Feature Density and Approximation Quality
Data Preparation & Feature Engineering DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding the relationship between feature density (sparsity) and function approximation error., Euclidean distance metrics, Spatial indexing for point retrieval, Normalization of density features, Approximation error bounds, Local variance estimation, Data Preparation, Feature Engineering, Statistical Learning Theory, Computational Geometry, Dimensionality Reduction, Sparsity Analysis, Local Density Estimation, Curse of Dimensionality, Kernel Density Estimation, Nearest Neighbor Search.
Implement a function 'evaluate approximation quality(data, query point, radius)' that calculates the local feature density as the number of data points within a Euclidean radius of the query point, and returns an approximation quality score defined as 'density / (1 + distance to nearest neighbor)'.