Related papers: Heaviside Low-Rank Support Matrix Machine
Support vector machines with ramp loss (dubbed as $L_r$-SVM) have attracted wide attention due to the boundedness of ramp loss. However, the corresponding optimization problem is non-convex and the given Karush-Kuhn-Tucker (KKT) conditions…
Sparse additive models have attracted much attention in high-dimensional data analysis due to their flexible representation and strong interpretability. However, most existing models are limited to single-level learning under the…
Maximum likelihood estimation (MLE) is a well-known estimation method used in many robotic and computer vision applications. Under Gaussian assumption, the MLE converts to a nonlinear least squares (NLS) problem. Efficient solutions to NLS…
Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…
Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most…
Support Vector Machines (SVMs) are popular tools for data mining tasks such as classification, regression, and density estimation. However, original SVM (C-SVM) only considers local information of data points on or over the margin.…
Support vector machines (SVM) can classify data sets along highly non-linear decision boundaries because of the kernel-trick. This expressiveness comes at a price: During test-time, the SVM classifier needs to compute the kernel…
As deep neural networks continue to revolutionize various application domains, there is increasing interest in making these powerful models more understandable and interpretable, and narrowing down the causes of good and bad predictions. We…
The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to…
In recent years, large language models (LLMs) have achieved strong performance on benchmark tasks, especially in zero or few-shot settings. However, these benchmarks often do not adequately address the challenges posed in the real-world,…
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…
Low rank matrix approximation (LRMA), which aims to recover the underlying low rank matrix from its degraded observation, has a wide range of applications in computer vision. The latest LRMA methods resort to using the nuclear norm…
Kernel-free quadratic surface support vector machines (QSVM) have recently gained traction due to their flexibility in modeling nonlinear decision boundaries without relying on kernel functions. However, the introduction of a full quadratic…
This paper concerns a fundamental class of convex matrix optimization problems. It presents the first algorithm that uses optimal storage and provably computes a low-rank approximation of a solution. In particular, when all solutions have…
Deploying Large Language Models (LLMs) on edge devices faces severe computational and memory constraints, limiting real-time processing and on-device intelligence. Hybrid architectures combining Structured State Space Models (SSMs) with…
This paper presents a novel hybrid Automatic Speech Recognition (ASR) system designed specifically for resource-constrained robots. The proposed approach combines Hidden Markov Models (HMMs) with deep learning models and leverages socket…
Graphical models for structured domains are powerful tools, but the computational complexities of combinatorial prediction spaces can force restrictions on models, or require approximate inference in order to be tractable. Instead of…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Localized support vector machines solve SVMs on many spatially defined small chunks and one of their main characteristics besides the computational benefit compared to global SVMs is the freedom of choosing arbitrary kernel and…