Related papers: Projection Pursuit through $\Phi$-Divergence Minim…
Clustering analysis by nonnegative low-rank approximations has achieved remarkable progress in the past decade. However, most approximation approaches in this direction are still restricted to matrix factorization. We propose a new low-rank…
This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the…
The problem of the minimization of least squares functionals with $\ell^1$ penalties is considered in an infinite dimensional Hilbert space setting. While there are several algorithms available in the finite dimensional setting there are…
In this paper we derive an exact full expression for the 2D probability distribution of the ellipticity of an object measured from data, only assuming Gaussian noise in pixel values. This is a generalisation of the probability distribution…
Sampling from circular distributions is a fundamental task in directional statistics. A key challenge in acceptance-rejection methods lies in selecting an efficient envelope density, as poor choices can lead to low acceptance rates and…
This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the…
Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…
Given a redundant dictionary $\Phi$, represented by an $M \times N$ matrix ($\Phi \in \mathbb{R}^{M \times N}$) and a target signal $y \in \mathbb{R}^M$, the \emph{sparse approximation problem} asks to find an approximate representation of…
Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are…
The maximum-entropy method is applied to the problem of reconstructing the projected mass density of a galaxy cluster using its gravitational lensing effects on background galaxies. We demonstrate the method by reconstructing the mass…
For many applications, such as computing the expected value of different magnitudes, sampling from a known probability density function, the target density, is crucial but challenging through the inverse transform. In these cases, rejection…
In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace…
Density estimation is a versatile technique underlying many data mining tasks and techniques,ranging from exploration and presentation of static data, to probabilistic classification, or identifying changes or irregularities in streaming…
We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…
A binary string transmitted via a memoryless i.i.d. deletion channel is received as a subsequence of the original input. From this, one obtains a posterior distribution on the channel input, corresponding to a set of candidate…
In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…
Autonomous drone pursuit requires not only detecting drones but also predicting their trajectories in a manner that enables kinematically feasible interception. Existing tracking methods optimize for prediction accuracy but ignore pursuit…
Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit…
Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering…