De-noising analysis of noisy data under mixed graphical models

Abstract

Graphical models are useful to characterize the dependence structure of variables and have been commonly used for analysis of complex structured data. While various estimation methods have been developed under different graphical models, those methods are, however, inadequate to handle noisy data with measurement error. The development of most existing approaches relies on the implicit yet stringent assumption that the associated variables must be measured precisely. This assumption is unrealistic for many applications because mismeasurement in variables is usually presented in the data collection process. In this paper, we consider analysis of error-prone data under graphical models. To understand the impact of measurement error, we first study the asymptotic bias of the naive analysis which disregards the feature of measurement error in the variables. Furthermore, we develop a de-noising estimation procedure to account for measurement error effects. Theoretical results are established for the proposed method and numerical studies are reported to assess the finite sample performance of our proposed method.