Conjugate-gradient Monte Carlo
Algorithms AIMech:ConjugateGradientMonteCarlo DRAFT
Aliases: CGMC
A population Markov sampler that obtains a local-optimization anchor from one population member and updates another member along the anchor line with a multiple-try transition targeting a radial-Jacobian-adjusted density.
Identity Notes & Concept Scope
This is Liu–Liang–Wong Section 4.2 CGMC, not the conjugate-gradient linear solver or direct optimization as a substitute for sampling. Its anchor comes from a different stream. The product target is an invariant population law, not a statement that transient streams are independent. 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
Maintain m≥2 population members targeting a product of pi. Choose a reference member x_r uniformly at random, and deterministically optimize along a gradient or conjugate-gradient direction of log pi to obtain anchor A=g(x_r). Choose x_c uniformly among the other members. For A≠x_c, define e=(A−x_c)/||A−x_c|| and the scalar line target f(r) proportional to |r|^(d−1)pi(A+r e), r on the whole real line. Apply a valid MTM transition along this line, starting at the scalar coordinate of x_c, and replace x_c by A+r_new e while retaining the other members. A scalar proposal and weight construction must respect the same unoriented line when traversed in reverse; a centered Gaussian scalar random-walk proposal of fixed variance with MTM-II target-density selection weights is a concrete compatible choice. The source’s product-invariance argument uses the anchor’s independence from the moved member under the product target.
⚠️ Curated Limitations & Negative Results
- The factor |r|^(d−1) is essential for an anchor line selected through the current point. Replacing the line target with pi(A+r e) alone is not this construction.
- The optimization anchor must be independent of the moved member under the product stationary law. Optimizing that same member and copying this acceptance scheme is not justified.
- The zero-length line A=x_c requires a defined degenerate-case policy; the displayed normalized direction is not evaluated at zero. Differentiability and the chosen deterministic optimization procedure have their own requirements.
- The compatible scalar-proposal statement is an explicit implementation constraint inferred from reversing the unoriented line, not a new algorithm attributed to the source.
- Invariance does not guarantee population exploration, convergence, independent transient streams or universally reliable convergence diagnostics. Optimization and multiple trials add cost.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:MarkovChain
Markov Chain
|
related_match | The procedure defines target-invariant Markov transitions under its stated assumptions, including a population state for CGMC. AIO MarkovChain describes a stochastic process/model and is exported beneath Network. This method-to-process related match is not equivalence, an is-a assertion or a claim of independent samples or a trained network. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Jun S. Liu, Faming Liang, Wing Hung Wong
|
primary paper
full_text
|
ID: doi:10.1080/01621459.2000.10473908
sha256:5329c50b3760…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T07:26:59Z
Updated: 2026-10-11T07:27:21Z
Source File:
data/curated/ConjugateGradientMonteCarlo.yaml