Amortized Monte Carlo Integration
Authors: Adam Golinski, Frank Wood, Tom Rainforth
ICML 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | It is therefore necessary to test its empirical performance to assert that gains are possible with inexact proposals. To this end, we investigate AMCI s performance on two illustrative examples. [...] As shown in Figure 1, AMCI outperformed SNIS in both the one- and five-dimensional cases. [...] Results are presented in Figure 2. AMCI again significantly outperformed the literature baseline of SNIS q2 |
| Researcher Affiliation | Academia | Adam Goli nski * 1 2 Frank Wood 3 Tom Rainforth * 1 1Department of Statistics, University of Oxford, United Kingdom 2Department of Engineering Science, University of Oxford, United Kingdom 3Department of Computer Science, University of British Columbia, Vancouver, Canada. |
| Pseudocode | No | No pseudocode or algorithm blocks are present in the paper. |
| Open Source Code | Yes | An implementation for AMCI and our experiments is available at http://github.com/talesa/amci. |
| Open Datasets | No | We start with the conceptually simple problem of calculating tail integrals for Gaussian distributions, namely p(x) = N(x; 0, Σ1) p(y|x) = N(y; x, Σ2) (24) f(x; θ) = YD i=1 1xi>θi p(θ) = UNIFORM(θ; [0, u D]D where D is the dimensionality, we set Σ2 = I, and Σ1 is a fixed covariance matrix (for details see Appendix C). [...] To demonstrate how AMCI might be used in a more realworld scenario, we now consider an illustrative example relating to cancer diagnostic decisions. [...] A detailed description of the model and proposal setup is in the Appendix C.3. |
| Dataset Splits | No | Though the exact process varies with context, the inference network is usually trained either by drawing latent-data sample pairs from the joint p(x, y) (Paige & Wood, 2016; Le et al., 2017; 2018b), or by drawing mini-batches from a large dataset using stochastic variational inference approaches (Hoffman et al., 2013; Kingma & Welling, 2014; Rezende et al., 2014; Ritchie et al., 2016). |
| Hardware Specification | No | No specific hardware details (like GPU/CPU models, memory, or specific computing environments) are provided for running the experiments. |
| Software Dependencies | No | We use normalizing flows (Rezende & Mohamed, 2015) to construct our proposals, providing a flexible and powerful means of representing the target distributions. |
| Experiment Setup | No | Training was done by using importance sampling to generate the values of θ and x as per (22) with q (θ, x) = p(θ) HALFNORMAL(x; θ, diag(Σ2)). |