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I have a distribution built on an interval for example [v_min, v_max], given a good estimate on the interval, the performance of the model can be good. If the interval is not the right interval, it will impede the performance of the model. Now I want to design such a deep learning model so that the neural network can learning a good interval. Since the network is quite different. The output is bounded and it has constraint v_min < v_max.

How can I design such a network?

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I think this question is a bit too vague to answer properly, but you can simply regress v_min and v_max-v_min to get your interval. Then you can train with L1 or L2 loss, or if you want, the JS or KL divergence between the true distribution and the distribution parameterized by the network output.

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