Bias-corrected estimator for intrinsic dimension and differential entropy--a visual multiscale approach
This work addresses bias issues in fundamental data analysis measures, offering a practical method for researchers in machine learning and statistics, though it appears incremental as it builds on existing estimators.
The paper tackles the systematic bias in estimators for intrinsic dimension and differential entropy by proposing a joint estimation and bias correction approach, showing that simultaneous estimation provides complementary insights across different observation scales.
Intrinsic dimension and differential entropy estimators are studied in this paper, including their systematic bias. A pragmatic approach for joint estimation and bias correction of these two fundamental measures is proposed. Shared steps on both estimators are highlighted, along with their useful consequences to data analysis. It is shown that both estimators can be complementary parts of a single approach, and that the simultaneous estimation of differential entropy and intrinsic dimension give meaning to each other, where estimates at different observation scales convey different perspectives of underlying manifolds. Experiments with synthetic and real datasets are presented to illustrate how to extract meaning from visual inspections, and how to compensate for biases.