KL Divergence: A New Metric for Quantifying Distribution Differences in Noisy Data

The previous section highlighted the limitations of the transfer matrix method when dealing with noisy data and inaccurate posterior estimates of noise probability. This arises primarily due to the discrepancy between probability distributions A and B. To address this, we propose a metric to quantify the difference between these distributions. We introduce a novel metric, Kullback–Leibler (KL) divergence, which measures the difference between two probability distributions. By calculating the KL divergence of sample-dependent noise, we can more accurately estimate the posterior distribution of noise probability, ultimately improving the efficacy of the transfer matrix method.