Sampling with Mirrored Stein Operators

Authors: Jiaxin Shi, Chang Liu, Lester Mackey

ICLR 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental In Sec. 5, we demonstrate the advantages of our algorithms on benchmark simplex-constrained problems from the literature, constrained sampling problems in post-selection inference (Taylor & Tibshirani, 2015; Lee et al., 2016; Tian et al., 2016), and unconstrained large-scale posterior inference with the Fisher information metric. Finally, we analyze the convergence of our mirrored algorithms in Sec. 6 and discuss our results in Sec. 7. 5 EXPERIMENTS We next conduct a series of simulated and real-data experiments to assess (1) distributional approximation on the simplex, (2) frequentist confidence interval construction for (constrained) post-selection inference, and (3) large-scale posterior inference with non-Euclidean geometry.
Researcher Affiliation Industry Jiaxin Shi1 Chang Liu2 Lester Mackey1 1 Microsoft Research New England 2 Microsoft Research Asia {jiaxinshi,chang.liu,lmackey}@microsoft.com
Pseudocode Yes Algorithm 1 Mirrored Stein Variational Gradient Descent & Stein Variational Mirror Descent
Open Source Code Yes https://github.com/thjashin/mirror-stein-samplers for Python and R code replicating all experiments.
Open Datasets Yes We first measure distributional approximation quality using two 20-dimensional simplex-constrained targets: the sparse Dirchlet posterior of Patterson & Teh (2013) extended to 20 dimensions and the quadratic simplex target of Ahn & Chewi (2020).
Dataset Splits Yes For each run, we randomly keep 20% of the dataset as test data, 20% of the remaining points as the validation set, and all the rest as the training set.
Hardware Specification Yes Results were recorded on an Intel(R) Xeon(R) CPU E5-2690 v4 @ 2.60GHz and an NVIDIA Tesla P100 PCIe 16GB.
Software Dependencies No The paper mentions 'Python and R code' in the reproducibility statement, but does not specify version numbers for any software libraries, frameworks, or specific solvers.
Experiment Setup Yes The bandwidth ℓis determined by the median heuristic (Garreau et al., 2017). We select τ from {0.98, 0.99} for all SVMD experiments. For unconstrained targets, we report, for each method, results from the best fixed step size ϵ {0.01, 0.05, 0.1, 0.5, 1} selected on a separate validation set. For constrained targets, we select step sizes adaptively to accommodate rapid density growth near the boundary; specifically, we use RMSProp (Hinton et al., 2012)...