Research map / Probabilistic and scientific modeling / Variational and generative sampling
On Nesting Monte Carlo Estimators
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase both inner and outer sample counts as the total budget grows | NMC for nonlinear nested expectations · Single-level nested expectation | Consistency: O(1/N + 1/M) | Helped |
| Hold the inner sample count fixed while increasing the outer count (ablation) | NMC · Analytic nested expectation | Bias | Hurt |
| Use the continuously differentiable bound and allocate N proportional to M^2 (ablation) | NMC · Analytic nested expectation | MSE convergence rate: O(1/\sqrt{T}) -> O(1/T^{2/3}) | Helped |
| Reformulate discrete-outcome BED as separate non-nested estimates | Bayesian experimental design estimator · Bayesian experimental design, discrete outcomes | Convergence rate: O(1/N+1/M^2) -> O(1/N) | Helped |
| Set N=1 and use the full budget for M | VAE/IWAE evidence estimator · Importance weighted autoencoder evidence estimate | MSE bound | Helped |
| Replace NMC with a single expectation when the outer function is linear | Nested expectation estimator · Linear outer function | MSE convergence rate: O(1/N) | Helped |
| Use independent auxiliary draws to combine products of expectations into one expectation | Nested estimator for products of expectations · Products of expectations with linear outer function | MSE convergence rate: O(1/N) | Helped |
| Use the finite-realization reformulation for the outer variable | Nested expectation estimator · Finite possible realizations of y | MSE convergence rate: O(1/N) | Helped |
| Keep inner query computation fixed across calls | Nested probabilistic-program queries · Probabilistic program nesting | Convergence rate: O(1/N) | Helped |
| Use asymptotically optimal sample allocation at a finite budget (ablation) | Repeated-nesting NMC · Repeated nesting, fixed budget T=10^6 | Log MSE: (0.5,0.5); (0.53,0.36); (0.38,0.45) | Mixed |
| Use the asymptotically optimal outer-sample exponent at finite T (ablation) | Single-level NMC allocation · Analytic nested expectation, finite budgets | Final error: 0.5 for T=10^3; 0.6 for T=10^7; 2/3 | Hurt |
Closest papers by meaning
- Optimal randomized multilevel Monte Carlo for repeatedly nested expectations (ICML 2023 · similarity 0.90)
- Nested Expectations with Kernel Quadrature (ICML 2025 · similarity 0.90)
- Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo is All you Need (ICML 2024 · similarity 0.86)
- On Estimating the Gradient of the Expected Information Gain in Bayesian Experimental Design (AAAI 2024 · similarity 0.86)
- Nesting Particle Filters for Experimental Design in Dynamical Systems (ICML 2024 · similarity 0.84)
- Fearless Stochasticity in Expectation Propagation (NeurIPS 2024 · similarity 0.83)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.