Related papers: Probabilistic Cross-Identification in Crowded Fiel…
Matching astronomical catalogs in crowded regions of the sky is challenging both statistically and computationally due to the many possible alternative associations. Budav\'ari and Basu (2016) modeled the two-catalog situation as an…
Building on previous Bayesian approaches, we introduce a novel formulation of probabilistic cross-identification, where detections are directly associated to (hypothesized) astronomical objects in a globally optimal way. We show that this…
This paper studies the optimal solution of the classical problem of detecting the location of multiple image occurrences in a two-dimensional, noisy measurement. Assuming the image occurrences do not overlap, we formulate this task as a…
Optimally selecting a subset of targets from a larger catalog is a common problem in astronomy and cosmology. A specific example is the selection of targets from an imaging survey for multi-object spectrographic follow-up. We present a new…
In this work, I present an optimization problem which consists of assigning entries of a stellar catalog to multiple entries of another stellar catalog such that the probability of such assignment is maximum. I show a way of modeling it as…
In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…
Multi-wavelength astronomical studies require cross-identification of detections of the same celestial objects in multiple catalogs based on spherical coordinates and other properties. Because of the large data volumes and spherical…
This paper is an invited commentary on Tamas Budavari's presentation, "On statistical cross-identification in astronomy," for the Statistical Challenges in Modern Astronomy V conference held at Pennsylvania State University in June 2011. I…
The optimized assignment of staff is of great significance for improving the production efficiency of the society. For specific tasks, the key to optimizing staffing is personnel scheduling. The assignment problem is classical in the…
Probabilistic mixture models have been widely used for different machine learning and pattern recognition tasks such as clustering, dimensionality reduction, and classification. In this paper, we focus on trying to solve the most common…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…
Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We…
In this paper, we consider the problem of finding the feature correspondences among a collection of feature sets, by using their point-wise unary features. This is a fundamental problem in computer vision and pattern recognition, which also…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
Cluster analysis faces two problems in high dimensions: first, the `curse of dimensionality' that can lead to overfitting and poor generalization performance; and second, the sheer time taken for conventional algorithms to process large…
The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions…
Context: The huge and still rapidly growing amount of galaxies in modern sky surveys raises the need of an automated and objective classification method. Unsupervised learning algorithms are of particular interest, since they discover…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure.…
In this paper, we propose an efficient clustering technique to solve the problem of clustering in the presence of obstacles. The proposed algorithm divides the spatial area into rectangular cells. Each cell is associated with statistical…