjustments without re-running the entire technique. The paper also demonstrates how these analytics may help several real-world use instances, explore affected person cohorts for studies, and develop stratified patient cohorts for hospital therapy. In the end, the paper observes how the proposed method may be exercised within the real world. Actively scalable inference for massive information analytics is pivotal in optimizing decision-making and allocation of assets. Typically, such inferences are made based on information accumulated from numerous sources, databases, unstructured data, and different digital sources. So one can ensure scalability, a complete cloud-primarily based platform has to be hired. This solution will permit the ***, deploying the essential records series and evaluation algorithms are prime here. It could permit the platform to recognize the styles inside the statistics and discover any ability correlations or traits. Additionally, predictive analytics and system mastering strategies may be incorporated to provide insights into the results of the information. In the long run, by leveraging those techniques, the platform can draw efficient inferences and appropriately compare situations in an agile and green way.. © 2023 IEEE.

关键词： adjustments an a lytics automated preserves statistics

Learning binary latent variable models: A tensor eigenpair approach

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arXiv 2018年

作者： Jaffe, Ariel Weiss, Roi Carmi, Shai Kluger, Yuval Nadler, Boaz Dept. of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot7610001 Israel Braun School of Public Health and Community Medicine Hebrew University of Jerusalem Jerusalem9112102 Israel Interdepartmental Program in Computational Biology and Bioinformatics Yale University New HavenCT06511 United States Dept. of Pathology Yale Cancer Center Yale University School of Medicine New HavenCT06520 United States Program of Applied Mathematics Yale University New HavenCT06511 United States

Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this problem, based on the eigenvectors of both the second order moment matrix and third order moment tensor of the observed data. We prove that under mild non-degeneracy conditions, our method consistently estimates the model parameters at the optimal parametric rate. Our tensor-based method generalizes previous orthogonal tensor decomposition approaches, where the hidden units were assumed to be either statistically independent or mutually exclusive. We illustrate the consistency of our method on simulated data and demonstrate its usefulness in learning a common model for population mixtures in genetics. Copyright © 2018, The Authors. All rights reserved.

关键词： Tensors

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Wire Before You Walk

Wire Before You Walk

Asilomar Conference on Signals, Systems & computers

作者： Tesfa Asmara Dhananjay Bhaskar Ian Adelstein Smita Krishnaswamy Michael Perlmutter Department of Computer Science Pomona College Claremont CA USA Mathematics and Statistics Pomona College Claremont CA USA Department of Genetics Yale School of Medicine New Haven CT USA Department of Mathematics Yale University New Haven CT USA Department of Computer Science Yale University New Haven CT USA Program for Applied Mathematics Yale University New Haven CT USA Computational Biology and Bioinformatics Program Yale University New Haven CT USA Wu Tsai Institute Yale University New Haven CT USA Department of Mathematics Boise State University Boise ID USA

Node embeddings aim to associate a vector to every vertex of a graph which can then be used for downstream tasks such as clustering, classification, or link prediction. Many popular node embeddings such as no $d$ e2vec and DeepWalk are based upon counting which nodes frequently co-occur in random walks of the graph. In this paper, we show that the performance of such algorithms can be improved by rewiring the edges of the graph through a variety of network indices before running DeepWalk. These rewirings effectively give the random walker an inductive bias and increase the accuracy of a logistic regression classifier applied to the node embedding on several benchmark data sets.

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