本文提出贝叶斯广义加性模型选择方法，利用组 LASSO 先验和辅助变量实现 MCMC 与快速平均场变分推断，并提供 R 包支持大规模数据应用。
摘要：
我们使用贝叶斯模型选择范式（如组最小绝对收缩和选择算子先验）来促进广义加性模型选择。我们的方法允许将连续预测变量的效应归类为零效应、线性效应或非线性效应。通过采用精心定制的辅助变量，得到了用于该方法实际实施的 Gibbsian Markov chain Monte Carlo 方案。此外，还获得了具有闭式更新的平均场变分算法。虽然精度稍低，但这种快速变分选项增强了对超大数据集的可扩展性。一个 R 语言软件包有助于实际使用。
英文摘要：
We use Bayesian model selection paradigms, such as group least absolute shrinkage and selection operator priors, to facilitate generalized additive model selection. Our approach allows for the effects of continuous predictors to be categorized as either zero, linear or non-linear. Employment of carefully tailored auxiliary variables results in Gibbsian Markov chain Monte Carlo schemes for practical implementation of the approach. In addition, mean field variational algorithms with closed form updates are obtained. Whilst not as accurate, this fast variational option enhances scalability to very large data sets. A package in the R language aids use in practice.
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National University of Singapore（新加坡国立大学）；Shenzhen University（深圳大学）
This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest model evidence, our proposed VBKS algorithm considers the kernel as a random variable and learns its belief from data such that the uncertainty of the kernel can be interpreted and exploited to avoid overconfident GP predictions. To achieve this, we represent the probabilistic kernel as an additional variational variable in a variational inference (VI) framewo…
University of Toronto（多伦多大学）；Riskfuel Analytics（Riskfuel分析公司）
We propose a hybrid method for generating arbitrage-free implied volatility (IV) surfaces consistent with historical data by combining model-free Variational Autoencoders (VAEs) with continuous time stochastic differential equation (SDE) driven models. We focus on two classes of SDE models: regime switching models and Lévy additive processes. By projecting historical surfaces onto the space of SDE model parameters, we obtain a distribution on the parameter subspace faithful to the data on which we then train a VAE. Arbitrage-free IV surfaces are then generated by sampling from the posterior di…
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We develop a privatised stochastic variational inference method for Latent Dirichlet Allocation (LDA). The iterative nature of stochastic variational inference presents challenges: multiple iterations are required to obtain accurate posterior distributions, yet each iteration increases the amount of noise that must be added to achieve a reasonable degree of privacy. We propose a practical algorithm that overcomes this challenge by combining: (1) an improved composition method for differential privacy, called the moments accountant, which provides a tight bound on the privacy cost of multiple v…
Hamilton Institute（汉密尔顿研究所）；Maynooth University（梅努斯大学）；Insight Centre for Data Analytics（洞察数据分析中心）
In plant breeding the presence of a genotype by environment (GxE) interaction has a strong impact on cultivation decision making and the introduction of new crop cultivars. The combination of linear and bilinear terms has been shown to be very useful in modelling this type of data. A widely-used approach to identify GxE is the Additive Main Effects and Multiplicative Interaction Effects (AMMI) model. However, as data frequently can be high-dimensional, Markov chain Monte Carlo (MCMC) approaches can be computationally infeasible. In this article, we consider a variational inference approach for…
