{"ID":2851188,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.20551","arxiv_id":"2510.20551","title":"Time-series Random Process Complexity Ranking Using a Bound on Conditional Differential Entropy","abstract":"Conditional differential entropy provides an intuitive measure for relatively ranking time-series complexity by quantifying uncertainty in future observations given past context. However, its direct computation for high-dimensional processes from unknown distributions is often intractable. This paper builds on the information theoretic prediction error bounds established by Fang et al. \\cite{fang2019generic}, which demonstrate that the conditional differential entropy \\textbf{$h(X_k \\mid X_{k-1},...,X_{k-m})$} is upper bounded by a function of the determinant of the covariance matrix of next-step prediction errors for any next step prediction model. We add to this theoretical framework by further increasing this bound by leveraging Hadamard's inequality and the positive semi-definite property of covariance matrices. To see if these bounds can be used to rank the complexity of time series, we conducted two synthetic experiments: (1) controlled linear autoregressive processes with additive Gaussian noise, where we compare ordinary least squares prediction error entropy proxies to the true entropies of various additive noises, and (2) a complexity ranking task of bio-inspired synthetic audio data with unknown entropy, where neural network prediction errors are used to recover the known complexity ordering. This framework provides a computationally tractable method for time-series complexity ranking using prediction errors from next-step prediction models, that maintains a theoretical foundation in information theory.","short_abstract":"Conditional differential entropy provides an intuitive measure for relatively ranking time-series complexity by quantifying uncertainty in future observations given past context. However, its direct computation for high-dimensional processes from unknown distributions is often intractable. This paper builds on the info...","url_abs":"https://arxiv.org/abs/2510.20551","url_pdf":"https://arxiv.org/pdf/2510.20551v1","authors":"[\"Jacob Ayers\",\"Richard Hahnloser\",\"Julia Ulrich\",\"Lothar Sebastian Krapp\",\"Remo Nitschke\",\"Sabine Stoll\",\"Balthasar Bickel\",\"Reinhard Furrer\"]","published":"2025-10-23T13:36:04Z","proceeding":"eess.SP","tasks":"[\"eess.SP\",\"cs.IT\",\"eess.AS\",\"stat.ME\",\"stat.ML\"]","methods":"[]","has_code":false}