CINDES: Classification induced neural density estimator and simulator
This work addresses theoretical and practical gaps in neural density estimation for researchers and practitioners, offering an incremental improvement with provable adaptive rates.
The paper tackles the challenges of implementing neural density estimators and their lack of theoretical guarantees for adaptive convergence, proposing a structure-agnostic estimator that is easy to implement and provably adapts faster to low-dimensional structures, with validation through simulations and real data.
Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical successes, implementation can be challenging due to the need to ensure non-negativity and unit-mass constraints, and theoretical understanding remains limited. In particular, it is unclear whether such estimators can adaptively achieve faster convergence rates when the underlying density exhibits a low-dimensional structure. This paper addresses these gaps by proposing a structure-agnostic neural density estimator that is (i) straightforward to implement and (ii) provably adaptive, attaining faster rates when the true density admits a low-dimensional composition structure. Another key contribution of our work is to show that the proposed estimator integrates naturally into generative sampling pipelines, most notably score-based diffusion models, where it achieves provably faster convergence when the underlying density is structured. We validate its performance through extensive simulations and a real-data application.