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Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

Recent critiques of Physics Education Research (PER) studies have revoiced the critical issues when drawing causal inferences from observational data where no intervention is present. In response to a call for a "causal reasoning primer", this paper discusses some of the fundamental issues underlying statistical causal inference. In reviewing these issues, we discuss well-established causal inference methods commonly applied in other fields and discuss their application to PER. Using simulated data sets, we illustrate (i) why analysis for causal inference should control for confounders but not control for mediators and colliders and (ii) that multiple proposed causal models can fit a highly correlated data set. Finally, we discuss how these causal inference methods can be used to represent and explain existing issues in quantitative PER. Throughout, we discuss a central issue: quantitative results from observational studies cannot support a researcher's proposed causal model over other alternative models. To address this issue, we propose an explicit role for observational studies in PER that draw statistical causal inferences: proposing future intervention studies and predicting their outcomes. Mirroring a broader connection between theoretical motivating experiments in physics, observational studies in PER can make quantitative predictions of the causal effects of interventions, and future intervention studies can test those predictions directly.

This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when compared to other popular approaches such as those based on k-nearest neighbors or on multiple imputations by chained equations. However, Gaussian mixture models are known to be non-robust to heterogeneous data, which can lead to poor estimation performance when the data is contaminated by outliers or follows non-Gaussian distributions. To overcome this issue, a new EM algorithm is investigated for mixtures of elliptical distributions with the property of handling potential missing data. This paper shows that this problem reduces to the estimation of a mixture of Angular Gaussian distributions under generic assumptions (i.e., each sample is drawn from a mixture of elliptical distributions, which is possibly different for one sample to another). In that case, the complete-data likelihood associated with mixtures of elliptical distributions is well adapted to the EM framework with missing data thanks to its conditional distribution, which is shown to be a multivariate $t$-distribution. Experimental results on synthetic data demonstrate that the proposed algorithm is robust to outliers and can be used with non-Gaussian data. Furthermore, experiments conducted on real-world datasets show that this algorithm is very competitive when compared to other classical imputation methods.

Learning on graphs is becoming prevalent in a wide range of applications including social networks, robotics, communication, medicine, etc. These datasets belonging to entities often contain critical private information. The utilization of data for graph learning applications is hampered by the growing privacy concerns from users on data sharing. Existing privacy-preserving methods pre-process the data to extract user-side features, and only these features are used for subsequent learning. Unfortunately, these methods are vulnerable to adversarial attacks to infer private attributes. We present a novel privacy-respecting framework for distributed graph learning and graph-based machine learning. In order to perform graph learning and other downstream tasks on the server side, this framework aims to learn features as well as distances without requiring actual features while preserving the original structural properties of the raw data. The proposed framework is quite generic and highly adaptable. We demonstrate the utility of the Euclidean space, but it can be applied with any existing method of distance approximation and graph learning for the relevant spaces. Through extensive experimentation on both synthetic and real datasets, we demonstrate the efficacy of the framework in terms of comparing the results obtained without data sharing to those obtained with data sharing as a benchmark. This is, to our knowledge, the first privacy-preserving distributed graph learning framework.

While Reinforcement Learning (RL) achieves tremendous success in sequential decision-making problems of many domains, it still faces key challenges of data inefficiency and the lack of interpretability. Interestingly, many researchers have leveraged insights from the causality literature recently, bringing forth flourishing works to unify the merits of causality and address well the challenges from RL. As such, it is of great necessity and significance to collate these Causal Reinforcement Learning (CRL) works, offer a review of CRL methods, and investigate the potential functionality from causality toward RL. In particular, we divide existing CRL approaches into two categories according to whether their causality-based information is given in advance or not. We further analyze each category in terms of the formalization of different models, ranging from the Markov Decision Process (MDP), Partially Observed Markov Decision Process (POMDP), Multi-Arm Bandits (MAB), and Dynamic Treatment Regime (DTR). Moreover, we summarize the evaluation matrices and open sources while we discuss emerging applications, along with promising prospects for the future development of CRL.

With the advances of data-driven machine learning research, a wide variety of prediction problems have been tackled. It has become critical to explore how machine learning and specifically deep learning methods can be exploited to analyse healthcare data. A major limitation of existing methods has been the focus on grid-like data; however, the structure of physiological recordings are often irregular and unordered which makes it difficult to conceptualise them as a matrix. As such, graph neural networks have attracted significant attention by exploiting implicit information that resides in a biological system, with interactive nodes connected by edges whose weights can be either temporal associations or anatomical junctions. In this survey, we thoroughly review the different types of graph architectures and their applications in healthcare. We provide an overview of these methods in a systematic manner, organized by their domain of application including functional connectivity, anatomical structure and electrical-based analysis. We also outline the limitations of existing techniques and discuss potential directions for future research.

Graphical causal inference as pioneered by Judea Pearl arose from research on artificial intelligence (AI), and for a long time had little connection to the field of machine learning. This article discusses where links have been and should be established, introducing key concepts along the way. It argues that the hard open problems of machine learning and AI are intrinsically related to causality, and explains how the field is beginning to understand them.

Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.