cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.11973537
title: Bayesian Semiparametric Analysis of Multivariate Continuous Responses, With Variable Selection

description: This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical challenges revolve around dealing with the unknown mean and variance functions and in particular, the correlation matrix. To tackle these problems, we have developed priors over the smooth functions and a Markov chain Monte Carlo algorithm for inference and model selection. Specifically, Dirichlet process mixtures of Gaussian distributions are used as the basis for a cluster-inducing prior over the elements of the correlation matrix. The smooth, multidimensional means and variances are represented using radial basis function expansions. The complexity of the model, in terms of variable selection and smoothness, is then controlled by spike-slab priors. A simulation study is presented, demonstrating performance as the response dimension increases. Finally, the model is fit to a number of real world datasets. An R package, scripts for replicating synthetic and real data examples, and a detailed description of the MCMC sampler are available in the supplementary materials online.
DOI: 10.6084/m9.figshare.12141090.v3
title: Building Representative Matched Samples With Multi-Valued Treatments in Large Observational Studies

description: In this article, we present a new way of matching in observational studies that overcomes three limitations of existing matching approaches. First, it directly balances covariates with multi-valued treatments without explicitly estimating the generalized propensity score. Second, it builds self-weighted matched samples that are representative of a target population by design. Third, it can handle large datasets, with hundreds of thousands of observations, in a couple of minutes. The key insights of this new approach to matching are balancing the treatment groups relative to a target population and positing a linear-sized mixed integer formulation of the matching problem. We formally show that this formulation is more effective than alternative quadratic-sized formulations, as its reduction in size does not affect its strength from the standpoint of its linear programming relaxation. We also show that this formulation can be used for matching with distributional covariate balance in polynomial time under certain assumptions on the covariates and that it can handle large datasets in practice even when the assumptions are not satisfied. This algorithmic characterization is key to handling large datasets. We illustrate this new approach to matching in both a simulation study and an observational study of the impact of an earthquake on educational attainment. With this approach, the results after matching can be visualized with simple and transparent graphical displays: while increasing levels of exposure to the earthquake have a negative impact on school attendance, there is no effect on college admission test scores. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.12141066
title: State-Dependent Kernel Selection for Conditional Sampling of Graphs

description: This article introduces new efficient algorithms for two problems: sampling conditional on vertex degrees in unweighted graphs, and conditional on vertex strengths in weighted graphs. The resulting conditional distributions provide the basis for exact tests on social networks and two-way contingency tables. The algorithms are able to sample conditional on the presence or absence of an arbitrary set of edges. Existing samplers based on MCMC or sequential importance sampling are generally not scalable; their efficiency can degrade in large graphs with complex patterns of known edges. MCMC methods usually require explicit computation of a Markov basis to navigate the state space; this is computationally intensive even for small graphs. Our samplers do not require a Markov basis, and are efficient both in sparse and dense settings. The key idea is to carefully select a Markov kernel on the basis of the current state of the chain. We demonstrate the utility of our methods on a real network and contingency table. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.11973558
title: Bayesian Variational Inference for Exponential Random Graph Models

description: Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging “doubly intractable” problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC) methods which yield Bayesian inference for ERGMs, such as the exchange algorithm, are asymptotically exact but computationally intensive, as a network has to be drawn from the likelihood at every step using, for instance, a “tie no tie” sampler. In this article, we develop a variety of variational methods for Gaussian approximation of the posterior density and model selection. These include nonconjugate variational message passing based on an adjusted pseudolikelihood and stochastic variational inference. To overcome the computational hurdle of drawing a network from the likelihood at each iteration, we propose stochastic gradient ascent with biased but consistent gradient estimates computed using adaptive self-normalized importance sampling. These methods provide attractive fast alternatives to MCMC for posterior approximation. We illustrate the variational methods using real networks and compare their accuracy with results obtained via MCMC and Laplace approximation. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.12066147
title: Predicting the Output From a Stochastic Computer Model When a Deterministic Approximation is Available

description: Statistically modeling the output of a stochastic computer model can be difficult to do accurately without a large simulation budget. We alleviate this problem by exploiting readily available deterministic approximations to efficiently learn about the respective stochastic computer models. This is done via the summation of two Gaussian processes; one responsible for modeling the deterministic approximation, the other responsible for using such approximation to better statistically model the stochastic computer model. The developed method provides high predictive performance and increased confidence that complicated features of a stochastic computer model are captured, even when the simulation budget is small. Several synthetic computer models are used to outline the capabilities of this method, and two real-world examples are used to display its practical utility. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.12141069
title: A Tree-Based Semi-Varying Coefficient Model for the COM-Poisson Distribution

description: We propose a tree-based semi-varying coefficient model for the Conway–Maxwell–Poisson (CMP or COM-Poisson) distribution which is a two-parameter generalization of the Poisson distribution and is flexible enough to capture both under-dispersion and over-dispersion in count data. The advantage of tree-based methods is their scalability to high-dimensional data. We develop CMPMOB, an estimation procedure for a semi-varying coefficient model, using model-based recursive partitioning (MOB). The proposed framework is broader than the existing MOB framework as it allows node-invariant effects to be included in the model. To simplify the computational burden of the exhaustive search employed in the original MOB algorithm, a new split point estimation procedure is proposed by borrowing tools from change point estimation methodology. The proposed method uses only the estimated score functions without fitting models for each split point and, therefore, is computationally simpler. Since the tree-based methods only provide a piece-wise constant approximation to the underlying smooth function, we further propose the CMPBoost semi-varying coefficient model which uses the gradient boosting procedure for estimation. The usefulness of the proposed methods are illustrated using simulation studies and a real example from a bike sharing system in Washington, DC. Supplementary files for this article are available online.
DOI: 10.6084/m9.figshare.12141090.v2
title: Building Representative Matched Samples With Multi-Valued Treatments in Large Observational Studies

description: In this article, we present a new way of matching in observational studies that overcomes three limitations of existing matching approaches. First, it directly balances covariates with multi-valued treatments without explicitly estimating the generalized propensity score. Second, it builds self-weighted matched samples that are representative of a target population by design. Third, it can handle large datasets, with hundreds of thousands of observations, in a couple of minutes. The key insights of this new approach to matching are balancing the treatment groups relative to a target population and positing a linear-sized mixed integer formulation of the matching problem. We formally show that this formulation is more effective than alternative quadratic-sized formulations, as its reduction in size does not affect its strength from the standpoint of its linear programming relaxation. We also show that this formulation can be used for matching with distributional covariate balance in polynomial time under certain assumptions on the covariates and that it can handle large datasets in practice even when the assumptions are not satisfied. This algorithmic characterization is key to handling large datasets. We illustrate this new approach to matching in both a simulation study and an observational study of the impact of an earthquake on educational attainment. With this approach, the results after matching can be visualized with simple and transparent graphical displays: while increasing levels of exposure to the earthquake have a negative impact on school attendance, there is no effect on college admission test scores. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.11973537.v3
title: Bayesian Semiparametric Analysis of Multivariate Continuous Responses, With Variable Selection

description: This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical challenges revolve around dealing with the unknown mean and variance functions and in particular, the correlation matrix. To tackle these problems, we have developed priors over the smooth functions and a Markov chain Monte Carlo algorithm for inference and model selection. Specifically, Dirichlet process mixtures of Gaussian distributions are used as the basis for a cluster-inducing prior over the elements of the correlation matrix. The smooth, multidimensional means and variances are represented using radial basis function expansions. The complexity of the model, in terms of variable selection and smoothness, is then controlled by spike-slab priors. A simulation study is presented, demonstrating performance as the response dimension increases. Finally, the model is fit to a number of real world datasets. An R package, scripts for replicating synthetic and real data examples, and a detailed description of the MCMC sampler are available in the supplementary materials online.
DOI: 10.6084/m9.figshare.11983836.v4
title: High-Dimensional Copula Variational Approximation Through Transformation

description: Variational methods are attractive for computing Bayesian inference when exact inference is impractical. They approximate a target distribution—either the posterior or an augmented posterior—using a simpler distribution that is selected to balance accuracy with computational feasibility. Here, we approximate an element-wise parametric transformation of the target distribution as multivariate Gaussian or skew-normal. Approximations of this kind are implicit copula models for the original parameters, with a Gaussian or skew-normal copula function and flexible parametric margins. A key observation is that their adoption can improve the accuracy of variational inference in high dimensions at limited or no additional computational cost. We consider the Yeo–Johnson and inverse G&H transformations, along with sparse factor structures for the scale matrix of the Gaussian or skew-normal. We also show how to implement efficient reparameterization gradient methods for these copula-based approximations. The efficacy of the approach is illustrated by computing posterior inference for three different models using six real datasets. In each case, we show that our proposed copula model distributions are more accurate variational approximations than Gaussian or skew-normal distributions, but at only a minor or no increase in computational cost. Supplementary materials comprising an online appendix, MATLAB code to implement the method, and the datasets employed, are available online.
DOI: 10.6084/m9.figshare.12141066.v2
title: State-Dependent Kernel Selection for Conditional Sampling of Graphs

description: This article introduces new efficient algorithms for two problems: sampling conditional on vertex degrees in unweighted graphs, and conditional on vertex strengths in weighted graphs. The resulting conditional distributions provide the basis for exact tests on social networks and two-way contingency tables. The algorithms are able to sample conditional on the presence or absence of an arbitrary set of edges. Existing samplers based on MCMC or sequential importance sampling are generally not scalable; their efficiency can degrade in large graphs with complex patterns of known edges. MCMC methods usually require explicit computation of a Markov basis to navigate the state space; this is computationally intensive even for small graphs. Our samplers do not require a Markov basis, and are efficient both in sparse and dense settings. The key idea is to carefully select a Markov kernel on the basis of the current state of the chain. We demonstrate the utility of our methods on a real network and contingency table. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.12066147.v2
title: Predicting the Output From a Stochastic Computer Model When a Deterministic Approximation is Available

description: Statistically modeling the output of a stochastic computer model can be difficult to do accurately without a large simulation budget. We alleviate this problem by exploiting readily available deterministic approximations to efficiently learn about the respective stochastic computer models. This is done via the summation of two Gaussian processes; one responsible for modeling the deterministic approximation, the other responsible for using such approximation to better statistically model the stochastic computer model. The developed method provides high predictive performance and increased confidence that complicated features of a stochastic computer model are captured, even when the simulation budget is small. Several synthetic computer models are used to outline the capabilities of this method, and two real-world examples are used to display its practical utility. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.11973531
title: Co-Clustering of Ordinal Data via Latent Continuous Random Variables and Not Missing at Random Entries

description: This article is about the co-clustering of ordinal data. Such data are very common on e-commerce platforms where customers rank the products/services they bought. In more detail, we focus on arrays of ordinal (possibly missing) data involving two disjoint sets of individuals/objects corresponding to the rows/columns of the arrays. Typically, an observed entry (<i>i</i>, <i>j</i>) in the array is an ordinal score assigned by the individual/row <i>i</i> to the object/column <i>j</i>. A new generative model for arrays of ordinal data is introduced along with an inference algorithm for parameters estimation. The model accounts for not missing at random data and relies on latent continuous random variables. The fitting allows to simultaneously co-cluster the rows and columns of an array. The estimation of the model parameters is performed via a classification expectation maximization algorithm. A model selection criterion is formally obtained to select the number of row and column clusters. To show that our approach reaches and often outperforms the state of the art, we carry out numerical experiments on synthetic data. Finally, applications on real datasets highlight the model capacity to deal with very sparse arrays. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.11973531.v2
title: Co-Clustering of Ordinal Data via Latent Continuous Random Variables and Not Missing at Random Entries

description: This article is about the co-clustering of ordinal data. Such data are very common on e-commerce platforms where customers rank the products/services they bought. In more detail, we focus on arrays of ordinal (possibly missing) data involving two disjoint sets of individuals/objects corresponding to the rows/columns of the arrays. Typically, an observed entry (<i>i</i>, <i>j</i>) in the array is an ordinal score assigned by the individual/row <i>i</i> to the object/column <i>j</i>. A new generative model for arrays of ordinal data is introduced along with an inference algorithm for parameters estimation. The model accounts for not missing at random data and relies on latent continuous random variables. The fitting allows to simultaneously co-cluster the rows and columns of an array. The estimation of the model parameters is performed via a classification expectation maximization algorithm. A model selection criterion is formally obtained to select the number of row and column clusters. To show that our approach reaches and often outperforms the state of the art, we carry out numerical experiments on synthetic data. Finally, applications on real datasets highlight the model capacity to deal with very sparse arrays. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.11973558.v3
title: Bayesian Variational Inference for Exponential Random Graph Models

description: Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging “doubly intractable” problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC) methods which yield Bayesian inference for ERGMs, such as the exchange algorithm, are asymptotically exact but computationally intensive, as a network has to be drawn from the likelihood at every step using, for instance, a “tie no tie” sampler. In this article, we develop a variety of variational methods for Gaussian approximation of the posterior density and model selection. These include nonconjugate variational message passing based on an adjusted pseudolikelihood and stochastic variational inference. To overcome the computational hurdle of drawing a network from the likelihood at each iteration, we propose stochastic gradient ascent with biased but consistent gradient estimates computed using adaptive self-normalized importance sampling. These methods provide attractive fast alternatives to MCMC for posterior approximation. We illustrate the variational methods using real networks and compare their accuracy with results obtained via MCMC and Laplace approximation. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.12141066.v1
title: State-Dependent Kernel Selection for Conditional Sampling of Graphs

description: This article introduces new efficient algorithms for two problems: sampling conditional on vertex degrees in unweighted graphs, and conditional on vertex strengths in weighted graphs. The resulting conditional distributions provide the basis for exact tests on social networks and two-way contingency tables. The algorithms are able to sample conditional on the presence or absence of an arbitrary set of edges. Existing samplers based on MCMC or sequential importance sampling are generally not scalable; their efficiency can degrade in large graphs with complex patterns of known edges. MCMC methods usually require explicit computation of a Markov basis to navigate the state space; this is computationally intensive even for small graphs. Our samplers do not require a Markov basis, and are efficient both in sparse and dense settings. The key idea is to carefully select a Markov kernel on the basis of the current state of the chain. We demonstrate the utility of our methods on a real network and contingency table. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.11973537.v2
title: Bayesian Semiparametric Analysis of Multivariate Continuous Responses, With Variable Selection

description: This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical challenges revolve around dealing with the unknown mean and variance functions and in particular, the correlation matrix. To tackle these problems, we have developed priors over the smooth functions and a Markov chain Monte Carlo algorithm for inference and model selection. Specifically, Dirichlet process mixtures of Gaussian distributions are used as the basis for a cluster-inducing prior over the elements of the correlation matrix. The smooth, multidimensional means and variances are represented using radial basis function expansions. The complexity of the model, in terms of variable selection and smoothness, is then controlled by spike-slab priors. A simulation study is presented, demonstrating performance as the response dimension increases. Finally, the model is fit to a number of real world datasets. An R package, scripts for replicating synthetic and real data examples, and a detailed description of the MCMC sampler are available in the supplementary materials online.
DOI: 10.6084/m9.figshare.11932974
title: Consensus Monte Carlo for Random Subsets Using Shared Anchors

description: We present a consensus Monte Carlo algorithm that scales existing Bayesian nonparametric models for clustering and feature allocation to big data. The algorithm is valid for any prior on random subsets such as partitions and latent feature allocation, under essentially any sampling model. Motivated by three case studies, we focus on clustering induced by a Dirichlet process mixture sampling model, inference under an Indian buffet process prior with a binomial sampling model, and with a categorical sampling model. We assess the proposed algorithm with simulation studies and show results for inference with three datasets: an MNIST image dataset, a dataset of pancreatic cancer mutations, and a large set of electronic health records. Supplementary materials for this article are available online.