Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures

Local likelihood estimation for covariance functions with spatially-varying parameters: the convoSPAT package for R

In spite of the interest in and appeal of convolution-based approaches for nonstationary spatial modeling, off-the-shelf software for model fitting does not as of yet exist. Convolution-based models are highly flexible yet notoriously difficult to fit, even with relatively small data sets. The general lack of pre-packaged options for model fitting makes it difficult to compare new methodology in nonstationary modeling with other existing methods, and as a result most new models are simply compared to stationary models. Using a convolution-based approach, we present a new nonstationary covarian…

A Bayesian Nonparametric Markovian Model for Nonstationary Time Series

Stationary time series models built from parametric distributions are, in general, limited in scope due to the assumptions imposed on the residual distribution and autoregression relationship. We present a modeling approach for univariate time series data, which makes no assumptions of stationarity, and can accommodate complex dynamics and capture nonstandard distributions. The model for the transition density arises from the conditional distribution implied by a Bayesian nonparametric mixture of bivariate normals. This implies a flexible autoregressive form for the conditional transition dens…

时间分区高斯过程混合模型

Time-partitioning Gaussian Process Mixture Model

本研究提出TPGPMM模型，用于识别时间序列的持续状态并建模非平稳依赖，通过贝叶斯非参数方法实现，在应用于金融数据时可识别与重大事件对齐的状态，且存在可解释性与预测准确性的权衡。

Some covariance models based on normal scale mixtures

Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new class is described that merges and generalizes various models presented in the literature, in particular models in Gneiting (J. Amer. Statist. Assoc. 97 (2002) 590--600) and Stein (Nonstationary spatial covariance functions (2005) Univ. Chicago). Furthermore, new models and a multivariate extension are introduced.

基于两阶段物理信息深度学习和统计混合模型的系数具有跳跃不连续性的偏微分方程反问题

Inverse Problems for Partial Differential Equations with Jump Discontinuities in Coefficients via Two-Stage Physics-Informed Deep Learning and Statistical Mixture Models

提出两阶段物理信息深度学习框架，结合神经网络采样与统计推断，解决系数具有跳跃不连续性的PDE反问题，实现参数识别与解重构。

Learning Temporally Causal Latent Processes from General Temporal Data

Our goal is to recover time-delayed latent causal variables and identify their relations from measured temporal data. Estimating causally-related latent variables from observations is particularly challenging as the latent variables are not uniquely recoverable in the most general case. In this work, we consider both a nonparametric, nonstationary setting and a parametric setting for the latent processes and propose two provable conditions under which temporally causal latent processes can be identified from their nonlinear mixtures. We propose LEAP, a theoretically-grounded framework that ext…

Clustering dynamics in a class of normalised generalised gamma dependent priors

Normalised generalised gamma processes are random probability measures that induce nonparametric prior distributions widely used in Bayesian statistics, particularly for mixture modelling. We construct a class of dependent normalised generalised gamma priors induced by a stationary population model of Moran type, which exploits a generalised Pólya urn scheme associated with the prior. We study the asymptotic scaling for the dynamics of the number of clusters in the sample, which in turn provides a dynamic measure of diversity in the underlying population. The limit is formalised to be a positi…

Scalable Bayesian transport maps for high-dimensional non-Gaussian spatial fields

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using Gaussian processes. This enables regularization and uncertainty quantification of the map estimation, while still resulting in a closed-form and invertible posterior map. We then focus on inferring the distribution of a nonstationary spatial field from a small number of replicates. We develop specific transport-map priors that are highly flexible and are motiv…

An Application of Bayesian Variable Selection to Spatial Concurrent Linear Models

Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the spatial processes, but in applications the data may display strong nonstationary patterns. In this article, we propose a Bayesian variable selection approach based on wavelet tools to address this problem. The proposed approach does not involve any stationarity assumptions on the priors, and instead we impose a mixture prior directly on each wavelet coefficient. W…

A semiparametric spatiotemporal Bayesian model for the bulk and extremes of the Fosberg Fire Weather Index

Large wildfires pose a major environmental concern, and precise maps of fire risk can improve disaster relief planning. Fosberg Fire Weather Index (FFWI) is often used to measure wildfire risk; FFWI exhibits non-Gaussian marginal distributions as well as strong spatiotemporal extremal dependence and thus, modeling FFWI using geostatistical models like Gaussian processes is questionable. Extreme value theory (EVT)-driven models like max-stable processes are theoretically appealing but are computationally demanding and applicable only for threshold exceedances or block maxima. Disaster managemen…

使用高斯过程学习参数化刚性常微分方程的解

Learning solutions of parameterized stiff ODEs using Gaussian processes

针对刚性ODE解的非平稳性导致高斯过程代理模型性能下降的问题，提出一种基于数据重新参数化的预处理方法，使解更平稳，从而以极小计算开销恢复GP性能。

DeRegiME：用于分布偏移下概率预测的深度制度混合

DeRegiME: Deep Regime Mixtures for Probabilistic Forecasting under Distribution Shift

DeRegiME通过引入稀疏变分高斯过程，实现了概率预测中的制度混合，解决了神经预测器在处理分布偏移时的不足，提升了预测密度的准确性。

Generalized Spectral Kernels

In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary kernels, and propose a family of spectral kernels that extends existing approaches such as spectral mixture kernels and sparse spectrum kernels. Our extension has two primary advantages. Firstly, unlike existing spectral approaches that yield infinite differentiability, the kernels we introduce allow learning the degree of differentiability of the latent fu…