2016/05/19 by Surojit Biswas, Biswas, Surojit · 1 citation
Computer Science · Mathematics · #A priori and a posteriori #Abundance (ecology) #Artificial intelligence #Computer science #Econometrics #FOS: Computer and information sciences #Filter (signal processing) #Gaussian Processes and Bayesian Inference #Heteroscedasticity #Lag #Logarithm #Mathematical analysis #Mathematics #Methodology (stat.ME) #Neural Networks and Applications #Object (grammar) #Realization (probability) #Sampling (signal processing) #Scaling #Statistics #Time Series Analysis and Forecasting #Transformation (genetics) #stat.ME
paper · pdf · doi:10.48550/arxiv.1605.06064
arxiv created 2016/05/19 · openalex publication_date 2016/05/19 · arxiv updated 2016/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Count or non-negative data are often log transformed to improve heteroscedasticity and scaling. To avoid undefined values where the data are zeros, a small pseudocount (e.g. 1) is added across the dataset prior to applying the transformation. This pseudocount considers neither the measured object's a priori abundance nor the confidence with which the measurement was made, making this practice convenient but statistically unfounded. I introduce here the latent logarithm, or lag. lag assumes that each observed measurement is a noisy realization of an unmeasured latent abundance. By taking the logarithm of this learned latent abundance, which reflects both sampling confidence/depth and the object's a priori abundance, lag provides a probabilistically coherent, stable, and intuitive alternative to the questionable, but conventional "log(x + pseudocount)."