Related papers: Non-Parametric Estimation of Manifolds from Noisy …
Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…
We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\rho$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example…
Large-scale nonsmooth optimization problems arise in many real-world applications, but obtaining exact function and subgradient values for these problems may be computationally expensive or even infeasible. In many practical settings, only…
Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
This paper aims at building the theoretical foundations for manifold learning algorithms in the space of absolutely continuous probability measures $\mathcal{P}_{\mathrm{a.c.}}(\Omega)$ with $\Omega$ a compact and convex subset of…
The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data…
3D point clouds are often perturbed by noise due to the inherent limitation of acquisition equipments, which obstructs downstream tasks such as surface reconstruction, rendering and so on. Previous works mostly infer the displacement of…
Computations on a manifold often involve constructing an operator on the tangent space and computing its inverse, which can be time-consuming in many applications. In order to reduce the computational costs and preserve the benign…
High-dimensional datasets often exhibit low-dimensional geometric structures, as suggested by the manifold hypothesis, which implies that data lie on a smooth manifold embedded in a higher-dimensional ambient space. While this insight…
The problem of source localization with ad hoc microphone networks in noisy and reverberant enclosures, given a training set of prerecorded measurements, is addressed in this paper. The training set is assumed to consist of a limited number…
A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…
Existing learning-based point cloud upsampling methods often overlook the intrinsic data distribution charac?teristics of point clouds, leading to suboptimal results when handling sparse and non-uniform point clouds. We propose a novel…
We consider inverse problems consisting of the reconstruction of an unknown signal $f$ from noisy measurements $y=Ff+\text{noise}$, where $Ff$ is a function on a Riemannian manifold without boundary $\mathcal M$. We consider the case when…
The success of Deep Neural Network (DNN) models significantly depends on the quality of provided annotations. In medical image segmentation, for example, having multiple expert annotations for each data point is common to minimize…
We give asymptotically tight estimates of tangent space variation on Riemannian submanifolds of Euclidean space with respect to the local feature size of the submanifolds. We show that the result follows directly from structural properties…
It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension…
Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…
The high-dimensional data setting, in which p >> n, is a challenging statistical paradigm that appears in many real-world problems. In this setting, learning a compact, low-dimensional representation of the data can substantially help…
This paper surveys and evaluates some popular state of the art methods for algorithmic curvature and normal estimation. In addition to surveying existing methods we also propose a new method for robust curvature estimation and evaluate it…