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Markov Chain Monte Carlo (MCMC) Methods
Published in Stephen Marsland, Machine Learning, 2014
A plot of 1,000 samples created by the Box–Muller scheme along with the zero mean, unit variance Gaussian line is shown in Figure 15.1. There is a more efficient algorithm for computing Gaussian-distributed random numbers known as the Ziggurat algorithm that should be investigated further if you require lower computational cost.
A kind of fast Gaussian particle filter based on Artificial Fish School Algorithm
Published in Journal of Control and Decision, 2022
Zhaihe Zhou, Jingmin Ma, Qiqi Liu, Qingxi Zeng, Xiangrui Tian
Provement: Each random variable at of the random vector is linearly transformed, , and the random vector . From the linear transformation invariance of the normal variable, it can be known that are independent of each other. Therefore, for the sample of The sample value obtained after the above linear transformation is the sample value of . Since each random variable of and is equal to Obey the same Gaussian distribution and are independent of each other, so is also the sample value of . The improved algorithm can be seen from Theorem 1. The generated particle swarm and the particle swarm generated by the GPF algorithm obey the same distribution. There is no essential difference between the improved GPF algorithm and the GPF algorithm except for the way of generating the particle swarm. Just compare the time required to generate the particle swarm, seeing the difference in the running time of the two algorithms. The linear transformation method to generate N particles requires N multiplications and N additions. The Gaussian distribution sampling method to generate N particles uses the more commonly used and fast Ziggurat algorithm (Chechik et al., 2007), which requires 4N Multiplication and 4 N additions. Using the acceptance-complement-based algorithm is 24% faster than the Zigg urat algorithm (Mason et al., 2000). It can be seen that the same number of particle sets are generated, and the time complexity of the linear transformation method is O(N), Gaussian The time complexity of the distributed sampling method is at least O(3N). The linear transformation method requires relatively less time, so using linear transformation instead of Gaussian sampling can increase the speed.