Randomized Local Network Computing: Derandomization Beyond Locally Checkable Labelings

2021 ◽  
Vol 8 (4) ◽  
pp. 1-25
Author(s):  
Laurent Feuilloley ◽  
Pierre Fraigniaud
Keyword(s):  
Monte Carlo ◽  
Distributed Algorithms ◽  
Deterministic Algorithm ◽  
Monte Carlo Algorithm ◽  
Local Network ◽  
Network Computing ◽  
Seminal Paper ◽  
Distributed Tasks

We carry on investigating the line of research questioning the power of randomization for the design of distributed algorithms. In their seminal paper, Naor and Stockmeyer [STOC 1993] established that, in the context of network computing in which all nodes execute the same algorithm in parallel, any construction task that can be solved locally by a randomized Monte-Carlo algorithm can also be solved locally by a deterministic algorithm. This result, however, holds only for distributed tasks such that the correctness of their solutions can be locally checked by a deterministic algorithm. In this article, we extend the result of Naor and Stockmeyer to a wider class of tasks. Specifically, we prove that the same derandomization result holds for every task such that the correctness of their solutions can be locally checked using a 2-sided error randomized Monte-Carlo algorithm.

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

scholarly journals Bayesian cumulative shrinkage for infinite factorizations

Biometrika ◽  
2020 ◽  
Vol 107 (3) ◽  
pp. 745-752 ◽  
Author(s):  
Sirio Legramanti ◽  
Daniele Durante ◽  
David B Dunson
Keyword(s):  
Monte Carlo ◽  
Factor Analysis ◽  
Monte Carlo Algorithm ◽  
Model Complexity ◽  
Latent Factors ◽  
Shrinkage Process ◽  
Shrinkage Prior ◽  
Performance Gains ◽  
Shrinkage Priors ◽  
Model Dimension

Summary The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data.

scholarly journals Neural Decoding Using a Parallel Sequential Monte Carlo Method on Point Processes with Ensemble Effect

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Kai Xu ◽  
Yiwen Wang ◽  
Fang Wang ◽  
Yuxi Liao ◽  
Qiaosheng Zhang ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Point Process ◽  
Goodness Of Fit ◽  
Point Processes ◽  
Sequential Monte Carlo ◽  
Neuronal Response ◽  
Position Estimation ◽  
Monte Carlo Algorithm ◽  
Sequential Monte Carlo Method ◽  
Proposed Model

Sequential Monte Carlo estimation on point processes has been successfully applied to predict the movement from neural activity. However, there exist some issues along with this method such as the simplified tuning model and the high computational complexity, which may degenerate the decoding performance of motor brain machine interfaces. In this paper, we adopt a general tuning model which takes recent ensemble activity into account. The goodness-of-fit analysis demonstrates that the proposed model can predict the neuronal response more accurately than the one only depending on kinematics. A new sequential Monte Carlo algorithm based on the proposed model is constructed. The algorithm can significantly reduce the root mean square error of decoding results, which decreases 23.6% in position estimation. In addition, we accelerate the decoding speed by implementing the proposed algorithm in a massive parallel manner on GPU. The results demonstrate that the spike trains can be decoded as point process in real time even with 8000 particles or 300 neurons, which is over 10 times faster than the serial implementation. The main contribution of our work is to enable the sequential Monte Carlo algorithm with point process observation to output the movement estimation much faster and more accurately.

scholarly journals Testing a Fourier-accelerated hybrid Monte Carlo algorithm

2002 ◽  
Vol 528 (3-4) ◽  
pp. 301-305 ◽  
Author(s):  
Simon Catterall ◽  
Sergey Karamov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Hybrid Monte Carlo
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