Related papers: Spline Regression with Automatic Knot Selection

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We develop a novel procedure for constructing confidence bands for components of a sparse additive model. Our procedure is based on a new kernel-sieve hybrid estimator that combines two most popular nonparametric estimation methods in the…

This paper addresses the problem of learning to sparsify stochastic linear bandits, where a decision-maker sequentially selects actions from a high-dimensional space subject to a sparsity constraint on the number of nonzero elements in the…

We introduce the arbitrary rectangle-range generalized elastic net penalty method, abbreviated to ARGEN, for performing constrained variable selection and regularization in high-dimensional sparse linear models. As a natural extension of…

The weights of a neural network are typically initialized at random, and one can think of the functions produced by such a network as having been generated by a prior over some function space. Studying random networks, then, is useful for a…

We propose a novel B-spline trajectory optimization method for autonomous racing. We consider the unavailability of sophisticated race car and race track dynamics in early-stage autonomous motorsports development and derive methods that…

We develop a novel preconditioning method for ridge regression, based on recent linear sketching methods. By equipping Stochastic Variance Reduced Gradient (SVRG) with this preconditioning process, we obtain a significant speed-up relative…

Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…

Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees,…

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Calibrating neural networks is of utmost importance when employing them in safety-critical applications where the downstream decision making depends on the predicted probabilities. Measuring calibration error amounts to comparing two…

Given a data set (t_i, y_i), i=1,..., n with the t_i in [0,1] non-parametric regression is concerned with the problem of specifying a suitable function f_n:[0,1] -> R such that the data can be reasonably approximated by the points (t_i,…

We propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors. This method is based on a combination of the minimax concave penalty and Laplacian quadratic…

Causal structure learning, also known as causal discovery, aims to estimate causal relationships between variables as a form of a causal directed acyclic graph (DAG) from observational data. One of the major frameworks is the order-based…

Heavy-tailed error distributions and predictors with anomalous values are ubiquitous in high-dimensional regression problems and can seriously jeopardize the validity of statistical analyses if not properly addressed. For more reliable…

In a conventional supervised learning setting, a machine learning model has access to examples of all object classes that are desired to be recognized during the inference stage. This results in a fixed model that lacks the flexibility to…

Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects…

The problem of fixed knot approximation is convex and there are several efficient approaches to solve this problem, yet, when the knots joining the affine parts are also variable, finding conditions for a best Chebyshev approximation…

In high-dimensional data settings, additional information on the features is often available. Examples of such external information in omics research are: (a) p-values from a previous study, (b) a summary of prior information, and (c) omics…

In this paper, we introduce Adaptive Cluster Lasso(ACL) method for variable selection in high dimensional sparse regression models with strongly correlated variables. To handle correlated variables, the concept of clustering or grouping…