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Learning from structured data is becoming increasingly important. However, most prior work on kernel methods has focused on learning from attribute-value data. Only recently, research started investigating kernels for structured data. This paper considers kernels for multi-instance problems-a class of concepts on individuals represented by sets. The main result of this paper is a kernel on multi-instance data that can be shown to separate positive and negative sets under natural assumptions. This kernel compares favorably with state of the art multi-instance learning algorithms in an empirical study. Finally, we give some concluding remarks and propose future work that might further improve the results.