We explore the relationship between causality, symmetry, and compression. We build on and generalize the known connection between learning and compression to a setting where causal models are not identifiable. We propose a framework where causality emerges as a consequence of compressing data across multiple environments. We define algorithmic causality as an alternative definition of causality when traditional assumptions for causal identifiability do not hold. We demonstrate how algorithmic causal and symmetric structures can emerge from minimizing upper bounds on Kolmogorov complexity, without knowledge of intervention targets. We hypothesize that these insights may also provide a novel perspective on the emergence of causality in machine learning models, such as large language models, where causal relationships may not be explicitly identifiable.

This study examines the potential causal relationship between head injury and the risk of developing Alzheimer's disease (AD) using Bayesian networks and regression models. Using a dataset of 2,149 patients, we analyze key medical history variables, including head injury history, memory complaints, cardiovascular disease, and diabetes. Logistic regression results suggest an odds ratio of 0.88 for head injury, indicating a potential but statistically insignificant protective effect against AD. In contrast, memory complaints exhibit a strong association with AD, with an odds ratio of 4.59. Linear regression analysis further confirms the lack of statistical significance for head injury (coefficient: -0.0245, p = 0.469) while reinforcing the predictive importance of memory complaints. These findings highlight the complex interplay of medical history factors in AD risk assessment and underscore the need for further research utilizing larger datasets and advanced causal modeling techniques.

Among other uses, neural networks are a powerful tool for solving deterministic and Bayesian inverse problems in real-time. In the Bayesian framework, variational autoencoders, a specialized type of neural network, enable the estimation of model parameters and their distribution based on observational data allowing to perform real-time inverse uncertainty quantification. In this work, we build upon existing research [Goh, H. et al., Proceedings of Machine Learning Research, 2022] by proposing a novel loss function to train variational autoencoders for Bayesian inverse problems. When the forward map is affine, we provide a theoretical proof of the convergence of the latent states of variational autoencoders to the posterior distribution of the model parameters. We validate this theoretical result through numerical tests and we compare the proposed variational autoencoder with the existing one in the literature. Finally, we test the proposed variational autoencoder on the Laplace equation.

Reliably labelling data typically requires annotations from multiple human workers. However, humans are far from being perfect. Hence, it is a common practice to aggregate labels gathered from multiple annotators to make a more confident estimate of the true label. Among many aggregation methods, the simple and well known Majority Vote (MV) selects the class label polling the highest number of votes. However, despite its importance, the optimality of MV's label aggregation has not been extensively studied. We address this gap in our work by characterising the conditions under which MV achieves the theoretically optimal lower bound on label estimation error. Our results capture the tolerable limits on annotation noise under which MV can optimally recover labels for a given class distribution. This certificate of optimality provides a more principled approach to model selection for label aggregation as an alternative to otherwise inefficient practices that sometimes include higher experts, gold labels, etc., that are all marred by the same human uncertainty despite huge time and monetary costs. Experiments on both synthetic and real world data corroborate our theoretical findings.

We present a federated learning approach for Bayesian model-based clustering of large-scale binary and categorical datasets. We introduce a principled 'divide and conquer' inference procedure using variational inference with local merge and delete moves within batches of the data in parallel, followed by 'global' merge moves across batches to find global clustering structures. We show that these merge moves require only summaries of the data in each batch, enabling federated learning across local nodes without requiring the full dataset to be shared. Empirical results on simulated and benchmark datasets demonstrate that our method performs well in comparison to existing clustering algorithms. We validate the practical utility of the method by applying it to large scale electronic health record (EHR) data.

A comprehensive understanding of causality is critical for navigating and operating within today's complex real-world systems. The absence of realistic causal models with known data generating processes complicates fair benchmarking. In this paper, we present the CausalMan simulator, modeled after a real-world production line. The simulator features a diverse range of linear and non-linear mechanisms and challenging-to-predict behaviors, such as discrete mode changes. We demonstrate the inadequacy of many state-of-the-art approaches and analyze the significant differences in their performance and tractability, both in terms of runtime and memory complexity. As a contribution, we will release the CausalMan large-scale simulator. We present two derived datasets, and perform an extensive evaluation of both.

Integrating expert knowledge, e.g. from large language models, into causal discovery algorithms can be challenging when the knowledge is not guaranteed to be correct. Expert recommendations may contradict data-driven results, and their reliability can vary significantly depending on the domain or specific query. Existing methods based on soft constraints or inconsistencies in predicted causal relationships fail to account for these variations in expertise. To remedy this, we propose L2D-CD, a method for gauging the correctness of expert recommendations and optimally combining them with data-driven causal discovery results. By adapting learning-to-defer (L2D) algorithms for pairwise causal discovery (CD), we learn a deferral function that selects whether to rely on classical causal discovery methods using numerical data or expert recommendations based on textual meta-data. We evaluate L2D-CD on the canonical T\"ubingen pairs dataset and demonstrate its superior performance compared to both the causal discovery method and the expert used in isolation. Moreover, our approach identifies domains where the expert's performance is strong or weak. Finally, we outline a strategy for generalizing this approach to causal discovery on graphs with more than two variables, paving the way for further research in this area.

Training Large Language Models (LLMs) with synthetic data is a prevalent practice in code generation. A key approach is self-training, where LLMs are iteratively trained on self-generated correct code snippets. In this case, the self-generated codes are drawn from a conditional distribution, conditioned on a specific seed description. However, the seed description is not the only valid representation that aligns with its intended meaning. With all valid descriptions and codes forming a joint space, codes drawn from the conditional distribution would lead to an underrepresentation of the full description-code space. As such, we propose Gibbs Fine-Tuning (GiFT), a novel self-training method inspired by Gibbs sampling. GiFT allows self-generated data to be drawn from the marginal distribution of the joint space, thereby mitigating the biases inherent in conditional sampling. We provide a theoretical analysis demonstrating the potential benefits of fine-tuning LLMs with code derived from the marginal distribution. Furthermore, we propose a perplexity-based code selection method to mitigate the imbalanced long-tail distribution of the self-generated codes. Empirical evaluation of two LLMs across four datasets demonstrates that GiFT achieves superior performance, particularly on more challenging benchmarks.

Depth estimation plays a pivotal role in advancing human-robot interactions, especially in indoor environments where accurate 3D scene reconstruction is essential for tasks like navigation and object handling. Monocular depth estimation, which relies on a single RGB camera, offers a more affordable solution compared to traditional methods that use stereo cameras or LiDAR. However, despite recent progress, many monocular approaches struggle with accurately defining depth boundaries, leading to less precise reconstructions. In response to these challenges, this study introduces a novel depth estimation framework that leverages latent space features within a deep convolutional neural network to enhance the precision of monocular depth maps. The proposed model features dual encoder-decoder architecture, enabling both color-to-depth and depth-to-depth transformations. This structure allows for refined depth estimation through latent space encoding. To further improve the accuracy of depth boundaries and local features, a new loss function is introduced. This function combines latent loss with gradient loss, helping the model maintain the integrity of depth boundaries. The framework is thoroughly tested using the NYU Depth V2 dataset, where it sets a new benchmark, particularly excelling in complex indoor scenarios. The results clearly show that this approach effectively reduces depth ambiguities and blurring, making it a promising solution for applications in human-robot interaction and 3D scene reconstruction.

Deep neural networks (DNNs) often exhibit biases toward certain categories during object recognition, even under balanced training data conditions. The intrinsic mechanisms underlying these biases remain unclear. Inspired by the human visual system, which decouples object manifolds through hierarchical processing to achieve object recognition, we propose a geometric analysis framework linking the geometric complexity of class-specific perceptual manifolds in DNNs to model bias. Our findings reveal that differences in geometric complexity can lead to varying recognition capabilities across categories, introducing biases. To support this analysis, we present the Perceptual-Manifold-Geometry library, designed for calculating the geometric properties of perceptual manifolds.