Most Likely Optimal Subsampled Markov Chain Monte Carlo

基于AI调优的马尔可夫链蒙特卡洛矩阵求逆的快速线性求解器

Fast Linear Solvers via AI-Tuned Markov Chain Monte Carlo-based Matrix Inversion

本文提出AI驱动框架，利用图神经代理模型和贝叶斯采集函数自动推荐MCMC参数，以更低搜索预算生成更优预条件子并加速Krylov求解器收敛。

Stochastic Precipitation Generation for the Chesapeake Bay Watershed using Hidden Markov Models with Variational Bayes Parameter Estimation

Stochastic precipitation generators (SPGs) are a class of statistical models which generate synthetic data that can simulate dry and wet rainfall stretches for long durations. Generated precipitation time series data are used in climate projections, impact assessment of extreme weather events, and water resource and agricultural management. We construct an SPG for daily precipitation data that is specified as a semi-continuous distribution at every location, with a point mass at zero for no precipitation and a mixture of two exponential distributions for positive precipitation. Our generators …

Improving Sampling Accuracy of Stochastic Gradient MCMC Methods via Non-uniform Subsampling of Gradients

Many Markov Chain Monte Carlo (MCMC) methods leverage gradient information of the potential function of target distribution to explore sample space efficiently. However, computing gradients can often be computationally expensive for large scale applications, such as those in contemporary machine learning. Stochastic Gradient (SG-)MCMC methods approximate gradients by stochastic ones, commonly via uniformly subsampled data points, and achieve improved computational efficiency, however at the price of introducing sampling error. We propose a non-uniform subsampling scheme to improve the sampling…

An adaptive MCMC method for multiple changepoint analysis with applications to large datasets

We consider the problem of Bayesian inference for changepoints where the number and position of the changepoints are both unknown. In particular, we consider product partition models where it is possible to integrate out model parameters for the regime between each changepoint, leaving a posterior distribution over a latent vector indicating the presence or not of a changepoint at each observation. The same problem setting has been considered by Fearnhead (2006) where one can use filtering recursions to make exact inference. However the complexity of this algorithm depends quadratically on the…

Adaptive Stress Testing for Autonomous Vehicles

This paper presents a method for testing the decision making systems of autonomous vehicles. Our approach involves perturbing stochastic elements in the vehicle's environment until the vehicle is involved in a collision. Instead of applying direct Monte Carlo sampling to find collision scenarios, we formulate the problem as a Markov decision process and use reinforcement learning algorithms to find the most likely failure scenarios. This paper presents Monte Carlo Tree Search (MCTS) and Deep Reinforcement Learning (DRL) solutions that can scale to large environments. We show that DRL can find …

Latent Community Adaptive Network Regression

The study of network data in the social and health sciences frequently concentrates on two distinct tasks (1) detecting community structures among nodes and (2) associating covariate information to edge formation. In much of this data, it is likely that the effects of covariates on edge formation differ between communities (e.g. age might play a different role in friendship formation in communities across a city). In this work, we introduce a latent space network model where coefficients associated with certain covariates can depend on latent community membership of the nodes. We show that ign…

An Infinite Hidden Markov Model With Similarity-Biased Transitions

We describe a generalization of the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) which is able to encode prior information that state transitions are more likely between "nearby" states. This is accomplished by defining a similarity function on the state space and scaling transition probabilities by pair-wise similarities, thereby inducing correlations among the transition distributions. We present an augmented data representation of the model as a Markov Jump Process in which: (1) some jump attempts fail, and (2) the probability of success is proportional to the similarity bet…

Bayesian Context Trees: Modelling and exact inference for discrete time series

We develop a new Bayesian modelling framework for the class of higher-order, variable-memory Markov chains, and introduce an associated collection of methodological tools for exact inference with discrete time series. We show that a version of the context tree weighting algorithm can compute the prior predictive likelihood exactly (averaged over both models and parameters), and two related algorithms are introduced, which identify the a posteriori most likely models and compute their exact posterior probabilities. All three algorithms are deterministic and have linear-time complexity. A family…

心理测试中用于检查反应动力学的马尔可夫链模型

Markov chain models for inspecting response dynamics in psychological testing

本研究引入一阶马尔可夫链模型和非对易可观测量的概念，探讨心理测试中早期反应对后续答案的锚定作用及序列依赖性，为测试和问卷反应模式的纵向分析提供了方法论框架。