Related papers: Application of Multivariate Adaptive Regression Sp…
In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are…
Protein Structure Prediction (PSP) is an unsolved problem in the field of computational biology. The problem of protein structure prediction is about predicting the native conformation of a protein, while its sequence of amino acids is…
Quantile regression is a powerful tool capable of offering a richer view of the data as compared to least-squares regression. Quantile regression is typically performed individually on a few quantiles or a grid of quantiles without…
Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between…
It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if…
Huntington disease (HD) is a neurodegenerative disease with progressively worsening symptoms. Accurately modeling time to HD diagnosis is essential for clinical trial design. Langbehn's model, the CAG-Age Product (CAP) model, the Prognostic…
We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth…
A fast and stable algorithm for estimating multidimensional adaptive P-spline models is presented. We call it as Separation of Overlapping Penalties (SOP) as it is an extension of the \textit{Separation of Anisotropic Penalties} (SAP)…
Modeling viral dynamics in HIV/AIDS studies has resulted in a deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear…
The paper motivates high dimensional smoothing with penalized splines and its numerical calculation in an efficient way. If smoothing is carried out over three or more covariates the classical tensor product spline bases explode in their…
Propensity scores are commonly used to reduce the confounding bias in non-randomized observational studies for estimating the average treatment effect. An important assumption underlying this approach is that all confounders that are…
When the data are sparse, optimization of hyperparameters of the kernel in Gaussian process regression by the commonly used maximum likelihood estimation (MLE) criterion often leads to overfitting. We show that choosing hyperparameters (in…
A common task is the determination of system parameters from spectroscopy, where one compares the experimental spectrum with calculated spectra, that depend on the desired parameters. Here we discuss an approach based on a machine learning…
In this paper, we propose a sparse least squares (SLS) optimization model for solving multilinear equations, in which the sparsity constraint on the solutions can effectively reduce storage and computation costs. By employing variational…
Density estimation plays a fundamental role in many areas of statistics and machine learning. Parametric, nonparametric and semiparametric density estimation methods have been proposed in the literature. Semiparametric density models are…
Modern neural networks are undeniably successful. Numerous studies have investigated how the curvature of loss landscapes can affect the quality of solutions. In this work we consider the Hessian matrix during network training. We reiterate…
This paper investigates the detection and estimation of a single change in high-dimensional linear models. We derive minimax lower bounds for the detection boundary and the estimation rate, which uncover a phase transition governed by the…
Establishing quantitative correlations between various molecular properties and chemical structures is of great technological importance for environmental and medical aspects. These approaches are referred to as Quantitative…
Computing the dispersion relation for two-dimensional photonic crystals is a notoriously challenging task: It involves solving parameterized Helmholtz eigenvalue problems with high-contrast coefficients. To resolve the challenge, we propose…
This paper proposes a general adaptive procedure for budget-limited predictor design in high dimensions called two-stage Sampling, Prediction and Adaptive Regression via Correlation Screening (SPARCS). SPARCS can be applied to high…