Despite the success of data driven approaches in transfer learning, the theoretical understanding of transfer learning from statistics or information theory is somewhat behind. A key challenge when conducting theoretical analyses for transfer learning problems is that the statistical correlation between source and target tasks are often unknown, and hence traditional mathematical tools in statistics and estimation theory are difficult to be applied. In this talk, we address this issue by formulating the transfer learning as an optimization problem for the testing loss over certain similarity constraints of the source and target tasks. Specifically, we first show that when the similarity between both tasks measured by a certain distance metric is given, the optimal linear transfer model can be computed. The optimal coefficient in such a model reveals how the sample complexity, model complexity, and the task similarity affect the knowledge transferring in transfer learning. Moreover, when the task similarity cannot be well estimated due to insufficient samples, we propose a minimax formulation, which only requires the similarity being bounded, and the resulting distribution estimator is robust against sample insufficiency. We show an approximately optimal distribution estimator for the minimax problem from the bounded normal mean problem, and develop similar knowledge transferring insights as in the linear transferring model. Finally, some experimental results validate the algorithms led by our theoretical approach. Speaker(s): Shao-Lun Huang, Room: 4127, Bldg: Earth Science Building, 2207 Main Mall, Vancouver, British Columbia, Canada, V6T1Z4