AIMech AI

Tempered expectation maximization

Algorithms AIMech:TemperedExpectationMaximization DRAFT
Aliases: Tempered EM
An entropy-tempered generalization of expectation maximization for finite latent-state models that alternates powered latent-joint responsibilities with weighted complete-log-likelihood parameter updates at a positive inverse temperature.
Identity Notes & Concept Scope This record denotes the deterministic free-energy fitting procedure described by Hofmann, with his held-out inverse-annealing schedule as an explicit realization. Ordinary EM is its beta=1 case. The procedure changes responsibilities and parameter fitting; it is neither replica-exchange MCMC nor a supervised confidence-mask schedule, and it does not introduce a new topic-model probability family. The short TEM acronym is not asserted as a globally unambiguous alias. Compared all 442 pinned AIO labels and scoped synonyms and 418 preceding native IDs, names and aliases. The initial normalized LDA hit denotes LinearDiscriminantAnalysis, whose full Gaussian-classifier record was read; the bare LDA alias is omitted from the new topic-model record. No normalized identity match remains for the final candidate names/aliases. Final full-checkout fixed-string searches, including ignored and hidden files in both worktree and main, return two lines each; both unique contents are existing frontier references. An additional broad LDA search returned 289 worktree and 237 main lines before the preceding batch merged; all 84 distinct contents were read, covering the existing classifier, topic-context references, unrelated programming mnemonics and namespace abbreviations. All 188 semantic label/synonym hits were read. Nineteen exact annotated AIO CLASS nodes and outgoing edges were inspected (18 verified unchanged from prior reading, Biclustering read here), along with their generated records and 16 native neighbors. The 35 contextual YAMLs were read or byte-verified after documented full reading. Absence is bounded to this snapshot, maintained corpus and inspected semantic neighborhood.

Claims & Grounded Evidence

1 Claim
Mechanism #method
For observations x with multiplicities n_x, finite latent states z, model parameters eta and a positive inverse temperature beta, minimize F_beta(q,eta)=sum_x n_x*sum_z q_xz*[log q_xz-beta*log p_eta(x,z)]. For fixed eta, on positive joint support use q_xz=p_eta(x,z)^beta/sum_j p_eta(x,j)^beta. For fixed q and beta>0, minimizing F_beta over eta is equivalent to maximizing the expected complete log likelihood; in PLSA this gives the usual normalized expected-count M-step with the tempered responsibilities. At beta=1 the E-step is the ordinary posterior. With 0<beta<1 it is flatter on its positive support. Hofmann’s inverse-annealing schedule first runs early-stopped EM at beta=1, then reduces beta multiplicatively, continues iterations while held-out performance improves, and stops decreasing beta when further improvements cease. At fixed beta, exact block updates optimize that temperature’s free energy; changing beta changes the objective.

⚠️ Curated Limitations & Negative Results

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes
AIO Target Class Mapping Relation Mapping Rationale
AIO:TrainingStrategy
TrainingStrategy
related_match Tempered EM is a specified latent-variable fitting procedure. The target broadly describes preprocessing/training strategies; related match avoids forcing this optimization algorithm under that wording as a subclass.
AIO:MachineLearningTask
Machine Learning Task
related_match The procedure estimates latent-model parameters rather than denoting a task or a probabilistic model. The relation records its learning role without equivalence or an is-a assertion.

Evidence Sources & Primary Literature

1 Source
Source ID Publication / Document Type / Access Reference & Checksum
method-source
Thomas Hofmann
primary paper
full_text
ID: arXiv:1301.6705v1
sha256:798ce8b95d01…

Curation Provenance

Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T23:19:29Z
Updated: 2026-10-11T23:19:29Z
Source File: data/curated/TemperedExpectationMaximization.yaml