Related papers: Varying Coefficient Model via Adaptive Spline Fitt…
Using a combination of the replica-exchange Monte Carlo algorithm and the multicanonical method, we investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudo-phase…
This paper considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable…
Forward uncertainty quantification in dynamical systems is challenging due to non-smooth or locally oscillating nonlinear behaviors. Spline dimensional decomposition (SDD) addresses such nonlinearity by partitioning input coordinates via…
Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…
Variable selection for structured covariates lying on an underlying known graph is a problem motivated by practical applications, and has been a topic of increasing interest. However, most of the existing methods may not be scalable to high…
There are many uses for linear fitting; the context here is interpolation and denoising of data, as when you have calibration data and you want to fit a smooth, flexible function to those data. Or you want to fit a flexible function to…
This paper presents a learning-based method to solve the traditional parameterization and knot placement problems in B-spline approximation. Different from conventional heuristic methods or recent AI-based methods, the proposed method does…
Time series are difficult to monitor, summarize and predict. Segmentation organizes time series into few intervals having uniform characteristics (flatness, linearity, modality, monotonicity and so on). For scalability, we require fast…
We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the…
We introduce a new algorithm, called adaptive sparse backfitting algorithm, for solving high dimensional Sparse Additive Model (SpAM) utilizing symmetric, non-negative definite smoothers. Unlike the previous sparse backfitting algorithm,…
Many separable nonlinear optimization problems can be approximated by their nonlinear objective functions with piecewise linear functions. A natural question arising from applying this approach is how to break the interval of interest into…
Changepoint detection is commonly formulated by minimizing the sum of in-sample losses to quantify the model's overall fit. However, for flexible modeling procedures -- especially those involving high-dimensional parameter spaces or…
In biomedical studies, we are often interested in the association between different types of covariates and the times to disease events. Because the relationship between the covariates and event times is often complex, standard survival…
We study the parameter estimation problem for a varying index coefficient model in high dimensions. Unlike the most existing works that iteratively estimate the parameters and link functions, based on the generalized Stein's identity, we…
In this notes we describe an algorithm for non-linear fitting which incorporates some of the features of linear least squares into a general minimum $\chi^2$ fit and provide a pure Python implementation of the algorithm. It consists of the…
Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…
It can be difficult to interpret a coefficient of an uncertain model. A slope coefficient of a regression model may change as covariates are added or removed from the model. In the context of high-dimensional data, there are too many model…
Human migration exhibits complex spatiotemporal dependence driven by environmental and socioeconomic forces. Modeling such patterns at scale requires methods that accommodate many random effects while remaining feasible when raw data or…
A basis expansion with regularization methods is much appealing to the flexible or robust nonlinear regression models for data with complex structures. When the underlying function has inhomogeneous smoothness, it is well known that…
We consider the problem of predicting an outcome variable using $p$ covariates that are measured on $n$ independent observations, in the setting in which flexible and interpretable fits are desirable. We propose the fused lasso additive…