  For various speech-related tasks, confidence scores from a speech recogniser
are a useful measure to assess the quality of transcriptions. In traditional
hidden Markov model-based automatic speech recognition (ASR) systems,
confidence scores can be reliably obtained from word posteriors in decoding
lattices. However, for an ASR system with an auto-regressive decoder, such as
an attention-based sequence-to-sequence model, computing word posteriors is
difficult. An obvious alternative is to use the decoder softmax probability as
the model confidence. In this paper, we first examine how some commonly used
regularisation methods influence the softmax-based confidence scores and study
the overconfident behaviour of end-to-end models. Then we propose a lightweight
and effective approach named confidence estimation module (CEM) on top of an
existing end-to-end ASR model. Experiments on LibriSpeech show that CEM can
mitigate the overconfidence problem and can produce more reliable confidence
scores with and without shallow fusion of a language model. Further analysis
shows that CEM generalises well to speech from a moderately mismatched domain
and can potentially improve downstream tasks such as semi-supervised learning.
