| Abstract: |
| Precision medicine seeks to provide personalized healthcare by tailoring treatments to individual patient characteristics, making the development of individualized treatment rules (ITR) a central task. Outcome weighted learning serves as a powerful framework for estimating optimal , often relying on the hinge loss function due to its favorable statistical properties. However, the non-smooth nature of the hinge loss function can lead to computational difficulties, particularly in high-dimensional or small-sample settings.
In this talk, we introduce and investigate a family of outcome weighted learning algorithms generated by convolution-type smoothed hinge loss functions and varying Gaussian kernels. We derive fast convergence rates for the excess value function of these proposed learning algorithms across different model selection strategies, showing that these rates are optimal under mild noise and margin conditions, up to logarithmic factors.
Numerical simulations support our theoretical findings and indicate that the convolution smoothed hinge loss functions outperform the standard hinge loss function in terms of both computational efficiency and treatment value. |
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