arXiv subjects

Daiki Morita

Publications and source records attributed to Daiki Morita.

5 recordsLinked to original sources

arXiv2026

Surprise Reduction and Nullification in Bayesian and Inverse Bayesian Inference under Ambiguous Prediction-Error Attribution

In non-stationary environments, prediction errors may signal environmental change or transient outliers, and adaptive systems must track such changes without overreacting to outliers. We distinguish surprise reduction, which updates beliefs to fit observations, from surprise nullification, which weakens constraints imposed by the predictive structure, and formalize both within Bayesian and inverse Bayesian (BIB) inference. Belief and likelihood updates are derived from variational objectives sharing a nullification strength, determined endogenously by minimizing surprise under the candidate post-update predictive distribution. In the Gaussian case, nullification expands belief and likelihood variances by a common factor relative to standard Bayesian updating, leaving the ratio unchanged. BIB thus defers attribution of the prediction error, committing to neither latent-state change nor observation-process uncertainty. The nullification strength is carried over as a candidate and is maintained or released according to the predictive surprise of the next observation. In a mean estimation task with outliers and changepoints, no scanned parameter setting of a Sage-Husa-type adaptive Kalman filter, fixed-strength BIB variant, or belief-forgetting-only variant outperforms BIB in both changepoint tracking and post-outlier stability. An oracle-informed reduced Bayesian model tracks changepoints better but is less stable after outliers. Although BIB maintains no explicit hypotheses about changepoints or outliers, it generates event-dependent dynamics. The learning rate increases after changepoints, whereas after outliers, nullification is released, and this increase is suppressed. Deferring attribution and letting subsequent observations differentiate the responses may constitute a principle of adaptive inference in non-stationary environments.

stat.ME↗

arXiv2025

Adaptive Inference through Bayesian and Inverse Bayesian Inference with Symmetry-Bias in Nonstationary Environments

This study proposes the novel Bayesian and inverse Bayesian (BIB) inference framework that incorporates symmetry bias into the Bayesian updating process to perform both conventional and inverse Bayesian updates concurrently. Conventional Bayesian inference is constrained by a fundamental trade-off between adaptability to abrupt environmental changes and accuracy during stable periods. The BIB framework addresses this limitation by dynamically modulating the learning rate via inverse Bayesian updates, thereby enhancing adaptive flexibility. The BIB model was evaluated in a sequential estimation task involving observations drawn from a Gaussian distribution with a stochastically time-varying mean, where it exhibited spontaneous bursts in the learning rate during environmental transitions, transiently entering high-sensitivity states that facilitated rapid adaptation. This burst-relaxation dynamic serves as a mechanism for balancing adaptability and accuracy. Furthermore, avalanche analysis, detrended fluctuation analysis, and power spectral analysis revealed that the BIB system likely operates near a critical state-a property not observed in standard Bayesian inference. This suggests that the BIB model uniquely achieves a coexistence of computational efficiency and critical dynamics, resolving the adaptability-accuracy trade-off while maintaining scale-free behavior. These findings offer a new computational perspective on scale-free dynamics in natural systems and provide valuable insights for the design of adaptive inference systems in nonstationary environments.

stat.ME↗

arXiv2025

A Simple Walk Model for Reproducing Power Laws in Human mobility

Identifying statistical patterns characterizing human trajectories is crucial for public health, traffic engineering, city planning, and epidemic modeling. Recent developments in global positioning systems and mobile phone networks have enabled the collection of substantial information on human movement. Analyses of these data have revealed various power laws in the temporal and spatial statistical patterns of human mobility. For example, jump size and waiting time distributions follow power laws. Zipf's law was also established for the frequency of visits to each location and rank. Relationship $S(t)\sim t^μ$ exists between time t and the number of sites visited up to that time t. Recently, a universal law of visitation for human mobility was established. Specifically, the number of people per unit area $ρ(r,f)$, who reside at distance r from a particular location and visit that location f times in a given period, is inversely proportional to the square of rf, i.e., $ρ(r,f) \propto (rf)^{-2}$ holds. The exploration and preferential return (EPR) model and its improved versions have been proposed to reproduce the above scaling laws. However, some rules that follow the power law are preinstalled in the EPR model. We propose a simple walking model to generate movements toward and away from a target via a single mechanism by relaxing the concept of approaching a target. Our model can reproduce the abovementioned power laws and some of the rules used in the EPR model are generated. These results provide a new perspective on why or how the scaling laws observed in human mobility behavior arise.

physics.soc-ph↗

arXiv2024

Walk model that continuously generates Brownian walks to Lévy walks depending on destination attractiveness

The Lévy walk, a type of random walk characterized by linear step lengths that follow a power-law distribution, is observed in the migratory behaviors of various organisms, ranging from bacteria to humans. Notably, Lévy walks with power exponents close to two, also known as Cauchy walks, are frequently observed, though their underlying causes remain elusive. This study proposes a walk model in which agents move toward a destination in multi-dimensional space and their movement strategy is parameterized by the extent to which they pursue the shortest path to the destination. This parameter is taken to represent the attractiveness of the destination to the agents. Our findings reveal that if the destination is very attractive, agents intensively search the area around it using Brownian walks, whereas if the destination is unattractive, they explore a distant region away from the point using Lévy walks with power exponents less than two. In the case where agents are unable to determine whether the destination is attractive or unattractive, Cauchy walks emerge. The Cauchy walker searches the region with a probability inversely proportional to the distance from the destination. This suggests that it preferentially searches the area close to the destination, while concurrently having the potential to extend the search area much further. Our model, which can change the search method and search area depending on the attractiveness of the destination, has the potential to be utilized for exploring the parameter space of optimization problems.

cs.MA↗

arXiv2023

Inverse square Levy walk emerging universally in goal-oriented tasks

The Levy walk in which the frequency of occurrence of step lengths follows a power-law distribution, can be observed in the migratory behavior of organisms at various levels. Levy walks with power exponents close to 2 are observed, and the reasons are unclear. This study aims to propose a model that universally generates inverse square Levy walks (called Cauchy walks) and to identify the conditions under which Cauchy walks appear. We demonstrate that Cauchy walks emerge universally in goal-oriented tasks. We use the term "goal-oriented" when the goal is clear, but this can be achieved in different ways, which cannot be uniquely determined. We performed a simulation in which an agent observed the data generated from a probability distribution in a two-dimensional space and successively estimated the central coordinates of that probability distribution. The agent has a model of probability distribution as a hypothesis for data-generating distribution and can modify the model such that each time a data point is observed, thereby increasing the estimated probability of occurrence of the observed data. To achieve this, the center coordinates of the model must be moved closer to those of the observed data. However, in the case of a two-dimensional space, arbitrariness arises in the direction of correction of the center; this task is goal oriented. We analyze two cases: a strategy that allocates the amount of modification randomly in the x- and y-directions, and a strategy that determines allocation such that movement is minimized. The results reveal that when a random strategy is used, the Cauchy walk appears. When the minimum strategy is used, the Brownian walk appears. The presence or absence of the constraint of minimizing the amount of movement may be a factor that causes the difference between Brownian and Levy walks.

cond-mat.stat-mech↗