Generative models such as diffusion models have achieved remarkable success in state-of-the-art image and text tasks. Recently, score-based diffusion models have extended their success beyond image generation, showing competitive performance with discriminative methods in image {\em classification} tasks~\cite{zimmermann2021score}. However, their application to classification in the {\em graph} domain, which presents unique challenges such as complex topologies, remains underexplored. We show how graph diffusion models can be applied for graph classification. We find that to achieve competitive classification accuracy, score-based graph diffusion models should be trained with a novel training objective that is tailored to graph classification. In experiments with a sampling-based inference method, our discriminative training objective achieves state-of-the-art graph classification accuracy.

Reinforcement learning (RL) and causal modelling naturally complement each other. The goal of causal modelling is to predict the effects of interventions in an environment, while the goal of reinforcement learning is to select interventions that maximize the rewards the agent receives from the environment. Reinforcement learning includes the two most powerful sources of information for estimating causal relationships: temporal ordering and the ability to act on an environment. This paper examines which reinforcement learning settings we can expect to benefit from causal modelling, and how. In online learning, the agent has the ability to interact directly with their environment, and learn from exploring it. Our main argument is that in online learning, conditional probabilities are causal, and therefore offline RL is the setting where causal learning has the most potential to make a difference. Essentially, the reason is that when an agent learns from their {\em own} experience, there are no unobserved confounders that influence both the agent's own exploratory actions and the rewards they receive. Our paper formalizes this argument. For offline RL, where an agent may and typically does learn from the experience of {\em others}, we describe previous and new methods for leveraging a causal model, including support for counterfactual queries.

Learning causal representations from observational and interventional data in the absence of known ground-truth graph structures necessitates implicit latent causal representation learning. Implicit learning of causal mechanisms typically involves two categories of interventional data: hard and soft interventions. In real-world scenarios, soft interventions are often more realistic than hard interventions, as the latter require fully controlled environments. Unlike hard interventions, which directly force changes in a causal variable, soft interventions exert influence indirectly by affecting the causal mechanism. However, the subtlety of soft interventions impose several challenges for learning causal models. One challenge is that soft intervention's effects are ambiguous, since parental relations remain intact. In this paper, we tackle the challenges of learning causal models using soft interventions while retaining implicit modeling. Our approach models the effects of soft interventions by employing a \textit{causal mechanism switch variable} designed to toggle between different causal mechanisms. In our experiments, we consistently observe improved learning of identifiable, causal representations, compared to baseline approaches.

The aim of the Prague Relational Learning Repository is to support machine learning research with multi-relational data. The repository currently contains 148 SQL databases hosted on a public MySQL server located at https://relational-data.org. The server is provided by getML to support the relational machine learning community(www.getml.com). A searchable meta-database provides metadata (e.g., the number of tables in the database, the number of rows and columns in the tables, the number of self-relationships). Many organizations maintain their data in relational databases, which support complex structured data.

A fundamental problem of causal discovery is cause-effect inference, learning the correct causal direction between two random variables. Significant progress has been made through modelling the effect as a function of its cause and a noise term, which allows us to leverage assumptions about the generating function class. The recently introduced heteroscedastic location-scale noise functional models (LSNMs) combine expressive power with identifiability guarantees. LSNM model selection based on maximizing likelihood achieves state-of-the-art accuracy, when the noise distributions are correctly specified. However, through an extensive empirical evaluation, we demonstrate that the accuracy deteriorates sharply when the form of the noise distribution is misspecified by the user. Our analysis shows that the failure occurs mainly when the conditional variance in the anti-causal direction is smaller than that in the causal direction. As an alternative, we find that causal model selection through residual independence testing is much more robust to noise misspecification and misleading conditional variance.

The graph classification task is to assign a discrete class label to an input graph. The dominant approach for neural graph classification is to compute an embedding for the input graph and perform the final classification in embedding space. The successful graph coarsening approach aggregates graph structural information at successively lower resolutions until a final embedding is obtained. Another direction for graph learning, so far unrelated, is graph generation. A graph generative model (GGM) aims to generate realistic graphs, often by sampling from a distribution over graphs. GGMs include the graph Variational Auto-Encoder (GVAE), auto-regressive methods, and most recently graph diffusion models.

Estimating the expected value of a graph statistic is an important inference task for using and learning graph models. This note presents a scalable estimation procedure for expected motif counts, a widely used type of graph statistic. The procedure applies for generative mixture models of the type used in neural and Bayesian approaches to graph data.

Conventional supervised learning methods typically assume i.i.d samples and are found to be sensitive to out-of-distribution (OOD) data. We propose Generative Causal Representation Learning (GCRL) which leverages causality to facilitate knowledge transfer under distribution shifts. While we evaluate the effectiveness of our proposed method in human trajectory prediction models, GCRL can be applied to other domains as well. First, we propose a novel causal model that explains the generative factors in motion forecasting datasets using features that are common across all environments and with features that are specific to each environment. Selection variables are used to determine which parts of the model can be directly transferred to a new environment without fine-tuning. Second, we propose an end-to-end variational learning paradigm to learn the causal mechanisms that generate observations from features. GCRL is supported by strong theoretical results that imply identifiability of the causal model under certain assumptions. Experimental results on synthetic and real-world motion forecasting datasets show the robustness and effectiveness of our proposed method for knowledge transfer under zero-shot and low-shot settings by substantially outperforming the prior motion forecasting models on out-of-distribution prediction. Our code is available at https://github.com/sshirahmad/GCRL.

Generative models for graph data are an important research topic in machine learning. Graph data comprise two levels that are typically analyzed separately: node-level properties such as the existence of a link between a pair of nodes, and global aggregate graph-level statistics, such as motif counts. This paper proposes a new multi-level framework that jointly models node-level properties and graph-level statistics, as mutually reinforcing sources of information. We introduce a new micro-macro training objective for graph generation that combines node-level and graph-level losses. We utilize the micro-macro objective to improve graph generation with a GraphVAE, a well-established model based on graph-level latent variables, that provides fast training and generation time for medium-sized graphs. Our experiments show that adding micro-macro modeling to the GraphVAE model improves graph quality scores up to 2 orders of magnitude on five benchmark datasets, while maintaining the GraphVAE generation speed advantage.

Statistical-Relational Model Discovery aims to find statistically relevant patterns in relational data. For example, a relational dependency pattern may stipulate that a user's gender is associated with the gender of their friends. As with propositional (non-relational) graphical models, the major scalability bottleneck for model discovery is computing instantiation counts: the number of times a relational pattern is instantiated in a database. Previous work on propositional learning utilized pre-counting or post-counting to solve this task. This paper takes a detailed look at the memory and speed trade-offs between pre-counting and post-counting strategies for relational learning. A pre-counting approach computes and caches instantiation counts for a large set of relational patterns before model search. A post-counting approach computes an instantiation count dynamically on-demand for each candidate pattern generated during the model search. We describe a novel hybrid approach, tailored to relational data, that achieves a sweet spot with pre-counting for patterns involving positive relationships (e.g. pairs of users who are friends) and post-counting for patterns involving negative relationships (e.g. pairs of users who are not friends). Our hybrid approach scales model discovery to millions of data facts.