Related papers: Probabilistic Detection and Estimation of Conic Se…
A perturbative approach is used to quantify the effect of noise in data points on fitted parameters in a general homogeneous linear model, and the results applied to the case of conic sections. There is an optimal choice of normalisation…
We propose a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown…
Estimating signals underlying noisy data is a significant problem in statistics and engineering. Numerous estimators are available in the literature, depending on the observation model and estimation criterion. This paper introduces a…
We develop an unsupervised, nonparametric, and scalable statistical learning method for detection of unknown objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that…
We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of…
In this paper, we further develop the approach, originating in [14 (arXiv:1311.6765),20 (arXiv:1604.02576)], to "computation-friendly" hypothesis testing and statistical estimation via Convex Programming. Specifically, we focus on…
Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…
We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of…
Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…
Given noisy data, function estimation is considered when the unknown function is known apriori to consist of a small number of regions where the function is either convex or concave. When the regions are known apriori, the estimate is…
Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems.…
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…
There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained…
Object parsing and segmentation from point clouds are challenging tasks because the relevant data is available only as thin structures along object boundaries or other features, and is corrupted by large amounts of noise. To handle this…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…
We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…
Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this…
A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias…
We present an efficient algorithm to compute tight upper bounds of collision probability between two objects with positional uncertainties, whose error distributions are represented with non-Gaussian forms. Our approach can handle noisy…