Strongly universally consistent nonparametric regression and classification with privatised data
| Autor: | Berrett, Thomas, Györfi, László, Walk, Harro |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we revisit the classical problem of nonparametric regression, but impose local differential privacy constraints. Under such constraints, the raw data $(X_1,Y_1),\ldots,(X_n,Y_n)$, taking values in $\mathbb{R}^d \times \mathbb{R}$, cannot be directly observed, and all estimators are functions of the randomised output from a suitable privacy mechanism. The statistician is free to choose the form of the privacy mechanism, and here we add Laplace distributed noise to a discretisation of the location of a feature vector $X_i$ and to the value of its response variable $Y_i$. Based on this randomised data, we design a novel estimator of the regression function, which can be viewed as a privatised version of the well-studied partitioning regression estimator. The main result is that the estimator is strongly universally consistent. Our methods and analysis also give rise to a strongly universally consistent binary classification rule for locally differentially private data. Comment: 25 pages |
| Databáze: | arXiv |
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