CATVI: Conditional and Adaptively Truncated Variational Inference for Hierarchical Bayesian Nonparametric Models

Nonparametric Bayesian label prediction on a large graph using truncated Laplacian regularization

This article describes an implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs. We consider a hierarchical Bayesian approach with a prior that is constructed by truncating a series expansion of the soft label function using the graph Laplacian eigenfunctions as basis functions. We compare our truncated prior to the untruncated Laplacian based prior in simulated and real data examples to illustrate the improved scalability in terms of size of the underlying graph.

Max-Margin Nonparametric Latent Feature Models for Link Prediction

Link prediction is a fundamental task in statistical network analysis. Recent advances have been made on learning flexible nonparametric Bayesian latent feature models for link prediction. In this paper, we present a max-margin learning method for such nonparametric latent feature relational models. Our approach attempts to unite the ideas of max-margin learning and Bayesian nonparametrics to discover discriminative latent features for link prediction. It inherits the advances of nonparametric Bayesian methods to infer the unknown latent social dimension, while for discriminative link predicti…

作为非参数条件概率估计的上下文学习：风险界与最优性

In-Context Learning as Nonparametric Conditional Probability Estimation: Risk Bounds and Optimality

该研究针对多类分类中上下文学习的期望超额风险，基于KL散度建立新神谕不等式，证明transformer与多层感知器的ICL估计器均能达到条件概率估计的极小极大最优速率，还提出了通过一致经验熵控制泛化误差的新方法。

Bayesian Nonparametric Inference of Switching Linear Dynamical Systems

Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. Our Bayesian nonparametric approach utilizes a hierarchical Dirichlet process prior to learn an unknown number of persistent, smooth dynamical modes. We additionally employ automatic relevance determination to infer a sparse set of dynamic dependencies allowing us to learn SLDS with varying state dimension or switching VAR process…

Optimum thresholding using mean and conditional mean square error

We consider a univariate semimartingale model for (the logarithm of) an asset price, containing jumps having possibly infinite activity (IA). The nonparametric threshold estimator of the integrated variance IV proposed in Mancini 2009 is constructed using observations on a discrete time grid, and precisely it sums up the squared increments of the process when they are below a threshold, a deterministic function of the observation step and possibly of the coefficients of X. All the threshold functions satisfying given conditions allow asymptotically consistent estimates of IV, however the finit…

贝叶斯非参数推断的独立有限近似

Independent finite approximations for Bayesian nonparametric inference

针对贝叶斯非参数中完全随机测度无限维推断难题，提出自动化独立有限近似AIFA方法，推导其误差界与选择准则，对比了与截断近似的理论效率和实际性能，拓展了独立有限近似的适用场景。