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Ioannis Papageorgiou

Publications and source records attributed to Ioannis Papageorgiou.

At least 19 recordsLinked to original sources
arXiv2026

A Spectral Approach to Survival Bounds for the Elephant Random Walk

We study a rate-one Poissonization of the one-dimensional elephant random walk killed upon reaching $\pm N$. For every fixed memory parameter $0<p<1$, we give a self-contained proof of two-sided exponential survival bounds on the rate scale $N^{-2}$, uniformly for sufficiently large $N$ and times $t\ge TN^3$. Our approach combines the classical Dirichlet Poincaré inequality with an $O(N/t)$ estimate on the memory-dependent perturbation and a quantitative initialization of the principal-eigenvector projection. The lower bound covers the critical and superdiffusive regimes $3/4\le p<1$ in this late-time range. The confined-path comparison used for initialization also gives a direct proof of the lower bound. The spectral argument controls the exponentially small forcing terms and jumps introduced by Poisson truncation.

math.PR↗
arXiv2026

Elephant Reinforced Galves-Löcherbach Networks

We introduce an infinite-dimensional Galves--Löcherbach system with bounded Elephant-type reinforced synaptic interactions. The reinforcement mechanism modifies the probabilities of excitatory and inhibitory synaptic updates while keeping their amplitudes uniformly bounded. We prove non-explosion by means of a Lyapunov estimate and establish a conditional Wasserstein contraction for the membrane-potential dynamics when the coupled systems share the same reinforcement profile. Finally, we derive the corresponding replica mean-field equation under the Poisson hypothesis.

math.PR↗
arXiv2026

Spiking Neural Networks with Elephant Reinforcement

We introduce a finite stochastic spiking-neuron network with Elephant-type memory, in which past firing activity modifies future excitability through a reinforcement-dependent threshold. For a bounded hard-threshold firing rate, we prove non-explosion of the finite system and obtain conditional exponential contraction in (1)-Wasserstein distance on a truncated potential space. We then formulate the corresponding replica mean-field dynamics and establish global existence, uniqueness in law, and non-explosion of the nonlinear process, together with a characterization of its invariant measures. Numerical experiments show that Elephant memory produces a (p)-dependent decline in firing activity, alters extinction behaviour, and yields finite-network dynamics closely matched by the replica mean-field approximation.

math.PR↗
arXiv2026

Fundamental limits of distributed multiclass classification from simple binary decisions

We consider the problem of constructing a $K$-class classifier from the combination of $O(\log K)$ simple binary classifiers -- this is a natural paradigm to construct a sophisticated classifier in a distributed manner with each agent performing a relatively straightforward task. We study the fundamental performance limits of such a classifier when the corresponding binary classifiers are hyperplanes. For a stylized Gaussian setting where the $K$ class centers are independent Gaussian points in $\mathbb R^d$ and the observations are corrupted by Gaussian noise, we derive explicit performance bounds across several decoding and dimensional regimes. Extensive simulation experiments provide strong empirical validation of the presented theoretical results.

stat.ML↗
arXiv2025

The Bayesian Context Trees State Space Model for time series modelling and forecasting

A hierarchical Bayesian framework is introduced for developing tree-based mixture models for time series, partly motivated by applications in finance and forecasting. At the top level, meaningful discrete states are identified as appropriately quantised values of some of the most recent samples. At the bottom level, a different, arbitrary base model is associated with each state. This defines a very general framework that can be used in conjunction with any existing model class to build flexible and interpretable mixture models. We call this the Bayesian Context Trees State Space Model, or the BCT-X framework. Appropriate algorithmic tools are described, which allow for effective and efficient Bayesian inference and learning; these algorithms can be updated sequentially, facilitating online forecasting. The utility of the general framework is illustrated in the particular instances when AR or ARCH models are used as base models. The latter results in a mixture model that offers a powerful way of modelling the well-known volatility asymmetries in financial data, revealing a novel, important feature of stock market index data, in the form of an enhanced leverage effect. In forecasting, the BCT-X methods are found to outperform several state-of-the-art techniques, both in terms of accuracy and computational requirements.

stat.ME↗
arXiv2025

Change-point Detection and Segmentation of Discrete Data using Bayesian Context Trees

A new Bayesian modelling framework is introduced for piece-wise homogeneous variable-memory Markov chains, along with a collection of effective algorithmic tools for change-point detection and segmentation of discrete time series. Building on the recently introduced Bayesian Context Trees (BCT) framework, the distributions of different segments in a discrete time series are described as variable-memory Markov chains. Inference for the presence and location of change-points is then performed via Markov chain Monte Carlo sampling. The key observation that facilitates effective sampling is that, using one of the BCT algorithms, the prior predictive likelihood of the data can be computed exactly, integrating out all the models and parameters in each segment. This makes it possible to sample directly from the posterior distribution of the number and location of the change-points, leading to accurate estimates and providing a natural quantitative measure of uncertainty in the results. Estimates of the actual model in each segment can also be obtained, at essentially no additional computational cost. Results on both simulated and real-world data indicate that the proposed methodology performs better than or as well as state-of-the-art techniques.

stat.ME↗
arXiv2025

The log-Sobolev inequality for spin systems of higher order interactions

We study the infinite-dimensional log-Sobolev inequality for spin systems on $\mathbb{Z}^d$ with interactions of power higher than quadratic. We assume that the one site measure without a boundary $e^{-ϕ(x)}dx/Z$ satisfies a log-Sobolev inequality and we determine conditions so that the infinite-dimensional Gibbs measure also satisfies the inequality. As a concrete application, we prove that a certain class of nontrivial Gibbs measures with non-quadratic interaction potentials on an infinite product of Heisenberg groups satisfy the log-Sobolev inequality.

math.PR↗
arXiv2023

Interacting systems of infinite spiking neurons with weights beyond uniform summability

We consider an infinite system of spiking neurons with a drift and both excitatory and inhibitory connections. We study conditions for non-explosiveness and the uniqueness of the invariant measure. In particular, we examine conditions that allow this infinite interacting system to go beyond the usual interactions of uniformly summable weights. As a result, we extend the Galves-Löcherbach model beyond the restrictive uniform summability of the model.

math.PR↗
arXiv2023

Context-tree weighting for real-valued time series: Bayesian inference with hierarchical mixture models

Real-valued time series are ubiquitous in the sciences and engineering. In this work, a general, hierarchical Bayesian modelling framework is developed for building mixture models for times series. This development is based, in part, on the use of context trees, and it includes a collection of effective algorithmic tools for learning and inference. A discrete context (or 'state') is extracted for each sample, consisting of a discretised version of some of the most recent observations preceding it. The set of all relevant contexts are represented as a discrete context-tree. At the bottom level, a different real-valued time series model is associated with each context-state, i.e., with each leaf of the tree. This defines a very general framework that can be used in conjunction with any existing model class to build flexible and interpretable mixture models. Extending the idea of context-tree weighting leads to algorithms that allow for efficient, exact Bayesian inference in this setting. The utility of the general framework is illustrated in detail when autoregressive (AR) models are used at the bottom level, resulting in a nonlinear AR mixture model. The associated methods are found to outperform several state-of-the-art techniques on simulated and real-world experiments.

stat.ME↗
arXiv2023

Truly Bayesian Entropy Estimation

Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been developed for this task, typically based either on universal data compression algorithms, or on statistical estimators of the underlying process distribution. In this work, we propose a fully-Bayesian approach for entropy estimation. Building on the recently introduced Bayesian Context Trees (BCT) framework for modelling discrete time series as variable-memory Markov chains, we show that it is possible to sample directly from the induced posterior on the entropy rate. This can be used to estimate the entire posterior distribution, providing much richer information than point estimates. We develop theoretical results for the posterior distribution of the entropy rate, including proofs of consistency and asymptotic normality. The practical utility of the method is illustrated on both simulated and real-world data, where it is found to outperform state-of-the-art alternatives.

stat.ME↗
arXiv2023

Posterior Representations for Bayesian Context Trees: Sampling, Estimation and Convergence

We revisit the Bayesian Context Trees (BCT) modelling framework for discrete time series, which was recently found to be very effective in numerous tasks including model selection, estimation and prediction. A novel representation of the induced posterior distribution on model space is derived in terms of a simple branching process, and several consequences of this are explored in theory and in practice. First, it is shown that the branching process representation leads to a simple variable-dimensional Monte Carlo sampler for the joint posterior distribution on models and parameters, which can efficiently produce independent samples. This sampler is found to be more efficient than earlier MCMC samplers for the same tasks. Then, the branching process representation is used to establish the asymptotic consistency of the BCT posterior, including the derivation of an almost-sure convergence rate. Finally, an extensive study is carried out on the performance of the induced Bayesian entropy estimator. Its utility is illustrated through both simulation experiments and real-world applications, where it is found to outperform several state-of-the-art methods.

stat.ME↗
arXiv2022

Bayesian Context Trees: Modelling and exact inference for discrete time series

We develop a new Bayesian modelling framework for the class of higher-order, variable-memory Markov chains, and introduce an associated collection of methodological tools for exact inference with discrete time series. We show that a version of the context tree weighting algorithm can compute the prior predictive likelihood exactly (averaged over both models and parameters), and two related algorithms are introduced, which identify the a posteriori most likely models and compute their exact posterior probabilities. All three algorithms are deterministic and have linear-time complexity. A family of variable-dimension Markov chain Monte Carlo samplers is also provided, facilitating further exploration of the posterior. The performance of the proposed methods in model selection, Markov order estimation and prediction is illustrated through simulation experiments and real-world applications with data from finance, genetics, neuroscience, and animal communication. The associated algorithms are implemented in the R package BCT.

stat.ME↗
arXiv2020

Asymptotic Analysis of the Elephant Random Walk

In this work we study asymptotic properties of a long range memory random walk known as elephant random walk. First we prove recurrence and positive recurrence for the elephant random walk. Then, we establish the transience regime of the model. Finally, under the Poisson Hypothesis, we study the replica mean field limit for this random walk and we obtain an upper bound for the expected distance of the walker from the origin.

math.PR↗
arXiv2020

Modified log-Sobolev inequality for a compact PJMP with degenerate jumps

We study the modified log-Sobolev inequality for a class of pure jump Markov processes that describe the interactions between brain neurons. In particular, we focus on a finite and compact process with degenerate jumps inspired by the model introduced by Galves and Löcherbach. As a result, we obtain concentration properties for empirical approximations of the process.

math.PR↗
arXiv2019

Concentration and Poincaré type inequalities for a degenerate pure jump Markov process

We study Talagrand concentration and Poincaré type inequalities for unbounded pure jump Markov processes. In particular we focus on processes with degenerate jumps that depend on the past of the whole system, based on the model introduced by Galves and Löcherbach in \cite{G-L}, in order to describe the activity of a biological neural network. As a result we obtain exponential rates of convergence to equilibrium.

math.PR↗
arXiv2019

Poincaré type inequalities for compact degenerate pure jump Markov processes

We aim in proving Poincaré inequalities for a class of pure jump Markov processes inspired by the model introduced in \cite{G-L} by Galves and Löcherbach to describe the behaviour of interacting brain neurons. In particular, we consider neurons with degenerate jumps, i.e. that lose their memory when they spike, while the probability of a spike depends on the actual position and thus the past of the whole neural system.

math.PR↗