STATISTICAL-MECHANICS OF THE MAXIMUM-LIKELIHOOD DENSITY-ESTIMATION

被引：25

作者：

BARKAI, N ^{[1
]}

SOMPOLINSKY, H ^{[1
]}

机构：

[1] HEBREW UNIV JERUSALEM,CTR NEURAL COMPUTAT,IL-91904 JERUSALEM,ISRAEL

来源：

PHYSICAL REVIEW E | 1994年 / 50卷 / 03期

关键词：

D O I：

10.1103/PhysRevE.50.1766

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

Estimating the density of data generated by Gaussian mixtures, using the maximum-likelihood criterion, is investigated. Solving the statistical mechanics of this problem we evaluate the quality of the estimation as a function of the number of data points, P = alpha N, N being the dimensionality of the points, in the limit of large N. Below a critical value of alpha, the estimated density consists of Gaussian centers that have zero overlap with the structure of the true mixture. We show numerically that estimating the centers by slowly reducing the estimated Gaussian width yields a good agreement with the theory even in the presence of many local minima.

引用

页码：1766 / 1769

页数：4

共 13 条

[1] SCALING LAWS IN LEARNING OF CLASSIFICATION TASKS [J].

BARKAI, N ;

SEUNG, HS ;

SOMPOLINSKY, H .

PHYSICAL REVIEW LETTERS, 1993, 70 (20) :3167-3170

[2] STATISTICAL-MECHANICS OF UNSUPERVISED STRUCTURE RECOGNITION [J].

BIEHL, M ;

MIETZNER, A .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1994, 27 (06) :1885-1897

[3] COMPLEXITY OPTIMIZED DATA CLUSTERING BY COMPETITIVE NEURAL NETWORKS [J].

BUHMANN, J ;

KUHNEL, H .

NEURAL COMPUTATION, 1993, 5 (01) :75-88

[4]

Duda R. O., 1973, PATTERN CLASSIFICATI, V3

[5]

LING D, 1983, PHYS REV B, V23, P262

[6]

MEZARD M, 1987, SPIN GLASS THEORY BE

[7]

RADNER RA, 1984, SIAM REV, V26, P195

[8] STATISTICAL-MECHANICS AND PHASE-TRANSITIONS IN CLUSTERING [J].

ROSE, K ;

GUREWITZ, E ;

FOX, GC .

PHYSICAL REVIEW LETTERS, 1990, 65 (08) :945-948

[9]

SIMPOLINSKY H, UNPUB

[10] REVERSIBILITY AND IRREVERSIBILITY IN SPIN-GLASSES - THE FREE-ENERGY SURFACE [J].

SOUKOULIS, CM ;

LEVIN, K ;

GREST, GS .

PHYSICAL REVIEW LETTERS, 1982, 48 (25) :1756-1759

← 1 2 →