1 results about "Linear dependency" patented technology

This invention relates to the fields of stochastic processes and Monte Carlo computation, and particularly to a method for constructing a Markov transition operator. The aim is to improve the spectral properties of traditional Markov operators by introducing a higher-order transition structure, thereby enhancing sampling efficiency. First, starting with a basic Markov transition operator that satisfies the invariance of the target distribution, this method, based on the Metropolis–Hastings (MH) framework, introduces a two-step hybrid update mechanism to construct a polynomial Markov operator. Through spectral structure analysis of this operator, its eigenvalue transformation relationship is established, and it is proven that it has a larger spectral gap and better convergence performance compared to the original operator, while also reducing the asymptotic variance of the corresponding statistics. Second, further analysis of the autocorrelation function and integration time shows that the Ishikawa-MCMC algorithm can effectively suppress linear dependencies between samples, resulting in a faster decay rate of the autocovariance, thereby reducing the Monte Carlo covariance. The operator construction method proposed in this invention overcomes the problem of slow convergence of traditional single transition operators under high-dimensional or complex distributions by integrating multi-order transition information. It provides a new operator design framework for Markov chain Monte Carlo algorithms and can be widely applied in fields such as Bayesian statistical inference, complex probability distribution sampling, and stochastic simulation.