Maximum pseudolikelihood estimation
Algorithms AIMech:MaximumPseudolikelihoodEstimation DRAFT
Aliases: MPLE
A parameter-estimation method that maximizes the product of a specified model’s sitewise full conditional probabilities or densities evaluated at the observed configuration.
Identity Notes & Concept Scope
The classical full-conditional pseudolikelihood uses every observed site. It is an estimation objective and does not specify a unique numerical optimizer. It is distinct from full joint maximum likelihood, independent-site coding likelihood, iterative conditional modes for state optimization, and iterative conditional estimation for incomplete-data parameters. A general loss assembled from unrelated conditionals is not automatically the pseudolikelihood of a compatible joint model. The paper discusses fixed-site spatial models without assuming stationarity or homogeneity; the local graph and parameterization must still be specified. No normalized identity match was found across all 442 pinned AIO labels and all scoped synonyms and 400 preceding native IDs, names and aliases. Full-checkout fixed-string searches included ignored and hidden files in worktree and main, yielding 35 and 35 matched lines; all 23 unique contents were read. Hits are citations, contextual statements and discovery leads rather than records of these identities. All 182 semantic label/synonym hits were read. Thirty-one fully annotated exact CLASS nodes and outgoing edges were inspected: 23 byte-equivalent to prior inspected nodes and eight freshly read. Thirty-nine contextual YAMLs comprise 31 generated and eight native records: 29 byte-verified after prior reading and 10 freshly read. Short acronyms were included in the normalized identity comparison. Absence is bounded to the pinned snapshot, maintained corpus and inspected semantic neighborhood.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
For an observed configuration x and a compatible family p_theta with well-defined full conditionals, form PL(theta;x)=product_i p_theta(x_i|x_(-i)) and maximize sum_i log p_theta(x_i|x_(-i)) over the admissible parameter space. In a Markov field, each factor depends only on the site’s neighbors; a global joint partition function cancels from that factor, although its local normalizer still must be evaluated. If the sites are partitioned into nonneighbor coding sets, the log pseudolikelihood is the sum of their conditional log likelihoods. This identity combines objectives, not the separately fitted parameter values. For the source’s proper common-conditional-variance Gaussian model with mean D*a, symmetric B=I-phi*H and variance sigma^2, the residual term is (x-D*a)^T B^2(x-D*a)/sigma^2. Its joint Gaussian likelihood instead includes log|B| and a single-B quadratic. Complete independence is a special case in which the product of full conditionals equals the joint likelihood.
⚠️ Curated Limitations & Negative Results
- The product of normalized full conditionals is generally not a normalized joint distribution over x. Its maximizer need not equal the joint-likelihood maximizer. Dividing that product by a parameter-dependent joint normalizer changes the objective.
- Conditionals must be compatible with the intended joint model and parameters must lie in its valid domain. Optimizing local expressions without these restrictions can produce inadmissible joint parameters. Gaussian variance positivity and precision positive definiteness remain necessary.
- The source gives a consistency sketch for an infinite bounded-degree site system with growing coding classes and additional regularity and boundary conditions. It is not a universal theorem for arbitrary growing graphs, fixed finite samples, misspecified models or every parameterization.
- Efficiency, uncertainty estimates and likelihood-ratio calibration do not automatically follow ordinary independent-sample likelihood formulas. Strong dependence, limited information, boundaries and model mismatch require separate assessment; the source offers no universal efficiency advantage.
- Gaussian least-squares expressions apply to the stated common-variance and compatible symmetric interaction parameterization. Design inverses, ratio denominators, finite maximizers and nonzero residual variance require checks. Alternating algebraic updates are not a proof of a global optimum.
- A partition into coding sets does not make the corresponding estimators or test statistics independent. The pseudolikelihood maximizer is not generally the arithmetic mean of coding-set maximizers. Original finite objective comparisons demonstrate this distinction; no empirical fitting, author code or benchmark was run.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:ProbabilisticGraphicalModel
Probabilistic Graphical Model
|
related_match | The inspected method estimates parameters of compatible spatial graphical probability models from their full conditionals. The pinned target describes a machine-learning task; a related mapping captures this graphical-model learning role without making an estimation algorithm a model or a subtype of the task. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Julian Besag
|
primary paper
full_text
|
ID: doi:10.2307/2987782
sha256:0db3c34554e1…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T22:02:22Z
Updated: 2026-10-11T22:02:22Z
Source File:
data/curated/MaximumPseudolikelihoodEstimation.yaml