Set Of Latent Variables Research Articles

Stochastic inversion of geophysical data by a conditional variational autoencoder

Recovering geologically realistic physical property models by geophysical inversion is a long-standing challenge. Generative neural networks offer a promising path to meet this challenge because they can produce spatially complex models that exhibit the characteristics of a set of training models, even when those characteristics are difficult to quantify. In the context of geophysical inversion, these characteristics may include faults, layers, and sharp contacts between rock units. Here, we develop a framework for incorporating prior geologic knowledge into geophysical inversions using conditional variational autoencoders (CVAEs). We train a CVAE to reconstruct training density models while honoring relative gravity data. Once trained, the decoder network of the CVAE inverts gravity data. The inputs to the decoder are observed gravity data and a set of latent variables that are sampled from a standard normal distribution. The decoder maps from the observed data and latent variables to density models such that the resulting models are consistent with the training models and the input data. Consequently, the inversion fits the observed data and incorporates the information embedded in the training models. The decoder can produce many inverted models instantaneously, sampling an approximation to the posterior model distribution efficiently. We find that the latent variables correspond to independent interpretable ways in which the model can vary while still honoring the observed data. We draw a connection to linear inverse theory, positing that the latent variables are analogous to the principal components of the local posterior model covariance.

A Unified Approach to Hierarchical Random Measures

AbstractHierarchical models enjoy great popularity due to their ability to handle heterogeneous groups of observations by leveraging on their underlying common structure. In a Bayesian nonparametric framework, the hierarchy is introduced at the level of group-specific random measures, and then translated to the observations’ level via suitable transformations. In this work, we propose a new strategy to derive closed-form expressions for the marginal and posterior distributions of each group. Indeed, by directly inserting a suitable set of latent variables into the generative model for the data, we unravel a common core shared by the different hierarchical constructions proposed in the Bayesian nonparametric literature. Specifically, we identify a key identity that underlies these models and highlight its role in the derivation of quantities of interest.

A framework of zero-inflated Bayesian negative binomial regression models for spatiotemporal data

Spatiotemporal data analysis with massive zeros is widely used in many areas such as epidemiology and public health. We use a Bayesian framework to fit zero-inflated negative binomial models and employ a set of latent variables from Pólya-Gamma distributions to derive an efficient Gibbs sampler. The proposed model accommodates varying spatial and temporal random effects through Gaussian process priors, which have both the simplicity and flexibility in modeling nonlinear relationships through a covariance function. To conquer the computation bottleneck that GPs may suffer when the sample size is large, we adopt the nearest-neighbor GP approach that approximates the covariance matrix using local experts. For the simulation study, we adopt multiple settings with varying sizes of spatial locations to evaluate the performance of the proposed model such as spatial and temporal random effects estimation and compare the result to other methods. We also apply the proposed model to the COVID-19 death counts in the state of Florida, USA from 3/25/2020 through 7/29/2020 to examine relationships between social vulnerability and COVID-19 deaths.

Human Joint Kinematics Diffusion-Refinement for Stochastic Motion Prediction

Stochastic human motion prediction aims to forecast multiple plausible future motions given a single pose sequence from the past. Most previous works focus on designing elaborate losses to improve the accuracy, while the diversity is typically characterized by randomly sampling a set of latent variables from the latent prior, which is then decoded into possible motions. This joint training of sampling and decoding, however, suffers from posterior collapse as the learned latent variables tend to be ignored by a strong decoder, leading to limited diversity. Alternatively, inspired by the diffusion process in nonequilibrium thermodynamics, we propose MotionDiff, a diffusion probabilistic model to treat the kinematics of human joints as heated particles, which will diffuse from original states to a noise distribution. This process not only offers a natural way to obtain the "whitened'' latents without any trainable parameters, but also introduces a new noise in each diffusion step, both of which facilitate more diverse motions. Human motion prediction is then regarded as the reverse diffusion process that converts the noise distribution into realistic future motions conditioned on the observed sequence. Specifically, MotionDiff consists of two parts: a spatial-temporal transformer-based diffusion network to generate diverse yet plausible motions, and a flexible refinement network to further enable geometric losses and align with the ground truth. Experimental results on two datasets demonstrate that our model yields the competitive performance in terms of both diversity and accuracy.

HONMF: integration analysis of multi-omics microbiome data via matrix factorization and hypergraph.

The accumulation of multi-omics microbiome data provides an unprecedented opportunity to understand the diversity of bacterial, fungal, and viral components from different conditions. The changes in the composition of viruses, bacteria, and fungi communities have been associated with environments and critical illness. However, identifying and dissecting the heterogeneity of microbial samples and cross-kingdom interactions remains challenging. We propose HONMF for the integrative analysis of multi-modal microbiome data, including bacterial, fungal, and viral composition profiles. HONMF enables identification of microbial samples and data visualization, and also facilitates downstream analysis, including feature selection and cross-kingdom association analysis between species. HONMF is an unsupervised method based on hypergraph induced orthogonal non-negative matrix factorization, where it assumes that latent variables are specific for each composition profile and integrates the distinct sets of latent variables through graph fusion strategy, which better tackles the distinct characteristics in bacterial, fungal, and viral microbiome. We implemented HONMF on several multi-omics microbiome datasets from different environments and tissues. The experimental results demonstrate the superior performance of HONMF in data visualization and clustering. HONMF also provides rich biological insights by implementing discriminative microbial feature selection and bacterium-fungus-virus association analysis, which improves our understanding of ecological interactions and microbial pathogenesis. The software and datasets are available at https://github.com/chonghua-1983/HONMF.

Attractor-Like Dynamics Extracted from Human Electrocorticographic Recordings Underlie Computational Principles of Auditory Bistable Perception.

In bistable perception, observers experience alternations between two interpretations of an unchanging stimulus. Neurophysiological studies of bistable perception typically partition neural measurements into stimulus-based epochs and assess neuronal differences between epochs based on subjects' perceptual reports. Computational studies replicate statistical properties of percept durations with modeling principles like competitive attractors or Bayesian inference. However, bridging neuro-behavioral findings with modeling theory requires the analysis of single-trial dynamic data. Here, we propose an algorithm for extracting nonstationary timeseries features from single-trial electrocorticography (ECoG) data. We applied the proposed algorithm to 5-min ECoG recordings from human primary auditory cortex obtained during perceptual alternations in an auditory triplet streaming task (six subjects: four male, two female). We report two ensembles of emergent neuronal features in all trial blocks. One ensemble consists of periodic functions that encode a stereotypical response to the stimulus. The other comprises more transient features and encodes dynamics associated with bistable perception at multiple time scales: minutes (within-trial alternations), seconds (duration of individual percepts), and milliseconds (switches between percepts). Within the second ensemble, we identified a slowly drifting rhythm that correlates with the perceptual states and several oscillators with phase shifts near perceptual switches. Projections of single-trial ECoG data onto these features establish low-dimensional attractor-like geometric structures invariant across subjects and stimulus types. These findings provide supporting neural evidence for computational models with oscillatory-driven attractor-based principles. The feature extraction techniques described here generalize across recording modality and are appropriate when hypothesized low-dimensional dynamics characterize an underlying neural system.SIGNIFICANCE STATEMENT Irrespective of the sensory modality, neurophysiological studies of multistable perception have typically investigated events time-locked to the perceptual switching rather than the time course of the perceptual states per se. Here, we propose an algorithm that extracts neuronal features of bistable auditory perception from largescale single-trial data while remaining agnostic to the subject's perceptual reports. The algorithm captures the dynamics of perception at multiple timescales, minutes (within-trial alternations), seconds (durations of individual percepts), and milliseconds (timing of switches), and distinguishes attributes of neural encoding of the stimulus from those encoding the perceptual states. Finally, our analysis identifies a set of latent variables that exhibit alternating dynamics along a low-dimensional manifold, similar to trajectories in attractor-based models for perceptual bistability.

TRUST XAI: Model-Agnostic Explanations for AI With a Case Study on IIoT Security

Despite artificial intelligence (AI)’s significant growth, its “black box” nature creates challenges in generating adequate trust. Thus, it is seldom utilized as a standalone unit in IoT high-risk applications, such as critical industrial infrastructures, medical systems, financial applications, etc. Explainable AI (XAI) has emerged to help with this problem. However, designing appropriately fast and accurate XAI is still challenging, especially in numerical applications. Here, we propose a universal XAI model, named the transparency relying upon statistical theory (TRUST), which is model-agnostic, high performing, and suitable for numerical applications. Simply put, TRUST XAI models the statistical behavior of the AI’s outputs in an AI-based system. Factor analysis is used to transform the input features into a new set of latent variables. We use mutual information (MI) to rank these variables and pick only the most influential ones on the AI’s outputs and call them “representatives” of the classes. Then, we use multimodal Gaussian (MMG) distributions to determine the likelihood of any new sample belonging to each class. We demonstrate the effectiveness of TRUST in a case study on cybersecurity of the Industrial Internet of Things (IIoT) using three different cybersecurity data sets. As IIoT is a prominent application that deals with numerical data. The results show that TRUST XAI provides explanations for new random samples with an average success rate of 98%. Compared with local interpretable model-agnostic explanations (LIME), a popular XAI model, TRUST is shown to be superior in the context of performance, speed, and the method of explainability. In the end, we also show how TRUST is explained to the user.

Enhanced Dynamic Dual-Latent Variable Model for Multirate Process Monitoring and Its Industrial Application

Quality-related process monitoring is an important tool to ensure process safety and product quality. However, the existence of process dynamics and multirate sampling makes it difficult to construct an efficient monitoring model. In order to handle process dynamics and multirate sampling, a multirate process monitoring method based on a dynamic dual-latent variable model is proposed. The model involves two sets of latent variables modeled as first-order Markov chains, which are used to capture both quality-related and quality-unrelated dynamic information. In addition, to deal with multiple sampling rates in the process data, the proposed model is combined with a multirate Kalman filtering technique. An expectation-maximization (EM) algorithm is used to estimate the unknown parameters, and a fault detection strategy is developed. The higher fault detection rate of the proposed method is verified by two application studies including a real industrial experiment and the Tennessee Eastman (TE) process.

Plantwide control design using latent variables: An integration between control allocation and a measurement combination approach

This paper presents a plantwide control design methodology based on a novel structure which consists of a decentralized strategy complemented by a control allocation (CA) module and a measurement combination (MC) block. Taking into account a principal components analysis (PCA) selection approach, the CA and MC modules perform a dimensional reduction of the original input–output variable space in order to obtain sets of latent variables (or principal components) as control actions and controlled variables. The use of principal components in the controller design provides several interesting features given that: (i) the conditioning of the subsystem to be controlled can be improved, (ii) when performing combinations of variables, the CA and MC modules act as steady-state decouplers and thus an apparently diagonal process is obtained, which favors the reduction of the variables interaction and the pairing problem is automatically solved, and (iii) they allow to naturally handle nonsquare systems. The proposed design procedure is implemented through a multiobjective bilevel mixed-integer nonlinear programming (BMINLP) optimization problem. The leader problem is based on the minimization of three functional costs: 1- the well-known sum of squared deviations (SSD) index, 2- the number of selected manipulated variables (actuators), and 3- the number of selected measurements (sensors). The inner optimization minimizes the relative gain array number (RGAN). This provides a good trade-off between the degree of conditioning/controllability and the complexity/cost of the resulting system. This problem is efficiently solved through genetic algorithms and allows to perform: (i) the selection of the manipulated variables (actuators) and the measurements (sensors) to be used, (ii) the computation of the matrices that characterize the CA and MC modules, and (iii) the stability analysis of the multivariable control structure. The overall design procedure only requires steady-state models of the process. The Tennessee Eastman case study is considered for the simulation and performance evaluation of the proposed solutions.

Integrated Deep-Learning and Physics-Based Models Improve Production Prediction

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 204864, “Integrating Deep-Learning and Physics-Based Models for Improved Production Prediction in Unconventional Reservoirs,” by Syamil M. Razak, SPE, Jodel Cornelio, SPE, and Atefeh Jahandideh, SPE, University of Southern California, et al. The paper has not been peer reviewed. _ The physics of fluid flow and transport processes in hydraulically fractured unconventional reservoirs is not well understood. As a result, predicted production behavior using conventional simulation often does not agree with observed field performance data. The discrepancy is caused by potential errors in the simulation model and the physical processes that take place in complex fractured rocks subjected to hydraulic fracturing. In the complete paper, the authors discuss the development of a deep-learning model to investigate the errors in simulation-based performance prediction in unconventional reservoirs. Introduction One of the major challenges for petroleum engineers working with unconventional reservoirs is a lack of models that accurately represent a physical relationship between the formation, completion and fluid properties, and production responses. Statistical predictive models typically are used to extract sets of input parameters that better represent the properties of the field. However, a major drawback with statistical models is their inability to extrapolate from the training data set. The authors propose a deep-learning predictive model based on a combination of physics and data to account for the errors that may have come from undiscovered physics or imperfect description of unconventional reservoirs. The model leverages the power of deep learning to account for systematic prediction inaccuracies resulting from incomplete knowledge about the reservoir model and the underlying flow processes. Deep neural network models trained with observed production responses and other related data in the field are used to enhance the prediction performance of simulation models with limited knowledge of flow physics in complex, unconventional reservoirs. The data the authors use for their model consist of the following: - Formation, completion, and fluid properties for physics-based reservoir simulation (xsim) - Corresponding simulated production responses (dsim) - Formation, completion, and fluid properties collected from the field (xfield) - Related observed production response data (dfield) The authors define simulation errors (derr) as the difference between dsim and dfield. Each derr is paired with xerr that is the concatenation of the corresponding xsim and xfield. The predictive model integrates a 1D convolutional autoencoder (AE) that extracts temporal trends in the simulation errors as a set of latent variables. These components are used to train deep regression neural networks to represent the complex relationship between the simulation errors and these latent variables.

Where do measures of health, social care and wellbeing fit within a wider measurement framework? Implications for the measurement of quality of life and the identification of bolt-ons

BackgroundThere is variability across studies in the dimensionality i.e., set of latent variables to which health, social care and wellbeing measures relate. This variability may impact the development of new measures and the identification of bolt-on dimensions. We examine the dimensionality of commonly used measures and identify a set of potential bolt-ons for the EQ-5D-5L. MethodsWe used the OMS dataset, an online survey of health, social care and wellbeing measures in patients and members of the general public. A content analysis provided a theoretical framework for results interpretation. Quantitative analyses were based on a pool of 79 items from 7 measures. Confirmatory factor analysis was used to assess health, social care and wellbeing measures dimensionality and their contribution to quality of life. The relationship between EQ-5D-5L items and the identified factors was used for bolt-ons identification. ResultsThe dimensionality comprised of seven factors, namely physical functioning, psychological symptoms, energy/sleep, physical pain, social functioning, needs and satisfaction. Health measures covered five of the seven factors identified, wellbeing measures three and the social care measure one. A list of candidate bolt-on items for the EQ-5D-5L was presented e.g., cognition, energy, dignity. ConclusionsThis study provides evidence on the dimensionality of health, social care and wellbeing measures and presents a list of candidate bolt-ons for the EQ-5D-5L.

Unsupervised probabilistic models for sequential Electronic Health Records

We develop an unsupervised probabilistic model for heterogeneous Electronic Health Record (EHR) data. Utilizing a mixture model formulation, our approach directly models sequences of arbitrary length, such as medications and laboratory results. This allows for subgrouping and incorporation of the dynamics underlying heterogeneous data types. The model consists of a layered set of latent variables that encode underlying structure in the data. These variables represent subject subgroups at the top layer, and unobserved states for sequences in the second layer. We train this model on episodic data from subjects receiving medical care in the Kaiser Permanente Northern California integrated healthcare delivery system. The resulting properties of the trained model generate novel insight from these complex and multifaceted data. In addition, we show how the model can be used to analyze sequences that contribute to assessment of mortality likelihood.

Analyzing the Safety Consequences of Pedestrian Spatial Violation at Mid-Blocks: A Bayesian Structural Equation Modeling Approach

The objective of this study is to understand the impact of a variety of factors on the frequency and severity of pedestrian-vehicle collisions that involve pedestrian spatial violations at mid-blocks. To that end, the historical collision records of the City of Hamilton between 2010 and 2017 were obtained, and collisions that had occurred at mid-blocks were filtered out. A Bayesian structural equation modeling (SEM) framework was developed to investigate the impact of a wide range of factors on such collisions. First, a classical SEM was developed to group the different factors into sets of latent variables. Four latent variables were defined, including location amenities and attractions, pedestrian/road network characteristics, exposure parameters, and location/collision-specific factors. The Bayesian SEM was then implemented to investigate the relationship between the latent variables and collisions. The results showed that the amenities and attractions of a location (e.g., parks, schools, bike-share stations, and bus stops) were the most influential factor on the frequency of collisions that involve spatial violation, followed by pedestrian network characteristics. Pedestrian network characteristics and location/collision-specific factors were found to be the most influential factors on the severity of collisions. The location of bike-share stations, pedestrian network connectivity, exposure to walkers, and the number of lanes were the four observed variables that explained the highest percentage of the variance in each latent group, respectively. The results of this study should assist engineers and planners to develop better design concepts to mitigate collisions that are caused by pedestrian spatial violations in urban areas.

Latent variable modeling and state estimation of non-stationary processes driven by monotonic trends

In certain non-stationary processes, the non-stationary dynamics is caused by degradation or wearing of certain process components. Such dynamics can be characterized by a latent monotonic signal. Meanwhile, there also exist stationary dynamics characterizing the regular process variables. It hence becomes pertinent to distinguish these two sets of latent variables for the monitoring of the process from both the stationary and non-stationary aspects. In this regard, we propose a methodology to achieve such a goal by modeling the latent monotonic trend as a closed skew-normal random walk model. The other stationary relations are characterized by a state-space model with Gaussian noises. The problem is solved as a simultaneous state and parameter estimation problem using the expectation–maximization algorithm. As a result of the closed skew-normal random walk model for the monotonic trend, the state estimation problem becomes a skew-normal filtering and smoothing problem. The effectiveness of the proposed method is verified through a numerical simulation, and the algorithm is applied to solve a Hot Lime Softener fouling predictive monitoring problem.

Unsupervised Channel Compression Methods in Motor Prostheses Design.

The development of high performance brain machine interfaces (BMIs) requires scaling recording channel count to enable simultaneous recording from large populations of neurons. Unfortunately, proposed implantable neural interfaces have power requirements that scale linearly with channel count. To facilitate the design of interfaces with reduced power requirements, we propose and evaluate an unsupervised-learning-based compressed sensing strategy. This strategy suggests novel neural interface architectures which compress neural data by methodically combining channels of spiking activity. We develop an entropy-based compression strategy that models the population of neurons as being generated from a lower dimensional set of latent variables and aims to minimize the loss of information in the latent variables due to compression. We evaluate compressed features by inferring the latent variables from these features and measuring the accuracy with which the activity of held out neurons and arm movements can be estimated. We apply these methods to different cortical regions (PMd and M1) and compare the proposed compression methods to a random projections strategy often employed for compressed sensing and to a supervised regression based channel dropping strategy traditionally applied in BMI applications.

Multiple Conformer Descriptors for QSAR Modeling.

The most widely used QSAR approaches are mainly based on 2D molecular representation which ignores stereoconfiguration and conformational flexibility of compounds. 3D QSAR uses a single conformer of each compound which is difficult to choose reasonably. 4D QSAR uses multiple conformers to overcome the issues of 2D and 3D methods. However, many of existing 4D QSAR models suffer from the necessity to pre-align conformers, while alignment-independent approaches often ignore stereoconfiguration of compounds. In this study we propose a QSAR modeling approach based on transforming chirality-aware 3D pharmacophore descriptors of individual conformers into a set of latent variables representing the whole conformer set of a molecule. This is achieved by clustering together all conformers of all training set compounds. The final representation of a compound is a bit string encoding cluster membership of its conformers. In our study we used Random Forest, but this representation can be used in combination with any machine learning method. We compared this approach with conventional 2D and 3D approaches using multiple data sets and investigated the sensitivity of the approach proposed to tuning parameters: number of conformers and clusters.

A Hybrid Scan Gibbs Sampler for Bayesian Models with Latent Variables

Gibbs sampling is a widely popular Markov chain Monte Carlo algorithm that can be used to analyze intractable posterior distributions associated with Bayesian hierarchical models. There are two standard versions of the Gibbs sampler: The systematic scan (SS) version, where all variables are updated at each iteration, and the random scan (RS) version, where a single, randomly selected variable is updated at each iteration. The literature comparing the theoretical properties of SS and RS Gibbs samplers is reviewed, and an alternative hybrid scan Gibbs sampler is introduced, which is particularly well suited to Bayesian models with latent variables. The word “hybrid” reflects the fact that the scan used within this algorithm has both systematic and random elements. Indeed, at each iteration, one updates the entire set of latent variables, along with a randomly chosen block of the remaining variables. The hybrid scan (HS) Gibbs sampler has important advantages over the two standard scan Gibbs samplers. First, the HS algorithm is often easier to analyze from a theoretical standpoint. In particular, it can be much easier to establish the geometric ergodicity of a HS Gibbs Markov chain than to do the same for the corresponding SS and RS versions. Second, the sandwich methodology developed in (Ann. Statist. 36 (2008) 532–554), which is also reviewed, can be applied to the HS Gibbs algorithm (but not to the standard scan Gibbs samplers). It is shown that, under weak regularity conditions, adding sandwich steps to the HS Gibbs sampler always results in a theoretically superior algorithm. Three specific Bayesian hierarchical models of varying complexity are used to illustrate the results. One is a simple location-scale model for data from the Student’s t distribution, which is used as a pedagogical tool. The other two are sophisticated, yet practical Bayesian regression models.

Geolocation Error Estimation and Correction on Long-Term MWRI Data

Due to the limitation of the satellite attitude measurement accuracy and the system servo control error of the payload scanning mechanism, an optimal use of Micro-Wave Radiation Imager (MWRI) observations requires high geolocation accuracy. In the operational system, the MWRI geolocation accuracy reaches 1 pixel, and there still exists room for improvement. In this article, we improve upon the coastline inflection point method (CIM) and propose to assign the accurate correspondence by employing a nonrigid point set registration method. First, the method identifies a set of latent variables to recognize outliers and then applies nonparametric geometric constraints to the correspondence as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> distribution. Second, the maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> (MAP) estimation is applied by the expectation–maximization (EM) algorithm to obtain correct inliers. The comparison with other methods demonstrates that the proposed method can provide more accurate estimation of geolocation bias. In addition, the pixel error and changes in spacecraft attitude with the long-term geolocation data in FY-3C MWRI before and after correction were analyzed during the period from April 1 to August 30, 2018. The results have shown that the geolocation errors are reduced from [0.50, 0.60] pixels to [0.20, 0.33] pixels in the along- and cross-track directions after the attitude correction. In addition, the reduction of the standard deviation shows that the geolocation quality of MWRI is improved.

Disentangled Representation Learning in Real-World Image Datasets via Image Segmentation Prior

We propose a novel method that can learn easy-to-interpret latent representations in real-world image datasets using a VAE-based model by splitting an image into several disjoint regions. Our method performs object-wise disentanglement by exploiting image segmentation and alpha compositing. With remarkable results obtained by unsupervised disentanglement methods for toy datasets, recent studies have tackled challenging disentanglement for real-world image datasets. However, these methods involve deviations from the standard VAE architecture, which has favorable disentanglement properties. Thus, for disentanglement in images of real-world image datasets with preservation of the VAE backbone, we designed an encoder and a decoder that embed an image into disjoint sets of latent variables corresponding to objects. The encoder includes a pre-trained image segmentation network, which allows our model to focus only on representation learning while adopting image segmentation as an inductive bias. Evaluations using real-world image datasets, CelebA and Stanford Cars, showed that our method achieves improved disentanglement and transferability.

Stated consideration and attribute thresholds in mode choice models: a hierarchical ICLV approach

Consideration of alternatives, as many other aspects related to the decision-making process, is not observable and challenging to measure. Even when supplementary information is collected during stated choice experiments, its use as an additional explanatory variable is discouraged due to potential endogeneity issues, measurement error and limited suitability for forecasting. To overcome these limitations, we propose an Integrated Choice and Latent Variable model where consideration of an alternative is treated as a latent variable. The novelty of the presented model is that the latent variable for consideration of an alternative itself is a function of another set of latent variables that represent thresholds applied by the decision maker to individual attributes (such as travel time and cost). The proposed hierarchical relationship between latent thresholds and latent consideration enables us to explain a share of otherwise purely random heterogeneity, and identify the structural drivers of consideration. The latter is of interest to policymakers and private operators.