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About this paper
Yuji Ito
Yuji Ito (Toyota Central R&D Labs., Inc.) established the exact analytical forms for the posterior mean, variance, and cumulative distribution function of Heteroscedastic Gaussian Processes, moving beyond approximation-based methods. This framework enabled the design of a chance-constrained tracking controller that significantly reduced constraint violations in simulations, achieving 34 violations compared to 116 and 349 for baselines, with competitive control costs.
Key insights
- The non-Gaussian nature of the overall Heteroscedastic Gaussian Process posterior can be managed by decomposing it; conditioning on the noise at training points reveals a conditional Gaussian posterior.
- Exact expressions for the posterior mean, variance, and cumulative distribution function (CDF) can be derived by performing expectations and integrations over the latent noise function parameters.
- Autonormalized importance sampling, combined with a proposal distribution constructed by moment-matching properties of the log-chi-squared approximation, provides a practical path to evaluate these analytically exact but intractable posterior forms.
Summary by alphaXiv.
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