2020/10/31 by Thomas B. Berrett, László Györfi, Berrett, Thomas +3 · 1 citation
Computer Science · Mathematics · #62G08 #62G20 #Advanced Causal Inference Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Methodology (stat.ME) #Privacy-Preserving Technologies in Data #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2011.00216
openalex publication_date 2020/10/31 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this paper we revisit the classical problem of nonparametric regression,\nbut impose local differential privacy constraints. Under such constraints, the\nraw data (X1,Y1),\…,(Xn,Yn), taking values in \ℝd \×\n\ℝ, cannot be directly observed, and all estimators are functions of\nthe randomised output from a suitable privacy mechanism. The statistician is\nfree to choose the form of the privacy mechanism, and here we add Laplace\ndistributed noise to a discretisation of the location of a feature vector Xi\nand to the value of its response variable Yi. Based on this randomised data,\nwe design a novel estimator of the regression function, which can be viewed as\na privatised version of the well-studied partitioning regression estimator. The\nmain result is that the estimator is strongly universally consistent. Our\nmethods and analysis also give rise to a strongly universally consistent binary\nclassification rule for locally differentially private data.\n