相关论文: Surrogate to Poincar\'e inequalities on manifolds …

In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of…

We study the properties of stochastic approximation applied to a tame nondifferentiable function subject to constraints defined by a Riemannian manifold. The objective landscape of tame functions, arising in o-minimal topology extended to a…

We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…

We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic…

Automated medical image segmentation is an essential task to aid/speed up diagnosis and treatment procedures in clinical practices. Deep convolutional neural networks have exhibited promising performance in accurate and automatic seminal…

Multi-task learning is a widely used technique for harnessing information from various tasks. Recently, the sparse orthogonal factor regression (SOFAR) framework, based on the sparse singular value decomposition (SVD) within the coefficient…

Simultaneous feature selection and non-linear function estimation is challenging in modeling, especially in high-dimensional settings where the number of variables exceeds the available sample size. In this article, we investigate the…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

Shape optimization based on shape calculus has received a lot of attention in recent years, particularly regarding the development, analysis, and modification of efficient optimization algorithms. In this paper we propose and investigate…

Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for…

For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…

Motivated by the minimax concave penalty based variable selection in high-dimensional linear regression, we introduce a simple scheme to construct structured semiconvex sparsity promoting functions from convex sparsity promoting functions…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

Gradient-based optimization is now ubiquitous across graphics, but unfortunately can not be applied to problems with undefined or zero gradients. To circumvent this issue, the loss function can be manually replaced by a ``surrogate'' that…

Unsupervised rank aggregation on score-based permutations, which is widely used in many applications, has not been deeply explored yet. This work studies the use of submodular optimization for rank aggregation on score-based permutations in…

Applying half-quadratic optimization to loss functions can yield the corresponding regularizers, while these regularizers are usually not sparsity-inducing regularizers (SIRs). To solve this problem, we devise a framework to generate an SIR…

We present an algorithm for approximating a function defined over a $d$-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not require any…

We address the problem of aligning real-world 3D data of garments, which benefits many applications such as texture learning, physical parameter estimation, generative modeling of garments, etc. Existing extrinsic methods typically perform…

The key task of machine learning is to minimize the loss function that measures the model fit to the training data. The numerical methods to do this efficiently depend on the properties of the loss function. The most decisive among these…

In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…