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Title: Kernelised Stein discrepancy for truncated density estimation Authors:  Daniel Williams - University of Bristol (United Kingdom) [presenting]
Song Liu - University of Bristol (United Kingdom)
Abstract: Often, observations are truncated by a pre-defined boundary. For example, if we want to analyse the storm location pattern in the USA, the observations are naturally limited to the area within the country's boundary. Estimating a truncated density model is difficult due to the intractable normalising constant: It ensures the density model integrates to one over the truncated domain. A score matching-based approach has been proposed to estimate truncated density models using a weighted objective function. However, it is unclear whether its weighting function is optimal for a specific dataset. A truncated kernelised Stein discrepancy (TKSD) approach is developed, which solves the density estimation problem in an entirely data-driven fashion. It adapts the regular kernelised Stein discrepancy (KSD) estimator to the truncated observation setting without a handpicked weighting function. By solving the Lagrangian dual optimisation problem, we develop an objective function that estimates any unnormalised density, including one with a truncated domain. Finally, experiments on toy and real-world datasets show the accuracy of our method achieves a convincing lead over previous works at a small cost of computation time.