Related papers: Scalable Higher-Order Tensor Product Spline Models

Predictive models are often used for real-time decision making. However, typical machine learning techniques ignore feature evaluation cost, and focus solely on the accuracy of the machine learning models obtained utilizing all the features…

We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical…

Derivative-free - or zeroth-order - optimization (DFO) has gained recent attention for its ability to solve problems in a variety of application areas, including machine learning, particularly involving objectives which are stochastic…

Many real-world combinatorial problems involve uncertain parameters, which can be predicted given contextual features and historical data. These `predict-then-optimize' or `contextual optimization' problems have gained significant…

We propose a new method to extract discriminant and explainable features from a particular machine learning model, i.e., a combination of the scattering transform and the multiclass logistic regression. Although this model is well-known for…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise…

Factorization machines (FMs) are a supervised learning approach that can use second-order feature combinations even when the data is very high-dimensional. Unfortunately, despite increasing interest in FMs, there exists to date no efficient…

In this dissertation, we concentrate on the challenging research issue of developing a spline-based modeling framework, which converts the conventional data (e.g., surface meshes) to tensor-product trivariate splines. This methodology can…

High-order clustering aims to identify heterogeneous substructures in multiway datasets that arise commonly in neuroimaging, genomics, social network studies, etc. The non-convex and discontinuous nature of this problem pose significant…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

A new statistical procedure, based on a modified spline basis, is proposed to identify the linear components in the panel data model with fixed effects. Under some mild assumptions, the proposed procedure is shown to consistently estimate…

Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…

In this work, we propose a framework that constructs reduced order models for nonlinear structural mechanics in a nonintrusive fashion, and can handle large scale simulations. We identify three steps that are carried out separately in time,…

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…

This paper demonstrates new methods and implementations of nonlinear solvers with higher-order of convergence, which is achieved by efficiently computing higher-order derivatives. Instead of computing full derivatives, which could be…

Real-world relations among entities can often be observed and determined by different perspectives/views. For example, the decision made by a user on whether to adopt an item relies on multiple aspects such as the contextual information of…

Large language models (LLMs) demonstrate outstanding performance in various tasks in machine learning and have thus become one of the most important workloads in today's computing landscape. However, deploying LLM inference poses challenges…

Logistic Regression (LR) is a widely used statistical method in empirical binary classification studies. However, real-life scenarios oftentimes share complexities that prevent from the use of the as-is LR model, and instead highlight the…

We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition…