2016/08/19 by Xinyang Yi, Constantine Caramanis, Yi, Xinyang +3 · 2 citations
Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1608.05749
openalex publication_date 2016/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of solving mixed random linear equations with k components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels (which sample corresponds to which model) are not observed. We give a tractable algorithm for the mixed linear equation problem, and show that under some technical conditions, our algorithm is guaranteed to solve the problem exactly with sample complexity linear in the dimension, and polynomial in k, the number of components. Previous approaches have required either exponential dependence on k, or super-linear dependence on the dimension. The proposed algorithm is a combination of tensor decomposition and alternating minimization. Our analysis involves proving that the initialization provided by the tensor method allows alternating minimization, which is equivalent to EM in our setting, to converge to the global optimum at a linear rate.