Understanding the complex and stochastic nature of Gene Regulatory Networks (GRNs) remains a central challenge in systems biology. Existing modeling paradigms often struggle to effectively capture the intricate, multi-factor regulatory logic and to rigorously manage the dual uncertainties of network structure and kinetic parameters. In response, this work introduces the Probabilistic Categorical GRN(PC-GRN) framework. It is a novel theoretical approach founded on the synergistic integration of three core methodologies. Firstly, category theory provides a formal language for the modularity and composition of regulatory pathways. Secondly, Bayesian Typed Petri Nets (BTPNs) serve as an interpretable,mechanistic substrate for modeling stochastic cellular processes, with kinetic parameters themselves represented as probability distributions. The central innovation of PC-GRN is its end-to-end generative Bayesian inference engine, which learns a full posterior distribution over BTPN models (P (G, Θ|D)) directly from data. This is achieved by the novel interplay of a GFlowNet, which learns a policy to sample network topologies, and a HyperNetwork, which performs amortized inference to predict their corresponding parameter distributions. The resulting framework provides a mathematically rigorous, biologically interpretable, and uncertainty-aware representation of GRNs, advancing predictive modeling and systems-level analysis.

Active Inference (AIF) offers a robust framework for decision-making, yet its computational and memory demands pose challenges for deployment, especially in resource-constrained environments. This work presents a methodology that facilitates AIF's deployment by integrating pymdp's flexibility and efficiency with a unified, sparse, computational graph tailored for hardware-efficient execution. Our approach reduces latency by over 2x and memory by up to 35%, advancing the deployment of efficient AIF agents for real-time and embedded applications.

Uncertainty estimation is pivotal in machine learning, especially for classification tasks, as it improves the robustness and reliability of models. We introduce a novel `Epistemic Wrapping' methodology aimed at improving uncertainty estimation in classification. Our approach uses Bayesian Neural Networks (BNNs) as a baseline and transforms their outputs into belief function posteriors, effectively capturing epistemic uncertainty and offering an efficient and general methodology for uncertainty quantification. Comprehensive experiments employing a Bayesian Neural Network (BNN) baseline and an Interval Neural Network for inference on the MNIST, Fashion-MNIST, CIFAR-10 and CIFAR-100 datasets demonstrate that our Epistemic Wrapper significantly enhances generalisation and uncertainty quantification.

The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these representations, effectively enabling us to learn a continuous distribution using discrete parameters. We consider both 2D densities and quantized neural networks, where we introduce a tractable learning approach using probabilistic circuits. This method offers a scalable solution to manage complex distributions and provides clear insights into model behavior. We validate our approach with various models, demonstrating inference efficiency without sacrificing accuracy. This work advances scalable, interpretable machine learning by utilizing discrete approximations for probabilistic computations.

Curriculum analytics (CA) studies curriculum structure and student data to ensure the quality of educational programs. An essential aspect is studying course properties, which involves assigning each course a representative difficulty value. This is critical for several aspects of CA, such as quality control (e.g., monitoring variations over time), course comparisons (e.g., articulation), and course recommendation (e.g., advising). Measuring course difficulty requires careful consideration of multiple factors: First, when difficulty measures are sensitive to the performance level of enrolled students, it can bias interpretations by overlooking student diversity. By assessing difficulty independently of enrolled students' performances, we can reduce the risk of bias and enable fair, representative assessments of difficulty. Second, from a measurement theoretic perspective, the measurement must be reliable and valid to provide a robust basis for subsequent analyses. Third, difficulty measures should account for covariates, such as the characteristics of individual students within a diverse populations (e.g., transfer status). In recent years, various notions of difficulty have been proposed. This paper provides the first comprehensive review and comparison of existing approaches for assessing course difficulty based on grade point averages and latent trait modeling. It further offers a hands-on tutorial on model selection, assumption checking, and practical CA applications. These applications include monitoring course difficulty over time and detecting courses with disparate outcomes between distinct groups of students (e.g., dropouts vs. graduates), ultimately aiming to promote high-quality, fair, and equitable learning experiences. To support further research and application, we provide an open-source software package and artificial datasets, facilitating reproducibility and adoption.

This allows for the use of gradient-based end-to-end training to integrate deep-learning and the classical inverse problem methods.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Markov Decision Process (MDP) provided that we can access the reward and transition function through a generative model.

A graphical model is a structured representation of the data generating process. The traditional method to reason over random variables is to perform inference in this graphical model. However, in many cases the generating process is only a poor approximation of the much more complex true data generating process, leading to suboptimal estimations.