From CDF to PDF --- A Density Estimation Method for High Dimensional Data
This work addresses a specific technical bottleneck in density estimation for data analysis, but it is incremental as it builds directly on prior research.
The paper tackles the problem of estimating probability density functions (PDFs) from cumulative distribution functions (CDFs) for high-dimensional data, improving upon an existing method by eliminating hyper-parameter tuning and enabling efficient higher-order derivative computation, with experiments on one-dimensional data showing promising results.
CDF2PDF is a method of PDF estimation by approximating CDF. The original idea of it was previously proposed in [1] called SIC. However, SIC requires additional hyper-parameter tunning, and no algorithms for computing higher order derivative from a trained NN are provided in [1]. CDF2PDF improves SIC by avoiding the time-consuming hyper-parameter tuning part and enabling higher order derivative computation to be done in polynomial time. Experiments of this method for one-dimensional data shows promising results.