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高维与机器学习:高维模型、正则化、变量选择与机器学习。
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Dynamic Factor Analysis of High-dimensional Recurrent Events

高维重复事件的动态因子分析

Recurrent event time data arise in many studies, including biomedicine, public health, marketing, and social media analysis. High-dimensional recurrent event data involving many event types and observations have become prevalent with advances in information technology. This paper proposes a semiparametric dynamic factor model for the dimension reduction of high-dimensional recurrent event data. The proposed model imposes a low-dimensional structure on the mean intensity…

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Non-parametric cure models through extreme-value tail estimation

基于极值尾部估计的非参数治愈模型

In survival analysis, the estimation of the proportion of subjects who will never experience the event of interest, termed the cure rate, has received considerable attention recently. Its estimation can be a particularly difficult task when follow-up is not sufficient, that is when the censoring mechanism has a smaller support than the distribution of the target data. In the latter case, non-parametric estimators were recently proposed using extreme value methodology,…

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Variable selection in balance regression with applications to microbiome compositional data

平衡回归中的变量选择及其在微生物组成分数据中的应用

Compositional data, where only relative abundances are available, are common in microbiome and other high-throughput sequencing studies. Log ratios between groups of variables serve as key biomarkers in these settings. However, selecting predictive log ratios is a combinatorial challenge, and existing greedy search-based methods are computationally expensive, limiting their applicability to high-dimensional data. We introduce the supervised log ratio (SLR) method, a novel…

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Relational Graph in Vector Autoregression: A Case Study on the Effect of the Great Recession on Connectivity of Economic Indicators

向量自回归中的关系图:大衰退与经济指标连接变化

Under a high-dimensional vector autoregressive (VAR) model, we propose a way of efficiently estimating both the stationary graph structure between the nodal time series and their temporal dynamics. The framework is then used to make inferences on the change in interdependencies between several economic indicators due to the impact of the Great Recession, the financial crisis that lasted from 2007 through 2009. There are several key advantages of the proposed framework; (1)…

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A Unified Approach for Estimating Various Treatment Effects in Causal Inference

因果推断中多类处理效应的统一估计方法

In this paper, we introduce a unified estimator to analyze various treatment effects in causal inference, including but not limited to the average treatment effect (ATE) and the quantile treatment effect (QTE). The proposed estimator is developed under the statistical functional and cumulative distribution function structure, which leads to a flexible and robust estimator and covers some frequent treatment effects. In addition, our approach also takes variable selection into…

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Sparklen: A Statistical Learning Toolkit for High-Dimensional Hawkes Processes in Python

Sparklen:面向高维霍克斯过程的 Python 统计学习工具包

This paper introduces Sparklen, a statistical learning toolkit for Hawkes processes in Python, designed to bring together efficiency and ease of use. The purpose of this package is to provide the Python community with a complete suite of cutting-edge tools specifically tailored for the study of exponential Hawkes processes, with a particular focus on highdimensional framework. It includes state-of-the-art estimation tools with built-in support for incorporating…

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An Artificial Trend Index for Private Consumption Using Google Trends

利用 Google Trends 构建私人消费趋势指数

In recent years, the use of databases that analyze trends, sentiments or news to make economic projections or create indicators has gained significant popularity, particularly with the Google Trends platform. This article explores the potential of Google search data to develop a new index that improves economic forecasts, with a particular focus on one of the key components of economic activity: private consumption (64\% of GDP in Peru). By selecting and estimating…

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Revisiting general source condition in learning over a Hilbert space

重审希尔伯特空间学习中的一般源条件

In Learning Theory, the smoothness assumption on the target function (known as source condition) is a key factor in establishing theoretical convergence rates for an estimator. The existing general form of the source condition, as discussed in learning theory literature, has traditionally been restricted to a class of functions that can be expressed as a product of an operator monotone function and a Lipschitz continuous function. In this note, we remove these restrictions…

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Statistical Inference for High-dimensional Matrix-variate Factor Models with Missing Observations

缺失观测下高维矩阵值因子模型的统计推断

This paper develops an inferential theory for high-dimensional matrix-variate factor models with missing observations. We propose an easy-to-use all-purpose method that involves two straightforward steps. First, we perform principal component analysis on two re-weighted covariance matrices to obtain the row and column loadings. Second, we utilize these loadings along with the matrix-variate data to derive the factors. We develop an inferential theory that establishes the…

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A general joint latent class model of longitudinal and survival data with the covariance modelling

带协方差建模的纵向与生存数据联合潜类别模型

Based on the proposed time-varying JLCM (Miao and Charalambous, 2022), the heterogeneous random covariance matrix can also be considered, and a regression submodel for the variance-covariance matrix of the multivariate latent random effects can be added to the joint latent class model. A general joint latent class model with heterogeneous random-effects modelling is a natural extension of the time-varying JLCM, which consists of the linear and the log link functions to model…

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Forecasting Labor Demand: Predicting JOLT Job Openings using Deep Learning Model

劳动需求预测:利用深度学习预测JOLTS职位空缺

This thesis studies the effectiveness of Long Short Term Memory model in forecasting future Job Openings and Labor Turnover Survey data in the United States. Drawing on multiple economic indicators from various sources, the data are fed directly into LSTM model to predict JOLT job openings in subsequent periods. The performance of the LSTM model is compared with conventional autoregressive approaches, including ARIMA, SARIMA, and Holt-Winters. Findings suggest that the LSTM…

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Minimax Rate-Optimal Inference for Individualized Quantile Treatment Effects in High-dimensional Models

高维模型中个体化分位数处理效应的极小极大速率最优推断

The quantification of treatment effects plays an important role in a wide range of applications, including policy making and bio-pharmaceutical research. In this article, we study the quantile treatment effect (QTE) while addressing two specific types of heterogeneities: (a) personalized heterogeneity, which captures the varying treatment effects for different individuals, and (b) quantile heterogeneity, which accounts for how the impact of covariates varies across different…

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Distributional bias compromises leave-one-out cross-validation

分布偏差影响留一交叉验证

Cross-validation is a common method for estimating the predictive performance of machine learning models. In a data-scarce regime, where one typically wishes to maximize the number of instances used for training the model, an approach called "leave-one-out cross-validation" is often used. In this design, a separate model is built for predicting each data instance after training on all other instances. Since this results in a single test instance available per model trained,…

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Principal Component Analysis When n < p: Challenges and Solutions

当 n < p 时的主成分分析:挑战与解决方案

Principal Component Analysis is a key technique for reducing the complexity of high-dimensional data while preserving its fundamental data structure, ensuring models remain stable and interpretable. This is achieved by transforming the original variables into a new set of uncorrelated variables (principal components) based on the covariance structure of the original variables. However, since the traditional maximum likelihood covariance estimator does not accurately converge…

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Prediction-Centric Uncertainty Quantification via MMD

以预测为中心的不确定性量化:基于MMD的方法

Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised Bayesian methodologies have been proposed for inference with misspecified models, but these are typically associated with vanishing parameter uncertainty as more data are observed. In the context of a misspecified deterministic mathematical…

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Multi-View Orthogonal Projection Regression with Application in Multi-omics integration

多视图正交投影回归及其在多组学整合中的应用

Multi-omics integration offers novel insights into complex biological mechanisms by utlizing the fused information from various omics datasets. However, the inherent within- and inter-modality correlations in multi-omics data present significant challenges for traditional variable selection methods, such as Lasso regression. These correlations can lead to multicollinearity, compromising the stability and interpretability of selected variables. To address these problems, we…

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Weighted Average Ensemble for Cholesky-based Covariance Matrix Estimation

基于Cholesky分解的协方差矩阵加权平均集成估计

The modified Cholesky decomposition (MCD) is an efficient technique for estimating a covariance matrix. However, it is known that the MCD technique often requires a pre-specified variable ordering in the estimation procedure. In this work, we propose a weighted average ensemble covariance estimation for high-dimensional data based on the MCD technique. It can flexibly accommodate the high-dimensional case and ensure the positive definiteness property of the resultant…

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Outcome-Informed Weighting for Robust ATE Estimation

利用结局信息加权的稳健平均处理效应估计

Reliable causal effect estimation from observational data requires adjustment for confounding and sufficient overlap in covariate distributions between treatment groups. However, in high-dimensional settings, lack of overlap often inflates the variance and weakens the robustness of inverse propensity score weighting (IPW) based estimators. Although many approaches that rely on covariate adjustment have been proposed to mitigate these issues, we instead shift the focus to the…

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Integrative Analysis of High-dimensional RCT and RWD Subject to Censoring and Hidden Confounding

删失与隐藏混杂下高维随机试验和真实世界数据的整合分析

In this study, we focus on estimating the heterogeneous treatment effect (HTE) for survival outcome. The outcome is subject to censoring and the number of covariates is high-dimensional. We utilize data from both the randomized controlled trial (RCT), considered as the gold standard, and real-world data (RWD), possibly affected by hidden confounding factors. To achieve a more efficient HTE estimate, such integrative analysis requires great insight into the data generation…

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A Shrinkage Likelihood Ratio Test for High-Dimensional Subgroup Analysis with a Logistic-Normal Mixture Model

逻辑斯蒂—正态混合模型下高维亚组分析的收缩似然比检验

In subgroup analysis, testing the existence of a subgroup with a differential treatment effect serves as protection against spurious subgroup discovery. Despite its importance, this hypothesis testing possesses a complicated nature: parameter characterizing subgroup classification is not identified under the null hypothesis of no subgroup. Due to this irregularity, the existing methods have the following two limitations. First, the asymptotic null distribution of test…

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Dynamic Investment Strategies Through Market Classification and Volatility: A Machine Learning Approach

基于市场分类与波动率的动态投资策略:机器学习方法

This study introduces a dynamic investment framework to enhance portfolio management in volatile markets, offering clear advantages over traditional static strategies. Evaluates four conventional approaches : equal weighted, minimum variance, maximum diversification, and equal risk contribution under dynamic conditions. Using K means clustering, the market is segmented into ten volatility-based states, with transitions forecasted by a Bayesian Markov switching model…

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Information-theoretic limits and approximate message-passing for high-dimensional time series

高维时间序列的信息论极限与近似消息传递

High-dimensional time series appear in many scientific setups, demanding a nuanced approach to model and analyze the underlying dependence structure. Theoretical advancements so far often rely on stringent assumptions regarding the sparsity of the underlying signal. In non-sparse regimes, analyses have primarily focused on linear regression models with the design matrix having independent rows. In this paper, we expand the scope by investigating a high-dimensional time…

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A Unified Framework for Semiparametrically Efficient Semi-Supervised Learning

半参数有效半监督学习的统一框架

We consider statistical inference under a semi-supervised setting where we have access to both a labeled dataset consisting of pairs $\{X_i, Y_i \}_{i=1}^n$ and an unlabeled dataset $\{ X_i \}_{i=n+1}^{n+N}$. We ask the question: under what circumstances, and by how much, can incorporating the unlabeled dataset improve upon inference using the labeled data? To answer this question, we investigate semi-supervised learning through the lens of semiparametric efficiency theory.…

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fabisearch: A Package for Change Point Detection in and Visualization of the Network Structure of Multivariate High-Dimensional Time Series in R

fabisearch:高维多元时间序列网络结构变点检测与可视化 R 包

Change point detection is a commonly used technique in time series analysis, capturing the dynamic nature in which many real-world processes function. With the ever increasing troves of multivariate high-dimensional time series data, especially in neuroimaging and finance, there is a clear need for scalable and data-driven change point detection methods. Currently, change point detection methods for multivariate high-dimensional data are scarce, with even less available in…

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