AMIS Adaptive Multiple Importance Sampling with Past-Weight Recycling
Algorithms AIMech:AMISAdaptiveMultipleImportanceSamplingWithPastWeightRecycling DRAFT
Aliases: Adaptive Multiple Importance Sampling, AMIS Past-Weight Recycling Importance Sampler, Cornuet-Marin-Mira-Robert Adaptive Multiple Importance Sampling
An adaptive importance sampling algorithm that iteratively updates parametric proposal distributions (such as multivariate Student-t densities fitted via weighted moment matching) while recycling all previously simulated particles at every iteration t by incrementally updating each past particle's Owen-Zhou deterministic multiple mixture denominator delta_i^l <- delta_i^l + N_t q_t(x_i^l) and recomputing importance weights omega_i^l = pi(x_i^l) / (delta_i^l / sum_{j=0}^t N_j) across the entire pooled trajectory.
Identity Notes & Concept Scope
No AIO class represents Adaptive Multiple Importance Sampling (AMIS); MarkovChain (AIO:MarkovChain) is the closest broad match covering iterative stochastic simulation and Monte Carlo sampling processes.
Claims & Grounded Evidence
4 Claims
Mechanism
#incremental-deterministic-mixture-past-weight-recycling
At each adaptation stage t = 1, ..., T, AMIS evaluates the new proposal density q_t(x; theta^{t-1}) on all previously generated particles x_i^l (0 <= l <= t-1) to incrementally update their unnormalized mixture denominators delta_i^l <- delta_i^l + N_t q_t(x_i^l) and importance weights omega_i^l = pi(x_i^l) / [delta_i^l / sum_{j=0}^t N_j] (Algorithm 1, Equations 2-5), achieving exact deterministic-mixture pooling in (T+1) sum_{t=0}^T N_t density evaluations.
Mechanism
#student-t-moment-matching-and-ess-scale-hierarchy-initialization
AMIS updates multivariate Student-t proposal parameters T_3(mu^t, Sigma^t) using the pooled deterministic-mixture importance weights across all stages 0 <= l <= t (Equation 6) and initializes the baseline covariance scale via a geometric hierarchy sigma_0 * 2^eta,eta in {-4,...,8}, selecting the scale that maximizes the Effective Sample Size (ESS) before launching sequential adaptation (Section 4).
Application
#banana-shaped-posterior-and-population-genetics-application
AMIS is applied to Bayesian posterior integration, marginal likelihood estimation, and population genetics coalescent inference, substantially increasing Effective Sample Size and reducing estimator mean squared error on strongly twisted banana-shaped target distributions compared to unrecycled Population Monte Carlo.
Limitation
#adaptive-proposal-dependence-bias-and-quadratic-stage-cost-limitation
Because adapted proposal parameters theta^t depend on earlier simulated particles, the retroactively reweighted terms for fixed stage sizes N_t are not strictly unbiased in finite samples (exhibiting bias when N_t = 1, Section 5) and require N_T -> infinity for asymptotic consistency (Lemma 1), while evaluating every new proposal on all past draws incurs O(T sum_{t=0}^T N_t) proposal evaluations.
⚠️ Curated Limitations & Negative Results
- Because adapted proposal parameters theta^t depend on earlier simulated particles, the retroactively reweighted terms for fixed stage sizes N_t are not strictly unbiased in finite samples (exhibiting bias when N_t = 1, Section 5) and require N_T -> infinity for asymptotic consistency (Lemma 1), while evaluating every new proposal on all past draws incurs O(T sum_{t=0}^T N_t) proposal evaluations.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:MarkovChain
Markov Chain
|
broad_match | AMIS is an iterative Monte Carlo sampling algorithm that adapts sequential proposal distributions across stages to approximate posterior and target expectations. |
Evidence Sources & Primary Literature
3 Sources| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
r833-primary-pdf
|
Jean-Marie Cornuet, Jean-Michel Marin, Antonietta Mira, Christian P. Robert
|
primary paper
full_text
|
ID: https://arxiv.org/abs/0907.1254
sha256:013bb11954af…
|
r833-arxiv-abs
|
Jean-Marie Cornuet, Jean-Michel Marin, Antonietta Mira, Christian P. Robert
|
primary paper
abstract_only
|
ID: https://arxiv.org/abs/0907.1254
sha256:5b75957b67d8…
|
r833-metadata-cr
|
Jean-Marie Cornuet, Jean-Michel Marin, Antonietta Mira, Christian P. Robert
|
primary paper
abstract_only
|
ID: https://arxiv.org/abs/0907.1254
sha256:117829116cb3…
|
Ontology & Grounding Topology
Open in interactive network graph →Curation Provenance
Curator: Antigravity
Method: ai_assisted
Model: Gemini
Created: 2026-10-19T15:16:00Z
Updated: 2026-10-19T15:16:00Z
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