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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning 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Approximate factor analysis model building via alternating I-divergence minimization
Lorenzo Finesso, Peter Spreij · 2008-12-10 · via math.ST updates on arXiv.org

Given a positive definite covariance matrix $\widehat Σ$, we strive to construct an optimal \emph{approximate} factor analysis model $HH^\top +D$, with $H$ having a prescribed number of columns and $D>0$ diagonal. The optimality criterion we minimize is the I-divergence between the corresponding normal laws. Lifting the problem into a properly chosen larger space enables us to derive an alternating minimization algorithm à la Csiszár-Tusnády for the construction of the best approximation. The convergence properties of the algorithm are studied, with special attention given to the case where $D$ is singular.

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