René's URL Explorer Experiment

{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"MPE does not return assignments for disconnected/isolated variables","articleBody":"## Problem\n\nWhen a probabilistic graphical model contains disconnected components or isolated variables (variables that don't appear in any pairwise/higher-order factors), the current MPE implementation does not include these variables in the returned assignment.\n\n## Example\n\nConsider a model with:\n- Variables: 0, 1, 2, 3\n- Factors: f(0,1), f(1,2) (variable 3 is isolated)\n\nCurrent behavior:\n```python\nassignment = mpe(model)\n# Returns: {0: x, 1: y, 2: z}  # Missing variable 3!\n```\n\nExpected behavior:\n```python\nassignment = mpe(model)\n# Returns: {0: x, 1: y, 2: z, 3: w}  # All variables included\n```\n\n## Root Cause\n\nThe contraction tree only includes tensors that are connected through shared variables. Isolated variables with only unary factors are not contracted into the tree and thus their optimal assignments are never computed.\n\n## Potential Solutions\n\n1. **Post-processing**: After contraction, identify variables not in the assignment and compute their optimal values from unary factors\n2. **Preprocessing**: Add dummy binary factors with uniform potentials to connect isolated components\n3. **Separate handling**: Detect disconnected components before contraction and solve each component separately\n\n## Discovered During\n\nUAI benchmark testing - some benchmark models have isolated variables or disconnected components.\n\n## Related\n\nPR #65 - Tropical einsum module with OMEinsum-style design","author":{"url":"https://github.com/GiggleLiu","@type":"Person","name":"GiggleLiu"},"datePublished":"2026-01-25T12:05:57.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":0},"url":"https://github.com/66/BPDecoderPlus/issues/66"}