Hierarchical Inference Research Articles

A hierarchical active inference model of spatial alternation tasks and the hippocampal-prefrontal circuit.

Cognitive problem-solving benefits from cognitive maps aiding navigation and planning. Physical space navigation involves hippocampal (HC) allocentric codes, while abstract task space engages medial prefrontal cortex (mPFC) task-specific codes. Previous studies show that challenging tasks, like spatial alternation, require integrating these two types of maps. The disruption of the HC-mPFC circuit impairs performance. We propose a hierarchical active inference model clarifying how this circuit solves spatial interaction tasks by bridging physical and task-space maps. Simulations demonstrate that the model's dual layers develop effective cognitive maps for physical and task space. The model solves spatial alternation tasks through reciprocal interactions between the two layers. Disrupting its communication impairs decision-making, which is consistent with empirical evidence. Additionally, the model adapts to switching between multiple alternation rules, providing a mechanistic explanation of how the HC-mPFC circuit supports spatial alternation tasks and the effects of disruption.

Causal inference predicts the transition from integration to segmentation in motion perception.

Motion provides a powerful sensory cue for segmenting a visual scene into objects and inferring the causal relationships between objects. Fundamental mechanisms involved in this process are the integration and segmentation of local motion signals. However, the computations that govern whether local motion signals are perceptually integrated or segmented remain unclear. Hierarchical Bayesian causal inference has recently been proposed as a model for these computations, yet a hallmark prediction of the model - its dependency on sensory uncertainty - has remained untested. We used a recently developed hierarchical stimulus configuration to measure how human subjects integrate or segment local motion signals while manipulating motion coherence to control sensory uncertainty. We found that (a) the perceptual transition from motion integration to segmentation shifts with sensory uncertainty, and (b) that perceptual variability is maximal around this transition point. Both findings were predicted by the model and challenge conventional interpretations of motion repulsion effects.

Inferring the distribution of the ionising photon escape fraction

The escape fraction of ionising photons from galaxies ($f_ esc $) is a key parameter for understanding how intergalactic hydrogen became reionised, but it remains mostly unconstrained. Measurements have been limited to the average value in galaxy ensembles and to handfuls of individual detections. To help understand which mechanisms govern ionising photon escape, here we infer the distribution of $f_ esc We developed a hierarchical Bayesian inference technique to estimate the population distribution of $f_ esc $ from the ratio of Lyman continuum to non-ionising UV flux measured from broadband photometry. We applied it to a sample of 148 $z 3.5$ star-forming galaxies from the VANDELS spectroscopic survey. We explored four physically motivated distributions: constant, log-normal, exponential, and bimodal, and recovered $ f_ esc for most models. We find the observations are best described by an exponential $f_ esc $ distribution with scale factor $ $. This indicates most galaxies in our sample exhibit very low escape fractions, while predicting substantial ionising photon leakage for only a few galaxies, implying a range of optical depths in the interstellar medium and/or time variability in ionising photon escape. We rule out a bimodal distribution at high significance, indicating that a purely bimodal model of ionising photon escape (due to very strong sightline and/or time variability) is not favoured. We compare our recovered exponential distribution with the SPHINX simulations and find that, while the simulation also predicts an exponential distribution, it significantly underpredicts our inferred mean. The distribution of $f_ esc $ can be a vital test for simulations in understanding ionising photon leakage, and is important to consider to gain a complete picture of reionisation.

The Heavier the Faster: A Subpopulation of Heavy, Rapidly Spinning and Quickly Evolving Binary Black Holes

Abstract The spins of binary black holes (BBHs) measured from gravitational waves contain valuable information about their formation pathways. In this study, we propose a new quantity, the “dimensionless net spin” (χ N), which relates to the sum of the angular momenta of the component black holes (BHs) in the system, offering a novel perspective for exploring the origins of BBHs. Through hierarchical Bayesian inference on χ N, we find strong evidence that its distribution is better described by two Gaussian components rather than one, and their branching ratios vary with total mass and redshift: there is a narrow peak at χ N ∼ 0.15 and an extended peak at χ N ∼ 0.3–0.6. The rapidly spinning systems likely dominate the high-mass end of the population and evolve with redshift more quickly. These findings present new challenges to the field binary formation scenario and suggest that dynamical processes may play a key role in the formation of high total mass BBHs.

Constrained cosmological simulations of the Local Group using Bayesian hierarchical field-level inference

We present a novel approach based on Bayesian field-level inference that provides representative initial conditions for simulation of the Local Group (LG) of galaxies and its neighbourhood, constrained by present-day observations. We extended the Bayesian Origin Reconstruction from Galaxies ( algorithm with a multi-resolution approach, allowing us to reach the smaller scales needed to apply the constraints. Our data model simultaneously accounts for observations of mass tracers within the dark haloes of the Milky Way (MW) and M31, for their observed separation and relative velocity, and for the quiet surrounding Hubble flow, represented by the positions and velocities of 31 galaxies at distances between one and four megaparsec. Our approach delivers representative posterior samples of realisations that are statistically and simultaneously consistent with all of these observations, leading to significantly tighter mass constraints than found if the individual datasets are considered separately. In particular, we estimate the virial masses of the MW and M31 to be $ (M_ 200c /M_ and $12.33 respectively, their sum to be $ 200c /M_ and the enclosed mass within spheres of radius $R$ to be $ (M(R)/M_ and $12.96 for $R=1$ Mpc and $3$ Mpc, respectively. The M31-MW orbit is nearly radial for most of our realisations, and most of them feature a dark matter sheet aligning approximately with the supergalactic plane, despite the surrounding density field not being used explicitly as a constraint. High-resolution, high-fidelity resimulations from initial conditions identified using the approximate simulations of our inference scheme continue to satisfy the observational constraints, demonstrating a route to future high-resolution, full-physics simulations of ensembles of LG look-alikes, all of which closely mirror the observed properties of the real system and its immediate environment.

Scalable spatiotemporal prediction with Bayesian neural fields

Spatiotemporal datasets, which consist of spatially-referenced time series, are ubiquitous in diverse applications, such as air pollution monitoring, disease tracking, and cloud-demand forecasting. As the scale of modern datasets increases, there is a growing need for statistical methods that are flexible enough to capture complex spatiotemporal dynamics and scalable enough to handle many observations. This article introduces the Bayesian Neural Field (BayesNF), a domain-general statistical model that infers rich spatiotemporal probability distributions for data-analysis tasks including forecasting, interpolation, and variography. BayesNF integrates a deep neural network architecture for high-capacity function estimation with hierarchical Bayesian inference for robust predictive uncertainty quantification. Evaluations against prominent baselines show that BayesNF delivers improvements on prediction problems from climate and public health data containing tens to hundreds of thousands of measurements. Accompanying the paper is an open-source software package (https://github.com/google/bayesnf) that runs on GPU and TPU accelerators through the Jax machine learning platform.

Hierarchical Bayesian modeling for calibration and uncertainty quantification of constitutive material models: Application to a uniaxial steel material model

Constitutive material models play an integral role in finite element (FE) modeling of structural components and systems and are governed by a set of parameters. The values of the material model parameters are important for the FE model to be able to predict the real structural behavior as closely as possible. Realistic cyclic material constitutive models well calibrated to experimental data are critical when predicting the nonlinear dynamic response of structural systems to extreme loads (e.g., earthquakes, high winds, blast). Hence, this study focuses on the inference and uncertainty quantification of material model parameters from an experimental dataset consisting of data from experiments on multiple specimens of the same kind, which is a topic of great interest to the structural modeling and simulation community. Traditionally, Bayesian inference is performed by pooling the data from all the specimens, or by considering the data from a single specimen, disregarding the inherent variability (aleatory uncertainty) among specimens of the same kind. Consequently, traditional approaches fail to capture the population distribution of material model parameters, which represents the aleatory specimen-to-specimen variability that is essential for conducting reliability analysis and uncertainty propagation studies. Moreover, these approaches cannot accurately simulate the response of new specimens. To overcome these limitations, this study introduces a novel application of hierarchical Bayesian inference for calibrating material model parameters. By simultaneously considering experimental data from multiple specimens of the same kind, hierarchical Bayesian modeling quantifies both epistemic uncertainty and aleatory specimen-to-specimen variability. In this study, the parameters of the well-known Giuffré-Menegotto-Pinto (GMP) uniaxial material model for reinforcing steel are calibrated and validated based on a dataset of experimental cyclic tests conducted on thirty-six steel specimens, or coupons, originating from three different manufacturing mills, complying to two different manufacturing standards, and subjected to different strain histories. These strain histories are similar to those experienced during seismic events by reinforcing steel bars within reinforced concrete structures. The material model parameters are calibrated using both the traditional and the hierarchical Bayesian approach and the results are compared. Based on the experimental dataset employed in this study, a joint probability distribution of the GMP material model parameters that quantifies both epistemic (due to finite sample size) and aleatory (coupon-to-coupon) variability or uncertainty is provided which can be used for uncertainty propagation in reliability and risk analyses of nonlinear dynamic systems.

Computational phenotyping of aberrant belief updating in individuals with schizotypal traits and schizophrenia

BackgroundPsychotic experiences are thought to emerge from various interrelated patterns of disrupted belief updating, such as overestimating the reliability of sensory information and misjudging task volatility. Yet, these substrates have never been jointly addressed under one computational framework and it is not clear to what degree they reflect trait-like computational patterns. MethodsWe introduced a novel hierarchical Bayesian model that describes how individuals simultaneously update their beliefs about the task volatility and noise in observation. We applied this model to data from a modified Predictive inference task in a test-retest study with healthy volunteers (N=45, 4 sessions) and examined the relationship between model parameters and schizotypal traits in a larger online sample (N = 437) and in a cohort of patients with schizophrenia (N = 100). ResultsThe interclass correlations were moderate to high for model parameters and excellent for averaged belief trajectories and precision-weighted learning rates estimated through hierarchical Bayesian inference. We found that uncertainty about the task volatility was related to schizotypal traits and to positive symptoms in patients, when learning to gain rewards. In contrast, negative symptoms in patients were associated with more rigid beliefs about observational noise, when learning to avoid losses. ConclusionThese findings suggest that individuals with schizotypal traits across the psychosis continuum are less likely to learn or utilize higher-order statistical regularities of the environment and showcase the potential of clinically relevant computational phenotypes for differentiating symptom groups in a transdiagnostic manner.

Inferring the spin distribution of binary black holes using deep learning

The spin characteristics of black holes offer valuable insights into the evolutionary pathways of their progenitor stars. This is crucial for understanding the broader population properties of black holes. Traditional hierarchical Bayesian inference techniques employed to discern these properties often demand substantial time, and consensus regarding the spin distribution of binary black hole (BBH) systems remains elusive. In this study, leveraging observations from GWTC-3, we adopted a machine learning approach to infer the spin distribution of black holes within BBH systems. Specifically, we developed a deep neural network (DNN) and trained it using data generated from a Beta distribution. Our training strategy, involving the segregation of data into 10 bins, not only expedites model training but also enhances the versatility and adaptability of the DNN to accommodate the growing volume of gravitational wave observations. Utilizing Monte Carlo-bootstrap (MC-bootstrap) to generate observation-simulated samples, we derived spin distribution parameters: for the larger BH sample and for the smaller BH sample. Within our constraints, the distributions of component spin magnitudes suggest the likelihood of both black holes in the BBH merger possessing non-zero spin.

Physical Side-Channel Attacks against Intermittent Devices

Intermittent (batteryless) devices operate solely using energy harvested from their environment. These devices turn on when they have energy and turn off during energy scarcity. Intermittent devices have recently become increasingly popular in smart buildings, manufacturing plants, and medical implantables as they eliminate the need for battery replacement and enable green computing. Despite their growing adoption in critical applications, the privacy implications of intermittent devices remain largely unexplored. In this paper, we introduce a novel remote side-channel attack. Our observation is that the network packet frequency of an intermittent device can be exploited to learn its turn-on/off patterns. From these patterns, we can infer the energy availability of a device, which reveals privacy-sensitive information about its operating environment, e.g., the presence or absence of individuals. To realize our attack, we develop a three-stage hierarchical inference framework that leverages the timestamped network packet sequence of intermittent devices. Our framework automatically extracts a set of temporal features from inter-packet-arrival timings. It then employs a series of models to uncover (1) whether a target intermittent device is present in the environment, (2) its energy harvester type (e.g., vibration or water flow), and (3) its energy availability conditions (e.g., high-vibration or no-vibration). To validate our attack effectiveness, we conduct experiments in two environments: a smart home and a miniature manufacturing plant equipped with three intermittent devices powered by solar energy, vibration, and temperature. By analyzing their energy availability patterns, we are able to infer user activities and presence in the smart home and the robot’s movement patterns in the manufacturing plant with an average accuracy of 85%. This sensitive information enables an adversary to launch domain-specific attacks, such as burglarizing a smart home when the user is asleep or timely tampering with plant sensors to cause maximum damage.

Hierarchical segmentation of surgical scenes in laparoscopy.

Segmentation of surgical scenes may provide valuable information for real-time guidance and post-operative analysis. However, in some surgical video frames there is unavoidable ambiguity, leading to incorrect predictions of class or missed detections. In this work, we propose a novel method that alleviates this problem by introducing a hierarchy and associated hierarchical inference scheme that allows broad anatomical structures to be predicted when fine-grained structures cannot be reliably distinguished. First, we formulate a multi-label segmentation loss informed by a hierarchy of anatomical classes and then train a network using this. Subsequently, we use a novel leaf-to-root inference scheme ("Hiera-Mix") to determine the trade-off between label confidence and granularity. This method can be applied to any segmentation model. We evaluate our method using a large laparoscopic cholecystectomy dataset with 65,000 labelled frames. We observed an increase in per-structure detection F1 score for the critical structures, when evaluated across their sub-hierarchies, compared to the baseline method: 6.0% for the cystic artery and 2.9% for the cystic duct, driven primarily by increases in precision of 11.3% and 4.7%, respectively. This corresponded to visibly improved segmentation outputs, with better characterisation of the undissected area containing the critical structures and fewer inter-class confusions. For other anatomical classes, which did not stand to benefit from the hierarchy, performance was unimpaired. Our proposed hierarchical approach improves surgical scene segmentation in frames with ambiguity, by more suitably reflecting the model's parsing of the scene. This may be beneficial in applications of surgical scene segmentation, including recent advancements towards computer-assisted intra-operative guidance.

Mathematical modelling, selection and hierarchical inference to determine the minimal dose in IFNα therapy against myeloproliferative neoplasms.

Myeloproliferative neoplasms (MPN) are blood cancers that appear after acquiring a driver mutation in a hematopoietic stem cell. These hematological malignancies result in the overproduction of mature blood cells and, if not treated, induce a risk of cardiovascular events and thrombosis. Pegylated IFN$\alpha $ is commonly used to treat MPN, but no clear guidelines exist concerning the dose prescribed to patients. We applied a model selection procedure and ran a hierarchical Bayesian inference method to decipher how dose variations impact the response to the therapy. We inferred that IFN$\alpha $ acts on mutated stem cells by inducing their differentiation into progenitor cells; the higher the dose, the higher the effect. We found that the treatment can induce long-term remission when a sufficient (patient-dependent) dose is reached. We determined this minimal dose for individuals in a cohort of patients and estimated the most suitable starting dose to give to a new patient to increase the chances of being cured.

Estimation of boreal forest biomass from ICESat-2 data using hierarchical hybrid inference

The ICESat-2, launched in 2018, carries the ATLAS instrument, which is a photon-counting spaceborne lidar that provides profile samples over the terrain. While primarily designed for snow and ice monitoring, there has been a great interest in using ICESat-2 to predict forest above-ground biomass density (AGBD). As ICESat-2 is on a polar orbit, it provides good spatial coverage of boreal forests.The aim of this study is to evaluate the estimation of mean AGBD from ICESat-2 data using a hierarchical modeling approach combined with rigorous statistical inference. We propose a hierarchical hybrid inference approach for uncertainty quantification of the average AGBD of the area of interest estimated directly from a sample of ICESat-2 lidar profiles. Our approach models the errors coming from the multiple modeling steps, including the allometric models used for predicting tree-level AGB. For testing the procedure, we have data from two adjacent study sites, denoted Valtimo and Nurmes, of which Valtimo site is used for model training and Nurmes for validation.The ICESat-2 estimated mean AGBD in the Nurmes validation area was 65.7 ± 1.9 Mg/ha (relative standard error of 2.9%). The local reference hierarchical model-based estimate obtained from wall-to-wall airborne lidar data was 63.9 ± 0.6 Mg/ha (relative standard error of 1.0%). The reference estimate was within the 95% confidence interval of the ICESat-2 hierarchical hybrid estimate. The small standard errors indicate that the proposed method is useful for AGBD assessment. However, some sources of error were not accounted for in the study and thus the real uncertainties are probably slightly larger than those reported.

Hierarchical fuzzy inference based on Bandler-Kohout subproduct

Fuzzy inference with the Bandler-Kohout subproduct (BKS) has been successfully applied in many fields such as fuzzy control, artificial intelligence, image processing, data mining, decision-making, prediction, classification and so on. However, one has to face with the rule explosion in these applications. To deal with this problem, hierarchical fuzzy systems with the compositional rule of inference (CRI) method have been constructed by a series of low-dimensional sub fuzzy systems. And it has been proved that hierarchical fuzzy inference method can efficiently restrain the explosion of fuzzy rules. Therefore, in order to increase the computational efficiency of the fuzzy inference based on the BKS when multi-input-single-output (MISO) fuzzy rules are involved, this paper mainly constructs two hierarchical fuzzy inference methods based on the BKS in which the if-then rules are respectively interpreted by fuzzy implications and ML-implications. Moreover, the validity of the two BKS hierarchical fuzzy inferences is studied with the GMP rules. Finally, two examples are employed to illustrate the computational efficiency of our proposed BKS hierarchical inference methods.

Pain perception as hierarchical Bayesian inference: A test case for the theory of constructed emotion.

An intriguing perspective about human emotion, the theory of constructed emotion considers emotions as generative models according to the Bayesian brain hypothesis. This theory brings fresh insight to existing findings, but its complexity renders it challenging to test experimentally. We argue that laboratory studies of pain could support the theory because although some may not consider pain to be a genuine emotion, the theory must at minimum be able to explain pain perception and its dysfunction in pathology. We review emerging evidence that bear on this question. We cover behavioral and neural laboratory findings, computational models, placebo hyperalgesia, and chronic pain. We conclude that there is substantial evidence for a predictive processing account of painful experience, paving the way for a better understanding of neuronal and computational mechanisms of other emotions.

Belief inference for hierarchical hidden states in spatial navigation

Uncertainty abounds in the real world, and in environments with multiple layers of unobservable hidden states, decision-making requires resolving uncertainties based on mutual inference. Focusing on a spatial navigation problem, we develop a Tiger maze task that involved simultaneously inferring the local hidden state and the global hidden state from probabilistically uncertain observation. We adopt a Bayesian computational approach by proposing a hierarchical inference model. Applying this to human task behaviour, alongside functional magnetic resonance brain imaging, allows us to separate the neural correlates associated with reinforcement and reassessment of belief in hidden states. The imaging results also suggest that different layers of uncertainty differentially involve the basal ganglia and dorsomedial prefrontal cortex, and that the regions responsible are organised along the rostral axis of these areas according to the type of inference and the level of abstraction of the hidden state, i.e. higher-order state inference involves more anterior parts.

Cosmology with Galaxy Photometry Alone

We present the first cosmological constraints using only the observed photometry of galaxies. Villaescusa-Navarro et al. recently demonstrated that the internal physical properties of a single simulated galaxy contain a significant amount of cosmological information. These physical properties, however, cannot be directly measured from observations. In this work, we present how we can go beyond theoretical demonstrations to infer cosmological constraints from actual galaxy observables (e.g., optical photometry) using neural density estimation and the CAMELS suite of hydrodynamical simulations. We find that the cosmological information in the photometry of a single galaxy is limited. However, we combine the constraining power of photometry from many galaxies using hierarchical population inference and place significant cosmological constraints. With the observed photometry of ∼20,000 NASA-Sloan Atlas galaxies, we constrain Ωm=0.323−0.095+0.075 and σ8=0.799−0.085+0.088 .

Eccentricity-induced systematic error on parametrized tests of general relativity: Hierarchical Bayesian inference applied to a binary black hole population

Eccentricity-induced systematic error on parametrized tests of general relativity: Hierarchical Bayesian inference applied to a binary black hole population

A comprehensive multi-fidelity surrogate framework based on Gaussian process for datasets with heterogeneous responses

In recent decades, the multi-fidelity (MF) surrogate framework has seen widespread application across various scenarios. This framework significantly enhances the efficiency of surrogate modeling by integrating data of varying fidelity levels. However, research on the MF surrogate has predominantly focused on regression settings, aiming at approximating continuous responses, with limited attention to classification problems involving discrete responses. Moreover, no existing studies have addressed a heterogeneous MF dataset, where the data types (continuous or discrete) vary between different fidelities. This paper introduces a comprehensive MF surrogate framework based on Gaussian process, designed to handle a wide range of MF dataset types. Our framework employs a hierarchical Kriging scheme and Bayesian inference, adaptable to any MF dataset type. Given the challenges posed by discrete data in analytical inference, we incorporate the Laplace approximation for the latent function associated with discrete data in our framework. Additionally, we introduce a local scaling factor specifically for low-correlation classification problems in MF settings. The superiority of our method over conventional ones is demonstrated through both synthetic and engineering examples. Notably, in an engineering example featuring a heterogeneous MF dataset, our proposed MF surrogate model achieves an error reduction exceeding 50%.

A novel method for post-earthquake functional evaluation of city building portfolios

Enhancing the seismic resilience of city building portfolios is crucial to mitigating the impact of seismic disasters. A novel method is proposed to evaluate the post-earthquake functionality of city building portfolios, which can serve as the foundation for assessing the seismic resilience of cities. This method incorporates multiple dimensions of functional evaluation, ranging from structural and nonstructural components to city building portfolios, elucidating the mechanism of functional assemblies from lower to higher dimensions. The calculation of the physical functionality of individual buildings relies on the functionalities of their structural and nonstructural components, which are determined using the functional mapping method. The impacts of infrastructure failures on the functionality of individual buildings are explored using the hierarchical belief rule base inference method based on the evidential reasoning algorithm (BRBI-ER). A technique that combines Point of Interest analysis and visual interpretation is utilized to classify building portfolios into three types: single-function building portfolios, multi-function building portfolios, and integrated-function building portfolios. A cumulative functional correlation model and an integrated functional correlation model using BRBI-ER are established to evaluate the functionality of these types of building portfolios. The results can contribute to predicting the risk of functional losses before earthquakes, guiding the recovery process after earthquakes, and taking proactive measures to improve the seismic resilience of cities.