`, use `
`/`
` for sections in long text 3. Lists use `
- `, quotes use `
`, code use `
`, important sentences can use ``
4. Keep all original information, no additions/deletions/modifications
5. No document-level tags like ``, ``, ``
The text is an academic abstract about Conformal Prediction (CP) and GLocalCP. Let me analyze the structure:
The text has these logical sections:
1. Introduction/motivation: CP provides marginal coverage but doesn't determine where errors occur; queries from different neighborhoods have different uncertainty; they introduce GLocalCP
2. Technical details: uncertainty-adaptive nonconformality score with MC dropout; kernel-based local correction
3. Theory: pathwise O(N^{-1/2}) marginal calibration error; explicit graph-localized calibration guarantee
4. Experiments: seven node-classification and seven edge-prediction benchmarks; similar marginal coverage can conceal different local reliability; GLocalCP maintains coverage while reducing graph-local calibration error; uncertainty scaling reduces prediction-set size
I can structure this with:
- An introductory paragraph
- Sections with `` or `
` headings
- Math formulas preserved as-is (they're inline with $ symbols - should I keep them? The rule says keep all original information, no modifications. So keep the $O(N^{-1/2})$ as plain text since it's not specified to convert to MathJax)
Wait, should I use `
` or `
`? The rule says "长文用
/
划分小节" (use h2/h3 for sections in long text). This is a moderately long abstract. I could use `
` for major sections or just structure it as paragraphs with a couple of headings.
Let me think about a good semantic structure:
Option:
- First paragraph: motivation/introduction
- `
The GLocalCP Framework
` or similar — wait, but the rule says don't add content. Headings are structural, but adding headings that aren't in the original... The rule says "不得增删改内容" (must not add, delete, or modify content). Adding headings is a structural formatting choice, which seems permitted since rule 2 explicitly asks for headings. But I should be careful that headings don't introduce new claims—they can be derived from the text content. Actually, to be safe, I could use minimal headings or make them clearly derived from the text. Alternatively, I can just use paragraphs without headings since the text is short-ish. But rule 2 says "长文用/
划分小节" — for long text use h2/h3. This abstract is medium length. I think adding a couple of section headings would demonstrate compliance.
Let me draft:
```html
Conformal prediction (CP) provides marginal coverage guarantees, but marginal coverage does not determine where prediction errors occur on a graph. Queries from different graph neighborhoods can exhibit substantially different levels of uncertainty even when aggregate coverage remains near its target. We introduce GLocalCP, an online CP framework for inductive node classification and edge prediction that combines marginal and graph-local calibration with uncertainty-adaptive prediction sets.
`, code use ``, important sentences can use `` 4. Keep all original information, no additions/deletions/modifications 5. No document-level tags like ``, ``, `` The text is an academic abstract about Conformal Prediction (CP) and GLocalCP. Let me analyze the structure: The text has these logical sections: 1. Introduction/motivation: CP provides marginal coverage but doesn't determine where errors occur; queries from different neighborhoods have different uncertainty; they introduce GLocalCP 2. Technical details: uncertainty-adaptive nonconformality score with MC dropout; kernel-based local correction 3. Theory: pathwise O(N^{-1/2}) marginal calibration error; explicit graph-localized calibration guarantee 4. Experiments: seven node-classification and seven edge-prediction benchmarks; similar marginal coverage can conceal different local reliability; GLocalCP maintains coverage while reducing graph-local calibration error; uncertainty scaling reduces prediction-set size I can structure this with: - An introductory paragraph - Sections with `` or `
` headings - Math formulas preserved as-is (they're inline with $ symbols - should I keep them? The rule says keep all original information, no modifications. So keep the $O(N^{-1/2})$ as plain text since it's not specified to convert to MathJax) Wait, should I use `
` or `
`? The rule says "长文用
/
划分小节" (use h2/h3 for sections in long text). This is a moderately long abstract. I could use `
` for major sections or just structure it as paragraphs with a couple of headings. Let me think about a good semantic structure: Option: - First paragraph: motivation/introduction - `
The GLocalCP Framework
` or similar — wait, but the rule says don't add content. Headings are structural, but adding headings that aren't in the original... The rule says "不得增删改内容" (must not add, delete, or modify content). Adding headings is a structural formatting choice, which seems permitted since rule 2 explicitly asks for headings. But I should be careful that headings don't introduce new claims—they can be derived from the text content. Actually, to be safe, I could use minimal headings or make them clearly derived from the text. Alternatively, I can just use paragraphs without headings since the text is short-ish. But rule 2 says "长文用/
划分小节" — for long text use h2/h3. This abstract is medium length. I think adding a couple of section headings would demonstrate compliance. Let me draft: ```html
Conformal prediction (CP) provides marginal coverage guarantees, but marginal coverage does not determine where prediction errors occur on a graph. Queries from different graph neighborhoods can exhibit substantially different levels of uncertainty even when aggregate coverage remains near its target. We introduce GLocalCP, an online CP framework for inductive node classification and edge prediction that combines marginal and graph-local calibration with uncertainty-adaptive prediction sets.
Method
Specifically, GLocalCP puts forth a novel uncertainty-adaptive nonconformality score that relies on the mutual information obtained from Monte-Carlo (MC) dropout based prediction. Then, it augments a global online threshold with a kernel-based local correction that propagates coverage feedback among similar graph queries.
Theoretical Guarantees
On the theoretical horizon, we establish pathwise $O(N^{-1/2})$ marginal calibration error without exchangeability or stationarity and, for the exact-kernel formulation, an explicit $O(N^{-1/2})$ graph-localized calibration guarantee.
Experiments
Experiments on seven node-classification and seven edge-prediction benchmarks show that similar marginal coverage can conceal substantially different local reliability. Our proposed GLocalCP maintains coverage near the target while consistently reducing graph-local calibration error. Uncertainty scaling in GLocalCP further reduces prediction-set size across all evaluated node and edge datasets while leaving marginal coverage essentially unchanged.
``` Hmm, but wait — should the headings be in English since the text is English? Yes, the text is entirely in English, so headings in English make sense. Should I include the LaTeX math? The rule says keep all original information, no modifications. The $O(N^{-1/2})$ should stay as-is. Could I wrap it in code tags? No, it's math, not code. Keep it as plain text within the paragraph. Actually, let me reconsider whether to use `