Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines

This article deals with symmetrical data that can be modelled based on Gaussian distribution. We consider a class of partially linear additive spatial autoregressive (PLASAR) models for spatial data. We develop a Bayesian free-knot splines approach to approximate the nonparametric functions. It can be performed to facilitate efficient Markov chain Monte Carlo (MCMC) tools to design a Gibbs sampler to explore the full conditional posterior distributions and analyze the PLASAR models. In order to acquire a rapidly-convergent algorithm, a modified Bayesian free-knot splines approach incorporated with powerful MCMC techniques is employed. The Bayesian estimator (BE) method is more computationally efficient than the generalized method of moments estimator (GMME) and thus capable of handling large scales of spatial data. The performance of the PLASAR model and methodology is illustrated by a simulation, and the model is used to analyze a Sydney real estate dataset.

An intelligent decision-making method for anti-jamming communication based on deep reinforcement learning

In order to solve the problem of intelligent anti-jamming decision-making in battlefield communication, this paper designs an intelligent decision-making method for communication anti-jamming based on deep reinforcement learning. Introducing experience replay and dynamic epsilon mechanism based on PHC under the framework of DQN algorithm, a dynamic epsilon-DQN intelligent decision-making method is proposed. The algorithm can better select the value of epsilon according to the state of the decision network and improve the convergence speed and decision success rate. During the decision-making process, the jamming signals of all communication frequencies are detected, and the results are input into the decision-making algorithm as jamming discriminant information, so that we can effectively avoid being jammed under the condition of no prior jamming information. The experimental results show that the proposed method adapts to various communication models, has a fast decision-making speed, and the average success rate of the convergent algorithm can reach more than 95%, which has a great advantage over the existing decision-making methods.

A triply cubic polynomials approach for globally convergent algorithm in coefficient inverse problems

In this paper, a triply cubic polynomials approach is proposed firstly for solving the globally convergent algorithm of coefficient inverse problems in three dimension. Using Taylor type expansion for three arguments to construct tripled cubic polynomials for the approximate solution as identifying coefficient function of parabolic initial-boundary problems, in which unknown coefficients appeared at nonlinear term. The presented computational approach is effective to execute in spatial 3D issues arising in real world. Further, the complete algorithm can be straightforwardly performed to lower or higher dimensions case

A triply cubic polynomials approach for globally convergent algorithm in coefficient inverse problems

In this paper, a triply cubic polynomials approach is proposed firstly for solving the globally convergent algorithm of coefficient inverse problems in three dimension. Using Taylor type expansion for three arguments to construct tripled cubic polynomials for the approximate solution as identifying coefficient function of parabolic initial-boundary problems, in which unknown coefficients appeared at nonlinear term. The presented computational approach is effective to execute in spatial 3D issues arising in real world. Further, the complete algorithm can be straightforwardly performed to lower or higher dimensions case

Efficient Algorithms for Rotation Averaging Problems

The rotation averaging problem is a fundamental task in computer vision applications. It is generally very difficult to solve due to the nonconvex rotation constraints. While a sufficient optimality condition is available in the literature, there is a lack of a fast convergent algorithm to achieve stationary points. In this paper, by exploring the problem structure, we first propose a block coordinate descent (BCD)-based rotation averaging algorithm with guaranteed convergence to stationary points. Afterwards, we further propose an alternative rotation averaging algorithm by applying successive upper-bound minimization (SUM) method. The SUM-based rotation averaging algorithm can be implemented in parallel and thus is more suitable for addressing large-scale rotation averaging problems. Numerical examples verify that the proposed rotation averaging algorithms have superior convergence performance as compared to the state-of-the-art algorithm. Moreover, by checking the sufficient optimality condition, we find from extensive numerical experiments that the proposed two algorithms can achieve globally optimal solutions.