Evaluating Probabilistic Inference in Deep Learning: Beyond Marginal Predictions

• URL: http://arxiv.org/abs/2107.09224v1
• Date: Tue, 20 Jul 2021 01:55:01 GMT
• Title: Evaluating Probabilistic Inference in Deep Learning: Beyond Marginal Predictions
• Authors: Xiuyuan Lu, Ian Osband, Benjamin Van Roy, Zheng Wen
• Abstract summary: We show that the commonly-used $tau=1$ can be insufficient to drive good decisions in many settings of interest. We also show that, as $tau$ grows, performing well according to $mathbfd_mathrmKLtau$ recovers universal guarantees for any possible decision.
• Score: 37.92747047688873
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A fundamental challenge for any intelligent system is prediction: given some inputs $X_1,..,X_\tau$ can you predict outcomes $Y_1,.., Y_\tau$. The KL divergence $\mathbf{d}_{\mathrm{KL}}$ provides a natural measure of prediction quality, but the majority of deep learning research looks only at the marginal predictions per input $X_t$. In this technical report we propose a scoring rule $\mathbf{d}_{\mathrm{KL}}^\tau$, parameterized by $\tau \in \mathcal{N}$ that evaluates the joint predictions at $\tau$ inputs simultaneously. We show that the commonly-used $\tau=1$ can be insufficient to drive good decisions in many settings of interest. We also show that, as $\tau$ grows, performing well according to $\mathbf{d}_{\mathrm{KL}}^\tau$ recovers universal guarantees for any possible decision. Finally, we provide problem-dependent guidance on the scale of $\tau$ for which our score provides sufficient guarantees for good performance.

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