Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation
Authors: David Holzmüller, Francis Bach
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our experimental study nonetheless confirms practical differences between the convergence rates of some of the investigated efficient algorithms, although it is limited to a toy problem and simple algorithms. |
| Researcher Affiliation | Academia | David Holzmüller david dot holzmuller at inria.fr Francis Bach EMAIL INRIA Ecole Normale Supérieure PSL Research University |
| Pseudocode | Yes | Algorithm 1 Rejection sampling with proposal distribution Pg limited to n function evaluations. ... Algorithm 2 Bisection sampling algorithm using a log-partition algorithm L. |
| Open Source Code | Yes | Our plots can be reproduced using the code at github.com/dholzmueller/sampling_experiments |
| Open Datasets | No | To further investigate the convergence behavior of some simple algorithms, we study them numerically on functions of the form f : [0, 1]3 R, x 7 β(x1 + x2 + x3). While these functions are simple (and concave), they pose a challenge to some general algorithms as they have a large range in relation to their Lipschitz constant. |
| Dataset Splits | No | The paper uses a synthetic function for its experiments (functions of the form f : [0, 1]3 R, x 7 β(x1 + x2 + x3)) and does not mention any dataset splits for this synthetic data, nor for any external dataset. |
| Hardware Specification | No | No specific hardware details (exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments are mentioned in the paper. |
| Software Dependencies | No | No specific ancillary software details (e.g., library or solver names with version numbers like Python 3.8, CPLEX 12.4) are mentioned in the paper. |
| Experiment Setup | Yes | Figure 2: Convergence of the (median) error |Lf Lf| for different values of β {0.1, 40, 10000}. For the stochastic methods MC and PC+MC, the median is taken over 10001 independent runs. ... Figure 3: Convergence of different sampling methods in terms of the empirical energy distance, computed using N = 106 samples for each distribution, to the true distribution Pf for β = 15. |