2020/10/12 by Yihong Wu, Pengkun Yang · 1 voice · 1 citation
Computer Science · Physics and Astronomy · #Bayesian Methods and Mixture Models #Gaussian Processes and Bayesian Inference #Scientific Research and Discoveries #cs.IT #math.ST
paper · pdf · doi:10.1561/0100000095
openalex publication_date 2020/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This survey provides an exposition of a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods, which have recently been applied to address several challenging problems in statistical inference successfully. Topics including polynomial approximation, polynomial interpolation and majorization, moment space and positive polynomials, orthogonal polynomials and Gaussian quadrature are discussed, with their major probabilistic and statistical applications in property estimation on large domains and learning mixture models. These techniques provide useful tools not only for the design of highly practical algorithms with provable optimality, but also for establishing the fundamental limits of the inference problems through the method of moment matching. The effectiveness of the polynomial method is demonstrated in concrete problems such as entropy and support size estimation, distinct elements problem, and learning Gaussian mixture models.