2001/05/29 by Natalia L. Komarova, Natalia Komarova, Komarova, Natalia +2
Computer Science · Mathematics · #26C10 #60E07 #60F15 #60J20 #91E40 #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #cs.LG #math.CO #math.DS #math.PR #msc:26C10 #msc:60E07 #msc:60F15 #msc:60J20 #msc:91E40
paper · pdf · doi:10.48550/arxiv.math/0105235
Minor revisions
openalex publication_date 2001/05/29 · arxiv created 2001/12/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the convergence properties of a pair of learning algorithms (learning with and without memory). This leads us to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the derivative of random polynomials (generated by picking their roots uniformly at random in the interval [0, 1], although our results extend to other distributions). This, in turn, requires the study of the statistical behavior of the harmonic mean of random variables as above, which leads us to delicate question of the rate of convergence to stable laws and tail estimates for stable laws. The reader can find the proofs of most of the results announced here in the paper entitled "Harmonic mean, random polynomials, and random matrices", by the same authors.