← 研踪 PaperTrailarXiv:2611.15698 · v1
Learning Mixtures of Exponential Family
首次提交 2026-11-12 00:37
版本更新 2026-11-12 00:37
雷达观测 2026-11-13 14:16
摘要
Motivated by causal inference and physical computing systems, we consider the problem of learning mixture of two bounded-support exponential-family distributions with a shared interaction parameter matrix and mixture component-specific linear parameter vectors. The unknown sequence of component labels belongs to a known structured class. We propose an estimator based on a convex loss that avoids the log-partition function; for each fixed label assignment, estimation is a convex optimization problem. We show that the conditional population loss uniquely identifies the interaction matrix and the linear parameter attached to each sample. For a global empirical minimizer, we establish finite-sample bounds on the interaction error in Frobenius norm and the average squared linear-parameter error. The bounds depend on the logarithm of the number of admissible label assignments, and, for fixed dimension and model bounds, imply consistency when this complexity grows sublinearly with sample size. Additional occupancy and separation conditions yield component and label recovery.
作者备注：Preliminary version appeared in ISIT 2026
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v1 · 2026-11-12 00:37 · 最新观测版本
Learning Mixtures of Exponential Family
Motivated by causal inference and physical computing systems, we consider the problem of learning mixture of two bounded-support exponential-family distributions with a shared interaction parameter matrix and mixture component-specific linear parameter vectors. The unknown sequence of component labels belongs to a known structured class. We propose an estimator based on a convex loss that avoids the log-partition function; for each fixed label assignment, estimation is a convex optimization problem. We show that the conditional population loss uniquely identifies the interaction matrix and the linear parameter attached to each sample. For a global empirical minimizer, we establish finite-sample bounds on the interaction error in Frobenius norm and the average squared linear-parameter error. The bounds depend on the logarithm of the number of admissible label assignments, and, for fixed dimension and model bounds, imply consistency when this complexity grows sublinearly with sample size. Additional occupancy and separation conditions yield component and label recovery.
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