Related papers: Dimension Reduction and MARS
Covariance matrix reconstruction has been the most widely used guiding objective in gridless direction-of-arrival (DoA) estimation for sparse linear arrays. Many semidefinite programming (SDP)-based methods fall under this category.…
A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and non-linear, therefore computationally expensive. An emulator-based methodology is…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…
We present a new class of methods for high-dimensional nonparametric regression and classification called sparse additive models (SpAM). Our methods combine ideas from sparse linear modeling and additive nonparametric regression. We derive…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
A new dimension reduction method based on Gaussian finite mixtures is proposed as an extension to sliced inverse regression (SIR). The model-based SIR (MSIR) approach allows the main limitation of SIR to be overcome, i.e., failure in the…
The article develops marginal models for multivariate longitudinal responses. Overall, the model consists of five regression submodels, one for the mean and four for the covariance matrix, with the latter resulting by considering various…
The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…
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…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
To deal with non-linear relations between the predictors and the response, we can use transformations to make the data look linear or approximately linear. In practice, however, transformation methods may be ineffective, and it may be more…
The Active Subspace (AS) method is a widely used technique for identifying the most influential directions in high-dimensional input spaces that affect the output of a computational model. The standard AS algorithm requires a sufficient…
We propose a method for estimating a covariance matrix that can be represented as a sum of a low-rank matrix and a diagonal matrix. The proposed method compresses high-dimensional data, computes the sample covariance in the compressed…
In this paper, we consider multivariate response regression models with high dimensional predictor variables. One way to model the correlation among the response variables is through the low rank decomposition of the coefficient matrix,…
Many applications of machine learning involve the analysis of large data frames-matrices collecting heterogeneous measurements (binary, numerical, counts, etc.) across samples-with missing values. Low-rank models, as studied by Udell et al.…
Motivated by recent data analyses in biomedical imaging studies, we consider a class of image-on-scalar regression models for imaging responses and scalar predictors. We propose using flexible multivariate splines over triangulations to…
Comprehensive evaluation of machine learning models is the key to make sure that they perform as robustly and consistently as desired. In order to summarize the experimental results and pick a winner, Critical Difference (CD) diagrams are…
Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for sufficient dimension reduction…