We study estimating inherent human disagreement (annotation label distribution) in natural language inference task. Post-hoc smoothing of the predicted label distribution to match the expected label entropy is very effective. Such simple manipulation can reduce KL divergence by almost half, yet will not improve majority label prediction accuracy or learn label distributions. To this end, we introduce a small amount of examples with multiple references into training. We depart from the standard practice of collecting a single reference per each training example, and find that collecting multiple references can achieve better accuracy under the fixed annotation budget. Lastly, we provide rich analyses comparing these two methods for improving label distribution estimation.
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