SCORE: Spectral Correlation Estimation for Multivariate Gaussians

Key points

• We propose SCORE: a scalable framework, combining scoring rule training with an expressive covariance approximation learned in spectral space.1
• For $d$-dimensional data, the learning task is decomposed into learning the marginal distributions and learning a structured correlation matrix, which enables dense dependencies with linear storage and $\mathcal{O}(d\log d)$ cost.1
• We utilize the closed form Gaussian kernel score for training, which remains defined even for degenerate covariances and admits bounded gradients during optimization.1
• We evaluate our model on a variety of tasks with a commonly assumed Gaussian domain: Time-series forecasting, monocular depth estimation, and spatial weather prediction, showing improved performance at lower computational cost.1

Sources (1)

• [1]SCORE: Spectral Correlation Estimation for Multivariate Gaussians
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 03:01 PM

  Neural network-based predictive modeling with high-dimensional structured Gaussian targets requires an efficient and numerically stable, yet expressive approximation of the covariance matrix.

  We propose SCORE: a scalable framework, combining scoring rule training with an expressive covariance approximation learned in spectral space.

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