Scalable Multivariate Histograms

通过聚类集实现多变量分布的可扩展学习

Scalable Learning of Multivariate Distributions via Coresets

本文提出一种新的聚类集构造方法，用于多变量条件变换模型，以提高其可扩展性和训练效率，通过重要性抽样实现数据缩减，确保对数似然在乘法误差范围内，适用于复杂分布和非线性关系的场景。

大规模高斯随机向量采样中的可扩展迭代方法

Scalable iterative methods for sampling from massive Gaussian random vectors

本文提出利用高斯马尔可夫随机场的近似方法加速Krylov子空间采样，同时应用于大规模多元高斯分布的正则化常数计算，提出O(n log n)的采样方案。

A Computational Framework for Multivariate Convex Regression and its Variants

We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to compute for large problems. Exploiting problem specific structure, we propose a scalable algorithmic framework based on the augmented Lagrangian method to compute the LSE. We develop a novel approach to obtain smooth convex approximations to the fitted (piecewise affine) convex LSE and provide formal bounds on the quality of approximation. When the number of samp…

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…

在线多变量正则化分布回归用于高维概率电力价格预测

Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting

本文提出一种在线算法，用于高维概率电力价格预测，通过结合多变量分布回归与在线坐标下降和LASSO正则化，实现对电力价格条件均值、方差和依赖结构的高效建模，并在德国日间市场数据中验证了其有效性。

可扩展正则化向量乘法误差模型用于正值金融时间序列

Scalable Regularized Vector Multiplicative Error Models for Positive-valued Financial Time Series

本文提出针对正值金融时间序列的log-vMEM模型正则化估计方法，结合分层滞后结构与多种惩罚，采用块坐标下降算法，并利用GPU加速积分提升计算可扩展性。

Multiscale Fisher's Independence Test for Multivariate Dependence

Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample size, making it difficult to apply them to massive data. Moreover, resampling is usually necessary to evaluate the statistical significance of the resulting test statistics at finite sample sizes, further worsening the computational burden. We introduce a scalable, resampling-free approach to testing the independence between two random vectors by breaking d…