A Quadrature Rule combining Control Variates and Adaptive Importance Sampling
Authors: Rémi Leluc, François Portier, Johan Segers, Aigerim Zhuman
NeurIPS 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The good behavior of the method is illustrated empirically on synthetic examples and real-world data for Bayesian linear regression. To compare the finite-sample performance of the AIS and AISCV estimators, we first present in Section 6.1 synthetic data examples involving the integration problem over the unit cube [0, 1]d and then with respect to some Gaussian mixtures as in [4]. The goal is to compute R gf dλ for vectors of integrands g : Rd Rp. We consider various dimensions d > 1 and several choices for the number of control variates m. Section 6.2 deals with real-world datasets in the context of Bayesian inference. |
| Researcher Affiliation | Academia | Rémi Leluc LTCI, Télécom Paris Institut Polytechnique de Paris, France EMAIL, François Portier CREST ENSAI, France EMAIL, Aigerim Zhuman LIDAM, ISBA UCLouvain, Belgium EMAIL, Johan Segers LIDAM, ISBA UCLouvain, Belgium EMAIL |
| Pseudocode | Yes | Algorithm 1 Adaptive Importance Sampling with Control Variates (AISCV) and Algorithm 2 Quadrature Rule AISCV post-hoc scheme |
| Open Source Code | Yes | For ease of reproducibility, the code, numerical details and additional results are available in the supplementary material. |
| Open Datasets | Yes | Classical datasets from [11] are considered : housing (N = 506; d = 13; m {12; 104}); abalone (N = 4177; d = 8; m {7; 44}); red wine (N = 1599; d = 11; m {10; 77}); and white wine (N = 4898; d = 11; m {10; 77}). |
| Dataset Splits | No | The paper does not provide specific dataset split information (e.g., train/validation/test percentages or counts) as commonly understood for model training and evaluation. |
| Hardware Specification | No | The paper does not provide specific hardware details such as GPU models, CPU types, or memory specifications used for running its experiments. |
| Software Dependencies | No | The paper mentions software like 'Tensorflow', 'Py Torch', and 'Pymc' but does not specify their version numbers or any other software dependencies with version details. |
| Experiment Setup | Yes | In all simulations, the sampling policy is taken within the family of multivariate Student t distributions of degree ν denoted by {qµ,Σ0 : µ Rd} with Σ0 = σ0Id(ν 2)/ν and ν > 2, σ0 > 0. ... The allocation policy is fixed to nt = 1000 and the number of stages is T {5; 10; 20; 30; 50}. The policy parameters are µ0 = (0.5, . . . , 0.5) Rd, ν = 8, and σ0 = 0.1. |