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In this article, we propose a new algorithm for supervised learning methods, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset of the original variables, an ideal…
This work proposes a new algorithm for training a re-weighted L2 Support Vector Machine (SVM), inspired on the re-weighted Lasso algorithm of Cand\`es et al. and on the equivalence between Lasso and SVM shown recently by Jaggi. In…
Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to allow for piecewise stationarity, where the model is allowed to change at given time points. We propose a three-stage procedure for…
We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the…
For their ability to capture non-linearities in the data and to scale to large training sets, local Support Vector Machines (SVMs) have received a special attention during the past decade. In this paper, we introduce a new local SVM method,…
We have made initial studies of the potential of support vector machines (SVM) for providing statistical models of nuclear systematics with demonstrable predictive power. Using SVM regression and classification procedures, we have created…
Relevance Vector Machine (RVM) is a supervised learning algorithm extended from Support Vector Machine (SVM) based on the Bayesian sparsity model. Compared with the regression problem, RVM classification is difficult to be conducted because…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Objective: Brain networks have gained increasing recognition as potential biomarkers in mental health studies, but there are limited approaches that can leverage complex brain networks for accurate classification. Our goal is to develop a…
In this paper, we consider the binary classification problem via distributed Support-Vector-Machines (SVM), where the idea is to train a network of agents, with limited share of data, to cooperatively learn the SVM classifier for the global…
The support vector machine (SVM) was originally designed for binary classifications. A lot of effort has been put to generalize the binary SVM to multiclass SVM (MSVM) which are more complex problems. Initially, MSVMs were solved by…
In human-centered environments such as restaurants, homes, and warehouses, robots often face challenges in accurately recognizing 3D objects. These challenges stem from the complexity and variability of these environments, including diverse…
Training multimodal process reward models (PRMs) is hard due to (i) distribution shift between training set and test set and (ii) quality imbalance across training data samples. While domain-level reweighting (e.g., DreamPRM) aligns…
It is important to identify the change point of a system's health status, which usually signifies an incipient fault under development. The One-Class Support Vector Machine (OC-SVM) is a popular machine learning model for anomaly detection…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
The support vector machine (SVM) is a well-established classification method whose name refers to the particular training examples, called support vectors, that determine the maximum margin separating hyperplane. The SVM classifier is known…
In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…
Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…
Parameter estimation is a growing area of interest in statistical signal processing. Some parameters in real-life applications vary in space as opposed to those that are static. Most common methods in estimating parameters involve solving…
Adaptive loss function formulation is an active area of research and has gained a great deal of popularity in recent years, following the success of deep learning. However, existing frameworks of adaptive loss functions often suffer from…