  Conventional automatic speech recognition (ASR) system uses second-order
minkowski loss during inference time which is suboptimal as it incorporates
only first order statistics in posterior estimation [2]. In this paper we have
proposed higher order minkowski loss (4th Order and 6th Order) during inference
time, without any changes during training time. The main contribution of the
paper is to show that higher order loss uses higher order statistics in
posterior estimation, which improves the prediction ability of acoustic model
in ASR system. We have shown mathematically that posterior probability obtained
due to higher order loss is function of second order posterior and thus the
method can be incorporated in standard ASR system in an easy manner. It is to
be noted that all changes are proposed during test(inference) time, we do not
make any change in any training pipeline. Multiple baseline systems namely,
TDNN1, TDNN2, DNN and LSTM are developed to verify the improvement incurred due
to higher order minkowski loss. All experiments are conducted on LibriSpeech
dataset and performance metrics are word error rate (WER) on "dev-clean",
"test-clean", "dev-other" and "test-other" datasets.
