🤖 AI Summary
Traditional implicit generative models (e.g., GANs) suffer from training instability, mode collapse, and inaccurate tail characterization when modeling heavy-tailed, high-dimensional multivariate distributions. To address these challenges, this paper proposes Pareto-ISL—a novel implicit score learning framework. Its core contributions are: (1) the first integration of generalized Pareto noise into implicit score learning (ISL), explicitly capturing heavy-tailed behavior; and (2) a random-projection-based multidimensional ISL loss, extending ISL beyond univariate settings to scalable high-dimensional implicit modeling. Experiments demonstrate that Pareto-ISL accurately reproduces both central and tail regions of multivariate heavy-tailed distributions, significantly mitigates mode collapse, exhibits robustness to hyperparameter choices, and scales linearly in computational complexity with dimensionality.
📝 Abstract
Traditional implicit generative models are capable of learning highly complex data distributions. However, their training involves distinguishing real data from synthetically generated data using adversarial discriminators, which can lead to unstable training dynamics and mode dropping issues. In this work, we build on the extit{invariant statistical loss} (ISL) method introduced in cite{de2024training}, and extend it to handle heavy-tailed and multivariate data distributions. The data generated by many real-world phenomena can only be properly characterised using heavy-tailed probability distributions, and traditional implicit methods struggle to effectively capture their asymptotic behavior. To address this problem, we introduce a generator trained with ISL, that uses input noise from a generalised Pareto distribution (GPD). We refer to this generative scheme as Pareto-ISL for conciseness. Our experiments demonstrate that Pareto-ISL accurately models the tails of the distributions while still effectively capturing their central characteristics. The original ISL function was conceived for 1D data sets. When the actual data is $n$-dimensional, a straightforward extension of the method was obtained by targeting the $n$ marginal distributions of the data. This approach is computationally infeasible and ineffective in high-dimensional spaces. To overcome this, we extend the 1D approach using random projections and define a new loss function suited for multivariate data, keeping problems tractable by adjusting the number of projections. We assess its performance in multidimensional generative modeling and explore its potential as a pretraining technique for generative adversarial networks (GANs) to prevent mode collapse, reporting promising results and highlighting its robustness across various hyperparameter settings.