Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Model
We study ridge-regularized log-density-ratio estimation in the Gaussian location model with a common covariance matrix. By affine invariance, the model is written as q $\sim$ N(0, I), p $\sim$ N($Δ$, I), with linear features, where $Δ$ is a mean vector. The variational estimator is the empirical Kullback-Leibler (KL) log-normalized fit with a squared L2-penalty on its nonconstant coefficient, and the spectral estimator recently introduced in [1] replaces a single variational problem by a continuum of ridge-regularized least-squares problems. We derive high-dimensional deterministic asymptotic equivalents when the numbers of observations and dimension tend to infinity with fixed ratios. Th...
| Authors | Francis Bach |
|---|---|
| Primary category | cs.LG |
| Published | 2 July 2026 |
| Last updated at source | 2 July 2026 |
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