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Consider having some complicated system to which you would like to fit some arbitrary (finite) basis to: you have a few examples of inputs and outputs. Give a matrix equation or algorithm that will predict other values that are close to the system's likely outputs based on the data assuming you know nothing about the system. Now, you find that the weights are too dependent on some parameters and are larger than you would like; in particular, you see that you'd like to enforce the average to be something close to a value g. How would you do this?
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Research Intern

Interviewed at D. E. Shaw Research

4.1★
Jun 17, 2016

Consider having some complicated system to which you would like to fit some arbitrary (finite) basis to: you have a few examples of inputs and outputs. Give a matrix equation or algorithm that will predict other values that are close to the system's likely outputs based on the data assuming you know nothing about the system. Now, you find that the weights are too dependent on some parameters and are larger than you would like; in particular, you see that you'd like to enforce the average to be something close to a value g. How would you do this?

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