Conditional Probability Distribution Research Articles

Condition Monitoring Using a Latent Space of Variational Autoencoder Trained Only on a Healthy Machine.

Machine learning generative models have opened up a new perspective for automated machine diagnostics. These methods improve decision-making by extracting features, classifying, and creating new observations using deep neural networks. Generative modeling aims to determine the joint distribution of input data. This contrasts traditional methods used in diagnostics based on discriminative models and the conditional probability distribution of the target variable at known feature values. In the variational autoencoder (VAE) algorithms trained by the authors, the parameters of diagnostic features are random variables, the distributions of which can be approximated based on data, and the identification of probability distributions is based on variational inference. Variational inference is a tool that deals with difficult statistical problems and is usually faster than classical methods. VAEs can detect anomalies, predict failures, and optimize processes. This paper proposes an unsupervised approach to fault diagnosis using only healthy data with automatic feature extraction from the continuous probabilistic latent subspace of the VAE encoder and reduction in PCA or t-SNE. The solution, verified in the example of simulation data, is a response to a common problem related to the lack or difficulty of obtaining marked data in defected states of devices and mechanical structures.

Ensemble probability distribution of annual runoff for the past 70 years in two main watersheds of China

ABSTRACT Water resources in China, especially in the major basins of the Songhua and Yangtze Rivers, are characterized by uneven distribution both temporally and spatially, leading to notable challenges in per capita water availability. In this study, we investigate the ensemble probability distribution of annual runoff over the past 70 years in two of China's major watersheds: the Songhua River and the Yangtze River. By dividing each basin into several regions from upstream to downstream, based on annual mean discharge as a proxy for annual runoff, we observed a significant correlation between the annual runoff of the control sections and that of the upstream and downstream regions in these large watersheds. Consequently, this study establishes the probability distribution of annual runoff for each region within the basins, anchored on the design annual runoff of the control sections, using the joint bivariate logarithmic normal distribution of two interrelated random variables. Furthermore, we developed a relationship between the conditional probability distribution and correlation diagram data, and a regression equation correlating regional annual runoff with the watershed control section's runoff. This investigation into the historical patterns of runoff over the past 70 years provides a comprehensive understanding of the dynamics in these critical watersheds.

Statistical evaluation of road traffic noise in complex sound environment by using fuzzy inference

In order to evaluate road traffic noise in a sound environment, it is necessary to predict the sound levels at evaluation points based on the observations at a reference point. In actual sound environment, road traffic noise shows various types of probability distribution of non-Gaussian distribution and nonstationary property. Furthermore, there potentially exist various nonlinear correlations in addition to the linear correlation between the sound levels at evaluation and reference points. Consequently, the relationship between both points cannot be represented by a simple linear model based on only the linear correlation and lower order statistics. In this study, a complex sound environment difficult to analyze by using usual structural method is considered. By introducing a nonlinear model based on conditional probability distribution with various correlations between the sound levels, and applying fuzzy inference, an evaluation method for road traffic noise is theoretically proposed in a suitable form for the complex sound environment with nonlinear, non-Gaussian and nonstationary properties. The effectiveness of the proposed method is experimentally confirmed by applying it to the observed road traffic noise data in a complex sound environment.

Evaluating the variance of individual halo properties in constrained cosmological simulations

ABSTRACT Constrained cosmological simulations play an important role in modelling the local Universe, enabling investigation of the dark matter content of local structures and their formation. We introduce an internal method for quantifying the extent to which the variance of individual halo properties is suppressed by the constraints imposed on the initial conditions. We apply it to the Constrained Simulations in BORG (CSiBORG) suite of 101 high-resolution realizations across the posterior probability distribution of initial conditions from the Bayesian Origin Reconstruction from Galaxies (BORG) algorithm. The method is based on the overlap of the initial Lagrangian patch of a halo in one simulation with those in another, measuring the degree to which the haloes’ particles are initially coincident. This addresses the extent to which the imposed large-scale structure constraints reduce the variance of individual halo properties. We find consistent reconstructions of $M\gtrsim 10^{14}~\mathrm{M}_\odot \, h^{-1}$ haloes, indicating that the constraints from the BORG algorithm are sufficient to pin down the masses, positions, and peculiar velocities of clusters to high precision, though we do not assess how well they reproduce observations of the local Universe. The effect of the constraints tapers off towards lower mass, and the halo spins and concentrations are largely unconstrained at all masses. We document the advantages of evaluating halo consistency in the initial conditions and describe how the method may be used to quantify our knowledge of the halo field given galaxy survey data analysed through the lens of probabilistic inference machines such as BORG.

Joint Short-term Power Forecasting of Hydro-Wind-Photovoltaic Considering Spatiotemporal Delay of Weather Processes

Regional integrated energy systems (RIES) represented by hydro, wind, and solar energy are crucial avenues for future clean energy development, fully leveraging their complementarity can facilitate the orderly supply of renewable energy, significantly enhance the level of new energy consumption, and make outstanding contributions to achieving carbon neutrality goals. However, run-of-river hydropower (RHP), wind power (WP), and photovoltaic (PV) are affected by the chaotic characteristics of the weather system, with significant random fluctuations, and their output characteristics have significant heterogeneity, which brings a big challenge for the complementary coordinated scheduling. The high-accuracy power prediction of RHP, WP, and PV in the region is one of the key means for solving the above problems. To meet this challenge, by analyzing the spatio-temporal correlation properties between weather processes and station output, a novel joint prediction framework for short-term power forecasting (STPF) of regional hydro-wind-PV clusters is proposed. Firstly, to solve the problem of significant heterogeneity of water, wind, and solar, a Differentiated Spatio-Temporal Mixture Network (DSTMN) is proposed, which differentially encodes the weather and power information at multiple locations, enabling the extraction of common features while preserving their specificities, which addresses the difficulty of representing the inherent correlation patterns between wide-area meteorological information and heterogeneous energy sources. Secondly, to further explore the spatio-temporal correlation between meteorological information and power information, to improve the forecasting performance of the model, a spatio-temporal-lagged correlation (STLC) that can quantify their spatio-temporal delays is proposed. By analyzing the correlation characteristics between regional grid numerical weather prediction (NWP) information and station output at different spatial and temporal scales, the optimal spatial location and delay time of NWP inputs under the current scenario are determined for each station. Based on this, the best NWP scene probabilistic transfer model is established based on the Rank Bayesian Ensemble (RBE) method. By fitting the conditional probability distribution of the current best NWP spatiotemporal location and the 2nd day’s best NWP spatiotemporal location, providing a reliable input for the STPF model. Finally, a case study with 164 hydro-wind-solar stations in China demonstrates the effectiveness of the proposed method. Specifically, we achieved an accuracy improvement of 0.46% — 11.03% on the 2nd day of forecasting compared to benchmark methods.

The Inherent Normativity of Concepts

Concept normativity is a prominent subject of inquiry in the philosophical literature on the nature of concepts. Concepts are said to be normative, in that the use of concepts to categorise is associated with an evaluation of the appropriateness of such categorisation measured against some objective external standard. Two broad groups of views have emerged in accounting for the normativity of concepts: a weaker view traces such normativity to the social practice in which the agent using the concept is embedded, while a stronger view traces such normativity to a first-person capacity of reflection. However, both views have drawbacks: the weaker view seems not to do justice to the basic sense of normativity associated with an individual agent using a concept, while the stronger view ties such normativity with the first-person conscious evaluation, which appears to be too strong. Here, we propose a different view of concepts using principles from the Active Inference framework. We reconceive concepts, defining them as Bayesian beliefs—that is, conditional probability distributions—that represent causes and contingencies in the world, their form grounded in the exchange between the agent and its environment. This allows us to present a different view on the source of normativity, with an emphasis on the structure of the agent itself as well as its interaction with the environment. On the Active Inference view, concepts are normative in that they are intrinsically connected to the self-evidencing nature of an agent, whose very structure implies an evaluation of the concepts it employs.

Guest Editorial: What Engineers Should Know About the Expanding Generative AI Toolkit

Generative artificial intelligence (AI) is the art of creating new things inspired by the old. To understand what generative AI does, ask yourself what you would do if you wanted to create a new hit song. You wouldn't want to start from scratch. Instead, you'd listen to 100 popular songs, analyze the rhythms, melodies, and chord progressions. You would learn how these elements are structured and combined. Then, with this knowledge you would use your creativity to mix and match them in new and exciting ways—resulting in a fresh, original song that may be the next big hit. That's essentially what generative AI does. It devours massive amounts of training data, whether it's music, images, text, or scientific data. It learns the underlying patterns and relationships within that data. Then, it uses this knowledge to generate entirely new content that shares characteristics with the training data, but with a unique twist. Generative AI operates like a master mimic, following a three-step process to create entirely new content. 1. Find the building blocks. As mentioned, generative AI begins by analyzing vast amounts of training data. The goal is to identify the underlying building blocks and structures that define the data. For example, different rooms in a house contain different objects—kitchens have different items than bedrooms. Think of it like understanding the grammar of a language or the architectural styles that make up different cityscapes. For example, generative AI trained on cat images would learn to recognize distinct features like ears, whiskers, and fur patterns. 2. Decipher the unwritten rules. Next, it calculates the conditional probability distribution of these structures. In other words, it finds the order and relationship between various structures and the building blocks. Imagine that kitchen again. We know that knives are more likely to be found near cutting boards than, say, pillows, and that a sofa is typically found in front of a TV in the living room. Generative AI quantifies such relationships which allows it to then understand the underlying rules of how likely certain elements are to co-occur and in what order. 3. Perform a bold and creative remix. Finally, armed with this knowledge of building blocks and the rules of their order and structure, generative AI can create entirely new samples. It combines the learned structures and their conditional probabilities in novel ways, producing something entirely new yet rooted in the representations extracted from the training data. This could be a photorealistic image of a cat with unique markings, a catchy song inspired by popular hits, or even a compelling scientific hypothesis based on existing research.

Assessment of dynamic hydrological drought risk from a non‐stationary perspective

AbstractThe stationarity hypothesis of hydrometeorological elements has been questioned in the context of global warming and intense human disturbance. The conventional drought index and methods of frequency analysis may no longer be applicable for hydrological drought risk evaluation under a changing environment. In this study, a new dynamic hydrological drought risk evaluation framework is proposed for application to the Hanjiang River basin (HRB), which simultaneously considers the non‐stationarity in the construction of drought index as well as in the frequency analysis. First, a non‐stationary standardized runoff index (NSRI) is developed using a generalized additive model for location, scale and shape (GAMLSS) framework. Then, hydrological drought characteristics including duration and severity are identified, and their marginal distributions are established. Finally, based on the dynamic copula, considering the non‐stationarity of the dependence structure, the dynamic joint probability distribution, conditional probability distribution and return period of the bivariate hydrological drought properties are analysed. Results showed that NSRI, which integrates the impacts of climate change and anthropogenic activities on the non‐stationarity of runoff series, had a better ability to capture runoff extremes than had SRI. In addition, it is indispensable to consider the non‐stationarity of the dependence structure between variables when discussing the multivariate joint risk of hydrological drought. The risk of hydrological drought in the study area has shown an increasing trend in the past 65 years, and the drought conditions from upstream to downstream have been alleviated first and then intensified. This study provides valuable information for regional drought risk estimation and water resources management from a non‐stationary perspective.

Assessing Multi-Scale Atmospheric Circulation Patterns for Improvements in Sub-Seasonal Precipitation Predictability in the Northern Great Plains

This study leverages the relationships between the Great Plains low-level jet (GP-LLJ) and the circumglobal teleconnection (CGT) to assess the enhancement of 30-day rainfall forecast in the Northern Great Plains (NGP). The assessment of 30-day simulated precipitation using the Climate Forecast System (CFS) is contrasted with the North American Regional Reanalysis, searching for sources of precipitation predictability associated with extended wet and drought events. We analyze the 30-day sources of precipitation predictability using (1) the characterization of dominant statistical modes of variability of 900 mb winds associated with the GP-LLJ, (2) the large-scale atmospheric patterns based on 200 mb geopotential height (HGT), and (3) the use of GP-LLJ and CGT conditional probability distributions using a continuous correlation threshold approach to identify when and where the forecast of NGP precipitation occurs. Two factors contributing to the predictability of precipitation in the NGP are documented. We found that the association between GP-LLJ and CGT occurs at two different scales—the interdiurnal and the sub-seasonal, respectively. The CFS reforecast suggests that the ability to forecast sub-seasonal precipitation improves in response to the enhanced simulation of the GP-LLJ and CGT. Using these modes of climate variability could improve predictive frameworks for water resources management, governance, and water supply for agriculture.

Stochastic filtering of reaction networks partially observed in time snapshots

Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state space. We consider the problem of estimating the conditional probability distribution of a stochastic reaction network given exact partial state observations in time snapshots. We propose a particle filtering method called the targeting method. Our approach takes into account that the reaction counts in between two observation snapshots satisfy linear constraints and also uses inhomogeneous Poisson processes as proposals for the reaction counts to facilitate exact interpolation. We provide rigorous analysis as well as numerical examples to illustrate our method and compare it with other alternatives.

LJCD-Net: Cross-Domain Jamming Generalization Diagnostic Network Based on Deep Adversarial Transfer.

Global Navigation Satellite Systems (GNSS) offer comprehensive position, navigation, and timing (PNT) estimates worldwide. Given the growing demand for reliable location awareness in both indoor and outdoor contexts, the advent of fifth-generation mobile communication technology (5G) has enabled expansive coverage and precise positioning services. However, the power received by the signal of interest (SOI) at terminals is notably low. This can lead to significant jamming, whether intentional or unintentional, which can adversely affect positioning receivers. The diagnosis of jamming types, such as classification, assists receivers in spectrum sensing and choosing effective mitigation strategies. Traditional jamming diagnosis methodologies predominantly depend on the expertise of classification experts, often demonstrating a lack of adaptability for diverse tasks. Recently, researchers have begun utilizing convolutional neural networks to re-conceptualize a jamming diagnosis as an image classification issue, thereby augmenting recognition performance. However, in real-world scenarios, the assumptions of independent and homogeneous distributions are frequently violated. This discrepancy between the source and target distributions frequently leads to subpar model performance on the test set or an inability to procure usable evaluation samples during training. In this paper, we introduce LJCD-Net, a deep adversarial migration-based cross-domain jamming generalization diagnostic network. LJCD-Net capitalizes on a fully labeled source domain and multiple unlabeled auxiliary domains to generate shared feature representations with generalization capabilities. Initially, our paper proposes an uncertainty-guided auxiliary domain labeling weighting strategy, which estimates the multi-domain sample uncertainty to re-weight the classification loss and specify the gradient optimization direction. Subsequently, from a probabilistic distribution standpoint, the spatial constraint imposed on the cross-domain global jamming time-frequency feature distribution facilitates the optimization of collaborative objectives. These objectives include minimizing both the source domain classification loss and auxiliary domain classification loss, as well as optimizing the inter-domain marginal probability and conditional probability distribution. Experimental results demonstrate that LJCD-Net enhances the recognition accuracy and confidence compared to five other diagnostic methods.

Reliability analysis of diesel engine cooling system based on improved Bayesian network

For the benefit of solving the problem of absoluteness of conditional probability distribution and difficulty in obtaining basic event probability in Bayesian networks, this paper studies the reliability of diesel engine cooling systems through leakage noise or gate intuitionistic fuzzy Bayesian network. Firstly, the leakage noise or gate is introduced into the intuitionistic fuzzy Bayesian network, which makes the results more realistic. Secondly, prior probability in the Bayesian network is obtained based on the similarity aggregation method of triangular intuitionistic fuzzy numbers. The results show that the introduction of leakage noise or gate, intuitionistic fuzzy set, and Bayesian network can solve the problem that the probability of basic events in a Bayesian network is difficult to obtain. The conditional probability table corrected by leakage noise or gate is more realistic and greatly reduces the workload. It is determined that the two weakest components of the cooling system are the thermostat and the water pump. The results show that the way in this paper can provide support for the reliability analysis of the complex system.

On the extreme wall shear stress events in a turbulent pipe flow

This study investigates the extreme wall shear stress events in a turbulent pipe flow by direct numerical simulation at a frictional Reynolds number Reτ≈500. A two-step conditional averaging scheme is implemented to identify the locations of extreme events and construct their spatial structures. Combined with the joint probability density functions of shear stresses, further evidence is provided for the argument that extreme positive events occur below an intense sweep event (Q4), and the formation of the backflow events is predominantly aided by an identifiable oblique vortex. Moreover, the conditional probability distribution of shear stress for varying thresholds used to define extreme events reveals that, when the threshold is above or below the mean, the probability distributions of the extreme positive events or the backflow events generally follow an exponential relationship, suggesting the extreme wall shear stress events are a threshold-independent process. Finally, the conditional space–time proper orthogonal decomposition is performed to extract the dominant modes and characterize the evolution of the extreme events from inception to dissipation, which exhibits morphological features of real flow structures. It is found that the observation of uθ modes can provide a basic representation of the entire variation process and the extreme values return to normal levels in a very short time.

Multi-Source and Multi-modal Deep Network Embedding for Cross-Network Node Classification

In recent years, to address the issue of networked data sparsity in node classification tasks, cross-network node classification (CNNC) leverages the richer information from a source network to enhance the performance of node classification in the target network, which typically has sparser information. However, in real-world applications, labeled nodes may be collected from multiple sources with multiple modalities (e.g., text, vision, and video). Naive application of single-source and single-modal CNNC methods may result in sub-optimal solutions. To this end, in this article, we propose a model called Multi-source and Multi-modal Cross-network Deep Network Embedding (M 2 CDNE) for cross-network node classification. In M 2 CDNE, we propose a deep multi-modal network embedding approach that combines the extracted deep multi-modal features to make the node vector representations network invariant. In addition, we apply dynamic adversarial adaptation to assess the significance of marginal and conditional probability distributions between each source and target network to make node vector representations label discriminative. Furthermore, we devise to classify nodes in the target network through the related source classifier and aggregate different predictions utilizing respective network weights, corresponding to the discrepancy between each source and target network. Extensive experiments performed on real-world datasets demonstrate that the proposed M 2 CDNE significantly outperforms the state-of-the-art approaches.

Maximum Likelihood Deconvolution of Beamforming Images with Signal-Dependent Speckle Fluctuations

Ocean Acoustic Waveguide Remote Sensing (OAWRS) typically utilizes large-aperture linear arrays combined with coherent beamforming to estimate the spatial distribution of acoustic scattering echoes. The conventional maximum likelihood deconvolution (DCV) method uses a likelihood model that is inaccurate in the presence of multiple adjacent targets with significant intensity differences. In this study, we propose a deconvolution algorithm based on a modified likelihood model of beamformed intensities (M-DCV) for estimation of the spatial intensity distribution. The simulated annealing iterative scheme is used to obtain the maximum likelihood estimation. An approximate expression based on the generalized negative binomial (GNB) distribution is introduced to calculate the conditional probability distribution of the beamformed intensity. The deconvolution algorithm is further simplified with an approximate likelihood model (AM-DCV) that can reduce the computational complexity for each iteration. We employ a direct deconvolution method based on the Fourier transform to enhance the initial solution, thereby reducing the number of iterations required for convergence. The M-DCV and AM-DCV algorithms are validated using synthetic and experimental data, demonstrating a maximum improvement of 73% in angular resolution and a sidelobe suppression of 15 dB. Experimental examples demonstrate that the imaging performance of the deconvolution algorithm based on a linear small-aperture array consisting of 16 array elements is comparable to that obtained through conventional beamforming using a linear large-aperture array consisting of 96 array elements. The proposed algorithm is applicable for Ocean Acoustic Waveguide Remote Sensing (OAWRS) and other sensing applications using linear arrays.

Predicting conditional probability distributions of redshifts of Active Galactic Nuclei using Hierarchical Correlation Reconstruction

ABSTRACT The Large Area Telescope (LAT) onboard the Fermi gamma-ray observatory continuously scans the sky in an energy range from 50 MeV to 1 TeV. The telescope has identified over 6000 gamma-ray emitting sources, approximately half of which are classified as active galactic nuclei (AGN). However, not all of these gamma-ray sources have known redshift values for the reason that redshift estimation following traditional methods can be an expensive, challenging task. Alternatively, as an effort to robustly predict the AGN redshift values, many researchers have recently turned to machine learning methods. However, while the focus has primarily been on predicting specific values, real-world data often allows us only to predict conditional probability distributions, constrained by conditional entropy [H(Y|X)]. In our study, we employ the Hierarchical Correlation Reconstruction approach to inexpensively predict complex conditional probability distributions, including multimodal ones. This is achieved through independent Mean Squared Error estimation of multiple moment-like parameters, combined into reconstruction of the conditional distribution. By employing linear regression for this purpose, we can develop interpretable models where coefficients describe the contributions of features to conditional moments. This article extends the original approach by incorporating Canonical Correlation Analysis for feature optimization and l1 ‘lasso’ regularization. Our primary focus is on the practical problem of predicting the redshift of AGN using data from the Fourth Fermi-LAT Data Release 3 (4LAC-DR3) data set.

Distilling dynamical knowledge from stochastic reaction networks

Stochastic reaction networks are widely used in the modeling of stochastic systems across diverse domains such as biology, chemistry, physics, and ecology. However, the comprehension of the dynamic behaviors inherent in stochastic reaction networks is a formidable undertaking, primarily due to the exponential growth in the number of possible states or trajectories as the state space dimension increases. In this study, we introduce a knowledge distillation method based on reinforcement learning principles, aimed at compressing the dynamical knowledge encoded in stochastic reaction networks into a singular neural network construct. The trained neural network possesses the capability to accurately predict the state conditional joint probability distribution that corresponds to the given query contexts, when prompted with rate parameters, initial conditions, and time values. This obviates the need to track the dynamical process, enabling the direct estimation of normalized state and trajectory probabilities, without necessitating the integration over the complete state space. By applying our method to representative examples, we have observed a high degree of accuracy in both multimodal and high-dimensional systems. Additionally, the trained neural network can serve as a foundational model for developing efficient algorithms for parameter inference and trajectory ensemble generation. These results collectively underscore the efficacy of our approach as a universal means of distilling knowledge from stochastic reaction networks. Importantly, our methodology also spotlights the potential utility in harnessing a singular, pretrained, large-scale model to encapsulate the solution space underpinning a wide spectrum of stochastic dynamical systems.

Prediction for underground seismic intensity measures using conditional generative adversarial networks

With the escalating development and utilization of subterranean spaces, the seismic hazards faced by underground structures are progressively increasing. However, owing to the challenges associated with acquiring underground seismic data and historical seismic design norms, pertinent regulations and research in this domain are scarce. This study focused on three crucial intensity measures in the seismic design process of underground structures peak ground acceleration (PGA), peak ground velocity (PGV), and peak ground displacement (PGD). The research leverages seismic data obtained from the California Strong Motion Instrumentation Program (CSMIP) to train and evaluate a conditional generative adversarial network (CGAN) model. This model was employed to establish a multivariate joint conditional probability distribution among the intensity measures at varying depths, facilitating the stochastic prediction of shallow intensity measures. In contrast to empirical formulas, the CGAN model eliminates the need for a predefined equation structure and enables the simultaneous prediction of multiple intensity measures. The performance of the model was evaluated by comparing the predictive accuracy of the CGAN model and empirical fitting formulas across diverse site conditions and depth intervals using metrics such as relative error coefficients. It can be concluded that the proposed CGAN model can accurately predict shallow seismic intensity measures, and the predictions conform to a specific conditional distribution while retaining the stochastic nature of seismic motion. Compared with empirical formula models, the CGAN model exhibited an enhanced predictive capability.

Modeling of Soil Water Distribution in a Small Mid-Latitude Watershed on the British Isle for Short Term Landslide and Flood Risk Assessment

The R-TopModel hydrological model coupled with two landslide and flood probability distribution models was applied to simulate the daily hydrological conditions of a small catchment in the Midlands of the British Isles, throughout 2017. Originally, the methodology was applied to a risk area in the tropical region. In this work, the application was extended to mid-latitude watersheds. The hydrographic basin around the Carsington Water dam (located in the Midlands of the Great Britain) is chosen because it presents risks. The model Nash-Sutcliffe Efficiency for the upstream discharge from the Carsington Water dam reached 50% with a correlation coefficient of the order of 70%, an acceptable value considering the seasonal effects of the dam on evapotranspiration and higher soil permeability. Modeling the distribution of soil moisture and excess surface water allowed obtaining the spatial distribution of the maximum conditional probability of landslides and floods in the Carsington Water catchment. These probability maps obtained are consistent with long-term susceptibility maps for Great Britain.

Statistical modelling of determinants of child stunting using secondary data and Bayesian networks: a UKRI Global Challenges Research Fund (GCRF) Action Against Stunting Hub protocol paper

IntroductionSeveral factors have been implicated in child stunting, but the precise determinants, mechanisms of action and causal pathways remain poorly understood. The objective of this study is to explore causal...