Additive　models　have　attracted　much　attention　for　high-dimensional　regression　estimation　and　variable　selection.　However,　the　existing　models　are　usually　limited　to　the　single-task　learning　framework　under　the　mean　squared　error　(MSE)　criterion,　where　the　utilization　of　variable　structure　depends　heavily　on　a　priori　knowledge　among　variables.　For　high-dimensional　observations　in　real　environment,　e.g.,　Coronal　Mass　Ejections　(CMEs)　data,　the　learning　performance　of　previous　methods　may　be　degraded　seriously　due　to　the　complex　non-Gaussian　noise　and　the　insufficiency　of　a　prior　knowledge　on　variable　structure.　To　tackle　this　problem,　we　propose　a　new　class　of　additive　models,　called　Multi-task　Additive　Models　(MAM),　by　integrating　the　mode-induced　metric,　the　structure-based　regularizer,　and　additive　hypothesis　spaces　into　a　bilevel　optimization　framework.　Our　approach　does　not　require　any　priori　knowledge　of　variable　structure　and　suits　for　high-dimensional　data　with　complex　noise,　e.g.,　skewed　noise,　heavy-tailed　noise,　and　outliers.　A　smooth　iterative　optimization　algorithm　with　convergence　guarantees　is　provided　to　implement　MAM　efficiently.　Experiments　on　simulations　and　the　CMEs　analysis　demonstrate　the　competitive　performance　of　our　approach　for　robust　estimation　and　automatic　structure　discovery.　©　2020　Neural　information　processing　systems　foundation.　All　rights　reserved.