Spike-and-Slab Generalized Additive Models and Scalable Algorithms for High-Dimensional Data

• URL: http://arxiv.org/abs/2110.14449v1
• Date: Wed, 27 Oct 2021 14:11:13 GMT
• Title: Spike-and-Slab Generalized Additive Models and Scalable Algorithms for High-Dimensional Data
• Authors: Boyi Guo, Byron C. Jaeger, A.K.M. Fazlur Rahman, D. Leann Long, Nengjun Yi
• Abstract summary: We propose hierarchical generalized additive models (GAMs) to accommodate high-dimensional data. We consider the smoothing penalty for proper shrinkage of curve and separation of smoothing function linear and nonlinear spaces. Two and deterministic algorithms, EM-Coordinate Descent and EM-Iterative Weighted Least Squares, are developed for different utilities.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: There are proposals that extend the classical generalized additive models (GAMs) to accommodate high-dimensional data ($p>>n$) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating smoothing functions, damaging predictive performance. Moreover, most of these GAMs consider an "all-in-all-out" approach for functional selection, rendering them difficult to answer if nonlinear effects are necessary. While some Bayesian models can address these shortcomings, using Markov chain Monte Carlo algorithms for model fitting creates a new challenge, scalability. Hence, we propose Bayesian hierarchical generalized additive models as a solution: we consider the smoothing penalty for proper shrinkage of curve interpolation and separation of smoothing function linear and nonlinear spaces. A novel spike-and-slab spline prior is proposed to select components of smoothing functions. Two scalable and deterministic algorithms, EM-Coordinate Descent and EM-Iterative Weighted Least Squares, are developed for different utilities. Simulation studies and metabolomics data analyses demonstrate improved predictive or computational performance against state-of-the-art models, mgcv, COSSO and sparse Bayesian GAM. The software implementation of the proposed models is freely available via an R package BHAM.

Related papers

• SIGMA: Scale-Invariant Global Sparse Shape Matching [50.385414715675076]
  We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for non-rigid shapes. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets.
  arXiv  Detail & Related papers  (2023-08-16T14:25:30Z)
• Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood Estimation for Latent Gaussian Models [69.22568644711113]
  We introduce probabilistic unrolling, a method that combines Monte Carlo sampling with iterative linear solvers to circumvent matrix inversions. Our theoretical analyses reveal that unrolling and backpropagation through the iterations of the solver can accelerate gradient estimation for maximum likelihood estimation. In experiments on simulated and real data, we demonstrate that probabilistic unrolling learns latent Gaussian models up to an order of magnitude faster than gradient EM, with minimal losses in model performance.
  arXiv  Detail & Related papers  (2023-06-05T21:08:34Z)
• Joint Graph Learning and Model Fitting in Laplacian Regularized Stratified Models [5.933030735757292]
  Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems. This paper shows the importance and sensitivity of graph weights in LRSM, and provably show that the sensitivity can be arbitrarily large. We propose a generic approach to jointly learn the graph while fitting the model parameters by solving a single optimization problem.
  arXiv  Detail & Related papers  (2023-05-04T06:06:29Z)
• A distribution-free mixed-integer optimization approach to hierarchical modelling of clustered and longitudinal data [0.0]
  We introduce an innovative algorithm that evaluates cluster effects for new data points, thereby increasing the robustness and precision of this model. The inferential and predictive efficacy of this approach is further illustrated through its application in student scoring and protein expression.
  arXiv  Detail & Related papers  (2023-02-06T23:34:51Z)
• Learning Graphical Factor Models with Riemannian Optimization [70.13748170371889]
  This paper proposes a flexible algorithmic framework for graph learning under low-rank structural constraints. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution. We leverage geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models.
  arXiv  Detail & Related papers  (2022-10-21T13:19:45Z)
• Adaptive LASSO estimation for functional hidden dynamic geostatistical model [69.10717733870575]
  We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hiddenstatistical models (f-HD) The algorithm is based on iterative optimisation and uses an adaptive least absolute shrinkage and selector operator (GMSOLAS) penalty function, wherein the weights are obtained by the unpenalised f-HD maximum-likelihood estimators.
  arXiv  Detail & Related papers  (2022-08-10T19:17:45Z)
• T-LoHo: A Bayesian Regularization Model for Structured Sparsity and Smoothness on Graphs [0.0]
  In graph-structured data, structured sparsity and smoothness tend to cluster together. We propose a new prior for high dimensional parameters with graphical relations. We use it to detect structured sparsity and smoothness simultaneously.
  arXiv  Detail & Related papers  (2021-07-06T10:10:03Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)
• Slice Sampling for General Completely Random Measures [74.24975039689893]
  We present a novel Markov chain Monte Carlo algorithm for posterior inference that adaptively sets the truncation level using auxiliary slice variables. The efficacy of the proposed algorithm is evaluated on several popular nonparametric models.
  arXiv  Detail & Related papers  (2020-06-24T17:53:53Z)
• Estimation of sparse Gaussian graphical models with hidden clustering structure [8.258451067861932]
  We propose a model to estimate the sparse Gaussian graphical models with hidden clustering structure. We develop a symmetric Gauss-Seidel based alternating direction method of the multipliers. Numerical experiments on both synthetic data and real data demonstrate the good performance of our model.
  arXiv  Detail & Related papers  (2020-04-17T08:43:31Z)
• Bayesian System ID: Optimal management of parameter, model, and measurement uncertainty [0.0]
  We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. We show that the log posterior has improved geometric properties compared with the objective function surfaces of traditional methods.
  arXiv  Detail & Related papers  (2020-03-04T22:48:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.