If sub-populations in a training mixture are close in total variation distance, the paper claims generalization bounds and regression rates match those of a single population, with thresholds that tighten as function classes get more complex.
Learning Mixtures of Linear Regressions with Nearly Optimal Complexity
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated component is also unknown. Previous works either assume strong assumptions on the data distribution or have high complexity. This paper proposes a fixed parameter tractable algorithm for the problem under general conditions, which achieves global convergence and the sample complexity scales nearly linearly in the dimension. In particular, different from previous works that require the data to be from the standard Gaussian, the algorithm allows the data from Gaussians with different covariances. When the conditional number of the covariances and the number of components are fixed, the algorithm has nearly optimal sample complexity $N = \tilde{O}(d)$ as well as nearly optimal computational complexity $\tilde{O}(Nd)$, where $d$ is the dimension of the data space. To the best of our knowledge, this approach provides the first such recovery guarantee for this general setting.
fields
stat.ML 1years
2025 1verdicts
REJECT 1representative citing papers
citing papers explorer
-
Learning and Generalization with Mixture Data
If sub-populations in a training mixture are close in total variation distance, the paper claims generalization bounds and regression rates match those of a single population, with thresholds that tighten as function classes get more complex.