Adaptive scaling Metropolis
Algorithms AIMech:AdaptiveScalingMetropolis DRAFT
Aliases: ASM
A random-walk Metropolis algorithm that adapts its proposal scale through stochastic approximation driven by the proposal acceptance probability relative to a chosen target rate.
Identity Notes & Concept Scope
The source’s ASM has fixed positive-definite shape and an adaptive scalar scale. This is distinct from covariance-shape adaptation and from RAM’s direction-dependent matrix update. The record uses the exponential-scale specialization of the source’s more general increasing scale map. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 181 prior native IDs/names/aliases. Ignored-inclusive searches of both full checkouts found prior discovery leads, neighboring sampler discussions and unrelated author-name/environment substrings. Existing random-walk Metropolis, delayed-rejection, fixed symmetric delayed-rejection and RAM records were inspected; shared components do not make these procedures equivalent.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
Fix shape Sigma positive definite and use a spherical proposal W. From retained x with pi(x)>0 and log scale S, propose Y=x+exp(S)Sigma^(1/2)W. Compute alpha=min(1,pi(Y)/pi(x)), accept Y with that probability or retain x, then update S_new=S+eta_n(alpha−alpha_star). Adapt after either outcome, using the acceptance probability rather than its Bernoulli realization. Choose alpha_star in (0,1) and positive step sizes with divergent sum and convergent sum of squares for the stated stochastic-approximation setting. The shape remains fixed; exp(S) multiplies standard deviation, so the covariance multiplier is exp(2S).
⚠️ Curated Limitations & Negative Results
- The stability and strong-law theorems in this version restrict alpha_star to (0,1/2), beyond the broader algorithm definition. Larger targets are discussed as expected extensions, not proved here.
- Compact-support regularity or the stated unbounded-target tail/contour assumptions and admissible proposal conditions are needed for the corresponding results. Positive step sizes alone are insufficient.
- The strong-law statements concern sample averages. The source explicitly distinguishes them from convergence in distribution of the adaptive sampled states.
- A target rate such as 0.234 is not a universal optimum, evidence of convergence or guarantee of good multimodal exploration.
- The inspected arXiv v3 submission date and later PDF footer differ; no later journal PDF inspection or numerical validation is claimed.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:MarkovChain
Markov Chain
|
related_match | This procedure adapts a family of Markov transition kernels that are target-invariant at frozen settings. Its sampled-state history is not assumed to be a homogeneous Markov chain, and adaptive validity requires separate assumptions. AIO MarkovChain is a process/model beneath Network; this is a related method-to-process mapping, not equivalence, an is-a assertion or a convergence guarantee. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Matti Vihola
|
primary paper
full_text
|
ID: arXiv:0903.4061v3
sha256:2de1293c2ed1…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T07:40:20Z
Updated: 2026-10-11T07:40:20Z
Source File:
data/curated/AdaptiveScalingMetropolis.yaml