Related papers: Granger Causality Detection with Kolmogorov-Arnold…

A major challenge of AI + Science lies in their inherent incompatibility: today's AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize…

Graph Representation Learning aims to create effective embeddings for nodes and edges that encapsulate their features and relationships. Graph Neural Networks (GNNs) leverage neural networks to model complex graph structures. Recently, the…

Kolmogorov-Arnold Networks (KANs) are emerging as a powerful framework for interpretable and efficient system identification in dynamic systems. By leveraging the Kolmogorov-Arnold representation theorem, KANs enable function approximation…

We consider the Granger causal structure learning problem from time series data. Granger causal algorithms predict a 'Granger causal effect' between two variables by testing if prediction error of one decreases significantly in the absence…

Effective molecular representation learning is crucial for advancing molecular property prediction and drug design. Mainstream molecular representation learning approaches are based on Graph Neural Networks (GNNs). However, these approaches…

In this paper, we introduce Wav-KAN, an innovative neural network architecture that leverages the Wavelet Kolmogorov-Arnold Networks (Wav-KAN) framework to enhance interpretability and performance. Traditional multilayer perceptrons (MLPs)…

Estimating causal relations is vital in understanding the complex interactions in multivariate time series. Non-linear coupling of variables is one of the major challenges inaccurate estimation of cause-effect relations. In this paper, we…

In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the…

Granger-Geweke causality (GGC) is a powerful and popular method for identifying directed functional (`causal') connectivity in neuroscience. In a recent paper, Stokes and Purdon [1] raise several concerns about its use. They make two…

The multilayer perceptron (MLP), a fundamental paradigm in current artificial intelligence, is widely applied in fields such as computer vision and natural language processing. However, the recently proposed Kolmogorov-Arnold Network (KAN),…

Kolmogorov-Arnold Networks (KANs) have gained attention as an alternative to traditional multilayer perceptrons (MLPs) for deep learning applications in computational physics, particularly for solving inverse problems with sparse data, as…

Survival analysis aims to model how covariates and time jointly shape the time-to-event distribution under right censoring. Classical methods such as the Cox model and generalised additive models (GAMs) require interactions and time-varying…

We consider the problem of learning models for forecasting multiple time-series systems together with discovering the leading indicators that serve as good predictors for the system. We model the systems by linear vector autoregressive…

An approach is proposed for inferring Granger causality between jointly stationary, Gaussian signals from quantized data. First, a necessary and sufficient rank criterion for the equality of two conditional Gaussian distributions is proved.…

We study Granger causality in the context of wide-sense stationary time series, where our focus is on the topological aspects of the underlying causality graph. We establish sufficient conditions (in particular, we develop the notion of a…

The Kolmogorov-Arnold representation theorem states that any continuous multivariable function can be exactly represented as a finite superposition of continuous single variable functions. Subsequent simplifications of this representation…

Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of…

Predictive modeling on web-scale tabular data with billions of instances and hundreds of heterogeneous numerical features faces significant scalability challenges. These features exhibit anisotropy, heavy-tailed distributions, and…

Kolmogorov-Arnold Networks represent a recent advancement in machine learning, with the potential to outperform traditional perceptron-based neural networks across various domains as well as provide more interpretability with the use of…

Recurrent Neural Networks (RNNs) have revolutionized many areas of machine learning, particularly in natural language and data sequence processing. Long Short-Term Memory (LSTM) has demonstrated its ability to capture long-term dependencies…