Direct loss minimization algorithms for sparse Gaussian processes
- URL: http://arxiv.org/abs/2004.03083v3
- Date: Tue, 27 Oct 2020 18:36:12 GMT
- Title: Direct loss minimization algorithms for sparse Gaussian processes
- Authors: Yadi Wei, Rishit Sheth, Roni Khardon
- Abstract summary: The paper provides a thorough investigation of Direct loss (DLM), which optimize the posterior to minimize predictive loss in sparse Gaussian processes.
The application of DLM in non-conjugate cases is more complex because the minimization of expectation in the log-loss DLM objective is often intractable.
- Score: 9.041035455989181
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The paper provides a thorough investigation of Direct loss minimization
(DLM), which optimizes the posterior to minimize predictive loss, in sparse
Gaussian processes. For the conjugate case, we consider DLM for log-loss and
DLM for square loss showing a significant performance improvement in both
cases. The application of DLM in non-conjugate cases is more complex because
the logarithm of expectation in the log-loss DLM objective is often intractable
and simple sampling leads to biased estimates of gradients. The paper makes two
technical contributions to address this. First, a new method using product
sampling is proposed, which gives unbiased estimates of gradients (uPS) for the
objective function. Second, a theoretical analysis of biased Monte Carlo
estimates (bMC) shows that stochastic gradient descent converges despite the
biased gradients. Experiments demonstrate empirical success of DLM. A
comparison of the sampling methods shows that, while uPS is potentially more
sample-efficient, bMC provides a better tradeoff in terms of convergence time
and computational efficiency.
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