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24
SelfAvoiding Random Dynamics on Integer Complex Systems
"... This paper introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binaryvalued systems, which allows for large moves in the state space. This is achieved by constructing selfavoiding walks (SAWs) in the state space. As a consequence, many bits are flipped in a single MCMC s ..."
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Cited by 4 (4 self)
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This paper introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binaryvalued systems, which allows for large moves in the state space. This is achieved by constructing selfavoiding walks (SAWs) in the state space. As a consequence, many bits are flipped in a single MCMC step. We name the algorithm SARDONICS, an acronym for SelfAvoiding Random Dynamics on Integer Complex Systems. The algorithm has several free parameters, but we show that Bayesian optimization can be used to automatically tune them. SARDONICS performs remarkably well in a broad number of sampling tasks: toroidal ferromagnetic and frustrated Ising models, 3D Ising models, restricted Boltzmann machines and chimera graphs arising in the design of quantum computers.
MCMC algorithms for subset simulation
 Manuscript, Engineering Risk Analysis Group, TU München
, 2013
"... Subset Simulation is an adaptive simulation method that efficiently solves structural reliability problems with many random variables. The method requires sampling from conditional distributions, which is achieved through Markov Chain Monte Carlo (MCMC) algorithms. This paper discusses different MCM ..."
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Cited by 4 (2 self)
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Subset Simulation is an adaptive simulation method that efficiently solves structural reliability problems with many random variables. The method requires sampling from conditional distributions, which is achieved through Markov Chain Monte Carlo (MCMC) algorithms. This paper discusses different MCMC algorithms proposed for Subset Simulation and introduces a novel approach for MCMC sampling in the standard normal space. Two variants of the algorithm are proposed: A basic variant, which is simpler than existing algorithms with equal accuracy and efficiency, and a more efficient variant with adaptive scaling. It is demonstrated that the proposed algorithm improves the accuracy of Subset Simulation, without the need for additional model evaluations.
Towards zero variance estimators for rare event probabilities
, 2012
"... Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events En: = (u(X1)+...+u(Xn)) ∈ An where the summands are i.i.d. and En is a large or moderate deviation event. The approximation of the conditional de ..."
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Cited by 2 (1 self)
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Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events En: = (u(X1)+...+u(Xn)) ∈ An where the summands are i.i.d. and En is a large or moderate deviation event. The approximation of the conditional density of the vector (X1,...,Xkn) with respect to En on long runs, when kn/n → 1, is handled. The maximal value of kn compatible with a given accuracy is discussed; simulated results are presented, which enlight the gain of the present approach over classical IS schemes. Detailed algorithms are proposed.
A large deviation based splitting estimation of power flow reliability
 In: Submitted
, 2015
"... Given the continued integration of intermittent renewable generators in electrical power grids, connection overloads are of increasing concern for grid operators. The risk of an overload due to injection variability can be described mathematically as a barrier crossing probability of a function of a ..."
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Given the continued integration of intermittent renewable generators in electrical power grids, connection overloads are of increasing concern for grid operators. The risk of an overload due to injection variability can be described mathematically as a barrier crossing probability of a function of a multidimensional stochastic process. Crude Monte Carlo is a wellknown technique to estimate probabilities, but it may be computationally too intensive in this case as typical modern power grids rarely exhibit connection overloads. In this paper we derive an approximate rate function for the overload probability using results from large deviations theory. Based on this large deviations approximation, we design a rare event simulation technique called splitting to estimate overload probabilities more efficiently than Crude Monte Carlo simulation. We show on example power grids with up to eleven stochastic power injections that for a fixed accuracy Crude Monte Carlo would require tens to millions as many samples than the proposed splitting technique required. We investigate the balance between accuracy and workload of three numerical approximations of the importance function. We justify the workload increase of large deviations based splitting compared to a naive one based on merely the Euclidean distance to the rare event set: for a fixed accuracy naive splitting requires over 60 times as much CPU time as large deviation based splitting. In these examples naive splitting — unlike large deviations based splitting — requires even more CPU time than CMC simulation, illustrating its pitfall. 1
Stochastic enumeration method for counting trees
"... Abstract. The problem of estimating the size of a backtrack tree is an important but hard problem in computational sciences. An efficient solution of this problem can have a major impact on the hierarchy of complexity classes. The first randomized procedure, which repeatedly generates random paths t ..."
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Abstract. The problem of estimating the size of a backtrack tree is an important but hard problem in computational sciences. An efficient solution of this problem can have a major impact on the hierarchy of complexity classes. The first randomized procedure, which repeatedly generates random paths through the tree, was introduced by Knuth. Unfortunately, as was noted by Knuth and a few other researchers, the estimator can introduce a large variance and become ineffective in the sense that it underestimates the cost of the tree. Recently, a new sequential algorithm called Stochastic Enumeration (SE) method was proposed by Rubinstein et al. The authors showed numerically that this simple algorithm can be very efficient for handling different counting problems, such as counting the number of satisfiability assignments and enumerating the number of perfect matchings in bipartite graphs. In this paper we introduce a rigorous analysis of SE and show that it results in significant variance reduction as compared to Knuth’s estimator. Moreover, we establish that for almost all random trees the SE algorithm is a fully polynomial time randomized approximation scheme (FPRAS) for the estimation of the overall tree size.
On the Use of Smoothing to Improve the Performance of the Splitting Method
, 2011
"... We present an enhanced version of the splitting method, called the smoothed splitting method (SSM), for counting associated with complex ..."
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We present an enhanced version of the splitting method, called the smoothed splitting method (SSM), for counting associated with complex
Dépôt légal – Bibliothèque et Archives nationales du Québec,
, 2015
"... Les textes publiés dans la série des rapports de recherche Les Cahiers du GERAD n’engagent que la responsabilite ́ de leurs auteurs. La publication de ces rapports de recherche est rendue possible grâce au soutien de HEC Montréal, Polytechnique Montréal, Universite ́ McGill, Universite ́ du Que ..."
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Les textes publiés dans la série des rapports de recherche Les Cahiers du GERAD n’engagent que la responsabilite ́ de leurs auteurs. La publication de ces rapports de recherche est rendue possible grâce au soutien de HEC Montréal, Polytechnique Montréal, Universite ́ McGill, Universite ́ du Québec a ̀ Montréal, ainsi que du Fonds de recherche du Québec – Nature et technologies.
Smoothed Splitting Method for Counting
, 2011
"... We present an enhanced version of the splitting method, called the smoothed splitting method (SSM), for counting associated with complex sets, such as the set defined by the constraints of an integer program and in particular for counting the number of satisfiability assignments. Like the convention ..."
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We present an enhanced version of the splitting method, called the smoothed splitting method (SSM), for counting associated with complex sets, such as the set defined by the constraints of an integer program and in particular for counting the number of satisfiability assignments. Like the conventional splitting algorithms, ours uses a sequential sampling plan to decompose a “difficult” problem into a sequence of “easy ” ones. The main difference between SSM and splitting is that it works with an auxiliary sequence of continuous sets instead of the original discrete ones. The rationale of doing so is that continuous sets are easier to handle. We show that while the proposed method and its standard splitting counterpart are similar in their CPU time and variability, the former is more robust and more flexible than the latter. In particular, it makes it simpler for tuning the parameters.