arXiv subjects

Esmail Abdul Fattah

Publications and source records attributed to Esmail Abdul Fattah.

7 recordsLinked to original sources

arXiv2026

Dense Matrices Are Alike; Sparse Matrices Are Sparse in Their Own Way: A Structure-Adaptive Tile Cholesky Factorization

Sparse direct Cholesky solvers fix one data structure for an entire matrix, but symmetric positive definite systems range from nearly dense to irregular, sometimes mixing both within one matrix. We let the data structure follow the sparsity structure, across matrices and across tiles within a matrix. Before numerical work starts, a lightweight selector captures the sparsity pattern of the Cholesky factor and routes the matrix, on one static shared-memory schedule, to one of three regimes: dense, sparse, or an intermediate semisparse regime. Dense tiles are stored in full; the semisparse regime uses a new active-column tile that keeps only the columns the factorization will touch, so banded or arrowhead-shaped structures common in spatial models still reach BLAS-3 efficiency. The approach suits the integrated nested Laplace approximation (INLA): one sparsity pattern factorized thousands of times with different values, so the one-time analysis cost is amortized and every factorization saving compounds. We evaluate the technique on 60 SPD matrices, comparing against MUMPS, PaStiX, CHOLMOD, symPACK, and Intel oneMKL PARDISO on Intel Xeon and AMD EPYC nodes; the selector alone achieves the lowest total factorization time in every regime. Summed over the suite, it beats the best fixed single-structure mode by 1.6 to 2.6x, and every alternative by 1.8 to 12.5x on Intel and 2.6 to 10.1x on AMD, with the largest gains on the most expensive factorizations. It trades more one-time analysis for less time per factorization, pulling ahead by the third factorization of a given pattern. As a first GPU extension, the dense route on one NVIDIA A100, with the factor resident on the device, runs 1.2 to 6.3x faster than on the faster CPU node, the margin widening with factor size. Solver, Python/R/Julia interfaces, benchmark suite, and results are open at https://github.com/esmail-abdulfattah/sTiles.

cs.PF↗

arXiv2026

PyINLA: Fast Bayesian Inference for Latent Gaussian Models in Python

Bayesian inference often relies on Markov chain Monte Carlo (MCMC) methods, particularly required for non-Gaussian data families. When dealing with complex hierarchical models, the MCMC approach can be computationally demanding in workflows that require repeated model fitting or when working with models of large dimensions with limited hardware resources. The Integrated Nested Laplace Approximations (INLA) is a deterministic alternative for models with non-Gaussian data that belong to the class of latent Gaussian models (LGMs), yielding accurate approximations to posterior marginals in many applied settings. The INLA method was implemented in C as a standalone program, inla, that is widely used in R through the INLA package. This paper introduces PyINLA, a dedicated Python package that provides a Pythonic interface directly to the inla program. Therefore, PyINLA enables specifying LGMs, running INLA-based inference, and accessing posterior summaries directly from Python while leveraging the established INLA implementation. We describe the package design and illustrate its use on representative models, including generalized linear mixed models, time series forecasting, disease mapping, and geostatistical prediction, demonstrating how deterministic Bayesian inference can be performed in Python using INLA in a way that integrates naturally with common scientific computing workflows.

stat.AP↗

arXiv2025

GPU-Accelerated Parallel Selected Inversion for Structured Matrices Using sTiles

Selected inversion is essential for applications such as Bayesian inference, electronic structure calculations, and inverse covariance estimation, where computing only specific elements of large sparse matrix inverses significantly reduces computational and memory overhead. We present an efficient implementation of a two-phase parallel algorithm for computing selected elements of the inverse of a sparse symmetric matrix A, which can be expressed as A = LL^T through sparse Cholesky factorization. Our approach leverages a tile-based structure, focusing on selected dense tiles to optimize computational efficiency and parallelism. While the focus is on arrowhead matrices, the method can be extended to handle general structured matrices. Performance evaluations on a dual-socket 26-core Intel Xeon CPU server demonstrate that sTiles outperforms state-of-the-art direct solvers such as Panua-PARDISO, achieving up to 13X speedup on large-scale structured matrices. Additionally, our GPU implementation using an NVIDIA A100 GPU demonstrates substantial acceleration over its CPU counterpart, achieving up to 5X speedup for large, high-bandwidth matrices with high computational intensity. These results underscore the robustness and versatility of sTiles, validating its effectiveness across various densities and problem configurations.

cs.PF↗

arXiv2025

sTiles: An Accelerated Computational Framework for Sparse Factorizations of Structured Matrices

This paper introduces sTiles, a GPU-accelerated framework for factorizing sparse structured symmetric matrices. By leveraging tile algorithms for fine-grained computations, sTiles uses a structure-aware task execution flow to handle challenging arrowhead sparse matrices with variable bandwidths, common in scientific and engineering fields. It minimizes fill-in during Cholesky factorization using permutation techniques and employs a static scheduler to manage tasks on shared-memory systems with GPU accelerators. sTiles balances tile size and parallelism, where larger tiles enhance algorithmic intensity but increase floating-point operations and memory usage, while parallelism is constrained by the arrowhead structure. To expose more parallelism, a left-looking Cholesky variant breaks sequential dependencies in trailing submatrix updates via tree reductions. Evaluations show sTiles achieves speedups of up to 8.41X, 9.34X, 5.07X, and 11.08X compared to CHOLMOD, SymPACK, MUMPS, and PARDISO, respectively, and a 5X speedup compared to a 32-core AMD EPYC CPU on an NVIDIA A100 GPU. Our generic software framework imports well-established concepts from dense matrix computations but they all require customizations in their deployments on hybrid architectures to best handle factorizations of sparse matrices with arrowhead structures.

cs.PF↗

arXiv2023

Non-stationary Bayesian Spatial Model for Disease Mapping based on Sub-regions

This paper aims to extend the Besag model, a widely used Bayesian spatial model in disease mapping, to a non-stationary spatial model for irregular lattice-type data. The goal is to improve the model's ability to capture complex spatial dependence patterns and increase interpretability. The proposed model uses multiple precision parameters, accounting for different intensities of spatial dependence in different sub-regions. We derive a joint penalized complexity prior for the flexible local precision parameters to prevent overfitting and ensure contraction to the stationary model at a user-defined rate. The proposed methodology can be used as a basis for the development of various other non-stationary effects over other domains such as time. An accompanying R package 'fbesag' equips the reader with the necessary tools for immediate use and application. We illustrate the novelty of the proposal by modeling the risk of dengue in Brazil, where the stationary spatial assumption fails and interesting risk profiles are estimated when accounting for spatial non-stationary.

stat.ME↗

arXiv2022

Approximate Bayesian Inference for the Interaction Types 1, 2, 3 and 4 with Application in Disease Mapping

We address in this paper a new approach for fitting spatiotemporal models with application in disease mapping using the interaction types 1,2,3, and 4. When we account for the spatiotemporal interactions in disease-mapping models, inference becomes more useful in revealing unknown patterns in the data. However, when the number of locations and/or the number of time points is large, the inference gets computationally challenging due to the high number of required constraints necessary for inference, and this holds for various inference architectures including Markov chain Monte Carlo (MCMC) and Integrated Nested Laplace Approximations (INLA). We re-formulate INLA approach based on dense matrices to fit the intrinsic spatiotemporal models with the four interaction types and account for the sum-to-zero constraints, and discuss how the new approach can be implemented in a high-performance computing framework. The computing time using the new approach does not depend on the number of constraints and can reach a 40-fold faster speed compared to INLA in realistic scenarios. This approach is verified by a simulation study and a real data application, and it is implemented in the R package INLAPLUS and the Python header function: inla1234().

stat.ME↗

arXiv2021

Smart Gradient -- An Adaptive Technique for Improving Gradient Estimation

Computing the gradient of a function provides fundamental information about its behavior. This information is essential for several applications and algorithms across various fields. One common application that require gradients are optimization techniques such as stochastic gradient descent, Newton's method and trust region methods. However, these methods usually requires a numerical computation of the gradient at every iteration of the method which is prone to numerical errors. We propose a simple limited-memory technique for improving the accuracy of a numerically computed gradient in this gradient-based optimization framework by exploiting (1) a coordinate transformation of the gradient and (2) the history of previously taken descent directions. The method is verified empirically by extensive experimentation on both test functions and on real data applications. The proposed method is implemented in the R package smartGrad and in C++.

math.NA↗