Black-box density function estimation using recursive partitioning
Authors: Erik Bodin, Zhenwen Dai, Neill Campbell, Carl Henrik Ek
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The algorithm shows competitive performance to recent state-of-the-art methods on synthetic and realworld problems including parameter inference for gravitational-wave physics. We compare with DNS quantitatively both for evidence and parameter estimation. For evidence estimation, we measure the median absolute error in log evidence (or log Z) over 20 runs with various budgets. For parameter estimation, we measure the error in estimated differential entropy, due to lack of summary statistics for multi-modal distributions. Results for a few functions with various challenging characteristics are shown in Figure 6, such as very small or elongated typical sets (see supplement for the functions). |
| Researcher Affiliation | Collaboration | 1University of Bristol, United Kingdom 2Spotify, United Kingdom 3University of Bath, United Kingdom 4University of Cambridge, United Kingdom. |
| Pseudocode | Yes | Algorithm 1 DEFER Input: General density function f defined over Ωwith unknown normalisation constant Z. Output: Approximation ˆf, ˆZ, as specified by the produced partitioning ΠT . Initialize t = 1 and initial partitioning Π1 = {Ω} repeat # makes density acquisitions at each iteration {Ωi} = to divide [ Πt] divide each partition Ωi, each one resulting in {Ωj} new partitions add all sets of {Ωj} into Πt remove the divided partitions {Ωi} from Πt set t t + 1 and update data structures until Nt Nmax |
| Open Source Code | Yes | We provide code and examples for such applications and more at https://github.com/bodin-e/defer. |
| Open Datasets | Yes | We apply DEFER to a simulated signal example from (Ashton et al., 2019). We apply DEFER to a Gaussian Process time-series regression model with a spectral mixture kernel (SMK) (Wilson & Adams, 2013). |
| Dataset Splits | No | The paper does not provide specific details about training, validation, or test dataset splits using exact percentages, sample counts, or citations to predefined splits. |
| Hardware Specification | No | The paper discusses runtime performance in terms of milliseconds per evaluation but does not specify any hardware details such as GPU/CPU models, memory, or specific computing environments used for the experiments. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers (e.g., Python 3.8, PyTorch 1.9). |
| Experiment Setup | Yes | Here, β is a positive parameter specifying what constitutes a non-trivial amount of upper bound mass of a partition in relation to the current estimate of average mass; we fix β = 1 for all the experiments in this work. In practice, we set M = min(5, D) and fix α = 20 for all experiments in this work. In practice we fix φ = 1.2 in all experiments in this work, which we found works well empirically with little to no benefit of targeted tuning. |