This paper describes a parameter estimation method for multi-label classification that does not rely on approximate inference. It is known that multi-label classification involving label correlation features is intractable, because the graphical model for this problem is a complete graph. Our solution is to exploit the sparsity of features, and express a model structure for each object by using a sparse graph. We can thereby apply the junction tree algorithm, allowing for efficient exact inference on sparse graphs. Experiments on three data sets for text categorization demonstrated that our method increases the accuracy for text categorization with a reasonable cost.