Related papers: The Efficient Shrinkage Path: Maximum Likelihood o…

Network service providers and customers are often concerned with aggregate performance measures that span multiple network paths. Unfortunately, forming such network-wide measures can be difficult, due to the issues of scale involved. In…

Variable selection in ultrahigh-dimensional linear regression is challenging due to its high computational cost. Therefore, a screening step is usually conducted before variable selection to significantly reduce the dimension. Here we…

In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. This inverse covariance matrix also prescribes the hedge trades in which a stock is hedged by all the other…

For many high-dimensional studies, additional information on the variables, like (genomic) annotation or external p-values, is available. In the context of binary and continuous prediction, we develop a method for adaptive group-regularized…

As regression is a widely studied problem, many methods have been proposed to solve it, each of them often requiring setting different hyper-parameters. Therefore, selecting the proper method for a given application may be very difficult…

The large amount of online data and vast array of computing resources enable current researchers in both industry and academia to employ the power of deep learning with neural networks. While deep models trained with massive amounts of data…

We analyze the statistics of the shortest and fastest paths on the road network between randomly sampled end points. To a good approximation, these optimal paths are found to be directed in that their lengths (at large scales) are linearly…

This paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from e.g. categorical regressors, (quasi-)experimental data or panel data models. The loss function is penalized by adding…

Inference and prediction of routes have become of interest over the past decade owing to a dramatic increase in package delivery and ride-sharing services. Given the underlying combinatorial structure and the incorporation of probabilities,…

Avoiding overfitting is a central challenge in machine learning, yet many large neural networks readily achieve zero training loss. This puzzling contradiction necessitates new approaches to the study of overfitting. Here we quantify…

It is well known that kernel ridge regression (KRR) is a popular nonparametric regression estimator. Nonetheless, in the presence of a large data set with size $n\gg 1,$ the KRR estimator has the drawback to require an intensive…

In this paper we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense…

We propose random hinge forests, a simple, efficient, and novel variant of decision forests. Importantly, random hinge forests can be readily incorporated as a general component within arbitrary computation graphs that are optimized…

In this paper we analyze a budgeted learning setting, in which the learner can only choose and observe a small subset of the attributes of each training example. We develop efficient algorithms for ridge and lasso linear regression, which…

We propose a quantum algorithm based on ridge regression model, which get the optimal fitting parameters w and a regularization hyperparameter {\alpha} by analysing the training dataset. The algorithm consists of two subalgorithms. One is…

A tree $\sigma$-spanner of a positively real-weighted $n$-vertex and $m$-edge undirected graph $G$ is a spanning tree $T$ of $G$ which approximately preserves (i.e., up to a multiplicative stretch factor $\sigma$) distances in $G$. Tree…

We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge…

In many areas, practitioners need to analyze large datasets that challenge conventional single-machine computing. To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here we study a fundamental…

We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…

Score-based methods are powerful across machine learning, but they face a paradox: theoretically path-independent, yet practically path-dependent. We resolve this by proving that practical training objectives differ from the ideal,…