IA Scholar Query: Inexact Matching of Large and Sparse Graphs Using Laplacian Eigenvectors.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 07 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Variational methods and its applications to computer vision
https://scholar.archive.org/work/dtthbdie4vf7nc4nxvyanwq7rq
Many computer vision applications such as image segmentation can be formulated in a "variational" way as energy minimization problems. Unfortunately, the computational task of minimizing these energies is usually difficult as it generally involves non convex functions in a space with thousands of dimensions and often the associated combinatorial problems are NP-hard to solve. Furthermore, they are ill-posed inverse problems and therefore are extremely sensitive to perturbations (e.g. noise). For this reason in order to compute a physically reliable approximation from given noisy data, it is necessary to incorporate into the mathematical model appropriate regularizations that require complex computations. The main aim of this work is to describe variational segmentation methods that are particularly effective for curvilinear structures. Due to their complex geometry, classical regularization techniques cannot be adopted because they lead to the loss of most of low contrasted details. In contrast, the proposed method not only better preserves curvilinear structures, but also reconnects some parts that may have been disconnected by noise. Moreover, it can be easily extensible to graphs and successfully applied to different types of data such as medical imagery (i.e. vessels, hearth coronaries etc), material samples (i.e. concrete) and satellite signals (i.e. streets, rivers etc.). In particular, we will show results and performances about an implementation targeting new generation of High Performance Computing (HPC) architectures where different types of coprocessors cooperate. The involved dataset consists of approximately 200 images of cracks, captured in three different tunnels by a robotic machine designed for the European ROBO-SPECT project.Erika Pellegrino, Panagiota Stathakiwork_dtthbdie4vf7nc4nxvyanwq7rqWed, 07 Sep 2022 00:00:00 GMTNeural Quantum States for Scientific Computing: Applications to Computational Chemistry and Finance
https://scholar.archive.org/work/z3junf2h2jdtvcdanbbffnwj4y
The variational quantum Monte Carlo (VQMC) method has received significant attention because of its ability to overcome the curse of dimensionality inherent in many-body quantum systems, by representing the exponentially complex quantum states variationally with machine learning models. We develop novel training strategies to improve the scalability of VQMC, and build parallelization frameworks for solving large-scale problems. The application of our method is extended to quantum chemistry and financial derivative pricing. For quantum chemistry, we build a pre-processing pipeline serving as an interface connecting molecular information and VQMC, and achieve remarkable performance in comparison with the classical approximate methods. On the other hand, we present a simple generalization of VQMC applicable to arbitrary linear PDEs, showcasing the technique in the Black-Scholes equation for pricing European contingent claims dependent on many underlying assets. We also introduce meta-learning and multi-fidelity active learning as exotic components to VQMC, which, under some reasonable assumptions on the problem formulation, can further improve the convergence and the sampling efficiency of our method.Tianchen Zhao, University, Mywork_z3junf2h2jdtvcdanbbffnwj4yTue, 06 Sep 2022 00:00:00 GMTOptimising Stable Radicals for the Electrochemical Generation of Reactive Intermediates
https://scholar.archive.org/work/eawknghuzvcrnn6sgpxgsoj7w4
This thesis concentrates on the electrochemical activation of stable-radical adducts to generate reactive intermediates for small molecule and polymer chemistry. The majority of this work concerns the computational modelling and design of such compounds using high-level, ab inito quantum chemistry methods. The main findings are as follows. It is first shown that adducts based on highly-stable Blatter and Kuhn-type radicals undergo mesolytic cleavage upon one-electron oxidation, generating reactive carbocations or carbon-centred radicals. Substituent effects are employed to optimise this chemistry, either to reduce the oxidation potential of the adduct to favour the production of radicals, or by altering the bond-dissociation free energy of mesolytic cleavage to control the rate of fragmentation. Computational chemistry is then used to explore the scope for stable-radical adducts as electrochemically activated alkylating agents. SN2-type methylations of pyridine are studied over a broad range of nitroxide, triazinyl, and verdazyl-based adducts (X-Me). Here, high oxidation potentials are found to render low SN2 barriers to methylation and thus more reactive agents, highlighting the suitability of commercially available, (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO), in this role. Modelling is also applied to study the triboelectrification of polymeric insulators. Here, material-specific charging properties and dissipation rates are found to be connected to the stability of anionic polymer fragments to oxidation, and cationic fragments to reduction. Computational methods are then used to study the low-frequency (Terahertz) vibrations in molecular crystals. A method benchmark is presented - identifying parameters that reliably produce accurate simulated spectra - along with several new analytical tools built for the assessment of spectral data.Fergus Rogers, University, The Australian Nationalwork_eawknghuzvcrnn6sgpxgsoj7w4Sat, 13 Aug 2022 00:00:00 GMTReview of data processing of functional optical microscopy for neuroscience
https://scholar.archive.org/work/y7zfqs3hm5bvjel4ifcqcmq2rq
Functional optical imaging in neuroscience is rapidly growing with the development of optical systems and fluorescence indicators. To realize the potential of these massive spatiotemporal datasets for relating neuronal activity to behavior and stimuli and uncovering local circuits in the brain, accurate automated processing is increasingly essential. We cover recent computational developments in the full data processing pipeline of functional optical microscopy for neuroscience data and discuss ongoing and emerging challenges.Hadas Benisty, Alexander Song, Gal Mishne, Adam S. Charleswork_y7zfqs3hm5bvjel4ifcqcmq2rqThu, 04 Aug 2022 00:00:00 GMTLet's Make Block Coordinate Descent Converge Faster: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence
https://scholar.archive.org/work/ioo5osphkzh6lkujg7daz2chhy
Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.Julie Nutini and Issam Laradji and Mark Schmidtwork_ioo5osphkzh6lkujg7daz2chhySun, 31 Jul 2022 00:00:00 GMTAutomatic coarsening in Algebraic Multigrid utilizing quality measures for matching-based aggregations
https://scholar.archive.org/work/gaapqivffbfdhcrl2p4elutapi
In this paper, we discuss the convergence of an Algebraic MultiGrid (AMG) method for general symmetric positive-definite matrices. The method relies on an aggregation algorithm, named coarsening based on compatible weighted matching, which exploits the interplay between the principle of compatible relaxation and the maximum product matching in undirected weighted graphs. The results are based on a general convergence analysis theory applied to the class of AMG methods employing unsmoothed aggregation and identifying a quality measure for the coarsening; similar quality measures were originally introduced and applied to other methods as tools to obtain good quality aggregates leading to optimal convergence for M-matrices. The analysis, as well as the coarsening procedure, is purely algebraic and, in our case, allows an a posteriori evaluation of the quality of the aggregation procedure which we apply to analyze the impact of approximate algorithms for matching computation and the definition of graph edge weights. We also explore the connection between the choice of the aggregates and the compatible relaxation convergence, confirming the consistency between theories for designing coarsening procedures in purely algebraic multigrid methods and the effectiveness of the coarsening based on compatible weighted matching. We discuss various completely automatic algorithmic approaches to obtain aggregates for which good convergence properties are achieved on various test cases.Pasqua D'Ambra, Fabio Durastante, Salvatore Filippone, Ludmil Zikatanovwork_gaapqivffbfdhcrl2p4elutapiSun, 31 Jul 2022 00:00:00 GMTAnalytic relations between networks: encoding, decoding, and causality
https://scholar.archive.org/work/utfsjdmub5d7jgppfgjolikhwq
Networks are common in physics, biology, computer science, and social science. Quantifying the relations (e.g., similarity) between networks paves the way for understanding the latent information shared across networks. However, fundamental metrics of relations, such as information divergence, mutual information, Fisher information, and causality, are not well-defined between networks. As a compromise, commonly used strategies (e.g., network embedding, matching, and kernel approaches) measure network relations in data-driven ways. These approaches are computation-oriented and inapplicable to analytic derivations in mathematics and physics. To resolve these issues, we present a theory to derive an optimal characterization of network topological properties. Our theory shows that a network can be fully represented by a Gaussian variable defined by the discrete Schrödinger operator, which simultaneously satisfies network-topology-dependent smoothness and maximum entropy properties. Based on this characterization, we can analytically measure diverse relations between networks in terms of topology properties. As illustrations, we primarily show how to define encoding (e.g., information divergence and mutual information), decoding (e.g., Fisher information), and causality (e.g., transfer entropy and Granger causality) between networks. We validate our framework on representative networks (e.g., evolutionary random network models, protein-protein interaction network, and chemical compound networks), and demonstrate that a series of science and engineering challenges (e.g., network evolution, clustering, and classification) can be tackled from a new perspective. A computationally efficient implementation of our theory is released as an open-source toolbox.Yang Tian, Hedong Hou, Guangzheng Xu, Yaoyuan Wang, Ziyang Zhang, Pei Sunwork_utfsjdmub5d7jgppfgjolikhwqFri, 29 Jul 2022 00:00:00 GMTPreconditioned iterative methods for optimal control problems with time-dependent PDEs as constraints
https://scholar.archive.org/work/cvyajxxvcfckffdt4jeujmttuu
In this work, we study fast and robust solvers for optimal control problems with Partial Differential Equations (PDEs) as constraints. Speci cally, we devise preconditioned iterative methods for time-dependent PDE-constrained optimization problems, usually when a higher-order discretization method in time is employed as opposed to most previous solvers. We also consider the control of stationary problems arising in uid dynamics, as well as that of unsteady Fractional Differential Equations (FDEs). The preconditioners we derive are employed within an appropriate Krylov subspace method. The fi rst key contribution of this thesis involves the study of fast and robust preconditioned iterative solution strategies for the all-at-once solution of optimal control problems with time-dependent PDEs as constraints, when a higher-order discretization method in time is employed. In fact, as opposed to most work in preconditioning this class of problems, where a ( first-order accurate) backward Euler method is used for the discretization of the time derivative, we employ a (second-order accurate) Crank-Nicolson method in time. By applying a carefully tailored invertible transformation, we symmetrize the system obtained, and then derive a preconditioner for the resulting matrix. We prove optimality of the preconditioner through bounds on the eigenvalues, and test our solver against a widely-used preconditioner for the linear system arising from a backward Euler discretization. These theoretical and numerical results demonstrate the effectiveness and robustness of our solver with respect to mesh-sizes and regularization parameter. Then, the optimal preconditioner so derived is generalized from the heat control problem to time-dependent convection{diffusion control with Crank- Nicolson discretization in time. Again, we prove optimality of the approximations of the main blocks of the preconditioner through bounds on the eigenvalues, and, through a range of numerical experiments, show the effectiveness and robustness of our approac [...]Santolo Leveque, University Of Edinburgh, John Pearson, Jacek Gondziowork_cvyajxxvcfckffdt4jeujmttuuMon, 27 Jun 2022 00:00:00 GMTTesting Positive Semidefiniteness Using Linear Measurements
https://scholar.archive.org/work/4hbovwuqinfnri53op23bdj6fe
We study the problem of testing whether a symmetric d × d input matrix A is symmetric positive semidefinite (PSD), or is ϵ-far from the PSD cone, meaning that λ_min(A) ≤ - ϵA_p, where A_p is the Schatten-p norm of A. In applications one often needs to quickly tell if an input matrix is PSD, and a small distance from the PSD cone may be tolerable. We consider two well-studied query models for measuring efficiency, namely, the matrix-vector and vector-matrix-vector query models. We first consider one-sided testers, which are testers that correctly classify any PSD input, but may fail on a non-PSD input with a tiny failure probability. Up to logarithmic factors, in the matrix-vector query model we show a tight Θ(1/ϵ^p/(2p+1)) bound, while in the vector-matrix-vector query model we show a tight Θ(d^1-1/p/ϵ) bound, for every p ≥ 1. We also show a strong separation between one-sided and two-sided testers in the vector-matrix-vector model, where a two-sided tester can fail on both PSD and non-PSD inputs with a tiny failure probability. In particular, for the important case of the Frobenius norm, we show that any one-sided tester requires Ω(√(d)/ϵ) queries. However we introduce a bilinear sketch for two-sided testing from which we construct a Frobenius norm tester achieving the optimal O(1/ϵ^2) queries. We also give a number of additional separations between adaptive and non-adaptive testers. Our techniques have implications beyond testing, providing new methods to approximate the spectrum of a matrix with Frobenius norm error using dimensionality reduction in a way that preserves the signs of eigenvalues.Deanna Needell, William Swartworth, David P. Woodruffwork_4hbovwuqinfnri53op23bdj6feFri, 08 Apr 2022 00:00:00 GMTKeyword spotting in handwritten document images using supervised and unsupervised representations
https://scholar.archive.org/work/p7zmrpqxejdbdjv37kjq7tjao4
Vast collections of documents available in image format need to be efficiently digitized for information retrieval purposes. Many approaches from the document analysis and recognition research community have been proposed to alleviate the search process.Άγγελος Γιώτης, University Of Ioanninawork_p7zmrpqxejdbdjv37kjq7tjao4Fri, 04 Mar 2022 00:00:00 GMTGraph Representation Learning in Computational Pathology
https://scholar.archive.org/work/juo4ac3sgzhazcm7z7qbi5n45u
hope you were able to learn as much as I learned from you. The (almost) five years that I spent in IBM Research would not have been the same without all my outstanding C-HCLS colleagues. I would like to thank Anca, with whom I shared the office for two years, for all the amazing discussions (and chocolate croissant), Kevin T. for never forgetting to send me the latest news about a big transfer to Barca or PSG, Sasha (Kim) and Sonali, for always bringing your joie-de-vivre. Of course, there is more at IBM than the C-HCLS group, and I would like to thank Pauline and Kevin P., with whom the coffee breaks were a breath of fresh air during the long working days. I am also grateful to Gabriel, who accompanied me throughout my studies at EPFL and IBM Research, first by offering me a semester project in the LTS5, then by putting me in relation with Maria, and finally by mentoring the beginning of my PhD. Your advice and trust have sincerely helped me, and I would not be where I am today without you. As the saying goes, work, love and play are the great balance wheels of man's being, and I think I have found this balance in Zurich. My life would not have been the same without all the amazing people around me. I would like to thank Malo, for being such a great riding/running partner, Cyril, for organizing amazing rooftop parties and for attempting to teach me the fundamentals of the rhythmic, Gaspard, for never forgetting to send me cat pictures, Pauline, for always organizing amazing weekend trips, Kevin P., for all those games of badminton and rackets at the lake, Manon, for bringing a little taste of the South of France to Zurich, Hugo for being (almost) as crazy as me with the Derrière le Miroir, Pol for all these discussions where we shared our love for Renoir, Charlotte for cooking the best homemade bread and cinnamon rolls in town, Hector for the Sunday night dinners at my place and the Catan games, Andrew, for teaching American slang, Alice, for the countless dinners at your place, Louis for the amazing trip to New York, Ahmed for the parties at Frieda's. Thank you for the countless memories that will remain forever in my mind. A special thanks to my flatmate, David, who has (so far) managed to put up with me, thanks for the pasta dishes, pancakes. Last, but certainly not least, thanks Tanja for your endless support over the past four years. You have been involved more than anyone else, and have always been there to listen and find the words in moments of doubt. This thesis would not have been the same if you had not been present. Finally, I want to thank my family, without whom I would not be here. Juliette, thank you for the interest you have always shown in my thesis, it has helped me a lot to improve my communication and vulgarization skills. Papi, thanks for sparking my curiosity as a child, my interest in science grew in large part because of you, and I will be forever appreciative. Papa et Maman, I am grateful for all that you have given me, without expecting anything in return, and I consider myself lucky to have been able to receive such support. You have always been able to find the balance, which can sometimes be fragile, between reminding us of the importance of education and giving us the freedom to grow outside the classroom. In all humility, look at this thesis as the materialization of your success as parents in providing a quality education to your children, something that you have achieved with flying colors for both Juliette and me.Guillaume Jaumework_juo4ac3sgzhazcm7z7qbi5n45uMon, 21 Feb 2022 00:00:00 GMTPerformance Guarantees for Spectral Initialization in Rotation Averaging and Pose-Graph SLAM
https://scholar.archive.org/work/pud3ryz4h5hglmeearmbqzj7qy
In this work we present the first initialization methods equipped with explicit performance guarantees adapted to the pose-graph simultaneous localization and mapping (SLAM) and rotation averaging (RA) problems. SLAM and rotation averaging are typically formalized as large-scale nonconvex point estimation problems, with many bad local minima that can entrap the smooth optimization methods typically applied to solve them; the performance of standard SLAM and RA algorithms thus crucially depends upon the quality of the estimates used to initialize this local search. While many initialization methods for SLAM and RA have appeared in the literature, these are typically obtained as purely heuristic approximations, making it difficult to determine whether (or under what circumstances) these techniques can be reliably deployed. In contrast, in this work we study the problem of initialization through the lens of spectral relaxation. Specifically, we derive a simple spectral relaxation of SLAM and RA, the form of which enables us to exploit classical linear-algebraic techniques (eigenvector perturbation bounds) to control the distance from our spectral estimate to both the (unknown) ground-truth and the global minimizer of the estimation problem as a function of measurement noise. Our results reveal the critical role that spectral graph-theoretic properties of the measurement network play in controlling estimation accuracy; moreover, as a by-product of our analysis we obtain new bounds on the estimation error for the maximum likelihood estimators in SLAM and RA, which are likely to be of independent interest. Finally, we show experimentally that our spectral estimator is very effective in practice, producing initializations of comparable or superior quality at lower computational cost compared to existing state-of-the-art techniques.Kevin J. Doherty, David M. Rosen, John J. Leonardwork_pud3ryz4h5hglmeearmbqzj7qyTue, 11 Jan 2022 00:00:00 GMTLecture Notes on Quantum Algorithms for Scientific Computation
https://scholar.archive.org/work/abqmzhmiozhkdlfehzz5lu3x7e
This is a set of lecture notes used in a graduate topic class in applied mathematics called "Quantum Algorithms for Scientific Computation" at the Department of Mathematics, UC Berkeley during the fall semester of 2021. These lecture notes focus only on quantum algorithms closely related to scientific computation, and in particular, matrix computation. The main purpose of the lecture notes is to introduce quantum phase estimation (QPE) and "post-QPE" methods such as block encoding, quantum signal processing, and quantum singular value transformation, and to demonstrate their applications in solving eigenvalue problems, linear systems of equations, and differential equations. The intended audience is the broad computational science and engineering (CSE) community interested in using fault-tolerant quantum computers to solve challenging scientific computing problems.Lin Linwork_abqmzhmiozhkdlfehzz5lu3x7eSat, 01 Jan 2022 00:00:00 GMTTheory and methods for stochastic, accelerated, and distributed optimization
https://scholar.archive.org/work/tdp4oy73cvgfrngt4jvsy24dim
This thesis consists of two parts. Part I (Chapters 1-3) concerns momentum-based first-order optimization algorithms for stochastic optimization where we have only access to stochastic (noisy) estimates of the gradient of the objective. This setting would arise frequently in several key problems in supervised learning such as risk minimization for classification or regression, or saddle-point problems for distributionally robust learning. When gradients are deterministic and do not contain any noise, it is well-known that momentum-based optimization algorithms such as Nesterov's accelerated gradient (AG) method or Polyak's heavy ball (HB) method have improved convergence rates compared to gradient descent methods. However, in the presence of persistent stochastic gradient errors; momentum-based algorithms amplify the noise in the gradients and are less robust to gradient errors unless the stepsize and the momentum parameters are very carefully tuned to the problem at hand. This motivates the study of the distribution of the iterates of the momentum algorithms as a function of the stepsize and momentum parameters where there is a lack of principled strategies to ensure the existence of a stationary distribution or to control the probability that the suboptimality exceeds a certain threshold. Especially, existing results for momentum methods provide only limited guarantees in expected suboptimality, but do not typically characterize deviations from the expected suboptimality. In Chapter 1, we show that many momentum algorithms such as AG, HB and their variants for constrained strongly convex optimization converge to their equilibrium with the accelerated rate under some conditions on the parameters and on the noise structure. These results shed further light into the effect of parameters and how much noise momentum algorithms can tolerate before being divergent. In Chapter 2, we consider the general class of momentum methods (GMM) subject to stochastic gradient noise which include AG and HB as special cases. Under [...]Bugra Canwork_tdp4oy73cvgfrngt4jvsy24dimSTATISTICAL INFERENCE ACROSS MULTIPLE NETWORKS: ADVANCEMENTS IN MULTIPLEX GRAPH MATCHING AND JOINT SPECTRAL NETWORK EMBEDDINGS
https://scholar.archive.org/work/77a4oyfvobfjhdeskr5g3wxy6u
Networks are commonly used to model and study complex systems that arise in a variety of scientific domains.One important network data modality is multiplex networks which are comprised of a collection of networks over a common vertex set. Multiplex networks can describe complex relational data where edges within each network can encode different relationship or interaction types. With the rise of network modeling of complex, multi-sample network data, there has been a recent emphasis on multiplex inference methods. In this thesis, we develop novel theory and methodology to study underlying network structures and perform statistical inference on multiple networks. While each chapter of the thesis has its own individual merit, synergistically they constitute a coherent multi-scale spectral network inference framework that accounts for unlabeled and correlated multi-sample network data. Together, these results significantly extend the reach of such procedures in the literature. In the first part of the thesis, we consider the inference task of aligning the vertices across a pair of multiplex networks, a key algorithmic step in routines that assume a priori node-aligned data. This general multiplex matching framework is then adapted to the task of detecting a noisy induced multiplex template network in a larger multiplex background network.Our methodology, which lifts the classical graph matching framework and the matched filters method of Sussman et al. (2018) to the multiple network setting, uses the template network to search for the "most" similar subgraph(s) in the background network, where the notion of similarity is measured via a multiplex graph matching distance. We present an algorithm which can efficiently match the template to a (induced or not induced) subgraph in the background that approximately minimizes a suitable graph matching distance, and we demonstrate the effectiveness of our approach both theoretically and empirically in synthetic and real-world data settings. In the second part of the thesi [...]Konstantinos Pantaziswork_77a4oyfvobfjhdeskr5g3wxy6uHigh Dimensional Optimization through the Lens of Machine Learning
https://scholar.archive.org/work/k2wd7h6ltnbbrez2udf6s5fvma
This thesis reviews numerical optimization methods with machine learning problems in mind. Since machine learning models are highly parametrized, we focus on methods suited for high dimensional optimization. We build intuition on quadratic models to figure out which methods are suited for non-convex optimization, and develop convergence proofs on convex functions for this selection of methods. With this theoretical foundation for stochastic gradient descent and momentum methods, we try to explain why the methods used commonly in the machine learning field are so successful. Besides explaining successful heuristics, the last chapter also provides a less extensive review of more theoretical methods, which are not quite as popular in practice. So in some sense this work attempts to answer the question: Why are the default Tensorflow optimizers included in the defaults?Felix Benningwork_k2wd7h6ltnbbrez2udf6s5fvmaFri, 31 Dec 2021 00:00:00 GMTMultiview Graph Learning for single-cell RNA sequencing data
https://scholar.archive.org/work/wggllbg7evbnbpcpcngklz7qdm
Characterizing the underlying topology of gene regulatory networks is one of the fundamental problems of systems biology. Ongoing developments in high throughput sequencing technologies has made it possible to capture the expression of thousands of genes at the single cell resolution. However, inherent cellular heterogeneity and high sparsity of the single cell datasets render void the application of regular Gaussian assumptions for constructing gene regulatory networks. Additionally, most algorithms aimed at single cell gene regulatory network reconstruction, estimate a single network ignoring group-level (cell-type) information present within the datasets. To better characterize single cell gene regulatory networks under different but related conditions we propose the joint estimation of multiple networks using multiview graph learning (mvGL). The proposed method is developed based on recent works in graph signal processing (GSP) for graph learning, where graph signals are assumed to be smooth over the unknown graph structure. Graphs corresponding to the different datasets are regularized to be similar to each other through a learned consensus graph. We further kernelize mvGL with the kernel selected to suit the structure of single cell data. An efficient algorithm based on prox-linear block coordinate descent is used to optimize mvGL. We study the performance of mvGL using synthetic data generated with a diverse set of parameters. We further show that mvGL successfully identifies well-established regulators in a mouse embryonic stem cell differentiation study and a cancer clinical study of medulloblastoma.Abdullah Karaaslanli, SATABDI SAHA, Selin Aviyente, Tapabrata Maitiwork_wggllbg7evbnbpcpcngklz7qdmMon, 08 Nov 2021 00:00:00 GMTRobust Distributed Accelerated Stochastic Gradient Methods for Multi-Agent Networks
https://scholar.archive.org/work/j4fwgjqwsrghxlwyxu2nujcb7i
We study distributed stochastic gradient (D-SG) method and its accelerated variant (D-ASG) for solving decentralized strongly convex stochastic optimization problems where the objective function is distributed over several computational units, lying on a fixed but arbitrary connected communication graph, subject to local communication constraints where noisy estimates of the gradients are available. We develop a framework which allows to choose the stepsize and the momentum parameters of these algorithms in a way to optimize performance by systematically trading off the bias, variance, robustness to gradient noise and dependence to network effects. When gradients do not contain noise, we also prove that distributed accelerated methods can achieve acceleration, requiring 𝒪(κlog(1/ε)) gradient evaluations and 𝒪(κlog(1/ε)) communications to converge to the same fixed point with the non-accelerated variant where κ is the condition number and ε is the target accuracy. To our knowledge, this is the first acceleration result where the iteration complexity scales with the square root of the condition number in the context of primal distributed inexact first-order methods. For quadratic functions, we also provide finer performance bounds that are tight with respect to bias and variance terms. Finally, we study a multistage version of D-ASG with parameters carefully varied over stages to ensure exact 𝒪(-k/√(κ)) linear decay in the bias term as well as optimal 𝒪(σ^2/k) in the variance term. We illustrate through numerical experiments that our approach results in practical algorithms that are robust to gradient noise and that can outperform existing methods.Alireza Fallah, Mert Gurbuzbalaban, Asuman Ozdaglar, Umut Simsekli, Lingjiong Zhuwork_j4fwgjqwsrghxlwyxu2nujcb7iMon, 04 Oct 2021 00:00:00 GMT