In statistical learning, various mathematical optimalities are used to characterize performances of different learning methods. They include minimax optimality from a worst-case standpoint and asymptotic efficiency from a rosy view that the regression function to be learned sits there to be discovered. When multiple models, e.g., trees, neural networks and support vector machines, are considere...
AbstractCan one learn a solution operator associated with a differential operator from pairs of solutions and righthand sides? If so, how many pairs are required? These two questions have received significant research attention in operator learning. More precisely, given input-output pairs from an unknown elliptic PDE, we will derive a theoretically rigorous scheme for learning the associated G...
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