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The decision tree is a flexible machine learning model that finds its success in numerous applications. It is usually fitted in a recursively greedy manner using CART. In this paper, we investigate the convergence rate of CART under a…

The generalized Ridge penalty is a powerful tool for dealing with overfitting and for high-dimensional regressions. The generalized Ridge regression can be derived as the mean of a posterior distribution with a Normal prior and a given…

Feature selection is a standard approach to understanding and modeling high-dimensional classification data, but the corresponding statistical methods hinge on tuning parameters that are difficult to calibrate. In particular, existing…

Analyzing classification model performance is a crucial task for machine learning practitioners. While practitioners often use count-based metrics derived from confusion matrices, like accuracy, many applications, such as weather…

We consider the sensitivity of real roots of polynomial systems with respect to perturbations of the coefficients. In particular - for a version of the condition number defined by Cucker, Krick, Malajovich, and Wschebor - we establish new…

We give the first specific conjectures on how frequently graphs satisfy sufficient conditions for being uniquely characterized by spectral information. These conjectures arise from a theoretical framework that we developed based on…

We develop a new approximative estimation method for conditional Shapley values obtained using a linear regression model. We develop a new estimation method and outperform existing methodology and implementations. Compared to the sequential…

The standard procedure to decide on the complexity of a CART regression tree is to use cross-validation with the aim of obtaining a predictor that generalises well to unseen data. The randomness in the selection of folds implies that the…

This paper shows that sequential statistical analysis techniques can be generalised to the problem of selecting between alternative forecasting methods using scoring rules. A return to basic principles is necessary in order to show that…

To use control charts in practice, the in-control state usually has to be estimated. This estimation has a detrimental effect on the performance of control charts, which is often measured for example by the false alarm probability or the…

The regsem package in R, an implementation of regularized structural equation modeling (RegSEM; Jacobucci, Grimm, and McArdle 2016), was recently developed with the goal of incorporating various forms of penalized likelihood estimation in a…

Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a…

Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To simultaneously achieve sparsity and positive…

Randomized experiments are the gold standard for estimating the average treatment effect (ATE). While covariate adjustment can reduce the asymptotic variances of the unbiased Horvitz-Thompson estimators for the ATE, it suffers from…

Calibration of expensive simulation models involves an emulator based on simulation outputs generated across various parameter settings to replace the actual model. Noisy outputs of stochastic simulation models require many simulation…

There are many advantages to use probability method for nonlinear system identification, such as the noises and outliers in the data set do not affect the probability models significantly; the input features can be extracted in probability…

Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…

The estimation of covariance matrices of multiple classes with limited training data is a difficult problem. The sample covariance matrix (SCM) is known to perform poorly when the number of variables is large compared to the available…