Variational Autoencoders (VAE) are popular generative models used to sample from complex data distributions. Despite their empirical success in various machine learning tasks, significant gaps remain in understanding their theoretical properties, particularly regarding convergence guarantees. This paper aims to bridge that gap by providing non-asymptotic convergence guarantees for VAE trained using both Stochastic Gradient Descent and Adam algorithms.We derive a convergence rate of $\mathcal{O}(\log n / \sqrt{n})$, where $n$ is the number of iterations of the optimization algorithm, with explicit dependencies on the batch size, the number of variational samples, and other key hyperparameters. Our theoretical analysis applies to both Linear VAE and Deep Gaussian VAE, as well as several VAE variants, including $\beta$-VAE and IWAE. Additionally, we empirically illustrate the impact of hyperparameters on convergence, offering new insights into the theoretical understanding of VAE training.

One of the main challenges of federated learning (FL) is handling non-independent and identically distributed (non-IID) client data, which may occur in practice due to unbalanced datasets and use of different data sources across clients. Knowledge sharing and model personalization are key strategies for addressing this issue. Clustered federated learning is a class of FL methods that groups clients that observe similarly distributed data into clusters, such that every client is typically associated with one data distribution and participates in training a model for that distribution along their cluster peers. In this paper, we present a unified Bayesian framework for clustered FL which associates clients to clusters. Then we propose several practical algorithms to handle the, otherwise growing, data associations in a way that trades off performance and computational complexity. This work provides insights on client-cluster associations and enables client knowledge sharing in new ways. The proposed framework circumvents the need for unique client-cluster associations, which is seen to increase the performance of the resulting models in a variety of experiments.

Causal learning from data has received much attention in recent years. One way of capturing causal relationships is by utilizing Bayesian networks. There, one recovers a weighted directed acyclic graph, in which random variables are represented by vertices, and the weights associated with each edge represent the strengths of the causal relationships between them. This concept is extended to capture dynamic effects by introducing a dependency on past data, which may be captured by the structural equation model, which is utilized in the present contribution to formulate a score-based learning approach. A mixed-integer quadratic program is formulated and an algorithmic solution proposed, in which the pre-generation of exponentially many acyclicity constraints is avoided by utilizing the so-called branch-and-cut ("lazy constraint") method. Comparing the novel approach to the state of the art, we show that the proposed approach turns out to produce excellent results when applied to small and medium-sized synthetic instances of up to 25 time-series. Lastly, two interesting applications in bio-science and finance, to which the method is directly applied, further stress the opportunities in developing highly accurate, globally convergent solvers that can handle modest instances.

Conventional medical artificial intelligence (AI) models face barriers in clinical application and ethical issues owing to their inability to handle the privacy-sensitive characteristics of medical data. We present a novel personalized federated learning (pFL) method for medical visual question answering (VQA) models, addressing privacy reliability challenges in the medical domain. Our method introduces learnable prompts into a Transformer architecture to efficiently train it on diverse medical datasets without massive computational costs. Then we introduce a reliable client VQA model that incorporates Dempster-Shafer evidence theory to quantify uncertainty in predictions, enhancing the model's reliability. Furthermore, we propose a novel inter-client communication mechanism that uses maximum likelihood estimation to balance accuracy and uncertainty, fostering efficient integration of insights across clients.

General-purpose navigation in challenging environments remains a significant problem in robotics, with current state-of-the-art approaches facing myriad limitations. Classical approaches struggle with cluttered settings and require extensive tuning, while learning-based methods face difficulties generalizing to out-of-distribution environments. This paper introduces X-Mobility, an end-to-end generalizable navigation model that overcomes existing challenges by leveraging three key ideas. First, X-Mobility employs an auto-regressive world modeling architecture with a latent state space to capture world dynamics. Second, a diverse set of multi-head decoders enables the model to learn a rich state representation that correlates strongly with effective navigation skills. Third, by decoupling world modeling from action policy, our architecture can train effectively on a variety of data sources, both with and without expert policies: off-policy data allows the model to learn world dynamics, while on-policy data with supervisory control enables optimal action policy learning. Through extensive experiments, we demonstrate that X-Mobility not only generalizes effectively but also surpasses current state-of-the-art navigation approaches. Additionally, X-Mobility also achieves zero-shot Sim2Real transferability and shows strong potential for cross-embodiment generalization.

This paper presents a novel Integer Programming (IP) approach for discovering the Markov Equivalent Class (MEC) of Bayesian Networks (BNs) through observational data. The MEC-IP algorithm utilizes a unique clique-focusing strategy and Extended Maximal Spanning Graphs (EMSG) to streamline the search for MEC, thus overcoming the computational limitations inherent in other existing algorithms. Our numerical results show that not only a remarkable reduction in computational time is achieved by our algorithm but also an improvement in causal discovery accuracy is seen across diverse datasets. These findings underscore this new algorithm's potential as a powerful tool for researchers and practitioners in causal discovery and BNSL, offering a significant leap forward toward the efficient and accurate analysis of complex data structures.

Understanding cognitive processes in multi-agent interactions is a primary goal in cognitive science. It can guide the direction of artificial intelligence (AI) research toward social decision-making in multi-agent systems, which includes uncertainty from character heterogeneity. In this paper, we introduce an episodic future thinking (EFT) mechanism for a reinforcement learning (RL) agent, inspired by cognitive processes observed in animals. To enable future thinking functionality, we first develop a multi-character policy that captures diverse characters with an ensemble of heterogeneous policies. Here, the character of an agent is defined as a different weight combination on reward components, representing distinct behavioral preferences. The future thinking agent collects observation-action trajectories of the target agents and uses the pre-trained multi-character policy to infer their characters. Once the character is inferred, the agent predicts the upcoming actions of target agents and simulates the potential future scenario. This capability allows the agent to adaptively select the optimal action, considering the predicted future scenario in multi-agent interactions. To evaluate the proposed mechanism, we consider the multi-agent autonomous driving scenario with diverse driving traits and multiple particle environments. Simulation results demonstrate that the EFT mechanism with accurate character inference leads to a higher reward than existing multi-agent solutions. We also confirm that the effect of reward improvement remains valid across societies with different levels of character diversity.

Dimensionality reduction (DR) offers a useful representation of complex high-dimensional data. Recent DR methods focus on hyperbolic geometry to derive a faithful low-dimensional representation of hierarchical data. However, existing methods are based on neighbor embedding, frequently ruining the continual relation of the hierarchies. This paper presents hyperboloid Gaussian process (GP) latent variable models (hGP-LVMs) to embed high-dimensional hierarchical data with implicit continuity via nonparametric estimation. We adopt generative modeling using the GP, which brings effective hierarchical embedding and executes ill-posed hyperparameter tuning. This paper presents three variants that employ original point, sparse point, and Bayesian estimations. We establish their learning algorithms by incorporating the Riemannian optimization and active approximation scheme of GP-LVM. For Bayesian inference, we further introduce the reparameterization trick to realize Bayesian latent variable learning. In the last part of this paper, we apply hGP-LVMs to several datasets and show their ability to represent high-dimensional hierarchies in low-dimensional spaces.

Procedural Content Generation (PCG) is defined as the automatic creation of game content using algorithms. PCG has a long history in both the game industry and the academic world. It can increase player engagement and ease the work of game designers. While recent advances in deep learning approaches in PCG have enabled researchers and practitioners to create more sophisticated content, it is the arrival of Large Language Models (LLMs) that truly disrupted the trajectory of PCG advancement. This survey explores the differences between various algorithms used for PCG, including search-based methods, machine learning-based methods, other frequently used methods (e.g., noise functions), and the newcomer, LLMs. We also provide a detailed discussion on combined methods. Furthermore, we compare these methods based on the type of content they generate and the publication dates of their respective papers. Finally, we identify gaps in the existing academic work and suggest possible directions for future research.

Intervention intuition is often used in model explanation where the intervention effect of a feature on the outcome is quantified by the difference of a model prediction when the feature value is changed from the current value to the baseline value. Such a model intervention effect of a feature is inherently association. In this paper, we will study the conditions when an intuitive model intervention effect has a causal interpretation, i.e., when it indicates whether a feature is a direct cause of the outcome. This work links the model intervention effect to the causal interpretation of a model. Such an interpretation capability is important since it indicates whether a machine learning model is trustworthy to domain experts. The conditions also reveal the limitations of using a model intervention effect for causal interpretation in an environment with unobserved features. Experiments on semi-synthetic datasets have been conducted to validate theorems and show the potential for using the model intervention effect for model interpretation.