Bethe Free Energy and Contrastive Divergence Approximations for Undirected Graphical Models
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
As the machine learning community tackles more complex and harder problems, the graph-ical models needed to solve such problems become larger and more complicated. As a result performing inference and learning exactly for such graphical models become ever more expen-sive, and approximate inference and learning techniques become ever more prominent. There are a variety of techniques for approximate inference and learning in the literature. This thesis contributes some new ideas in the products of experts (PoEs) class of models (Hin-ton, 2002), and the Bethe free energy approximations (Yedidia et al., 2001). For PoEs, our contribution is in developing new PoE models for continuous-valued do-mains. We developed RBMrate, a model for discretized continuous-valued data. We applied it to face recognition to demonstrate its abilities. We also developed energy-based models (EBMs) – flexible probabilistic models where the building blocks consist of energy terms com-puted using a feed-forward network. We show that standard square noiseless independent components analysis (ICA) (Bell and Sejnowski, 1995) can be viewed as a restricted form of EBMs. Extending this relationship with ICA, we describe sparse and over-complete represen-tations of data where the inference process is trivial since it is simply an EBM. For Bethe free energy approximations, our contribution is a theory relating belief propaga-tion and iterative scaling. We show that both belief propagation and iterative scaling updates can be derived as fixed point equations for constrained minimization of the Bethe free energy. This allows us to develop a new algorithm to directly minimize the Bethe free energy, and to ap-ply the Bethe free energy to learning in addition to inference. We also describe improvements to the efficiency of standard learning algorithms for undirected graphical models (Jirouˇsek and
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it