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Denoising Diffusion Probabilistic models have become increasingly popular due to their ability to offer probabilistic modeling and generate diverse outputs. This versatility inspired their adaptation for image segmentation, where multiple predictions of the model can produce segmentation results that not only achieve high quality but also capture the uncertainty inherent in the model. Here, powerful architectures were proposed for improving diffusion segmentation performance. However, there is a notable lack of analysis and discussions on the differences between diffusion segmentation and image generation, and thorough evaluations are missing that distinguish the improvements these architectures provide for segmentation in general from their benefit for diffusion segmentation specifically. In this work, we critically analyse and discuss how diffusion segmentation for medical images differs from diffusion image generation, with a particular focus on the training behavior. Furthermore, we conduct an assessment how proposed diffusion segmentation architectures perform when trained directly for segmentation. Lastly, we explore how different medical segmentation tasks influence the diffusion segmentation behavior and the diffusion process could be adapted accordingly. With these analyses, we aim to provide in-depth insights into the behavior of diffusion segmentation that allow for a better design and evaluation of diffusion segmentation methods in the future.

For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to translate propositional or first-order formulae into loss functions deployed for optimisation in machine learning. At the same time, recent attempts to give programming language support for verification of neural networks showed that DLs can be used to compile verification properties to machine-learning backends. This situation is calling for stronger guarantees about the soundness of such compilers, the soundness and compositionality of DLs, and the differentiability and performance of the resulting loss functions. In this paper, we propose an approach to formalise existing DLs using the Mathematical Components library in the Coq proof assistant. Thanks to this formalisation, we are able to give uniform semantics to otherwise disparate DLs, give formal proofs to existing informal arguments, find errors in previous work, and provide formal proofs to missing conjectured properties. This work is meant as a stepping stone for the development of programming language support for verification of machine learning.

In addressing control problems such as regulation and tracking through reinforcement learning, it is often required to guarantee that the acquired policy meets essential performance and stability criteria such as a desired settling time and steady-state error prior to deployment. Motivated by this necessity, we present a set of results and a systematic reward shaping procedure that (i) ensures the optimal policy generates trajectories that align with specified control requirements and (ii) allows to assess whether any given policy satisfies them. We validate our approach through comprehensive numerical experiments conducted in two representative environments from OpenAI Gym: the Inverted Pendulum swing-up problem and the Lunar Lander. Utilizing both tabular and deep reinforcement learning methods, our experiments consistently affirm the efficacy of our proposed framework, highlighting its effectiveness in ensuring policy adherence to the prescribed control requirements.

Meshfree simulation methods are emerging as compelling alternatives to conventional mesh-based approaches, particularly in the fields of Computational Fluid Dynamics (CFD) and continuum mechanics. In this publication, we provide a comprehensive overview of our research combining Machine Learning (ML) and Fraunhofer's MESHFREE software (www.meshfree.eu), a powerful tool utilizing a numerical point cloud in a Generalized Finite Difference Method (GFDM). This tool enables the effective handling of complex flow domains, moving geometries, and free surfaces, while allowing users to finely tune local refinement and quality parameters for an optimal balance between computation time and results accuracy. However, manually determining the optimal parameter combination poses challenges, especially for less experienced users. We introduce a novel ML-optimized approach, using active learning, regression trees, and visualization on MESHFREE simulation data, demonstrating the impact of input combinations on results quality and computation time. This research contributes valuable insights into parameter optimization in meshfree simulations, enhancing accessibility and usability for a broader user base in scientific and engineering applications.

Models with intractable normalizing functions have numerous applications. Because the normalizing constants are functions of the parameters of interest, standard Markov chain Monte Carlo cannot be used for Bayesian inference for these models. A number of algorithms have been developed for such models. Some have the posterior distribution as their asymptotic distribution. Other ``asymptotically inexact'' algorithms do not possess this property. There is limited guidance for evaluating approximations based on these algorithms. Hence it is very hard to tune them. We propose two new diagnostics that address these problems for intractable normalizing function models. Our first diagnostic, inspired by the second Bartlett identity, is in principle broadly applicable to Monte Carlo approximations beyond the normalizing function problem. We develop an approximate version of this diagnostic that is applicable to intractable normalizing function problems. Our second diagnostic is a Monte Carlo approximation to a kernel Stein discrepancy-based diagnostic introduced by Gorham and Mackey (2017). We provide theoretical justification for our methods and apply them to several algorithms in challenging simulated and real data examples including an Ising model, an exponential random graph model, and a Conway--Maxwell--Poisson regression model, obtaining interesting insights about the algorithms in these contexts.

Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.

Analyzing observational data from multiple sources can be useful for increasing statistical power to detect a treatment effect; however, practical constraints such as privacy considerations may restrict individual-level information sharing across data sets. This paper develops federated methods that only utilize summary-level information from heterogeneous data sets. Our federated methods provide doubly-robust point estimates of treatment effects as well as variance estimates. We derive the asymptotic distributions of our federated estimators, which are shown to be asymptotically equivalent to the corresponding estimators from the combined, individual-level data. We show that to achieve these properties, federated methods should be adjusted based on conditions such as whether models are correctly specified and stable across heterogeneous data sets.

Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.

It is always well believed that modeling relationships between objects would be helpful for representing and eventually describing an image. Nevertheless, there has not been evidence in support of the idea on image description generation. In this paper, we introduce a new design to explore the connections between objects for image captioning under the umbrella of attention-based encoder-decoder framework. Specifically, we present Graph Convolutional Networks plus Long Short-Term Memory (dubbed as GCN-LSTM) architecture that novelly integrates both semantic and spatial object relationships into image encoder. Technically, we build graphs over the detected objects in an image based on their spatial and semantic connections. The representations of each region proposed on objects are then refined by leveraging graph structure through GCN. With the learnt region-level features, our GCN-LSTM capitalizes on LSTM-based captioning framework with attention mechanism for sentence generation. Extensive experiments are conducted on COCO image captioning dataset, and superior results are reported when comparing to state-of-the-art approaches. More remarkably, GCN-LSTM increases CIDEr-D performance from 120.1% to 128.7% on COCO testing set.