PAC-Bayesian Theory Meets Bayesian Inference
Authors: Pascal Germain, Francis Bach, Alexandre Lacoste, Simon Lacoste-Julien
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In Section 6, we study the Bayesian model selection from a PAC-Bayesian perspective, and illustrate our finding on classical Bayesian regression tasks. (...) To produce Figures 1a and 1b, we reimplemented the toy experiment of Bishop [5, Section 3.5.1]. (...) Figure 1c compares the values of the PAC-Bayesian bounds presented in this paper on a synthetic dataset... |
| Researcher Affiliation | Collaboration | Pascal Germain Francis Bach Alexandre Lacoste Simon Lacoste-Julien INRIA Paris École Normale Supérieure, firstname.lastname@inria.fr Google, allac@google.com |
| Pseudocode | No | The paper does not contain any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statement about releasing source code for the methodology described. |
| Open Datasets | No | To produce Figures 1a and 1b, we reimplemented the toy experiment of Bishop [5, Section 3.5.1]. That is, we generated a learning sample of 15 data points according to y = sin(x) + , where x is uniformly sampled in the interval [0, 2 ] and N(0, 1/4) is a Gaussian noise. (...) Figure 1c compares the values of the PAC-Bayesian bounds presented in this paper on a synthetic dataset, where each input x2R20 is generated by a Gaussian x N(0, I). The associated output y2R is given by y=w x + , with kw k= 1/9. |
| Dataset Splits | No | No specific validation dataset splits were mentioned. The paper discusses 'training samples' and evaluating 'generalization risk (computed on a test sample of size 1000)'. |
| Hardware Specification | No | No specific hardware details (e.g., GPU/CPU models, memory) used for running experiments were mentioned. The paper only describes the synthetic data generation and the models learned. |
| Software Dependencies | No | No specific software dependencies with version numbers were mentioned. |
| Experiment Setup | Yes | More precisely, for a polynomial model of degree d, we map input x 2 R to a vector φ(x) = [1, x1, x2, . . . , xd] 2 Rd+1, and we fix parameters σ^2 = 1/0.005 and σ'^2 = 1/2. (...) We perform Bayesian linear regression in the input space, i.e., φ(x)=x, fixing σ^2 = 1/100 and σ'^2=2. |