Related papers: Escaping the Curse of Dimensionality in Similarity…
The aim of this paper is to propose a geometric framework for modelling similarity search in large and multidimensional data spaces of general nature, which seems to be flexible enough to address such issues as analysis of complexity,…
Frank--Wolfe methods avoid projections, but over curved feasible regions the full-space linear minimization oracle (LMO) can itself become the computational bottleneck. We introduce random-subspace Frank--Wolfe (RSFW), the first…
Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that…
This work approximates high-dimensional density functions with an ANOVA-like sparse structure by the mixture of wrapped Gaussian and von Mises distributions. When the dimension $d$ is very large, it is complex and impossible to train the…
Overparameterization and overfitting are common concerns when designing and training deep neural networks, that are often counteracted by pruning and regularization strategies. However, these strategies remain secondary to most learning…
High-dimensional statistical learning (HDSL) has wide applications in data analysis, operations research, and decision-making. Despite the availability of multiple theoretical frameworks, most existing HDSL schemes stipulate the following…
While the SLIM approach obtained high ranking-accuracy in many experiments in the literature, it is also known for its high computational cost of learning its parameters from data. For this reason, we focus in this paper on variants of…
This work studies the problem of learning appropriate low dimensional image representations. We propose a generic algorithmic framework, which leverages two classic representation learning paradigms, i.e., sparse representation and the…
In recent years, a lot of attention has been devoted to efficient nearest neighbor search by means of similarity-preserving hashing. One of the plights of existing hashing techniques is the intrinsic trade-off between performance and…
Deep learning usually relies on training large-scale data samples to achieve better performance. However, over-fitting based on training data always remains a problem. Scholars have proposed various strategies, such as feature dropping and…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…
Structured constraints in Machine Learning have recently brought the Frank-Wolfe (FW) family of algorithms back in the spotlight. While the classical FW algorithm has poor local convergence properties, the Away-steps and Pairwise FW…
Unsupervised feature selection is an important method to reduce dimensions of high dimensional data without labels, which is benefit to avoid ``curse of dimensionality'' and improve the performance of subsequent machine learning tasks, like…
Complex data mining has wide application value in many fields, especially in the feature extraction and classification tasks of unlabeled data. This paper proposes an algorithm based on self-supervised learning and verifies its…
Conditional Gradient algorithms (aka Frank-Wolfe algorithms) form a classical set of methods for constrained smooth convex minimization due to their simplicity, the absence of projection steps, and competitive numerical performance. While…
Online optimization has been a successful framework for solving large-scale problems under computational constraints and partial information. Current methods for online convex optimization require either a projection or exact gradient…
High-dimensional measurements are often correlated which motivates their approximation by factor models. This holds also true when features are engineered via low-dimensional interactions or kernel tricks. This often results in over…
In this paper, we study the problem of speeding up a type of optimization algorithms called Frank-Wolfe, a conditional gradient method. We develop and employ two novel inner product search data structures, improving the prior fastest…
Frank-Wolfe methods are projection-free algorithms for constrained optimization whose practical performance often depends critically on the choice of step size. Classical closed-loop step-size rules typically require prior knowledge of a…
We study the integration and approximation problems for monotone and convex bounded functions that depend on $d$ variables, where $d$ can be arbitrarily large. We consider the worst case error for algorithms that use finitely many function…