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Using Decomposed Error for Reproducing Implicit Understanding of algorithms

EVOLUTIONARY COMPUTATION 2024年第1期32卷 49-68页

作者： Owen, Caitlin A. Dick, Grant Whigham, Peter A. Univ Otago Dept Informat Sci Dunedin New Zealand

Reproducibility is important for having confidence in evolutionary machine learning algorithms. Although the focus of reproducibility is usually to recreate an aggregate prediction error score using fixed random seeds, this is not sufficient. Firstly, multiple runs of an algorithm, without a fixed random seed, should ideally return statistically equivalent results. Secondly, it should be confirmed whether the expected behaviour of an algorithm matches its actual behaviour, in terms of how an algorithm targets a reduction in prediction error. Confirming the behaviour of an algorithm is not possible when using a total error aggregate score. Using an error decomposition framework as a methodology for improving the reproducibility of results in evolutionary computation addresses both of these factors. By estimating decomposed error using multiple runs of an algorithm and multiple training sets, the framework provides a greater degree of certainty about the prediction error. Also, decomposing error into bias, variance due to the algorithm (internal variance), and variance due to the training data (external variance) more fully characterises evolutionary algorithms. This allows the behaviour of an algorithm to be confirmed. Applying the framework to a number of evolutionary algorithms shows that their expected behaviour can be different to their actual behaviour. Identifying a behaviour mismatch is important in terms of understanding how to further refine an algorithm as well as how to effectively apply an algorithm to a problem.

关键词： Genetic programming evolutionary machine learning error decomposition bias-variance trade-off stochastic algorithms geometric semantic genetic programming ensemble learning symbolic regression

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Deep Neural Network-based Inverse Analysis with Application to a Rockfill Dam

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KSCE JOURNAL OF CIVIL ENGINEERING 2024年第1期28卷 155-168页

作者： Shahzadi, Gullnaz Soulaimani, Azzeddine Ecole Technol Super Dept Mech Engn Montreal PQ H3C 1K3 Canada

The availability of significant computational resources has played an essential role in developing advanced numerical models for the design and safety evaluation of complex structures such as rockfill dams. Determining the geomechanical parameters is deemed a crucial but challenging task for effective modelling. The general approach involves using in situ or laboratory tests or experimental relationships from the literature to assess these parameters. These measures, however, do not accurately reflect the actual situation. This paper proposes a data driven approach using deep neural networks and non-deterministic optimization algorithms to identify the soil parameters that will lead to displacements that best approximate the measured data. The methodology is applied to a rockfill dam recently built in Quebec, for which some measurements of inclinometer displacements are available. A finite element model (FEM) of two dimensions generates numerical solutions. A comparative study is performed to account for the heterogeneity of the materials by decomposing the computational domain into subdomains. Subsequently, the inverse analysis uses the surrogate model instead of the full FEM model for rapid computations. A suitable objective function is defined to account for large oscillations in the measurement data. Non-intrusive stochastic optimization algorithms such as Genetic algorithm (GA), Particle Swarm Optimization (PSO), and Differential evolution (DE) are evaluated for the minimization problem. Finally, the case study confirms the capability of the proposed methodology to identify the relevant dam parameters, provide some insights into the performance, and compare three optimization algorithms.

关键词： Deep neural networks Inverse analysis Uncertainty analysis stochastic algorithms Rockfill dam

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Analysis of the applicability and results of swarm intelligence tools for the positioning of Energy Storage Systems

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2024年 163卷

作者： Divasson-J, Asier Santamaria, Itxaso Aranzabal Landaribar, Miren T. Bedialauneta Aguirre, Paula Castillo Univ Deusto Unibertsitate Etorb 24 Bilbao 48007 Biscay Spain Univ Basque Country UPV EHU Ingeniero Torres Quevedo Pl 1 Bilbao 48013 Biscay Spain Univ Basque Country UPV EHU Otaola Hiribidea 29 Gipuzkoa 20600 Eibar Spain

The integration of renewable energy is transforming traditional energy systems, blurring the distinction between producers and consumers and shifting towards a distributed grid network. This change demands innovative approaches to optimize Energy Storage Systems (ESS) and manage grid incidents efficiently, all without significant infrastructural changes. While optimization algorithms like Swarm Intelligence are gaining traction, critical aspects, such as worst-case scenario analysis in distribution networks, remain underexplored. This study addresses this gap by applying stochastic optimization techniques to determine the optimal placement and capacity of ESS in a medium voltage radial distribution system, using the IEEE 33-bus model. The findings highlight the importance of considering worst-case scenarios, offering a balanced evaluation of current methodologies. This research provides valuable insights for improving system flexibility and resilience, contributing to more effective and practical energy optimization strategies in real-world applications.

关键词： Energy storage systems Distribution systems Electrical systems Optimization stochastic algorithms

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Asset and Factor Risk Budgeting: a balanced approach

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QUANTITATIVE FINANCE 2025年第2期25卷 181-195页

作者： Cetingoz, Adil Rengim Gueant, Olivier Univ Paris 1 Pantheon sorbonne Ctr Econ Sorbonne 106 Blvd Hop F-75642 Paris 13 France

Portfolio optimization methods have evolved significantly since Markowitz introduced the mean-variance framework in 1952. While the theoretical appeal of this approach is undeniable, its practical implementation poses important challenges, primarily revolving around the intricate task of estimating expected returns. As a result, practitioners and scholars have explored alternative methods that prioritize risk management and diversification. One such approach is Risk Budgeting, where portfolio risk is allocated among assets according to predefined risk budgets. The effectiveness of Risk Budgeting in achieving true diversification can, however, be questioned, given that asset returns are often influenced by a small number of risk factors. From this perspective, one question arises: is it possible to allocate risk at the factor level using the Risk Budgeting approach? First, we introduce a comprehensive framework to address this question by introducing risk measures directly associated with risk factor exposures and demonstrating the desirable mathematical properties of these risk measures, making them suitable for optimization. Then, we propose a novel framework to find portfolios that effectively balance the risk contributions from both assets and factors. Leveraging standard stochastic algorithms, our framework enables the use of a wide range of risk measures to construct diversified portfolios.

关键词： Diversification Factor models Factor investing Portfolio optimization Risk budgeting Risk measures stochastic algorithms

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Nonsmooth Optimization over the Stiefel Manifold and Beyond: Proximal Gradient Method and Recent Variants

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SIAM REVIEW 2024年第2期66卷 319-352页

作者： Chen, Shixiang Ma, Shiqian So, Anthony Man-Cho Zhang, Tong Univ Sci & Technol China Sch Math Sci Hefei Anhui Peoples R China Rice Univ Dept Computat Appl Math & Operat Res Houston TX 77005 USA Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China Hong Kong Univ Sci & Technol Clear Water Bay Hong Kong Peoples R China

We consider optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. Existing methods for solving this class of problems converge slowly in practice, involve subproblems that can be as difficult as the original problem, or lack rigorous convergence guarantees. In this paper, we propose a manifold proximal gradient method (ManPG) for solving this class of problems. We prove that the proposed method converges globally to a stationary point and establish its iteration complexity for obtaining an \epsilon -stationary point. Furthermore, we present numerical results on the sparse PCA and compressed modes problems to demonstrate the advantages of the proposed method. We also discuss some recent advances related to ManPG for Riemannian optimization with nonsmooth objective functions.

关键词： manifold optimization Stiefel manifold nonsmooth proximal gradient method iteration complexity semismooth Newton method stochastic algorithms zeroth-order algorithms

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SQuadMDS: A lean stochastic Quartet MDS improving global structure preservation in neighbor embedding like t-SNE and UMAP

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NEUROCOMPUTING 2022年 503卷 17-27页

作者： Lambert, Pierre de Bodt, Cyril Verleysen, Michel Lee, John A. UCLouvain ICTEAM ELEN Pl Levant 3bte L5-03-02 B-1348 Louvain La Neuve Belgium MIT Media Lab Human Dynam Grp 20 Ames StWiesner Bldg E15 Cambridge MA 02139 USA UCLouvain IREC MIRO Ave Hippocrate 55 B1-54-07 B-1200 Brussels Belgium

Multidimensional scaling is a process that aims to embed high dimensional data into a lower -dimensional space;this process is often used for the purpose of data visualisation. Common multidimen-sional scaling algorithms tend to have high computational complexities, making them inapplicable on large data sets. This work introduces a stochastic, force directed approach to multidimensional scaling with a time and space complexity of O eth N THORN , with N data points. The method can be combined with force directed layouts of the family of neighbour embedding such as t-SNE, to produce embeddings that pre-serve both the global and the local structures of the data. Experiments assess the quality of the embeddings produced by the standalone version and its hybrid extension both quantitatively and qualitatively, showing competitive results outperforming state-of-the-art approaches. Codes are available at https://***/PierreLambert3/SQuaD-MDS-and-FItSNE-hybrid. (C) 2022 Elsevier B.V. All rights reserved.

关键词： Dimensionality reduction t-SNE UMAP Neighbor embedding MDS Global structure stochastic algorithms Data visualization Distance preservation

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stochastic Neuromorphic Circuits for Solving MAXCUT 37

Stochastic Neuromorphic Circuits for Solving MAXCUT

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37th IEEE International Parallel and Distributed Processing Symposium (IPDPS)

作者： Theilman, Bradley H. Wang, Yipu Parekht, Ojas Severa, William Smith, J. Darby Aimone, James B. Sandia Natl Labs Neural Explorat & Res Lab POB 5800 Albuquerque NM 87185 USA Sandia Natl Labs Discrete Math & Optimizat Albuquerque NM USA

ISBN: (纸本)9798350337662

Finding the maximum cut of a graph (MAXCUT) is a classic optimization problem that has motivated parallel algorithm development. While approximate algorithms to MAXCUT offer attractive theoretical guarantees and demonstrate compelling empirical performance, such approximation approaches can shift the dominant computational cost to the stochastic sampling operations. Neuromorphic computing, which uses the organizing principles of the nervous system to inspire new parallel computing architectures, offers a possible solution. One ubiquitous feature of natural brains is stochasticity: the individual elements of biological neural networks possess an intrinsic randomness that serves as a resource enabling their unique computational capacities. By designing circuits and algorithms that make use of randomness similarly to natural brains, we hypothesize that the intrinsic randomness in microelectronics devices could be turned into a valuable component of a neuromorphic architecture enabling more efficient computations. Here, we present neuromorphic circuits that transform the stochastic behavior of a pool of random devices into useful correlations that drive stochastic solutions to MAXCUT. We show that these circuits perform favorably in comparison to software solvers and argue that this neuromorphic hardware implementation provides a path for scaling advantages. This work demonstrates the utility of combining neuromorphic principles with intrinsic randomness as a computational resource for new computational architectures.

关键词： discrete optimization MAXCUT neuromorphic computing stochastic algorithms

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stochastic BIAS-ACCELERATED SUBSET SELECTION ALGORITHM FOR JOINT LEARNING OF SAMPLING PATTERN AND RECONSTRUCTION IN ACCELERATED MRI 20

STOCHASTIC BIAS-ACCELERATED SUBSET SELECTION ALGORITHM FOR J...

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20th IEEE International Symposium on Biomedical Imaging (ISBI)

作者： Zibetti, Marcelo V. W. Regatte, Ravinder R. NYU Grossman Sch Med New York NY 10003 USA

ISBN: (纸本)9781665473583

This work proposes and illustrates a stochastic version of the bias-accelerated subset selection (BASS) algorithm used to learn the sampling pattern (SP) in accelerated Cartesian MRI problems. Recently, BASS was combined with ADAM for joint learning of the SP and deep learning reconstruction. However, BASS originally uses all the data in each iteration, taking a long processing time when the training dataset is large. Here, we illustrate that BASS is also very stable when only a small fraction of the dataset is used at each iteration. This version, called stochastic BASS (SBASS), can substantially reduce the SP training time for large datasets, obtaining similar quality measurements of the learned pair of SP and reconstruction.

关键词： MRI learning deep learning sampling pattern stochastic algorithms

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Discrete Optimization Algorithm Based on Probability Distribution with Transformation of Target Values

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PROGRAMMING AND COMPUTER SOFTWARE 2024年第6期50卷 445-456页

作者： Sarin, K. S. Tomsk State Univ Control Syst & Radioelect Tomsk 634050 Russia

Problems of search optimization in a discrete space, particularly, in a binary space where a variable can take only two values, are of great practical importance. This paper proposes a new population-based discrete optimization algorithm that uses probability distributions of variables. The distributions determine the probability of taking one or another discrete value and are generated by transforming target values of solutions into their weight coefficients. The performance of the algorithm is evaluated using unimodal and multimodal test functions with binary variables. The experimental results demonstrate the high efficiency of the proposed algorithm in terms of convergence rate and stability.

关键词： optimization methods discrete optimization binary optimization metaheuristics stochastic algorithms and probability distribution

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Application of deterministic, stochastic, and hybrid methods for cloud provider selection

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JOURNAL OF CLOUD COMPUTING-ADVANCES SYSTEMS AND APPLICATIONS 2022年第1期11卷 1-23页

作者： de Moraes, Lucas Borges Parpinelli, Rafael Stubs Fiorese, Adriano Dept Comp Sci DCC Joinville SC Brazil Grad Program Appl Comp PPGCA Joinville SC Brazil Santa Catarina State Univ UDESC Joinville SC Brazil

Cloud Computing popularization inspired the emergence of many new cloud service providers. The significant number of cloud providers available drives users to complex or even impractical choice of the most suitable one to satisfy his needs without automation. The Cloud Provider Selection (CPS) problem addresses that choice. Hence, this work presents a general approach for solving the CPS problem using as selection criteria performance indicators compliant with the Cloud Service Measurement Initiative Consortium - Service Measurement Index framework (CSMIC-SMI). To accomplish that, deterministic (CPS-Matching and CPS-DEA), stochastic (Evolutionary algorithms: CPS-GA, CPS-BDE, and CPS-DDE), and hybrid (Matching-GA, Matching-BDE, and Matching-DDE) selection optimization methods are developed and employed. The evaluation uses a synthetic database created from several real cloud provider indicator values in experiments comprising scenarios with different user needs and several cloud providers indicating that the proposed approach is appropriate for solving the cloud provider selection problem, showing promising results for a large-scale application. Particularly, comparing which approach chooses the most appropriate cloud provider the better, the hybrid one presents better results, achieving the best average hit percentage, dealing with simple and multi-cloud user requests.

关键词： Cloud provider selection problem Cloud provider ranking Evolutionary computing Natural computing Performance indicator Hybrid methods stochastic algorithms Deterministic algorithms

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