Mixed regression is a statistical technique used to model the relationship between two or more dependent variables and an independent variable. In this article, we propose a new approach to mixed regression that takes into account the complexity of the problem and provides optimal rates of convergence. Our method is based on a convex formulation that simplifies the analysis and enables us to derive new results on the performance of identification algorithms.
Main Ideas
- The authors introduce two components to the mixed regression problem: a balanced mixture and an unbalanced mixture.
- They assume that the hidden variables are i.i.d with a known distribution, and the noise is Gaussian with unknown variance.
- They propose a new evaluation index (12) that combines events based on the clustering of the data into two categories.
- The authors analyze the RHS of the evaluation index term by term and derive new results on the performance of identification algorithms.
Conclusion
Our proposed method provides a more general approach to mixed regression than existing results, which only consider the balanced mixture. By taking into account the complexity of the problem and using a convex formulation, we are able to provide optimal rates of convergence and improve the analysis of identification algorithms. This work has important implications for the field of statistics and machine learning, as it provides a more robust and accurate way to model the relationship between dependent variables and an independent variable.
