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Efficient approximation of branching random walk Gibbs measures

ELECTRONIC JOURNAL OF PROBABILITY 2022年第none期27卷 1-18页

作者： Ho, Fu-Hsuan Maillard, Pascal CNRS Inst Math Toulouse UMR5219 Toulouse France Univ Toulouse 3 Paul Sabatier Inst Math Toulouse 118 Route Narbonne F-31062 Toulouse 9 France

Disordered systems such as spin glasses have been used extensively as models for high-dimensional random landscapes and studied from the perspective of optimization algorithms. In a recent paper by L. Addario-Berry and the second author, the continuous random energy model (CREM) was proposed as a simple toy model to study the efficiency of such algorithms. The following question was raised in that paper: what is the threshold ??G, at which sampling (approximately) from the Gibbs measure at inverse temperature ?? becomes algorithmically hard? This paper is a first step towards answering this question. We consider the branching random walk, a time-homogeneous version of the continuous random energy model. We show that a simple greedy search on a renormalized tree yields a linear-time algorithm which approximately samples from the Gibbs measure, for every ?? ??c, the (static) critical point. More precisely, we show that for every ?? 0, there exists such an algorithm such that the specific relative entropy between the law sampled by the algorithm and the Gibbs measure of inverse temperature ?? is less than ?? with high probability. In the supercritical regime ?? > ??c, we provide the following hardness result. Under a mild regularity condition, for every ?? > 0, there exists z > 0 such that the running time of any given algorithm approximating the Gibbs measure stochastically dominates a geometric random variable with parameter e???z N on an event with probability at least 1 ??? ??.

关键词： algorithmic hardness branching random walk Gibbs measure Kullback-Leibler divergence sampling algorithm

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Remarks on some misconceptions about unequal probability sampling without replacement

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COMPUTER SCIENCE REVIEW 2023年 47卷

作者： Tille, Yves Univ Neuchatel Inst Stat Bellevaux 51 CH-2000 Neuchatel Switzerland

Before computer scientists became interested in unequal probability sampling methods, they were widely studied by survey statisticians. We show that sometimes the same sampling methods have been proposed again without reference to existing methods. We also show that methods that are not correct and that were widely discussed in the 1950s are being proposed again. We review the most common errors and misunderstandings about these methods. (c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Entropy Inclusion probability Poisson sampling sampling algorithm Weighted sampling

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Calculating the interaction index of a fuzzy measure: A polynomial approach based on sampling

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FUZZY SETS AND SYSTEMS 2023年 466卷

作者： Gutierrez, Inmaculada Castro, Javier Gomez, Daniel Espinola, Rosa Univ Complutense Madrid Fac Stat Madrid Spain Univ Complutense Madrid Inst Evaluac Sanitaria Madrid Spain

In this paper we address the problem of fuzzy measures index calculation. On the basis of fuzzy sets, Murofushi and Soneda proposed an interaction index to deal with the relations between two individuals. This index was later extended in a common frame-work by Grabisch. Both indices are fundamental in the literature of fuzzy measures. Nevertheless, the corresponding calculation still presents a highly complex problem for which no approximation solution has been proposed yet. Then, using a representation of the Shapley based on orders, here we suggest an alternative calculation of the interaction index, both for the simple case of pairs of individuals, and for the more complex situation in which any set could be considered. This alternative representation facilitates the handling of these indices. Moreover, we draw on this representation to define two polynomial methods based on sampling to estimate the interaction index, as well as a method to approximate the generalized version of it. We provide some computational results to test the goodness of the proposed algorithms.& COPY;2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Fuzzy measures Interaction Index Interaction representation Shapley value sampling algorithm

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Polynomial time perfect sampler for discretized Dirichlet distribution

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Workshop on the Grammer of Technology Development

作者： Matsui, Tomomi Kijima, Shuji Univ Tokyo Dept Math Informat Grad Sch Informat Sci & Technol Bunkyo Ku Tokyo 1138656 Japan

ISBN: (纸本)9784431752318

In this paper, we propose a perfect (exact) sampling algorithm according to a discretized Dirichlet distribution. The Dirichlet distribution appears as prior and posterior distribution for the multinomial distribution in many statistical methods in bioinformatics. Our algorithm is a monotone coupling from the past algorithm, which is a Las Vegas type randomized algorithm. We propose a new Markov chain whose limit distribution is a discretized Dirichlet distribution. Our algorithm simulates transitions of the chain O(n(3) In Delta) times where n is the dimension (the number of parameters) and 1/Delta is the grid size for discretization. Thus the obtained bound does not depend on the magnitudes of parameters. In each transition, we need to sample a random variable according to a discretized beta distribution (2-dimensional Dirichlet distribution). To show the polynomiality, we employ the path coupling method carefully and show that our chain is rapidly mixing.

关键词： coupling from the past (CFTP) Dirichlet distribution Markov chain Monte Carlo path coupling sampling algorithm

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Trajectory tracking in 2D under fuzzy controller with variable sampling

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Journal of Electrical Systems and Information Technology 2015年第3期2卷 338-346页

作者： Ján Cigánek

The paper deals with an effective approach of the robust controller design based on the fuzzy logic, and algorithms for variable sampling of trajectory points to improve the control performance of trajectory tracking. The proposed controller design and sampling algorithms are verified in the case study of the selected mechatronic system. All presented results are reached in co-simulation of two different modeling environments, Matlab-Simulink and MSC Adams. MSC Adams is used for the dynamics of the mechatronic system and Matlab-Simulink for the control part of the co-simulation, respectively.

关键词： Control system Co-simulation Fuzzy logic Mechatronic system sampling algorithm Trajectory tracking

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Intelligent sampling of high-dimensional joint mobility space for analysis of articular function

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METHODS IN ECOLOGY AND EVOLUTION 2023年第2期14卷 569-582页

作者： Bishop, Peter J. Brocklehurst, Robert J. Pierce, Stephanie E. Harvard Univ Museum Comparat Zool Cambridge MA 02138 USA Harvard Univ Dept Organism & Evolutionary Biol Cambridge MA 02138 USA Queensland Museum Geosci Program Brisbane Qld Australia

Studies of joint structure and function have played a central role in understanding palaeobiology and major functional transitions in evolutionary history, where fossilized hard parts (e.g. bones) are often all that remain. Current digital methods for quantifying articular function depend on exhaustively sampling all possible joint poses, but this is computationally intensive, becoming prohibitively so with more degrees of freedom. This has impeded more sophisticated analyses or broader application of these methods to more diverse questions and species. The present study introduces 'APSE' (Accelerated Pose Searching with Electrostatics), an iterative algorithm for rapidly and intelligently sampling high-dimensional joint pose space to quantify articular function and mobility. Key features of the algorithm are: known viable joint poses inform the search for new poses in successive generations;the search preferentially targets under-explored regions of pose space, while avoiding over-explored regions;large swaths of inviable pose space are never evaluated, thus minimizing wasted time;and parallelizability. The efficacy of the algorithm was benchmarked with diverse theoretical and biological joints. As a case study to demonstrate its utility, APSE was used to investigate mobility in the enigmatic shoulder joint of the extinct 'pelycosaur'-grade synapsid Dimetrodon, the function of which has been widely debated. APSE produces high-dimensional joint mobility assessments with greater precision than state-of-the-art exhaustive sampling methods. More viable poses are identified at a greater sampling density, but in a fraction of the time taken by current methods (hours, not days or weeks). Results for Dimetrodon shoulder mobility indicate strong coupling between most degrees of freedom across the joint's full range of motion, a stark contrast to the flexible shoulder of most extant tetrapods. APSE provides a time-efficient means to quantitatively measure articular function

关键词： articular function Dimetrodon evolutionary biomechanics joint mobility range of motion sampling algorithm

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The relative importance of data points in systems biology and parameter estimation

The relative importance of data points in systems biology an...

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IEEE International Conference on Bioinformatics and Biomedicine (IEEE BIBM)

作者： Jeong, Jenny Qiu, Peng Georgia Inst Technol Elect & Comp Engn Atlanta GA 30332 USA Georgia Inst Technol Biomed Engn Atlanta GA 30332 USA Emory Univ Atlanta GA 30322 USA

ISBN: (纸本)9781509030507

Estimating model parameters is a crucial step to understand the behavior of biological systems. To perform parameter estimation, a commonly used formulation is the least square method that minimizes the mean squared error. This method finds the model parameters that minimize the sum of the squared error between experimental data and model predictions. However, such a formulation can misguide parameter estimation and the understanding of the system. This is mainly because least square formulation typically treats all data points equally, while the reality is that not all data points are of equal importance. Another common issue in systems biology is that the amount of experimental data is almost always limited compared to the model complexity, making parameter estimation challenging and ill-conditioned. Ignoring the relative importance of data points may amplify the ill-conditioned nature of the problem. Therefore, we propose to give different weight to each data point when formulating the least square cost function. The weight of each data point is defined by an uncertainty measure for the data point given the others, quantifying each data point's unique information that cannot be inferred from other data points. To test our algorithm, we used a G1/S transition model with two dynamic variables and 12 parameters, developed a sampling algorithm to obtain collections of parameter settings close to the best fit, and demonstrated the benefits of the proposed weighted cost function formulation.

关键词： parameter estimation optimization weighted cost function sampling algorithm

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Fuzzy Tracking Controller for Shape Optimized Robotic System 23

Fuzzy Tracking Controller for Shape Optimized Robotic System

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23rd International Conference on Robotics in Alpe-Adria-Danube Region (IEEE RAAD)

作者： Ciganek, Jan Noge, Filip Galik, Gabriel Gogola, Roman Slovak Univ Technol Bratislava Fac Elect Engn & Informat Technol Inst Automot Mech Bratislava Slovakia

ISBN: (纸本)9781479967988

The paper deals with an effective approach of the robust controller design, based on the fuzzy logic. We developed algorithms with variable sampling for trajectory tracking. The proposed controller design and sampling algorithms are verified on the case study of the chosen mechatronic system. All numerical and graphical results are obtained in Co-simulation of combination two different modeling systems - Matlab-Simulink and MSC Adams. The paper shows the methodology of energy cost reduction using shape optimized model based on the system analysis made in system ANSYS.

关键词： Control System Co-simulation Fuzzy Logic Matlab-Simulink MSC Adams Robotic System sampling algorithm Soft Computing System Analysis Trajectory Tracking

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Fast One-to-Many Reliability Estimation for Uncertain Graphs 31st

Fast One-to-Many Reliability Estimation for Uncertain Graphs

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31st International Conference on Database and Expert Systems Applications (DEXA)

作者： Yanagisawa, Junya Shiokawa, Hiroaki Univ Tsukuba Grad Sch Sci & Technol Tsukuba Ibaraki Japan Univ Tsukuba Ctr Computat Sci Tsukuba Ibaraki Japan

ISBN: (纸本)9783030590031;9783030590024

Uncertain graphs commonly represent noisy and unreliable real-world datasets in various applications. One fundamental primitive on uncertain graphs is reliability, which evaluates the connection robustness between two specific nodes. Although reliability is helpful to analyzeuncertain graphs, it is computationally expensive because (1) the reliability estimation is #P-hard problem and (2) many applications require reliability computations among all possible pairs of nodes. To overcome the aforementioned problems, we present a novel algorithm called Sharing RCSS+, which efficiently computes the reliability among all possible pairs of nodes. Our extensive experiments on both real-world and synthetic uncertain graphs clarified that Sharing RCSS+ achieves a more efficient estimation than the state-of-the-art methods.

关键词： Uncertain graphs Reliability sampling algorithm

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ONBRA: Rigorous Estimation of the Temporal Betweenness Centrality in Temporal Networks 22

ONBRA: Rigorous Estimation of the Temporal Betweenness Centr...

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31st ACM Web Conference (WWW)

作者： Santoro, Diego Sarpe, Ilie Univ Padua Dept Informat Engn Padua Italy

ISBN: (纸本)9781450390965

In network analysis, the betweenness centrality of a node informally captures the fraction of shortest paths visiting that node. The computation of the betweenness centrality measure is a fundamental task in the analysis of modern networks, enabling the identification of the most central nodes in such networks. Additionally to being massive, modern networks also contain information about the time at which their events occur. Such networks are often called temporal networks. The temporal information makes the study of the betweenness centrality in temporal networks (i.e., temporal betweenness centrality) much more challenging than in static networks (i.e., networks without temporal information). Moreover, the exact computation of the temporal betweenness centrality is often impractical on even moderately-sized networks, given its extremely high computational cost. A natural approach to reduce such computational cost is to obtain high-quality estimates of the exact values of the temporal betweenness centrality. In this work we present ONBRA, the first sampling-based approximation algorithm for estimating the temporal betweenness centrality values of the nodes in a temporal network, providing rigorous probabilistic guarantees on the quality of its output. ONBRA is able to compute the estimates of the temporal betweenness centrality values under two different optimality criteria for the shortest paths of the temporal network. In addition, ONBRA outputs high-quality estimates with sharp theoretical guarantees leveraging on the empirical Bernstein bound, an advanced concentration inequality. Finally, our experimental evaluation shows that ONBRA significantly reduces the computational resources required by the exact computation of the temporal betweenness centrality on several real world networks, while reporting high-quality estimates with rigorous guarantees.

关键词： Temporal networks Temporal betweenness centrality sampling algorithm Probabilistic analysis

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