Approximate Post-Selective Inference for Regression with the Group LASSO
Authors: Snigdha Panigrahi, Peter W MacDonald, Daniel Kessler
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments on simulated data and data from the Human Connectome Project demonstrate that our method recovers the effects of parameters within the selected groups while paying only a small price for bias adjustment. (Abstract) and We demonstrate the potential of our methods in numerical experiments and in a human neuroimaging application in Section 7. (Section 1) |
| Researcher Affiliation | Academia | Snigdha Panigrahi EMAIL Peter W. Mac Donald EMAIL Department of Statistics University of Michigan Ann Arbor, MI 48109-1107, USA Daniel Kessler EMAIL Department of Statistics and Department of Psychiatry University of Michigan Ann Arbor, MI 48109-1107, USA |
| Pseudocode | Yes | Algorithm 1 A Prototype Implementation of our Selection-informed Bayesian Method SELECT: (y, X, Ω, G, {λg}g G) Optimize (3) b E = E, b U = U, b Z = Z STEPS: Set up parameters for (Laplace) (Orthonormal completion) Calculate U (see Theorem 2) (Parameters) Calculate R, s, Θ, P, q, Σ (see Theorem 5) STEPS: Implementation for a generic gradient-based sampler (Initialize) Sample: β(1) E = bβE, Step Size: η, Proposal Scale: χ, Number of Samples: K for k = 1, 2, . . . , K 1 do (Laplace) Solve γ (k) = argminγ R|GE| n1 2(γ Pβ(k) E q) ( Σ) 1(γ Pβ(k) E q) + Barr(γ) o (Jacobian) Calculate J (k) (see Theorem 5) (Gradient) Calculate log πE(β(k) E | bβE, NE) (see Theorem 5) (Update) β(k+1) E β(k) E + ηχ log πE(β(k) E | bβE, NE) + 2ηϵ(k), ϵ(k) N(0, χ). |
| Open Source Code | Yes | The code for our experiments in the paper is available here: https://github.com/ snigdhagit/selective-inference/tree/group_LASSO/selection/randomized. |
| Open Datasets | Yes | We apply our method to a subset (n = 785) of human neuroimaging data from the Human Connectome Project (HCP) (Van Essen et al., 2013), a landmark study undertaken by a consortium involving Washington University, the University of Minnesota, and Oxford University. and The preprocessed version of the data set used in our analysis, which had undergone the processing stream described in Glasser et al. (2013), was downloaded from the HCP s Connectome DB platform (Marcus et al., 2011). |
| Dataset Splits | Yes | Split , the sample splitting method follows the same procedure as Naive except that this method partitions the data at a prespecified ratio r, that is, Split applies the usual Group LASSO to [rn] randomly chosen subsamples without replacement to obtain E and then uses the remaining (holdout) samples to fit a linear model restricted to E for interval estimation. and We consider the level of isotropic Gaussian randomization to be 1:1, 2:1, and 9:1 by setting the variance parameter τ 2 according to (23) after replacing σ2 with ˆσ2 = (n p) 1 y X (X X) 1 X y 2 for r = 1/2, 2/3, 9/10, respectively. |
| Hardware Specification | No | This research was supported in part through computational resources and services provided by Advanced Research Computing (ARC), a division of Information and Technology Services (ITS) at the University of Michigan, Ann Arbor. In addition, this work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562. No specific hardware models (e.g., GPU/CPU) or specifications are mentioned. |
| Software Dependencies | No | Contrasts were obtained using in-house processing scripts that use SPM12. No specific version number is provided for SPM12 or any other software. |
| Experiment Setup | Yes | In practice, we set η = 1 and determine χ from the inverse of the Hessian of our (negative-log) posterior. Completing our specifications, the inferential results we report in Section 7 are based upon 1500 draws of the Langevin sampler. We discard the first 100 samples as burn-in and retain the remainder for uncertainty estimation. Barr(γ) = P g GE log(1 + (γg) 1). we fix σ = 3 in our experiments. and For the selection step, we set the grouped penalty weights to be λg = λ|g|/pg for solving the Group LASSO... |