Related papers: Modelling multimodal photometric redshift regressi…
Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…
We study a practical algorithm for sparse principal component analysis (PCA) of incomplete and noisy data. Our algorithm is based on the semidefinite program (SDP) relaxation of the non-convex $l_1$-regularized PCA problem. We provide…
Computational time reversal imaging can be used to locate the position of multiple scatterers in a known background medium. The current methods for computational time reversal imaging are based on the null subspace projection operator,…
We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
We aim to determine the most effective approach for estimating uncertainties in quasar photo-$z$ and to evaluate the ability of different models to reconstruct the true redshift distribution under varying data quality. We use photometric…
We develop machinery to design efficiently computable and consistent estimators, achieving estimation error approaching zero as the number of observations grows, when facing an oblivious adversary that may corrupt responses in all but an…
We allow for nonlinear effects in the likelihood analysis of peculiar velocities, and obtain ~35%-lower values for the cosmological density parameter and for the amplitude of mass-density fluctuations. The power spectrum in the linear…
The large amount of data collected by LiDAR sensors brings the issue of LiDAR point cloud compression (PCC). Previous works on LiDAR PCC have used range image representations and followed the predictive coding paradigm to create a basic…
We consider the problem of estimating an unknown coordinate-wise monotone function given noisy measurements, known as the isotonic regression problem. Often, only a small subset of the features affects the output. This motivates the sparse…
This article discusses a generalization of the 1-dimensional multi-reference alignment problem. The goal is to recover a hidden signal from many noisy observations, where each noisy observation includes a random translation and random…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
In our previous work, a reduced order model (ROM) for a stochastic system was made, where noisy data was projected onto principal component analysis (PCA)-derived basis vectors to obtain an accurate reconstruction of the noise-free data.…
This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead…
In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…
We describe a novel end-to-end approach using Machine Learning to reconstruct the power spectrum of cosmological density perturbations at high redshift from observed quasar spectra. State-of-the-art cosmological simulations of structure…
Equation learning aims to infer differential equation models from data. While a number of studies have shown that differential equation models can be successfully identified when the data are sufficiently detailed and corrupted with…
Inferring unknown conic sections on the basis of noisy data is a challenging problem with applications in computer vision. A major limitation of the currently available methods for conic sections is that estimation methods rely on the…
We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…
In this paper, we expand the theory of depth-unbiased source localization to unbiased parameter estimation and signal reconstruction of an arbitrary number of non-zero parameters to be recovered. The topic touches on the concept of exact…