Minimum Weight Perfect Matching via Blossom Belief Propagation

Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of combinatorial optimization problems including minimum weight matching, shortest path, network flow and vertex cover under the following common assumption: the respective Linear Programming (LP) relaxation is tight, i.e., no integrality gap is present. However, when LP shows an integrality gap, no model has been known which can be solved systematically via sequential applications of BP. In this paper, we develop the first such algorithm, coined Blossom-BP, for solving the minimum weight matching problem over arbitrary graphs. Each step of the sequential algorithm requires applying BP over a modified graph constructed by contractions and expansions of blossoms, i.e., odd sets of vertices. Our scheme guarantees termination in O(n^2) of BP runs, where n is the number of vertices in the original graph. In essence, the Blossom-BP offers a distributed version of the celebrated Edmonds' Blossom algorithm by jumping at once over many sub-steps with a single BP. Moreover, our result provides an interpretation of the Edmonds' algorithm as a sequence of LPs

Hierarchical Graph Generation with K2K^2-trees

Generating graphs from a target distribution is a significant challenge across many domains, including drug discovery and social network analysis. In this work, we introduce a novel graph generation method leveraging $K^2$-tree representation which was originally designed for lossless graph compression. Our motivation stems from the ability of the $K^2$-trees to enable compact generation while concurrently capturing the inherent hierarchical structure of a graph. In addition, we make further contributions by (1) presenting a sequential $K^2$-tree representation that incorporates pruning, flattening, and tokenization processes and (2) introducing a Transformer-based architecture designed to generate the sequence by incorporating a specialized tree positional encoding scheme. Finally, we extensively evaluate our algorithm on four general and two molecular graph datasets to confirm its superiority for graph generation.Comment: 22 pages (10 appendices

Symmetric Exploration in Combinatorial Optimization is Free!

Recently, deep reinforcement learning (DRL) has shown promise in solving combinatorial optimization (CO) problems. However, they often require a large number of evaluations on the objective function, which can be time-consuming in real-world scenarios. To address this issue, we propose a "free" technique to enhance the performance of any deep reinforcement learning (DRL) solver by exploiting symmetry without requiring additional objective function evaluations. Our key idea is to augment the training of DRL-based combinatorial optimization solvers by reward-preserving transformations. The proposed algorithm is likely to be impactful since it is simple, easy to integrate with existing solvers, and applicable to a wide range of combinatorial optimization tasks. Extensive empirical evaluations on NP-hard routing optimization, scheduling optimization, and de novo molecular optimization confirm that our method effortlessly improves the sample efficiency of state-of-the-art DRL algorithms. Our source code is available at https://github.com/kaist-silab/sym-rd.Comment: 20 pages (including 9 pages of the appendix), 12 figure

EPIC: Graph Augmentation with Edit Path Interpolation via Learnable Cost

Graph-based models have become increasingly important in various domains, but the limited size and diversity of existing graph datasets often limit their performance. To address this issue, we propose EPIC (Edit Path Interpolation via learnable Cost), a novel interpolation-based method for augmenting graph datasets. Our approach leverages graph edit distance to generate new graphs that are similar to the original ones but exhibit some variation in their structures. To achieve this, we learn the graph edit distance through a comparison of labeled graphs and utilize this knowledge to create graph edit paths between pairs of original graphs. With randomly sampled graphs from a graph edit path, we enrich the training set to enhance the generalization capability of classification models. We demonstrate the effectiveness of our approach on several benchmark datasets and show that it outperforms existing augmentation methods in graph classification tasks

Learning Debiased Classifier with Biased Committee

Neural networks are prone to be biased towards spurious correlations between classes and latent attributes exhibited in a major portion of training data, which ruins their generalization capability. We propose a new method for training debiased classifiers with no spurious attribute label. The key idea is to employ a committee of classifiers as an auxiliary module that identifies bias-conflicting data, i.e., data without spurious correlation, and assigns large weights to them when training the main classifier. The committee is learned as a bootstrapped ensemble so that a majority of its classifiers are biased as well as being diverse, and intentionally fail to predict classes of bias-conflicting data accordingly. The consensus within the committee on prediction difficulty thus provides a reliable cue for identifying and weighting bias-conflicting data. Moreover, the committee is also trained with knowledge transferred from the main classifier so that it gradually becomes debiased along with the main classifier and emphasizes more difficult data as training progresses. On five real-world datasets, our method outperforms prior arts using no spurious attribute label like ours and even surpasses those relying on bias labels occasionally.Comment: Conference on Neural Information Processing Systems (NeurIPS), New Orleans, 202

Diffusion Tensor Imaging: Exploring the Motor Networks and Clinical Applications

With the advances in diffusion magnetic resonance (MR) imaging techniques, diffusion tensor imaging (DTI) has been applied to a number of neurological conditions because DTI can demonstrate microstructures of the brain that are not assessable with conventional MR imaging. Tractography based on DTI offers gross visualization of the white matter fiber architecture in the human brain in vivo. Degradation of restrictive barriers and disruption of the cytoarchitecture result in changes in the diffusion of water molecules in various pathological conditions, and these conditions can also be assessed with DTI. Yet many factors may influence the ability to apply DTI clinically, so these techniques have to be used with a cautious hand

Morbidity and related factors among elderly people in South Korea: results from the Ansan Geriatric (AGE) cohort study

BACKGROUND: A thorough examination of the morbidity and comorbidity profiles among the elderly and an evaluation of the related factors are required to improve the delivery of health care to the elderly and to estimate the cost of that care. In South Korea where the aged population is rapidly increasing, however, to date only one study using a limited sample (84 subjects) has provided information on morbidity and related factors among the elderly. Using a large, stratified, random sample (2,767 subjects) from the population-based Ansan Geriatric study, the present study sought to assess the morbidity and comorbidity, and to determine the relationships of these variables with sociodemographic and health characteristics in elderly people in South Korea. METHODS: A total of 2,767 subjects (1,215 men and 1,552 women) aged 60–84 years were randomly selected from September 2002 to August 2003 in Ansan, South Korea. Data on sociodemographic and health characteristics, and clinical diagnosis were collected using questionnaires. When available, the medical records and medications taken by the subjects were also cross-checked. RESULTS: Of the total subjects, 78.0% reported diagnosed disease, 11.0% had been cured, and 46.8% had been diagnosed with more than two diseases. The mean number of morbidities per person among elderly Koreans was 1.62 ± 1.35 (mean ± standard deviation), and women had a greater number of diseases per person than did men. The most common morbidities were chronic diseases such as hypertension, arthritis, and diabetes mellitus. In women, osteoporosis and arthritis were the second and third most prevalent diseases, respectively. Morbidity was significantly associated with gender, employment, household income, alcohol intake, self-assessed health status, and worries about health. CONCLUSION: These data will enhance understanding of the patterns of health problems among elderly Koreans and will contribute to the application of appropriate intervention strategies