Trustworthy prediction in Deep Neural Networks (DNNs), including Pre-trained Language Models (PLMs) is important for safety-critical applications in the real world. However, DNNs often suffer from uncertainty estimation, such as miscalibration. In particular, approaches that require multiple stochastic inference can mitigate this problem, but the expensive cost of inference makes them impractical. In this study, we propose $k$-Nearest Neighbor Uncertainty Estimation ($k$NN-UE), which is an uncertainty estimation method that uses the distances from the neighbors and label-existence ratio of neighbors. Experiments on sentiment analysis, natural language inference, and named entity recognition show that our proposed method outperforms the baselines or recent density-based methods in confidence calibration, selective prediction, and out-of-distribution detection. Moreover, our analyses indicate that introducing dimension reduction or approximate nearest neighbor search inspired by recent $k$NN-LM studies reduces the inference overhead without significantly degrading estimation performance when combined them appropriately.

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