arXiv subjects

Abdolnasser Sadeghkhani

Publications and source records attributed to Abdolnasser Sadeghkhani.

6 recordsLinked to original sources

arXiv2026

Scalable Bayesian structure learning of directed acyclic graphs via Laplace approximation, with an application to breast cancer gene expression networks

Structure learning of directed acyclic graphs (DAGs) from observational data is a foundational task in causal discovery and is widely used to infer regulatory networks from medical and genomic measurements. The Bayesian formulation quantifies model uncertainty and admits prior biological knowledge, but its practical use has been hampered by the super-exponential growth of the DAG space and by the intractability of the node-marginal likelihood under flexible, non-conjugate priors. Existing closed-form solutions are largely confined to the conjugate Normal--Inverse-Gamma prior. We develop a Laplace-approximated Bayesian scoring function for the non-conjugate Normal--Gamma prior on the modified Cholesky parameterisation of the precision matrix, embed it in a Metropolis--Hastings sampler over DAGs, and couple the latent Gaussian network to a binary clinical outcome through a probit link. We show that the node-marginal integral is of generalised inverse-Gaussian form, so that its exact value is a modified Bessel function of the second kind and the proposed scoring function is its leading large-argument asymptotic; the posterior of each conditional variance is likewise generalised inverse-Gaussian and is sampled exactly. In simulation, the proposed prior improves on the conjugate baseline and on the PC, greedy-equivalence-search, NOTEARS, and DAGMA benchmarks at sample sizes typical of clinical cohorts. On two real datasets, the Sachs protein-signalling network, scored against its validated consensus graph, and the Wisconsin Diagnostic Breast Cancer data, the method recovers known structure and, through the DAG-probit extension, predicts malignancy from nuclear morphometry with a cross-validated ROC-AUC of $0.94$ using a sparse, interpretable set of direct predictors.

stat.ME↗

arXiv2026

Bayesian DAG Structure Learning with Simultaneous Shrinkage Covariance Estimation under Scale-Mixture Error Distributions in the Proportional High-Dimensional Regime

We propose a unified Bayesian framework namely robust DAG-Cholesky horseshoe (R-DACH) for joint directed acyclic graph (DAG) structure learning and precision matrix estimation in the high-dimensional proportional asymptotic regime $p/n \to c \in (0,\infty)$, under the scale mixture of normal errors. The construction places a global-local horseshoe-type prior directly on the strictly lower-triangular entries of the modified Cholesky factor of the DAG-Markov precision matrix, so that sparsity in the Cholesky parameters induces a coherent parent-set selection consistent with a topological ordering of the variables. A per-observation inverse-gamma scale mixture yields automatic robustness to heavy-tailed and contaminated observations and admits Student-$t$, Laplace, and slash distributions as special cases. We design a partially-collapsed blocked Gibbs sampler that traverses the joint space of orderings, sparsity patterns and continuous parameters. Simulations across $(n,p)$ configurations with $p$ up to several hundreds confirm the theoretical rates and demonstrate substantial gains over graphical-horseshoe, DAG-Wishart, and PC-based competitors under contamination. An application to RNA-seq gene-expression data from \emph{The Cancer Genome Atlas} reveals biologically interpretable regulatory structure that competing methods fail to recover.

stat.ME↗

arXiv2024

Multivariate Interval-Valued Models in Frequentist and Bayesian Schemes

In recent years, addressing the challenges posed by massive datasets has led researchers to explore aggregated data, particularly leveraging interval-valued data, akin to traditional symbolic data analysis. While much recent research, with the exception of Samdai et al. (2023) who focused on the bivariate case, has primarily concentrated on parameter estimation in single-variable scenarios, this paper extends such investigations to the multivariate domain for the first time. We derive maximum likelihood (ML) estimators for the parameters and establish their asymptotic distributions. Additionally, we pioneer a theoretical Bayesian framework, previously confined to the univariate setting, for multivariate data. We provide a detailed exposition of the proposed estimators and conduct comparative performance analyses. Finally, we validate the effectiveness of our estimators through simulations and real-world data analysis.

stat.ME↗

arXiv2019

Predicting the scoring time in hockey

In this paper, we propose a Bayesian predictive density estimator to predict the time until the r-th goal is scored in a hockey game, using ancillary information such as their performances in the past, points and specialists' opinions. To be more specific, we consider a gamma distribution as a waiting scoring model. The proposed density estimator belongs to an interesting new version of weighted beta prime distribution and outperforms the other estimator in the literature. The efficiency of our estimator is evaluated using frequentist risk along with measuring the prediction error from the old dataset, 2016-17, to the current season (2018-19) of the National Hockey League.

stat.AP↗

arXiv2018

Bayesian predictive densities as an interpretation of a class of Skew--Student $t$ distributions with application to medical data

This paper describes a new Bayesian interpretation of a class of skew--Student $t$ distributions. We consider a hierarchical normal model with unknown covariance matrix and show that by imposing different restrictions on the parameter space, corresponding Bayes predictive density estimators under Kullback-Leibler loss function embrace some well-known skew--Student $t$ distributions. We show that obtained estimators perform better in terms of frequentist risk function over regular Bayes predictive density estimators. We apply our proposed methods to estimate future densities of medical data: the leg-length discrepancy and effect of exercise on the age at which a child starts to walk.

stat.ME↗

arXiv2017

On predictive density estimation with additional information

Based on independently distributed $X_1 \sim N_p(θ_1, σ^2_1 I_p)$ and $X_2 \sim N_p(θ_2, σ^2_2 I_p)$, we consider the efficiency of various predictive density estimators for $Y_1 \sim N_p(θ_1, σ^2_Y I_p)$, with the additional information $θ_1 - θ_2 \in A$ and known $σ^2_1, σ^2_2, σ^2_Y$. We provide improvements on benchmark predictive densities such as plug-in, the maximum likelihood, and the minimum risk equivariant predictive densities. Dominance results are obtained for $α-$divergence losses and include Bayesian improvements for reverse Kullback-Leibler loss, and Kullback-Leibler (KL) loss in the univariate case ($p=1$). An ensemble of techniques are exploited, including variance expansion (for KL loss), point estimation duality, and concave inequalities. Representations for Bayesian predictive densities, and in particular for $\hat{q}_{π_{U,A}}$ associated with a uniform prior for $θ=(θ_1, θ_2)$ truncated to $\{θ\in \mathbb{R}^{2p}: θ_1 - θ_2 \in A \}$, are established and are used for the Bayesian dominance findings. Finally and interestingly, these Bayesian predictive densities also relate to skew-normal distributions, as well as new forms of such distributions.

math.ST↗