Sparse regression has been a popular approach to perform variable selection and enhance the prediction accuracy and interpretability of the resulting statistical model. Existing approaches focus on offline regularized regression, while the online scenario has rarely been studied. In this paper, we propose a novel online sparse linear regression framework for analyzing streaming data when data points arrive sequentially. Our proposed method is memory efficient and requires less stringent restricted strong convexity assumptions. Theoretically, we show that with a properly chosen regularization parameter, the $\ell_2$-norm statistical error of our estimator diminishes to zero in the optimal order of $\tilde{O}({\sqrt{s/t}})$, where $s$ is the sparsity level, $t$ is the streaming sample size, and $\tilde{O}(\cdot)$ hides logarithmic terms. Numerical experiments demonstrate the practical efficiency of our algorithm.

This paper proposes an incremental solution to Fast Subclass Discriminant Analysis (fastSDA). We present an exact and an approximate linear solution, along with an approximate kernelized variant. Extensive experiments on eight image datasets with different incremental batch sizes show the superiority of the proposed approach in terms of training time and accuracy being equal or close to fastSDA solution and outperforming other methods.