Authors:
(1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk;
(2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Table of Links Abstract and 1 Introduction 2 Related Work 3 Framework 4 Main Results 5 A Case Study on Shortest-Path Distance 6 Conclusion and Discussion, and References 7 Proof of Theorem 1 8 Proof of Theorem 2 9 Procedure for Solving Eq. (6) 10 Additional Experiments Details and Results 11 Other Potential Applications 8 Proof of Theorem 2 Before diving into the detailed proof, we present an outline of the structure of the proof and prove a lemma which we use in the proof of the theorem. Outline of the proof for the thereom 1. Suppose we are given Vi and Vj , two test groups which satisfy the premise of the theorem; 2. Then, we can approximate and bound the loss of each vertex in these groups based on the nearest vertex in the training set by extending the result from Theorem 1; 3. If we can show that there exists a constant independent of the property of each test group, then we obtain the results of Theorem 2. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk; (2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Authors: Authors: (1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk; (2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Work 2 Related Work 3 Framework 3 Framework 4 Main Results 4 Main Results 5 A Case Study on Shortest-Path Distance 5 A Case Study on Shortest-Path Distance 6 Conclusion and Discussion, and References 6 Conclusion and Discussion, and References 7 Proof of Theorem 1 7 Proof of Theorem 1 8 Proof of Theorem 2 8 Proof of Theorem 2 9 Procedure for Solving Eq. (6) 9 Procedure for Solving Eq. (6) 10 Additional Experiments Details and Results 10 Additional Experiments Details and Results 11 Other Potential Applications 11 Other Potential Applications 8 Proof of Theorem 2 Before diving into the detailed proof, we present an outline of the structure of the proof and prove a lemma which we use in the proof of the theorem. Outline of the proof for the thereom Outline of the proof for the thereom 1. Suppose we are given Vi and Vj , two test groups which satisfy the premise of the theorem; 2. Then, we can approximate and bound the loss of each vertex in these groups based on the nearest vertex in the training set by extending the result from Theorem 1; 3. If we can show that there exists a constant independent of the property of each test group, then we obtain the results of Theorem 2. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

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