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We consider the least squares regression problem, penalized with a combination of the $\ell_{0}$ and squared $\ell_{2}$ penalty functions (a.k.a. $\ell_0 \ell_2$ regularization). Recent work shows that the resulting estimators are of key…
We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is…
Lane detection is typically tackled with a two-step pipeline in which a segmentation mask of the lane markings is predicted first, and a lane line model (like a parabola or spline) is fitted to the post-processed mask next. The problem with…
As a variant of the routing and wavelength assignment problem (RWAP), the RWAP with partial path protection (RWAP-PPP) designs a reliable optical-fiber network for telecommunications. It assigns paths and wavelengths to meet communication…
A local Bundle Adjustment (BA) on a sliding window of keyframes has been widely used in visual SLAM and proved to be very effective in lowering the drift. But in lidar SLAM, BA method is hardly used because the sparse feature points (e.g.,…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
Linear discriminant analysis (LDA) is a fundamental classification and dimension reduction method that achieves Bayes optimality under Gaussian mixture, but often struggles in high-dimensional settings where the covariance matrix cannot be…
A new package for nonlinear least squares fitting is introduced in this paper. This package implements a recently developed algorithm that, for certain types of nonlinear curve fitting, reduces the number of nonlinear parameters to be…
Structural pruning techniques are essential for deploying multimodal large language models (MLLMs) across various hardware platforms, from edge devices to cloud servers. However, current pruning methods typically determine optimal…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
Training neural networks with large batch is of fundamental significance to deep learning. Large batch training remarkably reduces the amount of training time but has difficulties in maintaining accuracy. Recent works have put forward…
Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares…
Variable selection in linear models plays a pivotal role in modern statistics. Hard-thresholding methods such as $l_0$ regularization are theoretically ideal but computationally infeasible. In this paper, we propose a new approach, called…
This paper proposes a method for solving multivariate regression and classification problems using piecewise linear predictors over a polyhedral partition of the feature space. The resulting algorithm that we call PARC (Piecewise Affine…
This paper investigates the control of nonlinear systems using a piecewise linear approximation framework. The proposed approach combines a PID controller with locally linearized models obtained by partitioning the nonlinear function into…
Ensuring code correctness remains a challenging problem even as large language models (LLMs) become increasingly capable at code-related tasks. While LLM-based program repair systems can propose bug fixes using only a user's bug report,…
We consider the estimation of the state transition matrix in vector autoregressive models, when time sequence data is limited but nonsequence steady-state data is abundant. To leverage both sources of data, we formulate the least squares…
Backpropagation (BP) is the cornerstone of today's deep learning algorithms, but it is inefficient partially because of backward locking, which means updating the weights of one layer locks the weight updates in the other layers.…
The least trimmed squares (LTS) is a reasonable formulation of robust regression whereas it suffers from high computational cost due to the nonconvexity and nonsmoothness of its objective function. The most frequently used FAST-LTS…
The Matching Augmentation Problem (MAP) has recently received significant attention as an important step towards better approximation algorithms for finding cheap $2$-edge connected subgraphs. This has culminated in a…