Multi-label　learning　has　been　widely　used　in　many　fields　to　solve　the　problem　of　assigning　multiple　related　categories　to　an　instance.　Nevertheless,　the　label　for　each　training　example　is　assumed　complete　in　most　of　the　current　multi-label　learning　methods.　As　a　matter　of　fact,　it　is　often　hard　to　obtain　training　samples　with　complete　labels,　thus　weakly　supervised　multi-label　learning　is　demanded,　which　has　become　a　hot　topic　in　recent　years.　Moreover,　the　missing　labels　would　further　aggravate　the　class　imbalance　in　multi-label　learning.　In　this　paper,　the　asymmetric　stage-wise　loss　function　is　introduced　to　make　positive　class　samples　farther　away　from　the　classification　boundary　than　negative　class　samples　by　adjusting　ramp　as　well　as　the　margin　parameters.　In　addition,　the　general　aggregate　loss　function　is　replaced　with　the　average　top-k　aggregate　loss　so　as　to　protect　the　non-typical　distributed　samples　from　being　sacrificed　in　the　aggregation　process　of　the　loss　function,　and　therefore　improve　the　identification　accuracy　of　minority　labels.　The　experiments　on　both　standard　and　large-scale　multi-label　data　sets　demonstrate　that　the　proposed　algorithm　can　solve　the　problem　of　class　imbalance　by　changing　the　sample　distribution　of　training　set,　thus　obtaining　competitive　performance.