Positive Curvature and Hamiltonian Monte Carlo
Authors: Christof Seiler, Simon Rubinstein-Salzedo, Susan Holmes
NeurIPS 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this paper, we present a theoretical analysis of HMC. ... Our main result quantifies how large T must be in order to obtain a good approximation to the above stated integral through its sample mean... Figure 1: Top left: Minimum and sample average of sectional curvatures for 14to 50-dimensional multivariate Gaussian π with identity covariance. For each dimension we run a HMC random walk with T = 104 steps. ... Figure 2: (Covariance structure with weak dependencies) Left: Sample means for 1000 simulations for the first coordinate of the 100 dimensional multivariate Gaussian. |
| Researcher Affiliation | Academia | Christof Seiler Simon Rubinstein-Salzedo Susan Holmes Department of Statistics Stanford University {cseiler,simonr}@stanford.edu, susan@stat.stanford.edu |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not provide an explicit statement or link for open-source code related to its methodology. |
| Open Datasets | No | The paper states: "For a book-length introduction to sampling from multivariate Gaussians, see [6]." and uses "sampling from a 100-dimensional multivariate Gaussian". This is a synthetic distribution/problem setup, not a publicly available dataset with concrete access information. |
| Dataset Splits | No | The paper discusses concepts like "burn-in time" and "running time" for Markov chains, which are not equivalent to standard training, validation, and test dataset splits typically found in supervised machine learning experiments. No specific data splits are mentioned for reproducibility in the context of dataset validation. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for running the experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers. |
| Experiment Setup | Yes | Example (Running time estimate). Now we give a concentration inequality simulation for sampling from a 100-dimensional multivariate Gaussian... and the following parameters Error bound r = 0.05 Starting point q0 = 0 Markov chain kernel P N(0, I100) Coarse Ricci curvature κ = 0.0024 Coarse diffusion constant σ2(q) = 100 Local dimension nq = 100 Lipschitz norm f Lip = 0.1 Eccentricity E(0) = 99.75 |