Then, we introduce a simple, but effective, statistical correction and demonstrate that it improves attribution-based explanations across various DNNs that span a wide range of prediction tasks in regulatory genomics. Here, we identify a previously overlooked source of noise in input gradients when the input features are categorical variables. However, the origins of all noise sources that afflict attribution maps are not yet fully understood. Many factors that influence the efficacy of attribution maps have been identified empirically, such as the smoothness properties of the learned function and learning (non-)robust features. This makes it difficult to deduce hypotheses of which patterns drive model predictions, which can then be validated with carefully designed in silico experiments. However, in practice, attribution methods often produce noisy feature importance maps with spurious importance scores. Some of the most popular attribution methods are gradient-based, where partial derivatives of the output with respect to the inputs are used, including saliency maps, integrated gradients, SmoothGrad, and expected gradients. Attribution methods also provide a natural way of quantifying the effect size of single-nucleotide mutations, both observed and counterfactual, which can help to prioritize disease-associated variants. To gain insights into the features learned by DNNs, post-hoc attribution methods provide an importance score for each nucleotide in a given sequence they often reveal biologically meaningful patterns, such as transcription factor binding motifs that are essential for gene regulation. Deep neural networks (DNNs) have demonstrated impressive performance across a wide variety of sequence-based prediction tasks in genomics, taking DNA sequences as input and predicting experimentally measured regulatory functions.
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