每日简报

协整回归变量：折叠凹惩罚何时超越 LASSOAI 解读

LASSO is one of the most popular regularization methods for high-dimensional regression models. While cointegration is common in practical applications of predictive regressions with many regressors, the convex penalty of LASSO overly suppresses the coefficients of cointegrated regressors and therefore fails to deliver consistent parameter estimation. We employ folded concave penalties (FCP), including the well-known SCAD and MCP, to address this issue. Using FCP, we…

循环重心编码器：预测、模拟及其在时间序列分析中的应用AI 解读

This dissertation has two parts. In the first part we theoretically develop a framework that extends the optimal transport barycenter problem from independent data with observed covariates to processes whose relevant covariate is their own history. Given a stationary stochastic process, our framework shows there exists an invertible transport map that extracts from it an iid component whose distribution is the barycenter of the conditional distributions of the input process…

矩阵值 CP 因子模型的识别问题与准极大似然估计AI 解读

Matrix-valued time series, arising in diverse fields such as economics, neuroscience, and recommender systems, have become increasingly prominent in modern data analysis. Among various modeling frameworks, the matrix-variate CP-factor model represents an important and widely applicable class for capturing low-rank structures in matrix time series. In this paper, we provide a unified treatment for the identification problem of CP factor models using both analytic and…

高维 Ornstein–Uhlenbeck 过程漂移项的稀疏估计AI 解读

We study sparsity-regularized maximum likelihood estimation for the drift parameter of high-dimensional non-stationary Ornstein--Uhlenbeck processes given repeated measurements of i.i.d. paths. In particular, we show that Lasso and Slope estimators can achieve the minimax optimal rate of convergence. We exhibit numerical experiments for sparse estimation methods and show their performance.