Real-Parameter Evolutionary Monte Carlo With Applications to Bayesian Mixture Models
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We propose an evolutionary Monte Carlo algorithm to sample from a target distribution with real-valued parameters. The attractive features of the algorithm include the ability to learn from the samples obtained in previous steps and the ability to improve the mixing of a system by sampling along a temperature ladder. The effectiveness of the algorithm is examined through three multimodal examples and Bayesian neural networks. The numerical results confirm that the real-coded evolutionary algorithm is a promising general approach for simulation and optimization.
Bayesian additive regression trees (BART) is a popular Bayesian ensemble model used in regression and classification analysis. Under this modeling framework, the regression function is approximated by an ensemble of decision trees, interpreted as weak learners. In this work, we propose a generalization of the BART model that has two main features: first, it automatically selects the number of decision trees using the given data; second, the model allows clusters of…
RBF 核高斯过程最大似然估计的精确渐近理论
Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications. A central component of a GP model is its kernel, which is typically specified through a parametric family. Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility. In practice, the…
大规模需求估计的贝叶斯机器学习方法
This work studies how Bayesian machine learning methods can be used for large-scale demand estimation with many product categories. I compare two model classes, a latent factorization model and a mixed logit model and two Bayesian estimation approaches, Markov Chain Monte Carlo (MCMC) and Variational Inference (VI). The analysis combines a simulation study with an application to supermarket scanner data. The results show that the latent factorization model benefits from…
相关任务间的经验贝叶斯谱部分汇聚
Spectral methods are central to high-dimensional statistics and machine learning, underlying procedures for covariance estimation, matrix denoising, representation learning, clustering, and latent variable modeling. In this work, we focus primarily on spectral estimators for high-dimensional factor models, where leading singular vectors of the data matrix are used to estimate latent structure and covariance parameters. In many modern applications, however, data are collected…
贝叶斯神经网络辅助多处理混合治愈生存模型:儿科肿瘤应用
Estimating covariate-conditional treatment effects in multi-arm oncology studies is complicated when treatment arms have common distributional features and a non-negligible fraction of patients achieve long-term remission. We propose a joint mixture cure model with covariate-dependent mixtures of log-normal kernels with treatment-specific inclusions. Both linear and neural-network-assisted non-linear covariate links are proposed. Specifically, the susceptible survival…
正则非光滑模型的归一化最大似然:测度论基础与几何采样
The Normalized Maximum Likelihood (NML) codelength, or stochastic complexity, represents a principled criterion for universal coding. While recent coarea-based formulations provided a calculation method for smooth models, this framework collapses for the non-smooth estimators ubiquitous in modern machine learning (e.g., Lasso, Sparse SVMs). In this work, we provide a rigorous framework for computing the NML for regular path-differentiable Lipschitz (PDL) estimators. By…