In the healthcare domain, time-series data are often irregularly sampled with varying intervals through outpatient visits, posing challenges for existing models designed for equally spaced sequential data. To address this, we propose Trajectory Generative Pre-trained Transformer (TrajGPT) for representation learning on irregularly-sampled healthcare time series. TrajGPT introduces a novel Selective Recurrent Attention (SRA) module that leverages a data-dependent decay to adaptively filter irrelevant past information. As a discretized ordinary differential equation (ODE) framework, TrajGPT captures underlying continuous dynamics and enables a time-specific inference for forecasting arbitrary target timesteps without auto-regressive prediction. Experimental results based on the longitudinal EHR data PopHR from Montreal health system and eICU from PhysioNet showcase TrajGPT's superior zero-shot performance in disease forecasting, drug usage prediction, and sepsis detection. The inferred trajectories of diabetic and cardiac patients reveal meaningful comorbidity conditions, underscoring TrajGPT as a useful tool for forecasting patient health evolution.

Massive MIMO (multiple-input multiple-output) detection is an important topic in wireless communication and various machine learning based methods have been developed recently for this task. Expectation propagation (EP) and its variants are widely used for MIMO detection and have achieved the best performance. However, EP-based solvers fail to capture the correlation between unknown variables, leading to a loss of information, and in addition, they are computationally expensive. In this paper, we show that the real-valued system can be modeled as spectral signal convolution on graph, through which the correlation between unknown variables can be captured. Based on this analysis, we propose graph convolution-enhanced expectation propagation (GCEPNet). GCEPNet incorporates data-dependent attention scores into Chebyshev polynomial for powerful graph convolution with better generalization capacity. It enables a better estimation of the cavity distribution for EP and empirically achieves the state-of-the-art (SOTA) MIMO detection performance with much faster inference speed. To our knowledge, we are the first to shed light on the connection between the system model and graph convolution, and the first to design the data-dependent coefficients for graph convolution.

This paper is concerned with success probabilities of some L2-norm regularized Babai detectors for MIMO detection. First, we extend the often used MMSE-SIC detector to two L2-norm regularized Babai detectors. Then, we derive the corresponding success probability formulae of the two detectors. To increase their success probabilities, we propose to maximize them with respect to the regularization parameter vector by a machine learning based method called ML-λ, as conventional optimization methods are very inefficient. This moves the exponential computational cost to offline training, and the method outputs an approximation to the optimal regularization parameter vector in polynomial time. Finally, we present some numerical simulations to demonstrate the performance of the new detectors.

Homophily principle, i.e., nodes with the same labels are more likely to be connected, has been believed to be the main reason for the performance superiority of Graph Neural Networks (GNNs) over Neural Networks on node classification tasks. Recent research suggests that, even in the absence of homophily, the advantage of GNNs still exists as long as nodes from the same class share similar neighborhood patterns. However, this argument only considers intra-class Node Distinguishability (ND) but neglects inter-class ND, which provides incomplete understanding of homophily on GNNs. In this paper, we first demonstrate such deficiency with examples and argue that an ideal situation for ND is to have smaller intra-class ND than inter-class ND. To formulate this idea and study ND deeply, we propose Contextual Stochastic Block Model for Homophily (CSBM-H) and define two metrics, Probabilistic Bayes Error (PBE) and negative generalized Jeffreys divergence, to quantify ND. With the metrics, we visualize and analyze how graph filters, node degree distributions and class variances influence ND, and investigate the combined effect of intra- and inter-class ND. Besides, we discovered the mid-homophily pitfall, which occurs widely in graph datasets. Furthermore, we verified that, in real-work tasks, the superiority of GNNs is indeed closely related to both intra- and inter-class ND regardless of homophily levels. Grounded in this observation, we propose a new hypothesis-testing based performance metric beyond homophily, which is non-linear, feature-based and can provide statistical threshold value for GNNs' the superiority. Experiments indicate that it is significantly more effective than the existing homophily metrics on revealing the advantage and disadvantage of graph-aware modes on both synthetic and benchmark real-world datasets.

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using graph structures based on the relational inductive bias (homophily assumption). While GNNs have been commonly believed to outperform NNs in real-world tasks, recent work has identified a non-trivial set of datasets where their performance compared to NNs is not satisfactory. Heterophily has been considered the main cause of this empirical observation and numerous works have been put forward to address it. In this paper, we first revisit the widely used homophily metrics and point out that their consideration of only graph-label consistency is a shortcoming. Then, we study heterophily from the perspective of post-aggregation node similarity and define new homophily metrics, which are potentially advantageous compared to existing ones. Based on this investigation, we prove that some harmful cases of heterophily can be effectively addressed by local diversification operation. Then, we propose the Adaptive Channel Mixing (ACM), a framework to adaptively exploit aggregation, diversification and identity channels to extract richer localized information in each baseline GNN layer. ACM is more powerful than the commonly used uni-channel framework for node classification tasks on heterophilic graphs. When evaluated on 10 benchmark node classification tasks, ACM-augmented baselines consistently achieve significant performance gain, exceeding state-of-the-art GNNs on most tasks without incurring significant computational burden. (Code: https://github.com/SitaoLuan/ACM-GNN)