Related papers: Dynamic Markov Blanket Detection for Macroscopic P…
Model discovery aims to uncover governing differential equations of dynamical systems directly from experimental data. Benchmarking such methods is essential for tracking progress and understanding trade-offs in the field. While prior…
Active classification, i.e., the sequential decision-making process aimed at data acquisition for classification purposes, arises naturally in many applications, including medical diagnosis, intrusion detection, and object tracking. In this…
Modern artificial intelligence excels at statistical interpolation within seen manifolds but fundamentally fails at the exact reasoning required for theoretical physics and mathematics. We identify the "Float Wall" -- a catastrophic…
Inverse problems involving partial differential equations (PDEs) with discontinuous coefficients are fundamental challenges in modeling complex spatiotemporal systems with heterogeneous structures and uncertain dynamics. Traditional…
Energy-Based Models (EBMs) have proven to be a highly effective approach for modelling densities on finite-dimensional spaces. Their ability to incorporate domain-specific choices and constraints into the structure of the model through…
This paper provides a graphical characterization of Markov blankets in chain graphs (CGs) under the Lauritzen-Wermuth-Frydenberg (LWF) interpretation. The characterization is different from the well-known one for Bayesian networks and…
Deep learning has revolutionised artificial intelligence (AI) by enabling automatic feature extraction and function approximation from raw data. However, it faces challenges such as a lack of out-of-distribution generalisation, catastrophic…
Autonomous agents require the capability to identify dynamic objects in their environment for safe planning and navigation. Incomplete and erroneous dynamic detections jeopardize the agent's ability to accomplish its task. Dynamic detection…
Based on a generative model (GM) and beliefs over hidden states, the free energy principle (FEP) enables an agent to sense and act by minimizing a free energy bound on Bayesian surprise. Inclusion of prior beliefs in the GM about desired…
Free energy principle (FEP) is a burgeoning theory in theoretical neuroscience that provides a universal law for modelling living systems of any scale. Expecting a digital twin mind from this first principle, we propose a macro-level…
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…
The maximum entropy principle (MEP) apparently allows us to derive, or justify, fundamental results of equilibrium statistical mechanics. Because of this, a school of thought considers the MEP as a powerful and elegant way to make…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…
General purpose intelligent learning agents cycle through (complex,non-MDP) sequences of observations, actions, and rewards. On the other hand, reinforcement learning is well-developed for small finite state Markov Decision Processes…
Consider $n$ random variables forming a Markov random field (MRF). The true model of the MRF is unknown, and it is assumed to belong to a binary set. The objective is to sequentially sample the random variables (one-at-a-time) such that the…
Labelled networks are an important class of data, naturally appearing in numerous applications in science and engineering. A typical inference goal is to determine how the vertex labels (or features) affect the network's structure. In this…
This thesis focuses on three fundamental aspects of biological systems; namely, entropy production, Bayesian mechanics, and the free-energy principle. The contributions are threefold: 1) We compute the entropy production for a greater class…
We discuss non-reversible Markov-chain Monte Carlo algorithms that, for particle systems, rigorously sample the positional Boltzmann distribution and that have faster than physical dynamics. These algorithms all feature a non-thermal…
Active learning optimizes the exploration of large parameter spaces by strategically selecting which experiments or simulations to conduct, thus reducing resource consumption and potentially accelerating scientific discovery. A key…