Graph Neural Machine: A New Model for Learning with Tabular Data
(2402.02862)Abstract
In recent years, there has been a growing interest in mapping data from different domains to graph structures. Among others, neural network models such as the multi-layer perceptron (MLP) can be modeled as graphs. In fact, MLPs can be represented as directed acyclic graphs. Graph neural networks (GNNs) have recently become the standard tool for performing machine learning tasks on graphs. In this work, we show that an MLP is equivalent to an asynchronous message passing GNN model which operates on the MLP's graph representation. We then propose a new machine learning model for tabular data, the so-called Graph Neural Machine (GNM), which replaces the MLP's directed acyclic graph with a nearly complete graph and which employs a synchronous message passing scheme. We show that a single GNM model can simulate multiple MLP models. We evaluate the proposed model in several classification and regression datasets. In most cases, the GNM model outperforms the MLP architecture.
Overview
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The paper introduces the Graph Neural Machine (GNM), a novel architecture for learning with tabular data that generalizes multi-layer perceptrons (MLPs) by using synchronous message passing in a nearly-complete graph.
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GNMs are shown to be universal function approximators that can simulate multiple MLPs within a single framework, offering improved results on classification and regression tasks.
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While GNMs have a larger parameter space which may lead to overfitting, they are found to be less susceptible to this issue than MLPs, particularly when using regularization and sparsity techniques.
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The practicality of using GNMs is supported by their compatibility with GPU parallelism, allowing for feasible application in real-world machine learning scenarios despite higher computational complexity.
Overview of Graph Neural Machine Model
Graph neural networks (GNNs) have extensively been applied across a breadth of domains where data is inherently structured as graphs. Traditional approaches such as multi-layer perceptrons (MLPs) are not optimized for capturing graph-based relationships in data, leaving a gap that GNNs adeptly fill. However, the relationship between GNNs and MLPs has prompted exploratory work in understanding how MLPs can be reinterpreted within the graph neural network framework. This paper delineates an innovative perspective showing that an MLP can be equivalently represented as an asynchronous message passing GNN based on the MLP’s graph structure.
Theoretical Insights
At the crux of this paper is the introduction of a novel architecture termed the Graph Neural Machine (GNM) for learning with tabular data. It underscores that GNMs are a generalization of MLPs, characterized by synchronous message passing within a nearly-complete graph structure devoid of the acyclic constraint. Specifically, GNMs enable the simulation of multiple MLP models within a singular framework, consequently demonstrating that GNM is a family of universal function approximators.
Empirical Evaluations
Quantitative analyses are conducted across several classification and regression datasets to validate the effectiveness of the proposed model. The GNM model consistently demonstrates superior or comparable results to the traditional MLP architecture. To elucidate these findings, in classification tasks, GNMs achieve marginally to significantly higher accuracy and F1 scores on a majority of the datasets tested. Remarkably, in regression contexts, the proposed model exhibits a pronounced outperformance over MLPs, suggesting a compelling advantage for GNMs in continuous output spaces.
Limitations and Practical Implications
Despite the robustness evinced by GNMs, the susceptibility to overfitting due to their large parameter space is a critical consideration. Regularization approaches and model sparsity stand as constructive strategies to potentially mitigate overfitting and enhance interpretability. The paper's experimental section denotes that GNMs are less prone to overfitting compared to MLPs when subject to the same parameter budgets.
Furthermore, albeit GNMs present with a greater computational complexity, this does not substantially affect the run time in practice, especially when leveraging GPUs' parallelism. This points to feasible employment of GNMs in real-world applications without prohibitive computational demands.
Conclusively, the GNM architecture signifies a substantial step in harmonizing traditional neural network approaches with graph-based learning, driving forward the potential for deeper and more comprehensive data analysis. The modeling flexibility and theoretical backing as universal approximators convey the substancial implications of GNMs in both academic research and applied machine learning settings.
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