Conditional Sparse Coding and Grouped Multivariate Regression
This method addresses regression in grouped datasets, such as in brain imaging, by balancing shared information and group-specific structure, but it is incremental as it builds on existing sparse coding techniques.
The paper tackles the problem of multivariate regression with grouped data by proposing conditional sparse coding, which estimates a shared dictionary of low-rank matrices and uses sparse combinations for group-specific models, showing improved performance in simulations and brain imaging experiments compared to reduced rank regression.
We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across groups, and a sparse linear combination of the dictionary elements is estimated to form a model within each group. We refer to the method as conditional sparse coding since it is a coding procedure for the response vectors Y conditioned on the covariate vectors X. This approach captures the shared information across the groups while adapting to the structure within each group. It exploits the same intuition behind sparse coding that has been successfully developed in computer vision and computational neuroscience. We propose an algorithm for conditional sparse coding, analyze its theoretical properties in terms of predictive accuracy, and present the results of simulation and brain imaging experiments that compare the new technique to reduced rank regression.