38 citations · 89 across the 29 of their papers we have counts for
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A Probabilistic Algorithm for Computing Data-Discriminants of Likelihood Equations
Jose Israel Rodriguez, Xiaoxian Tang
An algebraic approach to the maximum likelihood estimation problem is to solve a very structured parameterized polynomial system called likelihood equations that have finitely many…
The Maximum Likelihood Data Singular Locus
Emil Horobet, Jose Israel Rodriguez
For general data, the number of complex solutions to the likelihood equations is constant and this number is called the (maximum likelihood) ML-degree of the model. In this article…
Multiprojective witness sets and a trace test
Jonathan D. Hauenstein, Jose Israel Rodriguez
In the field of numerical algebraic geometry, positive-dimensional solution sets of systems of polynomial equations are described by witness sets. In this paper, we define multipro…
The maximum likelihood degree of mixtures of independence models
Jose Israel Rodriguez, Botong Wang
The maximum likelihood degree (ML degree) measures the algebraic complexity of a fundamental optimization problem in statistics: maximum likelihood estimation. In this problem, one…
Critical points via monodromy and local methods
Abraham Martin del Campo, Jose Israel Rodriguez
In many areas of applied mathematics and statistics, it is a fundamental problem to find the best representative of a model by optimizing an objective function. This can be done by…
Data-Discriminants of Likelihood Equations
Jose Israel Rodriguez, Xiaoxian Tang
Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statist…