We propose PathBoost, a gradient tree boosting method for graph-level classification and regression that learns discriminative path-based features directly from the input graph structure. Building on a previous work, which was tailored to a specific chemistry application, PathBoost introduces three key extensions: (i) adaptation to binary classification through gradient boosting with a logistic loss, (ii) incorporation of multiple node and edge attributes into the path feature space via a prefix-based decomposition, and (iii) automatic anchor node selection based on categorical attribute diversity, eliminating the need for the user to specify the starting point of the considered path features. We compared PathBoost to graph neural networks and graph kernel approaches on several benchmark datasets, obtaining better results in half of them, and comparable results in the rest. PathBoost shows better performances on graphs with larger average node counts. Overall, the results demonstrate that path-based boosting methods can be competitive with more complex black-box approaches.

This lack of hierarchical structure is especially problematic for the task of graph classification, where the goal is to predict thelabelassociatedwithan entiregraph.

We demonstrate the practical merits and limitations of existing theoretical tests and their bootstrapped variants.

To address this issue, we present the first analysis for instance weighting transfer learning that considers the presence of labeled target examples. The contribution of our work is two-fold.1. We address the question ofhow to measure the divergence between two domains given label informationforthetargetdomain.

Thegraphkernelfunction can be utilized toclassify graphs via standard kernel methods such assupport vector machines or k-nearest neighbors.

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Technically,various methods of both categories exploit the link between graph data and linear algebra by representing graphs by their (normalized) adjacency matrix. Such methods are often defined or can be interpreted in terms ofwalks. On the other hand, the Weisfeiler-Leman heuristic for graph isomorphism testing has attracted great interest in machine learning [33, 34].

Wepostulate thatthevector ofFGW distances to a set of template graphs has a strong discriminative power, which is then fed to anon-linear classifier forfinalpredictions.

While graphs with continuous node attributes arise in many applications, stateof-the-art graph kernels for comparing continuous-attributed graphs suffer from a high runtime complexity.

The purpose of this review is to introduce the reader to graph kernels and the corresponding literature, with an emphasis on those with direct application to chemoinformatics. Graph kernels are functions that allow for the inference of properties of molecules and compounds, which can help with tasks such as finding suitable compounds in drug design. The use of kernel methods is but one particular way two quantify similarity between graphs. We restrict our discussion to this one method, although popular alternatives have emerged in recent years, most notably graph neural networks.