Recent studies on Graph Neural Networks(GNNs) provide both empirical and theoretical evidence supporting their effectiveness in capturing structural patterns on both homophilic and certain heterophilic graphs. Notably, most real-world homophilic and heterophilic graphs are comprised of a mixture of nodes in both homophilic and heterophilic structural patterns, exhibiting a structural disparity. However, the analysis of GNN performance with respect to nodes exhibiting different structural patterns, e.g., homophilic nodes in heterophilic graphs, remains rather limited. In the present study, we provide evidence that Graph Neural Networks(GNNs) on node classification typically perform admirably on homophilic nodes within homophilic graphs and heterophilic nodes within heterophilic graphs while struggling on the opposite node set, exhibiting a performance disparity. We theoretically and empirically identify effects of GNNs on testing nodes exhibiting distinct structural patterns. We then propose a rigorous, non-i.i.d PAC-Bayesian generalization bound for GNNs, revealing reasons for the performance disparity, namely the aggregated feature distance and homophily ratio difference between training and testing nodes. Furthermore, we demonstrate the practical implications of our new findings via (1) elucidating the effectiveness of deeper GNNs; and (2) revealing an over-looked distribution shift factor on graph out-of-distribution problem and proposing a new scenario accordingly.

Designing flexible probabilistic models over tree topologies is important for developing efficient phylogenetic inference methods. To do that, previous works often leverage the similarity of tree topologies via hand-engineered heuristic features which would require pre-sampled tree topologies and may suffer from limited approximation capability. In this paper, we propose a deep autoregressive model for phylogenetic inference based on graph neural networks (GNNs), called ARTree. By decomposing a tree topology into a sequence of leaf node addition operations and modeling the involved conditional distributions based on learnable topological features via GNNs, ARTree can provide a rich family of distributions over the entire tree topology space that have simple sampling algorithms and density estimation procedures, without using heuristic features. We demonstrate the effectiveness and efficiency of our method on a benchmark of challenging real data tree topology density estimation and variational Bayesian phylogenetic inference problems.

Assessing causal effects in the presence of unobserved confounding is a challenging problem. Existing studies leveraged proxy variables or multiple treatments to adjust for the confounding bias. In particular, the latter approach attributes the impact on a single outcome to multiple treatments, allowing estimating latent variables for confounding control. Nevertheless, these methods primarily focus on a single outcome, whereas in many real-world scenarios, there is greater interest in studying the effects on multiple outcomes. Besides, these outcomes are often coupled with multiple treatments. Examples include the intensive care unit (ICU), where health providers evaluate the effectiveness of therapies on multiple health indicators. To accommodate these scenarios, we consider a new setting dubbed as multiple treatments and multiple outcomes. We then show that parallel studies of multiple outcomes involved in this setting can assist each other in causal identification, in the sense that we can exploit other treatments and outcomes as proxies for each treatment effect under study. We proceed with a causal discovery method that can effectively identify such proxies for causal estimation. The utility of our method is demonstrated in synthetic data and sepsis disease.

Bayesian methods for solving inverse problems are a powerful alternative to classical methods since the Bayesian approach offers the ability to quantify the uncertainty in the solution. In recent years, data-driven techniques for solving inverse problems have also been remarkably successful, due to their superior representation ability. In this work, we incorporate data-based models into a class of Langevin-based sampling algorithms for Bayesian inference in imaging inverse problems. In particular, we introduce NF-ULA (Normalizing Flow-based Unadjusted Langevin algorithm), which involves learning a normalizing flow (NF) as the image prior. We use NF to learn the prior because a tractable closed-form expression for the log prior enables the differentiation of it using autograd libraries. Our algorithm only requires a normalizing flow-based generative network, which can be pre-trained independently of the considered inverse problem and the forward operator. We perform theoretical analysis by investigating the well-posedness and non-asymptotic convergence of the resulting NF-ULA algorithm. The efficacy of the proposed NF-ULA algorithm is demonstrated in various image restoration problems such as image deblurring, image inpainting, and limited-angle X-ray computed tomography (CT) reconstruction. NF-ULA is found to perform better than competing methods for severely ill-posed inverse problems.

Patterns of microcircuitry suggest that the brain has an array of repeated canonical computational units. Yet neural representations are distributed, so the relevant computations may only be related indirectly to single-neuron transformations. It thus remains an open challenge how to define canonical distributed computations. We integrate normative and algorithmic theories of neural computation into a mathematical framework for inferring canonical distributed computations from large-scale neural activity patterns. At the normative level, we hypothesize that the brain creates a structured internal model of its environment, positing latent causes that explain its sensory inputs, and uses those sensory inputs to infer the latent causes. At the algorithmic level, we propose that this inference process is a nonlinear message-passing algorithm on a graph-structured model of the world. Given a time series of neural activity during a perceptual inference task, our framework finds (i) the neural representation of relevant latent variables, (ii) interactions between these variables that define the brain's internal model of the world, and (iii) message-functions specifying the inference algorithm. These targeted computational properties are then statistically distinguishable due to the symmetries inherent in any canonical computation, up to a global transformation. As a demonstration, we simulate recordings for a model brain that implicitly implements an approximate inference algorithm on a probabilistic graphical model. Given its external inputs and noisy neural activity, we recover the latent variables, their neural representation and dynamics, and canonical message-functions. We highlight features of experimental design needed to successfully extract canonical computations from neural data. Overall, this framework provides a new tool for discovering interpretable structure in neural recordings.

Despite advances in artificial intelligence-enhanced trading methods, developing a profitable automated trading system remains challenging in the rapidly evolving cryptocurrency market. This study aims to address these challenges by developing a reinforcement learning-based automated trading system for five popular altcoins~(cryptocurrencies other than Bitcoin): Binance Coin, Ethereum, Litecoin, Ripple, and Tether. To this end, we present CausalReinforceNet, a framework framed as a decision support system. Designed as the foundational architecture of the trading system, the CausalReinforceNet framework enhances the capabilities of the reinforcement learning agent through causal analysis. Within this framework, we use Bayesian networks in the feature engineering process to identify the most relevant features with causal relationships that influence cryptocurrency price movements. Additionally, we incorporate probabilistic price direction signals from dynamic Bayesian networks to enhance our reinforcement learning agent's decision-making. Due to the high volatility of the cryptocurrency market, we design our framework to adopt a conservative approach that limits sell and buy position sizes to manage risk. We develop two agents using the CausalReinforceNet framework, each based on distinct reinforcement learning algorithms. The results indicate that our framework substantially surpasses the Buy-and-Hold benchmark strategy in profitability. Additionally, both agents generated notable returns on investment for Binance Coin and Ethereum.

Automated Market Makers (AMMs) are major centers of matching liquidity supply and demand in Decentralized Finance. Their functioning relies primarily on the presence of liquidity providers (LPs) incentivized to invest their assets into a liquidity pool. However, the prices at which a pooled asset is traded is often more stale than the prices on centralized and more liquid exchanges. This leads to the LPs suffering losses to arbitrage. This problem is addressed by adapting market prices to trader behavior, captured via the classical market microstructure model of Glosten and Milgrom. In this paper, we propose the first optimal Bayesian and the first model-free data-driven algorithm to optimally track the external price of the asset. The notion of optimality that we use enforces a zero-profit condition on the prices of the market maker, hence the name ZeroSwap. This ensures that the market maker balances losses to informed traders with profits from noise traders. The key property of our approach is the ability to estimate the external market price without the need for price oracles or loss oracles. Our theoretical guarantees on the performance of both these algorithms, ensuring the stability and convergence of their price recommendations, are of independent interest in the theory of reinforcement learning. We empirically demonstrate the robustness of our algorithms to changing market conditions.

The core of the performance-driven computational design is to trace the sensitivity of variations of some performance indicators to the differences between design alternatives. Therefore any argument about the utility of AI for performancebased design must necessarily discuss the representation of such differences, as explicitly as possible. The existing data models and data representations in the field of Architecture, Engineering, and Construction (AEC), such as CAD and BIM are heavily focused on geometrically representing building elements and facilitating the process of construction management. Unfortunately, the field of AEC does not currently have a structured discourse based on an explicit representation of decision variables and outcomes of interest. Specifically, the notion of design representation and the idea of data modelling for representing "what needs to be attained from buildings" is rather absent in the literature.

Structure learning is essential for Bayesian networks (BNs) as it uncovers causal relationships, and enables knowledge discovery, predictions, inferences, and decision-making under uncertainty. Two novel algorithms, FSBN and SSBN, based on the PC algorithm, employ local search strategy and conditional independence tests to learn the causal network structure from data. They incorporate d-separation to infer additional topology information, prioritize conditioning sets, and terminate the search immediately and efficiently. FSBN achieves up to 52% computation cost reduction, while SSBN surpasses it with a remarkable 72% reduction for a 200-node network. SSBN demonstrates further efficiency gains due to its intelligent strategy. Experimental studies show that both algorithms match the induction quality of the PC algorithm while significantly reducing computation costs. This enables them to offer interpretability and adaptability while reducing the computational burden, making them valuable for various applications in big data analytics.

Educational Data Mining (EDM) has emerged as a vital field of research, which harnesses the power of computational techniques to analyze educational data. With the increasing complexity and diversity of educational data, Deep Learning techniques have shown significant advantages in addressing the challenges associated with analyzing and modeling this data. This survey aims to systematically review the state-of-the-art in EDM with Deep Learning. We begin by providing a brief introduction to EDM and Deep Learning, highlighting their relevance in the context of modern education. Next, we present a detailed review of Deep Learning techniques applied in four typical educational scenarios, including knowledge tracing, undesirable student detecting, performance prediction, and personalized recommendation. Furthermore, a comprehensive overview of public datasets and processing tools for EDM is provided. Finally, we point out emerging trends and future directions in this research area.