Related papers: Structure-adaptive manifold estimation

Given the necessity of connecting the unconnected, covering blind spots has emerged as a critical task in the next-generation wireless communication network. A direct solution involves obtaining a coverage manifold that visually showcases…

We propose the AdaPtive Noise Augmentation (PANDA) procedure to regularize the estimation and inference of generalized linear models (GLMs). PANDA iteratively optimizes the objective function given noise augmented data until convergence to…

In the multidimensional setting, we consider the errors-in-variables model. We aim at estimating the unknown nonparametric multivariate regression function with errors in the covariates. We devise an adaptive estimator based on projection…

We study the problem of nonparametric estimation under $\bL_p$-loss, $p\in [1,\infty)$, in the framework of the convolution structure density model on $\bR^d$. This observation scheme is a generalization of two classical statistical models,…

Nonlinear embedding manifold learning methods provide invaluable visual insights into the structure of high-dimensional data. However, due to a complicated nonconvex objective function, these methods can easily get stuck in local minima and…

We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…

The purpose of this paper is to study the problem of estimating a compactly supported density of probability from noisy observations of its moments. In fact, we provide a statistical approach to the famous Hausdorff classical moment…

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…

In this paper, we consider an unknown functional estimation problem in a general nonparametric regression model with the feature of having both multiplicative and additive noise.We propose two new wavelet estimators in this general context.…

A central goal of neuroscience is to understand how activity in the nervous system is related to features of the external world, or to features of the nervous system itself. A common approach is to model neural responses as a weighted…

With the burst development of neural networks in recent years, the task of normal estimation has once again become a concern. By introducing the neural networks to classic methods based on problem-specific knowledge, the adaptability of the…

In this manuscript, we propose an efficient manifold denoiser based on landmark diffusion and optimal shrinkage under the complicated high dimensional noise and compact manifold setup. It is flexible to handle several setups, including the…

Normal estimation for 3D point clouds is a fundamental task in 3D geometry processing. The state-of-the-art methods rely on priors of fitting local surfaces learned from normal supervision. However, normal supervision in benchmarks comes…

Orientation learning plays a pivotal role in many tasks. However, the rotation group SO(3) is a Riemannian manifold. As a result, the distortion caused by non-Euclidean geometric nature introduces difficulties to the incorporation of local…

In this paper, we propose a normal estimation method for unstructured 3D point clouds. This method, called Nesti-Net, builds on a new local point cloud representation which consists of multi-scale point statistics (MuPS), estimated on a…

The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of…

The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…

Point clouds are popular 3D representations for real-life objects (such as in LiDAR and Kinect) due to their detailed and compact representation of surface-based geometry. Recent approaches characterise the geometry of point clouds by…

Standard system identification methods often provide inconsistent estimates with closed-loop data. With the prediction error method (PEM), this issue is solved by using a noise model that is flexible enough to capture the noise spectrum.…

We present a robust multiple manifolds structure learning (RMMSL) scheme to robustly estimate data structures under the multiple low intrinsic dimensional manifolds assumption. In the local learning stage, RMMSL efficiently estimates local…