A variational approach to empirical mode estimation
Résumé
Mode estimation, which locates the values at which a probability distribution is maximal, is a critical task in statistical analysis, with applications spanning inverse problems, clustering, and image analysis. While traditional methods focus on single-mode detection, identifying multiple modes is often essential for capturing the data underlying structure. We introduce empirical Natural Variational Annealing (eNVA) that can achieve this task for distributions possibly only available through samples. eNVA is an extension of the recent Natural Variational Annealing (NVA) optimization framework. Using the flexibility of a variational formulation, eNVA accommodates variational distributions within the exponential family and generalizes the Gaussian mean-shift algorithm. Furthermore, the multiple mode estimation challenge can be tackled efficiently with our eNVA-GM variant, using Gaussian mixtures (GM) as variational distributions and allowing adaptive search strategies, such as temperature annealing, to balance exploration and exploitation principles. Insights demonstrate the robustness and versatility of eNVA in addressing complex multimodal problems.
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