Nonparametric Inference for Max-Stable Dependence

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…

Bayesian Nonparametric Modeling of Higher Order Markov Chains

We consider the problem of flexible modeling of higher order Markov chains when an upper bound on the order of the chain is known but the true order and nature of the serial dependence are unknown. We propose Bayesian nonparametric methodology based on conditional tensor factorizations, which can characterize any transition probability with a specified maximal order. The methodology selects the important lags and captures higher order interactions among the lags, while also facilitating calculation of Bayes factors for a variety of hypotheses of interest. We design efficient Markov chain Monte…

An overview of nonparametric tests of extreme-value dependence and of some related statistical procedures

An overview of existing nonparametric tests of extreme-value dependence is presented. Given an i.i.d.\ sample of random vectors from a continuous distribution, such tests aim at assessing whether the underlying unknown copula is of the {\em extreme-value} type or not. The existing approaches available in the literature are summarized according to how departure from extreme-value dependence is assessed. Related statistical procedures useful when modeling data with this type of dependence are briefly described next. Two illustrations on real data sets are then carried out using some of the stati…

在线学习中非线性能力轨迹与学习者异质性建模：一种贝叶斯非参数动态IRT框架

Modeling Nonlinear Ability Trajectories and Learner Heterogeneity in Online Learning: A Bayesian Nonparametric Dynamic IRT Framework

提出贝叶斯非参数动态IRT框架，用B样条基函数捕捉非线性效应，MFM先验自动确定聚类数，克服线性假设、预设聚类数和无法追踪纵向动态的局限，应用于198名大学生数据，识别出四种学习者轮廓。

Nonparametric inference for competing risks current status data with continuous, discrete or grouped observation times

New methods and theory have recently been developed to nonparametrically estimate cumulative incidence functions for competing risks survival data subject to current status censoring. In particular, the limiting distribution of the nonparametric maximum likelihood estimator and a simplified "naive estimator" have been established under certain smoothness conditions. In this paper, we establish the large-sample behavior of these estimators in two additional models, namely when the observation time distribution has discrete support and when the observation times are grouped. These asymptotic res…

A class of goodness-of-fit tests for spatial extremes models based on max-stable processes

Parametric max-stable processes are increasingly used to model spatial extremes. Starting from the fact that the dependence structure of a max-stable process is completely characterized by an extreme-value copula, a class of goodness-of-fit tests is proposed based on the comparison between a nonparametric and a parametric estimator of the corresponding unknown multivariate Pickands dependence function. Because of the high-dimensional setting under consideration, these functional estimators are only compared at a specific set of points at which they coincide, up to a multiplicative constant, wi…

Nonparametric estimation of multivariate extreme-value copulas

Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to certain shape constraints that arise from an integral transform of an underlying measure called spectral measure. Multivariate extensions are provided of certain rank-based nonparametric estimators of the Pickands dependence function. The shape constraint that the estimator should itself be a Pickands dependence function is enforced by replacing an initial estima…

高维分布的非参数变点检测与推断

Nonparametric Change-Point Detection and Inference for High-Dimensional Distributions

针对高维分布中均值协方差不变但分布改变且受影响坐标未知的问题，提出基于标准秩比较的非参数变点检测方法，结合和/最大扫描与柯西组合适应稀疏性，无需矩假设，可扩展多变点检测，模拟和实际数据验证有效。

Nonparametric Maximum Entropy Probability Density Estimation

Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found by maximizing a log-likelihood function based on single order statistics after transforming through a sequence of trial cumulative distribution functions that iteratively improve using a Monte Carlo random search method. Improvement is quantified by assessing the random variables against the statistical properties of sampled uniform random data. Quality is de…

Nonparametric Bayesian grouping methods for spatial time-series data

We describe an approach for identifying groups of dynamically similar locations in spatial time-series data based on a simple Markov transition model. We give maximum-likelihood, empirical Bayes, and fully Bayesian formulations of the model, and describe exhaustive, greedy, and MCMC-based inference methods. The approach has been employed successfully in several studies to reveal meaningful relationships between environmental patterns and disease dynamics.

经验贝叶斯估计与推断：基于光滑非参数最大似然法

Empirical Bayes Estimation and Inference via Smooth Nonparametric Maximum Likelihood

针对非参数最大似然估计的离散性和慢对数解卷积率，引入高斯平滑层，提出光滑NPMLE，实现多项式解卷积率、近参数去噪性能及后验一致估计，并构建最优边际覆盖集。

Nonparametric survival analysis and vaccine efficacy using Dempster-Shafer analysis

We introduce an extension of nonparametric DS inference for arbitrary univariate CDFs to the case in which some failure times are (right)-censored, and then apply this to the problem of assessing evidence regarding assertions about relative risks across two populations. The approach enables exploration of the sensitivity of survival analyses to assumed independence of the missing data process and the failure proces. We present an application to the partially efficacious RV144 (HIV-1) vaccine trial, and show that the strength of conclusions of vaccine efficacy depend on assumptions about the ma…

A copula approach for dependence modeling in multivariate nonparametric time series

This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences only the conditional mean and the conditional variance of each of the time series but the distribution of the standardized innovations is not influenced by the covariate and is stable in time. The joint distribution of the time series is then determined by the conditional means, the conditional variances and the marginal distributions of the innovations, which …

二元分类与政策价值中的非参数均匀推断

Nonparametric Uniform Inference in Binary Classification and Policy Values

本文提出了一种非参数均匀推断方法，用于成本敏感二元分类和政策价值的推断，通过严格凸替代损失函数实现点识别，并在模拟和实际应用中验证了其有效性。

An Encoding Approach for Stable Change Point Detection

Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis. We develop a structural subsampling procedure such that the observations are encoded into multiple sequences of Bernoulli variables. A maximum likelihood approach in conjunction with a newly developed searching algorithm is implemented to detect change points on each Bernoulli process separately. Then, aggregation statistics are proposed to collectively syn…

高维非参数时间序列回归模型中跳跃的推断

High-dimensional inference on jumps in nonparametric time series regression models

研究高维异质非参数时间序列条件均值函数中跳跃的同时推断，提出两个统一检验，推导跳跃估计量协方差结构近似并建立高斯近似，模拟和实证表明方法在多种依赖性下有效，能揭示显著非平滑效应。

无标签直方图的非参数推断

Nonparametric Inference on Unlabeled Histograms

本文提出用混合分布建模无标签直方图多重集，研究非参数最大似然估计及其最优收敛速率，并给出高效插件估计量，在合成、真实数据及大语言模型实验中验证了方法的实用价值。

外推感知的非参数统计推断

Extrapolation-Aware Nonparametric Statistical Inference

本文扩展非参数统计模型，提出基于观测支撑集内方向导数极值的外推假设与一致界估计方法，用于预测和不确定性量化。