Related papers: Escaping Poor Local Minima in Large Scale Robust E…
With the rapid development of large language models (LLMs) and the growing demand for personalized content, recommendation systems have become critical in enhancing user experience and driving engagement. Collaborative filtering algorithms,…
The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…
In this paper two formulations for the robust optimization of the size of the permanent magnet in a synchronous machine are discussed. The optimization is constrained by a partial differential equation to describe the electromagnetic…
Image segmentation is an important component of many image understanding systems. It aims to group pixels in a spatially and perceptually coherent manner. Typically, these algorithms have a collection of parameters that control the degree…
Random feature mapping (RFM) is a popular method for speeding up kernel methods at the cost of losing a little accuracy. We study kernel ridge regression with random feature mapping (RFM-KRR) and establish novel out-of-sample error upper…
Non-negative matrix factorization (NMF) is a key technique for feature extraction and widely used in source separation. However, existing algorithms may converge to poor local minima, or to one of several minima with similar objective value…
The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…
We consider the problem of minimizing a strongly convex smooth function where the gradients are subject to additive worst-case deterministic errors that are square-summable. We study the trade-offs between the convergence rate and…
Deep recommender systems (DRS) often face challenges in balancing computational efficiency and model accuracy, especially when handling high-dimensional input features. Existing methods either focus on improving accuracy while neglecting…
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$). In this regime,…
Nonlinear regression methods, such as local optimization algorithms, are widely used in the extraction of nanostructure profile parameters in optical scatterometry. The success of local optimization algorithms heavily relies on the…
Solving large-scale optimization problems is a bottleneck and is very important for machine learning and multiple kinds of scientific problems. Subspace-based methods using the local approximation strategy are one of the most important…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…
This paper introduces a simple but highly efficient ensemble for robust texture classification, which can effectively deal with translation, scale and changes of significant viewpoint problems. The proposed method first inherits the spirit…
Modern machine learning applications have witnessed the remarkable success of optimization algorithms that are designed to find flat minima. Motivated by this design choice, we undertake a formal study that (i) formulates the notion of flat…
Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier…
Moment-based estimation is a theoretically attractive approach to parametric inference, especially when likelihood-based estimation is unavailable, misspecified, or computationally inconvenient. However, the moment equations involve sample…
Designing efficient optimizers for large language models (LLMs) with low-memory requirements and fast convergence is an important and challenging problem. This paper makes a step towards the systematic design of such optimizers through the…
A robust estimator for a wide family of mixtures of linear regression is presented. Robustness is based on the joint adoption of the Cluster Weighted Model and of an estimator based on trimming and restrictions. The selected model provides…