A Fast and Flexible Algorithm for the Graph-Fused Lasso
This work addresses computational bottlenecks in graph-based signal processing, offering incremental improvements in speed and flexibility for researchers and practitioners in fields like machine learning and statistics.
The authors tackled the problem of efficiently solving the graph-fused lasso (GFL) for parameter estimation by proposing a new algorithm that decomposes the graph into trails, enabling faster and more flexible solutions compared to previous methods, with empirical results showing tradeoffs in preprocessing time and convergence rate.
We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to decompose the graph into a set of trails which can then each be solved efficiently using techniques for the ordinary (1D) fused lasso. We leverage these trails in a proximal algorithm that alternates between closed form primal updates and fast dual trail updates. The resulting techinque is both faster than previous GFL methods and more flexible in the choice of loss function and graph structure. Furthermore, we present two algorithms for constructing trail sets and show empirically that they offer a tradeoff between preprocessing time and convergence rate.