  


A New Computational Approach to Density Estimation with Semidefinite Programming
Tadayoshi Fushiki (fushikiism.ac.jp) Abstract: Density estimation is a classical and important problem in statistics. The aim of this paper is to develop a new computational approach to density estimation based on semidefinite programming (SDP), a new technology developed in optimization in the last decade. We express a density as the product of a nonnegative polynomial and a base density such as normal distribution, exponential distribution and uniform distribution. The difficult nonnegativity constraint imposed on the polynomial is expressed as a semidefinite constraint. Under the condition that the base density is specified, the maximum likelihood estimation of the coefficients of the polynomial is formulated as a variant of SDP which can be solved in polynomialtime with the recently developed interiorpoint methods. Since the base density typically contains just one or two parameters, if the likelihood function is easily maximized with respect to the polynomial part by SDP, then it is possible to compute the global maximum of the likelihood function by further maximizing the partiallymaximized likelihood function with respect to the base density parameter. The primaldual interiorpoint algorithms are used to solve the variant of SDP. The proposed model is flexible enough to express such properties as unimodality and symmetry which would be reasonably imposed on the density function. Akaike information criterion (AIC) is used to choose the best model. Through applications to several instances we demonstrate flexibility of the model and performance of the proposed procedure. Keywords: density estimation, semidefinite programming, maximum likelihood estimation, AIC, statistics Category 1: Applications  Science and Engineering (Statistics ) Category 2: Applications  Science and Engineering (DataMining ) Category 3: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Citation: Research Memorandum No. 898, The Institute of Statistical Mathematics, 467 MinamiAzabul, Minatoku, Tokyo, 1068569, Japan, Novermber 2003. Download: [Postscript][PDF] Entry Submitted: 11/29/2003 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  