Sophia: The Hutchinson Diagonal Estimate
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The problem, from first principles
Sophia needs the Hessian diagonal, but forming the full Hessian is too costly. The Hutchinson estimator uses random +1 and -1 probes: multiplying a Hessian-vector product by the probe, element-wise, gives an unbiased diagonal estimate.
From theory to code
Implement hutchinson_estimate(Hu, u), the element-wise probe times the Hessian-vector product.
Constraints
- The probe entries are plus or minus one.
Hints
Hint 1
Multiply the Hessian-vector product by the probe, element by element.
Keywords
research-papersoptimizationsecond-order
Python
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