Robust adaptive Metropolis
Algorithms AIMech:RobustAdaptiveMetropolis DRAFT
Aliases: RAM
An adaptive random-walk Metropolis algorithm that updates the proposal shape factor by a rank-one transformation driven by the proposal direction and the difference between its acceptance probability and a chosen target rate.
Identity Notes & Concept Scope
This is Vihola’s RAM update, which avoids estimating the target covariance. It differs from covariance-based adaptive Metropolis, scale-only adaptation and a fixed random-walk kernel. RAM here denotes this sampler, not computer memory. The history-dependent state sequence is not assumed to be a homogeneous Markov chain. No normalized match was found across all 442 pinned AIO labels/scoped synonyms and 175 prior native IDs/names/aliases. Full-checkout searches included ignored and hidden files in both worktrees; the only text hit was an unrelated installed-package checksum substring. Existing general Metropolis-Hastings, Metropolis-within-Gibbs and random-walk records were inspected to resolve these specialization boundaries.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
Let q be a spherical density, S a lower-triangular factor with positive diagonal, x satisfy pi(x)>0, eta_n lie in (0,1] and decay to zero, and alpha_star lie in (0,1). Draw U from q and propose y=x+S U. Set alpha=min(1,pi(y)/pi(x)), accept y with this probability or retain x. Whether accepted or rejected, choose the next positive-diagonal Cholesky factor S_new satisfying S_new S_new^T=S[I+eta_n(alpha−alpha_star)UU^T/||U||²]S^T. The update uses the acceptance probability, not the binary acceptance outcome; the normalized direction U determines the rank-one adjustment. It expands that component when alpha exceeds the target and contracts it when alpha is smaller.
⚠️ Curated Limitations & Negative Results
- Spherical continuous proposals make U=0 a null event; numerical implementations still need a zero-norm guard and stable factor updates.
- Positive definiteness of each update does not prove long-run stability. The source’s strong-law result assumes target/proposal regularity and step-size conditions and holds on an event where shape eigenvalues stay bounded away from zero and infinity.
- The paper explicitly leaves unrestricted stability unproved. Enforcing fixed eigenvalue bounds by rejecting a proposed shape update is a separate safeguard that can alter the limiting shape.
- A chosen acceptance rate is a tuning target, not a universal optimum or convergence diagnostic. Strong multimodality can remain difficult; no benchmark or arbitrary-heavy-tail convergence guarantee is asserted.
- The exact inspected arXiv v2 bytes have a later title-page footer date. This record does not claim to have inspected the later journal version.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:MarkovChain
Markov Chain
|
related_match | RAM adapts a family of random-walk Metropolis transition kernels, each target-invariant at a fixed shape. Its history-dependent sampled-state sequence is not assumed to be a homogeneous Markov chain. AIO MarkovChain describes the underlying process/model concept beneath Network, so this is a related method-to-process mapping, not equivalence, a subclass assertion or a proof of adaptive convergence. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Matti Vihola
|
primary paper
full_text
|
ID: arXiv:1011.4381v2
sha256:dc508f247e17…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T07:26:59Z
Updated: 2026-10-11T07:26:59Z
Source File:
data/curated/RobustAdaptiveMetropolis.yaml