2011/03/08 by José Bento, José Maurício S. Bento, Bento, José +4
Computer Science · Economics, Econometrics and Finance · Mathematics · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Finance (q-fin.ST) #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and financial applications #cs.IT #cs.LG #math.IT #math.ST #q-fin.ST #stat.ML #stat.TH
paper · pdf · doi:10.48550/arxiv.1103.1689
6 pages, 2 figures, conference version
openalex publication_date 2011/03/08 · arxiv created 2011/03/09 · arxiv updated 2011/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider the problem of learning the drift coefficient of a stochastic differential equation from a sample path. In this paper, we assume that the drift is parametrized by a high dimensional vector. We address the question of how long the system needs to be observed in order to learn this vector of parameters. We prove a general lower bound on this time complexity by using a characterization of mutual information as time integral of conditional variance, due to Kadota, Zakai, and Ziv. This general lower bound is applied to specific classes of linear and non-linear stochastic differential equations. In the linear case, the problem under consideration is the one of learning a matrix of interaction coefficients. We evaluate our lower bound for ensembles of sparse and dense random matrices. The resulting estimates match the qualitative behavior of upper bounds achieved by computationally efficient procedures.