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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