Maximum Likelihood Estimation and Polynomial System Solving
نویسندگان
چکیده
This article presents an alternative method to find the global maximum likelihood estimates of the mixing probabilities of a mixture of multinomial distributions. For these mixture models it is shown that the maximum likelihood estimates of the mixing probabilities correspond with the roots of a multivariate polynomial system. A new algorithm, set in a linear algebra framework, is presented which allows to find all these roots by solving a generalized eigenvalue problem.
منابع مشابه
Bearing Fault Detection Based on Maximum Likelihood Estimation and Optimized ANN Using the Bees Algorithm
Rotating machinery is the most common machinery in industry. The root of the faults in rotating machinery is often faulty rolling element bearings. This paper presents a technique using optimized artificial neural network by the Bees Algorithm for automated diagnosis of localized faults in rolling element bearings. The inputs of this technique are a number of features (maximum likelihood estima...
متن کاملTowards algebraic methods for maximum entropy estimation
We show that various formulations (e.g., dual and Kullback-Csiszar iterations) of estimation of maximum entropy (ME) models can be transformed to solving systems of polynomial equations in several variables for which one can use celebrated Gröbner bases methods. Posing of ME estimation as solving polynomial equations is possible, in the cases where feature functions (sufficient statistic) that ...
متن کاملOn Maximum Likelihood Estimation in Log-Linear Models
In this article, we combine results from the theory of linear exponential families, polyhedral geometry and algebraic geometry to provide analytic and geometric characterizations of log-linear models and maximum likelihood estimation. Geometric and combinatorial conditions for the existence of the Maximum Likelihood Estimate (MLE) of the cell mean vector of a contingency table are given for gen...
متن کاملTwo-stage estimation using copula function
Maximum likelihood estimation of multivariate distributions needs solving a optimization problem with large dimentions (to the number of unknown parameters) but two- stage estimation divides this problem to several simple optimizations. It saves significant amount of computational time. Two methods are investigated for estimation consistency check. We revisit Sankaran and Nair's bivari...
متن کاملMATHEMATICAL ENGINEERING TECHNICAL REPORTS Estimation of Exponential-Polynomial Distribution by Holonomic Gradient Descent
We study holonomic gradient decent for maximum likelihood estimation of exponentialpolynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of the distribution is the set of positive reals. We show that the maximum likelihood estimate (MLE) can be easily computed by the holonomic gradient descent, even...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012