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利用混合整数规划检测时间序列变点AI 解读

We use cutting-edge mixed integer optimization (MIO) methods to develop a framework for detection and estimation of structural breaks in time series regression models. The framework is constructed based on the least squares problem subject to a penalty on the number of breakpoints. We restate the l0-penalized regression problem as a quadratic programming problem with integer- and real-valued arguments and show that MIO is capable of finding provably optimal solutions using a…

从树集成中提取可解释模型：计算与统计视角AI 解读

Tree ensembles are non-parametric methods widely recognized for their accuracy and ability to capture complex interactions. While these models excel at prediction, they are difficult to interpret and may fail to uncover useful relationships in the data. We propose an estimator to extract compact sets of decision rules from tree ensembles. The extracted models are accurate and can be manually examined to reveal relationships between the predictors and the response. A key…

通过精确融合与稀疏正则化对类别特征建模AI 解读

Abstract We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a) clustering of the regression coefficients to collapse some of the categorical levels together; and (b) sparsity of the regression coefficients. We present novel mixed integer programming formulations for our estimator, and develop a custom…

基于离散优化的分组变量选择：计算与统计视角AI 解读

We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on optimal solutions for the ℓ0-regularized formulation, a problem that is relatively unexplored due to computational challenges. Our methodology covers both high-dimensional linear regression and nonparametric sparse additive modeling with…

非理性亢奋：校正概率估计中的偏差AI 解读

We consider the common setting where one observes probability estimates for a large number of events, such as default risks for numerous bonds. Unfortunately, even with unbiased estimates, selecting events corresponding to the most extreme probabilities can result in systematically underestimating the true level of uncertainty. We develop an empirical Bayes approach “excess certainty adjusted probabilities” (ECAP), using a variant of Tweedie’s formula, which updates…

通过 ℓ1 融合惩罚实现凸聚类AI 解读

Summary We study the large sample behaviour of a convex clustering framework, which minimizes the sample within cluster sum of squares under an l 1 fusion constraint on the cluster centroids. This recently proposed approach has been gaining in popularity; however, its asymptotic properties have remained mostly unknown. Our analysis is based on a novel representation of the sample clustering procedure as a sequence of cluster splits determined by a sequence of maximization…

函数型加性回归AI 解读

We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar response, $Y$, in two key respects. First, FAR uses a penalized least squares optimization approach to efficiently deal with high-dimensional problems involving a large number of functional predictors. Second, FAR extends beyond the…

高维自适应非线性交互结构的变量选择AI 解读

Numerous penalization based methods have been proposed for fitting a traditional linear regression model in which the number of predictors, p, is large relative to the number of observations, n. Most of these approaches assume sparsity in the underlying coefficients and perform some form of variable selection. Recently, some of this work has been extended to nonlinear additive regression models. However, in many contexts one wishes to allow for the possibility of…

DASSO：Dantzig 选择器与 Lasso 的联系AI 解读

Summary We propose a new algorithm, DASSO, for fitting the entire coefficient path of the Dantzig selector with a similar computational cost to the least angle regression algorithm that is used to compute the lasso. DASSO efficiently constructs a piecewise linear path through a sequential simplex-like algorithm, which is remarkably similar to the least angle regression algorithm. Comparison of the two algorithms sheds new light on the question of how the lasso and Dantzig…

变量纳入与收缩算法AI 解读

The Lasso is a popular and computationally efficient procedure for automatically performing both variable selection and coefficient shrinkage on linear regression models. One limitation of the Lasso is that the same tuning parameter is used for both variable selection and shrinkage. As a result, it typically ends up selecting a model with too many variables to prevent overshrinkage of the regression coefficients. We suggest an improved class of methods called variable…

混合收敛速率的渐近分析AI 解读

A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from uniform limit theorems for rescaled and reparametrized criterion functions. The new method can handle cases where the standard approach does not yield the complete limiting behavior of the estimator. The asymptotic analysis depends on a…