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In the presence of impulsive noise, and missing observations, accurate online prediction of time-varying graph signals poses a crucial challenge in numerous application domains. We propose the Adaptive Least Mean $p^{th}$ Power Graph Neural Networks (LMP-GNN), a universal framework combining adaptive filter and graph neural network for online graph signal estimation. LMP-GNN retains the advantage of adaptive filtering in handling noise and missing observations as well as the online update capability. The incorporated graph neural network within the LMP-GNN can train and update filter parameters online instead of predefined filter parameters in previous methods, outputting more accurate prediction results. The adaptive update scheme of the LMP-GNN follows the solution of a $l_p$-norm optimization, rooting to the minimum dispersion criterion, and yields robust estimation results for time-varying graph signals under impulsive noise. A special case of LMP-GNN named the Sign-GNN is also provided and analyzed, Experiment results on two real-world datasets of temperature graph and traffic graph under four different noise distributions prove the effectiveness and robustness of our proposed LMP-GNN.

Efficient and robust prediction of graph signals is challenging when the signals are under impulsive noise and have missing data. Exploiting graph signal processing (GSP) and leveraging the simplicity of the classical adaptive sign algorithm, we propose an adaptive algorithm on graphs named the Graph Normalized Sign (GNS). GNS approximated a normalization term into the update, therefore achieving faster convergence and lower error compared to previous adaptive GSP algorithms. In the task of the online prediction of multivariate temperature data under impulsive noise, GNS outputs fast and robust predictions.

Graph Neural Networks have a limitation of solely processing features on graph nodes, neglecting data on high-dimensional structures such as edges and triangles. Simplicial Convolutional Neural Networks (SCNN) represent higher-order structures using simplicial complexes to break this limitation albeit still lacking time efficiency. In this paper, we propose a novel neural network architecture on simplicial complexes named Binarized Simplicial Convolutional Neural Networks (Bi-SCNN) based on the combination of simplicial convolution with a binary-sign forward propagation strategy. The usage of the Hodge Laplacian on a binary-sign forward propagation enables Bi-SCNN to efficiently and effectively represent simplicial features that have higher-order structures than traditional graph node representations. Compared to the previous Simplicial Convolutional Neural Networks, the reduced model complexity of Bi-SCNN shortens the execution time without sacrificing the prediction performance and is less prone to the over-smoothing effect. Experimenting with real-world citation and ocean-drifter data confirmed that our proposed Bi-SCNN is efficient and accurate.

The problem of how to take the right actions to make profits in sequential process continues to be difficult due to the quick dynamics and a significant amount of uncertainty in many application scenarios. In such complicated environments, reinforcement learning (RL), a reward-oriented strategy for optimum control, has emerged as a potential technique to address this strategic decision-making issue. However, reinforcement learning also has some shortcomings that make it unsuitable for solving many financial problems, excessive resource consumption, and inability to quickly obtain optimal solutions, making it unsuitable for quantitative trading markets. In this study, we use two methods to overcome the issue with contextual information: contextual Thompson sampling and reinforcement learning under supervision which can accelerate the iterations in search of the best answer. In order to investigate strategic trading in quantitative markets, we merged the earlier financial trading strategy known as constant proportion portfolio insurance (CPPI) into deep deterministic policy gradient (DDPG). The experimental results show that both methods can accelerate the progress of reinforcement learning to obtain the optimal solution.

Quantitative markets are characterized by swift dynamics and abundant uncertainties, making the pursuit of profit-driven stock trading actions inherently challenging. Within this context, reinforcement learning (RL), which operates on a reward-centric mechanism for optimal control, has surfaced as a potentially effective solution to the intricate financial decision-making conundrums presented. This paper delves into the fusion of two established financial trading strategies, namely the constant proportion portfolio insurance (CPPI) and the time-invariant portfolio protection (TIPP), with the multi-agent deep deterministic policy gradient (MADDPG) framework. As a result, we introduce two novel multi-agent RL (MARL) methods, CPPI-MADDPG and TIPP-MADDPG, tailored for probing strategic trading within quantitative markets. To validate these innovations, we implemented them on a diverse selection of 100 real-market shares. Our empirical findings reveal that the CPPI-MADDPG and TIPP-MADDPG strategies consistently outpace their traditional counterparts, affirming their efficacy in the realm of quantitative trading.

The adaptive estimation of coexisting temporal vertex (node) and edge signals on graphs is a critical task when a change in edge signals influences the temporal dynamics of the vertex signals. However, the current Graph Signal Processing algorithms mostly consider only the signals existing on the graph vertices and have neglected the fact that signals can reside on the edges. We propose an Adaptive Joint Vertex-Edge Estimation (AJVEE) algorithm for jointly estimating time-varying vertex and edge signals through a time-varying regression, incorporating both vertex signal filtering and edge signal filtering. Accompanying AJVEE is a newly proposed Adaptive Least Mean Square procedure based on the Hodge Laplacian (ALMS-Hodge), which is inspired by classical adaptive filters combining simplicial filtering and simplicial regression. AJVEE is able to operate jointly on the vertices and edges by merging two ALMS-Hodge algorithms specified on the vertices and edges into a unified formulation. A more generalized case extending AJVEE beyond the vertices and edges is being discussed. Experimenting on real-world traffic networks and population mobility networks, we have confirmed that our proposed AJVEE algorithm could accurately and jointly track time-varying vertex and edge signals on graphs.

In algorithm optimization in reinforcement learning, how to deal with the exploration-exploitation dilemma is particularly important. Multi-armed bandit problem can optimize the proposed solutions by changing the reward distribution to realize the dynamic balance between exploration and exploitation. Thompson Sampling is a common method for solving multi-armed bandit problem and has been used to explore data that conform to various laws. In this paper, we consider the Thompson Sampling approach for multi-armed bandit problem, in which rewards conform to unknown asymmetric $\alpha$-stable distributions and explore their applications in modelling financial and wireless data., Comment: 8 pages, 4 figures

Efficient and robust online processing technique of irregularly structured data is crucial in the current era of data abundance. In this paper, we propose a graph/network version of the classical adaptive Sign algorithm for online graph signal estimation under impulsive noise. Recently introduced graph adaptive least mean squares algorithm is unstable under non-Gaussian impulsive noise and has high computational complexity. The Graph-Sign algorithm proposed in this work is based on the minimum dispersion criterion and therefore impulsive noise does not hinder its estimation quality. Unlike the recently proposed graph adaptive least mean p-th power algorithm, our Graph-Sign algorithm can operate without prior knowledge of the noise distribution. The proposed Graph-Sign algorithm has a faster run time because of its low computational complexity compared to the existing adaptive graph signal processing algorithms. Experimenting on steady-state and time-varying graph signals estimation utilizing spectral properties of bandlimitedness and sampling, the Graph-Sign algorithm demonstrates fast, stable, and robust graph signal estimation performance under impulsive noise modeled by alpha stable, Cauchy, Student's t, or Laplace distributions.

Understanding the source of the superior generalization ability of NNs remains one of the most important problems in ML research. There have been a series of theoretical works trying to derive non-vacuous bounds for NNs. Recently, the compression of information stored in weights (IIW) is proved to play a key role in NNs generalization based on the PAC-Bayes theorem. However, no solution of IIW has ever been provided, which builds a barrier for further investigation of the IIW's property and its potential in practical deep learning. In this paper, we propose an algorithm for the efficient approximation of IIW. Then, we build an IIW-based information bottleneck on the trade-off between accuracy and information complexity of NNs, namely PIB. From PIB, we can empirically identify the fitting to compressing phase transition during NNs' training and the concrete connection between the IIW compression and the generalization. Besides, we verify that IIW is able to explain NNs in broad cases, e.g., varying batch sizes, over-parameterization, and noisy labels. Moreover, we propose an MCMC-based algorithm to sample from the optimal weight posterior characterized by PIB, which fulfills the potential of IIW in enhancing NNs in practice., Comment: ICLR'22 (Spotlight)

Counterfactual learning for dealing with missing-not-at-random data (MNAR) is an intriguing topic in the recommendation literature since MNAR data are ubiquitous in modern recommender systems. Missing-at-random (MAR) data, namely randomized controlled trials (RCTs), are usually required by most previous counterfactual learning methods for debiasing learning. However, the execution of RCTs is extraordinarily expensive in practice. To circumvent the use of RCTs, we build an information-theoretic counterfactual variational information bottleneck (CVIB), as an alternative for debiasing learning without RCTs. By separating the task-aware mutual information term in the original information bottleneck Lagrangian into factual and counterfactual parts, we derive a contrastive information loss and an additional output confidence penalty, which facilitates balanced learning between the factual and counterfactual domains. Empirical evaluation on real-world datasets shows that our CVIB significantly enhances both shallow and deep models, which sheds light on counterfactual learning in recommendation that goes beyond RCTs.

In this paper, we present a novel statistical model, $\textit{the generalized-Gaussian-Rician}$ (GG-Rician) distribution, for the characterization of synthetic aperture radar (SAR) images. Since accurate statistical models lead to better results in applications such as target tracking, classification, or despeckling, characterizing SAR images of various scenes including urban, sea surface, or agricultural, is essential. The proposed statistical model is based on the Rician distribution to model the amplitude of a complex SAR signal, the in-phase and quadrature components of which are assumed to be generalized-Gaussian distributed. The proposed amplitude GG-Rician model is further extended to cover the intensity SAR signals. In the experimental analysis, the GG-Rician model is investigated for amplitude and intensity SAR images of various frequency bands and scenes in comparison to state-of-the-art statistical models that include $\mathcal{K}$, Weibull, Gamma, and Lognormal. In order to decide on the most suitable model, statistical significance analysis via Kullback-Leibler divergence and Kolmogorov-Smirnov statistics are performed. The results demonstrate the superior performance and flexibility of the proposed model for all frequency bands and scenes and its applicability on both amplitude and intensity SAR images. The Matlab package is available at https://github.com/oktaykarakus/GG-Rician-SAR-Image-Modelling., Comment: 20 Pages, 11 figures, 5 tables

Developing techniques for adversarial attack and defense is an important research field for establishing reliable machine learning and its applications. Many existing methods employ Gaussian random variables for exploring the data space to find the most adversarial (for attacking) or least adversarial (for defense) point. However, the Gaussian distribution is not necessarily the optimal choice when the exploration is required to follow the complicated structure that most real-world data distributions exhibit. In this paper, we investigate how statistics of random variables affect such random walk exploration. Specifically, we generalize the Boundary Attack, a state-of-the-art black-box decision based attacking strategy, and propose the L\'evy-Attack, where the random walk is driven by symmetric $\alpha$-stable random variables. Our experiments on MNIST and CIFAR10 datasets show that the L\'evy-Attack explores the image data space more efficiently, and significantly improves the performance. Our results also give an insight into the recently found fact in the whitebox attacking scenario that the choice of the norm for measuring the amplitude of the adversarial patterns is essential.

Reversible jump Markov chain Monte Carlo (RJMCMC) is a Bayesian model estimation method which has been used for trans-dimensional sampling. In this study, we propose utilization of RJMCMC beyond trans-dimensional sampling. This new interpretation, which we call trans-space RJMCMC, reveals the undiscovered potential of RJMCMC by exploiting the original formulation to explore spaces of different classes or structures. This provides flexibility in using different types of candidate classes in the combined model space such as spaces of linear and nonlinear models or of various distribution families. As an application for the proposed method, we have performed a special case of trans-space sampling, namely trans-distributional RJMCMC in impulsive data modeling. In many areas such as seismology, radar, image, using Gaussian models is a common practice due to analytical ease. However, many noise processes do not follow a Gaussian character and generally exhibit events too impulsive to be successfully described by the Gaussian model. We test the proposed method to choose between various impulsive distribution families to model both synthetically generated noise processes and real-life measurements on power line communications (PLC) impulsive noises and 2-D discrete wavelet transform (2-D DWT) coefficients., Comment: 22 pages, 9 figures

Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In this paper, we introduce stable graphical (SG) models, a class of multivariate stable densities that can also be represented as Bayesian networks whose edges encode linear dependencies between random variables. One major hurdle to the extensive use of stable distributions is the lack of a closed-form analytical expression for their densities. This makes penalized maximum-likelihood based learning computationally demanding. We establish theoretically that the Bayesian information criterion (BIC) can asymptotically be reduced to the computationally more tractable minimum dispersion criterion (MDC) and develop StabLe, a structure learning algorithm based on MDC. We use simulated datasets for five benchmark network topologies to empirically demonstrate how StabLe improves upon ordinary least squares (OLS) regression. We also apply StabLe to microarray gene expression data for lymphoblastoid cells from 727 individuals belonging to eight global population groups. We establish that StabLe improves test set performance relative to OLS via ten-fold cross-validation. Finally, we develop SGEX, a method for quantifying differential expression of genes between different population groups.