Sparse Latent Factor Forecaster (SLFF) with Iterative Inference for Transparent Multi-Horizon Commodity Futures Prediction

Amortized variational inference in latent-variable forecasters creates a deployment gap: the test-time encoder approximates a training-time optimization-refined latent, but without access to future targets. This gap introduces unnecessary forecast error and interpretability challenges. In this work, we propose the Sparse Latent Factor Forecaster with Iterative Inference (SLFF), addressing this through (i) a sparse coding objective with L1 regularization for low-dimensional latents, (ii) unrolled proximal gradient descent (LISTA-style) for iterative refinement during training, and (iii) encoder alignment to ensure amortized outputs match optimization-refined solutions. Under a linearized decoder assumption, we derive a design-motivating bound on the amortization gap based on encoder-optimizer distance, with convergence rates under mild conditions; empirical checks confirm the bound is predictive for the deployed MLP decoder. To prevent mixed-frequency data leakage, we introduce an information-set-aware protocol using release calendars and vintage macroeconomic data. Interpretability is formalized via a three-stage protocol: stability (Procrustes alignment across seeds), driver validity (held-out regressions against observables), and behavioral consistency (counterfactuals and event studies). Using commodity futures (Copper, WTI, Gold; 2005--2025) as a testbed, SLFF demonstrates significant improvements over neural baselines at 1- and 5-day horizons, yielding sparse factors that are stable across seeds and correlated with observable economic fundamentals (interpretability remains correlational, not causal). Code, manifests, diagnostics, and artifacts are released.