Latent Gaussian Models Research Articles

Spatio‐temporal occupancy models with INLA

Abstract Modern methods for quantifying, predicting and mapping species distributions have played a crucial part in biodiversity conservation. Occupancy models have become a popular choice for analysing species occurrence data due to their ability to separate out the observational error induced by imperfect detection of a species, and the sources of bias affecting the occupancy process. However, the spatial and temporal variation in occupancy that is not accounted for by environmental covariates is often ignored or modelled through simple spatial structures as the computational costs of fitting explicit spatio‐temporal models is too high. In this work, we demonstrate how Integrated Nested Laplace Approximation (INLA) may be used to fit complex spatio‐temporal occupancy models and how the R‐INLA package can provide a user‐friendly interface to make such complex models available to users. We show how occupancy models, provided some simplification on the detection process is assumed, can be framed as latent Gaussian models and, as such, benefit from the powerful INLA framework. A large selection of complex modelling features, and random effect models, including spatio‐temporal models, have already been implemented in R‐INLA. These also become available for occupancy models, providing the user with an efficient, reliable and flexible toolbox. We illustrate how INLA provides a flexible and computationally efficient framework for developing and fitting complex occupancy models using two complex case studies. Through these, we show how different spatio‐temporal models that include spatial‐varying trends, smooth terms and spatio‐temporal random effects can be fitted to aggregated detection/non‐detection data. At the cost of limiting the complexity of the detection model structure, INLA can incorporate a range of rather complex structures in the ecological process of interest and hence, extend the functionality of occupancy models. The limitations of occupancy models in terms of scalability for large spatio‐temporal data sets remain a challenge and an active area of research. INLA‐based occupancy models provide an alternative inferential and computational framework to fit complex spatio‐temporal occupancy models. The need for new and more flexible computationally efficient approaches to fit such models makes INLA an attractive option for addressing complex ecological problems, and a promising area of research.

Trivariate Joint Modeling for Family Data with Longitudinal Counts, Recurrent Events and a Terminal Event with Application to Lynch Syndrome.

Trivariate joint modeling for longitudinal count data, recurrent events, and a terminal event for family data has increased interest in medical studies. For example, families with Lynch syndrome (LS) are at high risk of developing colorectal cancer (CRC), where the number of polyps and the frequency of colonoscopy screening visits are highly associated with the risk of CRC among individuals and families. To assess how screening visits influence polyp detection, which in turn influences time to CRC, we propose a clustered trivariate joint model. The proposed model facilitates longitudinal count data that are zero-inflated and over-dispersed and invokes individual-specific and family-specific random effects to account for dependence among individuals and families. We formulate our proposed model as a latent Gaussian model to use the Bayesian estimation approach with the integrated nested Laplace approximation algorithm and evaluate its performance using simulation studies. Our trivariate joint model is applied to a series of 18 families from Newfoundland, with the occurrence of CRC taken as the terminal event, the colonoscopy screening visits as recurrent events, and the number of polyps detected at each visit as zero-inflated count data with overdispersion. We showed that our trivariate model fits better than alternative bivariate models and that the cluster effects should not be ignored when analyzing family data. Finally, the proposed model enables us to quantify heterogeneity across families and individuals in polyp detection and CRC risk, thus helping to identify individuals and families who would benefit from more intensive screening visits.

Mapping socio-economic status using mixed data: a hierarchical Bayesian approach

Abstract We propose a Bayesian hierarchical model to estimate a socio-economic status (SES) index based on mixed dichotomous and continuous variables. In particular, we extend Quinn’s ([2004]. Bayesian factor analysis for mixed ordinal and continuous responses. Political Analysis, 12(4), 338–353. https://doi.org/10.1093/pan/mph022) and Schliep and Hoeting’s ([2013]. Multilevel latent Gaussian process model for mixed discrete and continuous multivariate response data. Journal of Agricultural, Biological, and Environmental Statistics, 18(4), 492–513. https://doi.org/10.1007/s13253-013-0136-z) factor analysis models for mixed dichotomous and continuous variables by allowing a spatial hierarchical structure of key parameters of the model. Unlike most SES assessment models proposed in the literature, the hierarchical nature of this model enables the use of census observations at the household level without needing to aggregate any information a priori. Therefore, it better accommodates the variability of the SES between census tracts and the number of households per area. The proposed model is used in the estimation of a socio-economic index using 10% of the 2010 Ghana census in the Greater Accra Metropolitan area. Out of the 20 observed variables, the number of people per room, access to water piping and flushable toilets differentiated high and low SES areas the best.

Data-driven subclassification of ANCA-associated vasculitis: model-based clustering of a federated international cohort

Antineutrophil cytoplasmic antibody (ANCA)-associated vasculitis is a heterogenous autoimmune disease. While traditionally stratified into two conditions, granulomatosis with polyangiitis (GPA) and microscopic polyangiitis (MPA), the subclassification of ANCA-associated vasculitis is subject to continued debate. Here we aim to identify phenotypically distinct subgroups and develop a data-driven subclassification of ANCA-associated vasculitis, using a large real-world dataset. In the collaborative data reuse project FAIRVASC (Findable, Accessible, Interoperable, Reusable, Vasculitis), registry records of patients with ANCA-associated vasculitis were retrieved from six European vasculitis registries: the Czech Registry of ANCA-associated vasculitis (Czech Republic), the French Vasculitis Study Group Registry (FVSG; France), the Joint Vasculitis Registry in German-speaking Countries (GeVas; Germany), the Polish Vasculitis Registry (POLVAS; Poland), the Irish Rare Kidney Disease Registry (RKD; Ireland), and the Skåne Vasculitis Cohort (Sweden). We performed model-based clustering of 17 mixed-type clinical variables using a parsimonious mixture of two latent Gaussian variable models. Clinical validation of the optimal cluster solution was made through summary statistics of the clusters' demography, phenotypic and serological characteristics, and outcome. The predictive value of models featuring the cluster affiliations were compared with classifications based on clinical diagnosis and ANCA specificity. People with lived experience were involved throughout the FAIRVASVC project. A total of 3868 patients diagnosed with ANCA-associated vasculitis between Nov 1, 1966, and March 1, 2023, were included in the study across the six registries (Czech Registry n=371, FVSG n=1780, GeVas n=135, POLVAS n=792, RKD n=439, and Skåne Vasculitis Cohort n=351). There were 2434 (62·9%) patients with GPA and 1434 (37·1%) with MPA. Mean age at diagnosis was 57·2 years (SD 16·4); 2006 (51·9%) of 3867 patients were men and 1861 (48·1%) were women. We identified five clusters, with distinct phenotype, biochemical presentation, and disease outcome. Three clusters were characterised by kidney involvement: one severe kidney cluster (555 [14·3%] of 3868 patients) with high C-reactive protein (CRP) and serum creatinine concentrations, and variable ANCA specificity (SK cluster); one myeloperoxidase (MPO)-ANCA-positive kidney involvement cluster (782 [20·2%]) with limited extrarenal disease (MPO-K cluster); and one proteinase 3 (PR3)-ANCA-positive kidney involvement cluster (683 [17·7%]) with widespread extrarenal disease (PR3-K cluster). Two clusters were characterised by relative absence of kidney involvement: one was a predominantly PR3-ANCA-positive cluster (1202 [31·1%]) with inflammatory multisystem disease (IMS cluster), and one was a cluster (646 [16·7%]) with predominantly ear-nose-throat involvement and low CRP, with mainly younger patients (YR cluster). Compared with models fitted with clinical diagnosis or ANCA status, cluster-assigned models demonstrated improved predictive power with respect to both patient and kidney survival. Our study reinforces the view that ANCA-associated vasculitis is not merely a binary construct. Data-driven subclassification of ANCA-associated vasculitis exhibits higher predictive value than current approaches for key outcomes. European Union's Horizon 2020 research and innovation programme under the European Joint Programme on Rare Diseases.

A geospatial analysis of local intermediate snail host distributions provides insight into schistosomiasis risk within under-sampled areas of southern Lake Malawi

BackgroundAlong the southern shoreline of Lake Malawi, the incidence of schistosomiasis is increasing with snails of the genera Bulinus and Biomphalaria transmitting urogenital and intestinal schistosomiasis, respectively. Since the underlying distribution of snails is partially known, often being focal, developing pragmatic spatial models that interpolate snail information across under-sampled regions is required to understand and assess current and future risk of schistosomiasis.MethodsA secondary geospatial analysis of recently collected malacological and environmental survey data was undertaken. Using a Bayesian Poisson latent Gaussian process model, abundance data were fitted for Bulinus and Biomphalaria. Interpolating the abundance of snails along the shoreline (given their relative distance along the shoreline) was achieved by smoothing, using extracted environmental rainfall, land surface temperature (LST), evapotranspiration, normalised difference vegetation index (NDVI) and soil type covariate data for all predicted locations. Our adopted model used a combination of two-dimensional (2D) and one dimensional (1D) mapping.ResultsA significant association between normalised difference vegetation index (NDVI) and abundance of Bulinus spp. was detected (log risk ratio − 0.83, 95% CrI − 1.57, − 0.09). A qualitatively similar association was found between NDVI and Biomphalaria sp. but was not statistically significant (log risk ratio − 1.42, 95% CrI − 3.09, 0.10). Analyses of all other environmental data were considered non-significant.ConclusionsThe spatial range in which interpolation of snail distributions is possible appears < 10km owing to fine-scale biotic and abiotic heterogeneities. The forthcoming challenge is to refine geospatial sampling frameworks with future opportunities to map schistosomiasis within actual or predicted snail distributions. In so doing, this would better reveal local environmental transmission possibilities.Graphical

Automatic cross-validation in structured models: Is it time to leave out leave-one-out?

Standard techniques such as leave-one-out cross-validation (LOOCV) might not be suitable for evaluating the predictive performance of models incorporating structured random effects. In such cases, the correlation between the training and test sets could have a notable impact on the model’s prediction error. To overcome this issue, an automatic group construction procedure for leave-group-out cross validation (LGOCV) has recently emerged as a valuable tool for enhancing predictive performance measurement in structured models. The purpose of this paper is (i) to compare LOOCV and LGOCV within structured models, emphasizing model selection and predictive performance, and (ii) to provide real data applications in spatial statistics using complex structured models fitted with INLA, showcasing the utility of the automatic LGOCV method. First, we briefly review the key aspects of the recently proposed LGOCV method for automatic group construction in latent Gaussian models. We also demonstrate the effectiveness of this method for selecting the model with the highest predictive performance by simulating extrapolation tasks in both temporal and spatial data analyses. Finally, we provide insights into the effectiveness of the LGOCV method in modeling complex structured data, encompassing spatio-temporal multivariate count data, spatial compositional data, and spatio-temporal geospatial data.

A flexible Bayesian tool for CoDa mixed models: logistic-normal distribution with Dirichlet covariance

Compositional Data Analysis (CoDa) has gained popularity in recent years. This type of data consists of values from disjoint categories that sum up to a constant. Both Dirichlet regression and logistic-normal regression have become popular as CoDa analysis methods. However, fitting this kind of multivariate models presents challenges, especially when structured random effects are included in the model, such as temporal or spatial effects. To overcome these challenges, we propose the logistic-normal Dirichlet Model (LNDM). We seamlessly incorporate this approach into the R-INLA package, facilitating model fitting and model prediction within the framework of Latent Gaussian Models. Moreover, we explore metrics like Deviance Information Criteria, Watanabe Akaike information criterion, and cross-validation measure conditional predictive ordinate for model selection in R-INLA for CoDa. Illustrating LNDM through two simulated examples and with an ecological case study on Arabidopsis thaliana in the Iberian Peninsula, we underscore its potential as an effective tool for managing CoDa and large CoDa databases.

Developing a dynamic quality prediction model for limited samples target grade based on transfer learning

In response to the dynamic demands of the market, this study addresses the challenge of frequent operational adjustments in a production line to accommodate diverse product grades. The resulting scarcity of data in the new operating conditions (target grade) impedes the development of reliable soft-sensor prediction models. A two-step learning method, termed S2-LGMNSSM-TS-T, is proposed. This method employs a semi-supervised latent Gaussian mixture nonlinear state space model (S2-LGMNSSM-TS) trained on both target and source data, providing a dynamic, one-step-ahead predictive soft sensor. To overcome data scarcity in the target grade, insights from the source are utilized. With a Gaussian mixture prior distribution, S2-LGMNSSM-TS identifies dynamic behaviors in both target and source grades. The enhanced S2-LGMNSSM-TS-T configuration focuses on target-grade predictions, leveraging source knowledge and mitigating data scarcity issues. A numerical example and an industrial case study demonstrate the model's effectiveness in improving target-grade predictions through source knowledge utilization.

Joint quantile disease mapping with application to malaria and G6PD deficiency.

Statistical analysis based on quantile methods is more comprehensive, flexible and less sensitive to outliers when compared to mean methods. Joint disease mapping is useful for inferring correlation between different diseases. Most studies investigate this link through multiple correlated mean regressions. We propose a joint quantile regression framework for multiple diseases where different quantile levels can be considered. We are motivated by the theorized link between the presence of malaria and the gene deficiency G6PD, where medical scientists have anecdotally discovered a possible link between high levels of G6PD and lower than expected levels of malaria initially pointing towards the occurrence of G6PD inhibiting the occurrence of malaria. Thus, the need for flexible joint quantile regression in a disease mapping framework arises. Our model can be used for linear and nonlinear effects of covariates by stochastic splines since we define it as a latent Gaussian model. We perform Bayesian inference using the R integrated nested Laplace approximation, suitable even for large datasets. Finally, we illustrate the model's applicability by considering data from 21 countries, although better data are needed to prove a significant relationship. The proposed methodology offers a framework for future studies of interrelated disease phenomena.

A graph theory based similarity metric enables comparison of subpopulation psychometric networks.

Network psychometrics leverages pairwise Markov random fields to depict conditional dependencies among a set of psychological variables as undirected edge-weighted graphs. Researchers often intend to compare such psychometric networks across subpopulations, and recent methodological advances provide invariance tests of differences in subpopulation networks. What remains missing, though, is an analogue to an effect size measure that quantifies differences in psychometric networks. We address this gap by complementing recent advances for investigating whether psychometric networks differ with an intuitive similarity measure quantifying the extent to which networks differ. To this end, we build on graph-theoretic approaches and propose a similarity measure based on the Frobenius norm of differences in psychometric networks' weighted adjacency matrices. To assess this measure's utility for quantifying differences between psychometric networks, we study how it captures differences in subpopulation network models implied by both latent variable models and Gaussian graphical models. We show that a wide array of network differences translates intuitively into the proposed measure, while the same does not hold true for customary correlation-based comparisons. In a simulation study on finite-sample behavior, we show that the proposed measure yields trustworthy results when population networks differ and sample sizes are sufficiently large, but fails to identify exact similarity when population networks are the same. From these results, we derive a strong recommendation to only use the measure as a complement to a significant test for network similarity. We illustrate potential insights from quantifying psychometric network similarities through cross-country comparisons of human values networks. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Implementation of Latent Gaussian Model in the Forecasting Process

This research aims to determine the implementation of the Latent Gaussian Model in the forecasting process. This research focuses on developing a forecasting model using the Multivariate Latent Gaussian Model (LGM) approach with shared components. which offers a more accurate representation without the assumption of stationarity and cointegration as it accommodates random components in the model. The forecasting results for the five KPPs are considered to have a very good level of accuracy with MAPE values &lt; 10%. This shows that LGM can achieve reliable forecasting when applied to the real life problems. This condition supports forecasting and can be an effective and targeted benchmark. The Latent Gaussian Model using the Bayesian Approach in parameter estimation can be utilized in forecasting Personal Income Tax Article 25/29. This is supported by the highly accurate MAPE value of 0.01%. The implementation of the developed model is not limited to forecasting Personal Income Tax Article 25/29. but can also be used in various other fields. With its hierarchical structure. the Bayesian approach proves to be an effective method for addressing complex modeling challenges.

Fitting latent non-Gaussian models using variational Bayes and Laplace approximations

–Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that contain inherently non-Gaussian features, such as sudden jumps or spikes, that adversely affect the inferences and predictions made using an LGM. These datasets require more general latent non-Gaussian models (LnGMs) that can handle automatically these non-Gaussian features. However, fast implementation and easy-to-use software are lacking, preventing the broad applicability of LnGMs. In this paper, we derive variational Bayes algorithms for fast and scalable inference of LnGMs. The approximation leads to an LGM that downweights extreme events in the latent process, reducing their influence and leading to more robust inferences. It can be applied to a wide range of models, such as autoregressive processes for time series, simultaneous autoregressive models for areal data, and spatial Matérn models. To facilitate Bayesian inference, we introduce the ngvb package, where LGMs implemented in R-INLA can be easily extended to LnGMs by adding a single line of code.

Delineating important killer whale foraging areas using a spatiotemporal logistic model

Conservation management planning for highly mobile species requires an understanding of the distribution of areas that are biologically important to the species of concern. Collecting data on the locations of animal behaviors linked to biological characteristics, such as foraging, can be used to spatially describe biological important areas. However, spatial modeling of free-ranging animal behavior can be challenging, as behavioral observations of animals are often clustered, and sampling is commonly conducted at a higher frequency than changes in behavioral states, resulting in data that are usually highly autocorrelated in space and time. Here, we fit latent Gaussian process models to observational behavioral data to generate spatially-explicit predictions of foraging behavior within the critical habitat of an endangered population of fish-eating killer whales (Orcinus orca) in southern British Columbia, Canada, and northern Washington State, USA. We compare spatial models treating temporal autocorrelation in behavior in three ways: (1) ignoring temporal autocorrelation entirely; (2) traditional data-thinning to remove temporal autocorrelation, and; (3) using a temporal Gaussian process to account for temporal autocorrelation. Comparisons of autocorrelative structures for each model and visual comparison of broad spatial patterns demonstrate that our third approach yields more accurate results than when ignoring temporal autocorrelation entirely and higher precision results than when applying data-thinning methods. Within the identified areas of critical habitat, our models indicate two primary regions of intense killer whale foraging activity, and we delineate areas wherein the probability of foraging was particularly high as candidate locations for conservation management actions. This study underscores the value of refining our understanding of high-use areas for at-risk species by incorporating animal behavior data to inform area-based conservation measures.

Joint species distribution modeling with competition for space

AbstractJoint species distribution models (JSDM) are among the most important statistical tools in community ecology. However, existing JSDMs cannot model mutual exclusion between species. We tackle this deficiency in the context of modeling plant percentage cover data, where mutual exclusion arises from limited growing space and competition for light. We propose a hierarchical JSDM where latent Gaussian variable models describe species' niche preferences and Dirichlet‐Multinomial distribution models the observation process and competition between species. We also propose a decision theoretic model comparison and validation approach to assess the goodness of JSDMs in four different types of predictive tasks. We apply our models and methods to a case study on modeling vegetation cover in a boreal peatland. Our results show that ignoring the interspecific interactions and competition reduces models' predictive performance and leads to biased estimates for total percentage cover. Models' relative predictive performance also depends on the predictive task highlighting that model comparison and assessment should resemble the true predictive task. Our results also demonstrate that the proposed JSDM can be used to simultaneously infer interspecific correlations in niche preference as well as mutual competition for space and through that provide novel insight into ecological research.

Using Auxiliary Information in Probability Survey Data to Improve Pseudo-Weighting in Nonprobability Samples: A Copula Model Approach

Abstract While probability sampling has been considered the gold standard of survey methods, nonprobability sampling is increasingly popular due to its convenience and low cost. However, nonprobability samples can lead to biased estimates due to the unknown nature of the underlying selection mechanism. In this article, we propose parametric and semiparametric approaches to integrate probability and nonprobability samples using common ancillary variables observed in both samples. In the parametric approach, the joint distribution of ancillary variables is assumed to follow the latent Gaussian copula model, which is flexible to accommodate both categorical and continuous variables. In contrast, the semiparametric approach requires no assumptions about the distribution of ancillary variables. In addition, logistic regression is used to model the mechanism by which population units enter the nonprobability sample. The unknown parameters in the copula model are estimated through the pseudo maximum likelihood approach. The logistic regression model is estimated by maximizing the sample likelihood constructed from the nonprobability sample. The proposed method is evaluated in the context of estimating the population mean. Our simulation results show that the proposed method is able to correct the selection bias in the nonprobability sample by consistently estimating the underlying inclusion mechanism. By incorporating additional information in the nonprobability sample, the combined method can estimate the population mean more efficiently than using the probability sample alone. A real-data application is provided to illustrate the practical use of the proposed method.

High-resolution global precipitation downscaling with latent Gaussian models and non-stationary stochastic partial differential equation structure

Abstract Obtaining high-resolution maps of precipitation data can provide key insights to stakeholders to assess a sustainable access to water resources at urban scale. Mapping a non-stationary, sparse process such as precipitation at very high spatial resolution requires the interpolation of global datasets at the location where ground stations are available with statistical models able to capture complex non-Gaussian global space–time dependence structures. In this work, we propose a new approach based on capturing the spatially varying anisotropy of a latent Gaussian process via a locally deformed stochastic partial differential equation (SPDE) with a buffer allowing for a different spatial structure across land and sea. The finite volume approximation of the SPDE, coupled with integrated nested Laplace approximation ensures feasible Bayesian inference for tens of millions of observations. The simulation studies showcase the improved predictability of the proposed approach against stationary and no-buffer alternatives. The proposed approach is then used to yield high-resolution simulations of daily precipitation across the United States.

A latent Gaussian process model for the spatial distribution of liquefaction manifestation

This paper presents a model for distributing zones of liquefaction and nonliquefaction for use in regional liquefaction risk analysis. There are two broad methodologies that have been used to evaluate liquefaction risk on the regional scale: (a) application of site-specific procedures using soil properties inferred from geology, or (b) application of geospatial proxies for liquefaction. The first approach will tend to predict similar liquefaction probabilities across broad areas with similar geology, water table depths, and shaking intensities. The second approach yields the probability of liquefaction, which can be interpreted as the portion of the area affected by liquefaction ([Formula: see text]). Neither approach, however, gives an informed prediction of the spatial distribution of liquefaction and the resulting displacements, which are particularly important for assessments of seismic risk for spatially distributed infrastructure systems. We propose a methodology for incorporating spatial correlation into a geospatial proxy for liquefaction to create maps of liquefaction and nonliquefaction for a given earthquake scenario. First, we describe a latent Gaussian process that is assumed to govern the spatial distribution of liquefaction. Next, a database of empirical observations of liquefaction is used to obtain the coefficients that describe that latent Gaussian process. The proposed model yields random realizations of maps of liquefaction and nonliquefaction conditioned on a map of [Formula: see text]. Such maps can be used to constrain the area over which displacements are estimated using soil properties inferred from geology and are therefore a critical component in reducing bias in assessments of liquefaction risk at the regional scale.

Spatio-temporal dependence modelling of extreme rainfall in South Africa: A Bayesian integrated nested Laplace approximation technique

The spatial and spatio-temporal dependence modeling to extreme value distributions have been used to analyze the extremes of daily maximum rainfall data across selected weather stations in South Africa combining generalized Pareto distribution (GPD) with the flexible Bayesian Latent Gaussian Model (LGM). The paper demonstrated the spatio-temporal GPD model for applications in extreme rainfall data that capture systematic variation through spatial and spatio-temporal modeling framework, in which the temporal constitutes the week and month as random separately. The paper uses the Bayesian integrated Nested Laplace approximation (INLA) algorithm to estimate marginal posterior means of the parameters and hyper-parameters for Bayesian spatio-temporal models. The Bayesian inferences using INLA technique were applied to obtain prediction of the return levels at each station, which incorporate uncertainty due to model estimation, as well as the randomness that is inherent in the processes.

Latent Gaussian Model Boosting.

Latent Gaussian models and boosting are widely used techniques in statistics and machine learning. Tree-boosting shows excellent prediction accuracy on many data sets, but potential drawbacks are that it assumes conditional independence of samples, produces discontinuous predictions for, e.g., spatial data, and it can have difficulty with high-cardinality categorical variables. Latent Gaussian models, such as Gaussian process and grouped random effects models, are flexible prior models which explicitly model dependence among samples and which allow for efficient learning of predictor functions and for making probabilistic predictions. However, existing latent Gaussian models usually assume either a zero or a linear prior mean function which can be an unrealistic assumption. This article introduces a novel approach that combines boosting and latent Gaussian models to remedy the above-mentioned drawbacks and to leverage the advantages of both techniques. We obtain increased prediction accuracy compared to existing approaches in both simulated and real-world data experiments.

Exploiting Low-Rank Latent Gaussian Graphical Model Estimation for Visual Sentiment Distributions

Currently, an increasing number of applications and services has encouraged users to openly express their emotions via images. Unlike visual sentiment classification, visual sentiment distribution learning exploits the overall distribution to represent the relative importance of sentiment labels. Considering that most relevant studies have failed to completely model correlation structures or explicitly apply them to unknown instances, in this paper, we proposed a low-rank latent Gaussian graphical model estimation (LGGME) method for visual sentiment distribution learning tasks. There are three main characteristics of LGGME: 1) an integrated inverse covariance matrix whose parameters characterize the latent correlation structures between and within features and sentiments is estimated based on the sparse Gaussian graphical model; 2) a multivariate normal assumption is assigned on the concatenated latent feature representations and the estimated sentiment distributions instead of the original observations for a reasonable surrogate; and 3) the latent feature representations are projected from a low-rank subspace, which is also available for unseen instances, and the estimated sentiment distributions are evaluated by KL divergence to ensure a suitable setting for distribution learning. We further developed an effective optimization algorithm based on the alternating direction method of multipliers (ADMM) for our objective function. The experimental results obtained on three publicly available datasets demonstrate the superiority of our proposed method.