Self-Assembly of Geometric Space from Random Graphs

We present a Euclidean quantum gravity model in which random graphs dynamically self-assemble into discrete manifold structures. Concretely, we consider a statistical model driven by a discretisation of the Euclidean Einstein-Hilbert action; contrary to previous approaches based on simplicial complexes and Regge calculus our discretisation is based on the Ollivier curvature, a coarse analogue of the manifold Ricci curvature defined for generic graphs. The Ollivier curvature is generally difficult to evaluate due to its definition in terms of optimal transport theory, but we present a new exact expression for the Ollivier curvature in a wide class of relevant graphs purely in terms of the numbers of short cycles at an edge. This result should be of independent intrinsic interest to network theorists. Action minimising configurations prove to be cubic complexes up to defects; there are indications that such defects are dynamically suppressed in the macroscopic limit. Closer examination of a defect free model shows that certain classical configurations have a geometric interpretation and discretely approximate vacuum solutions to the Euclidean Einstein-Hilbert action. Working in a configuration space where the geometric configurations are stable vacua of the theory, we obtain direct numerical evidence for the existence of a continuous phase transition; this makes the model a UV completion of Euclidean Einstein gravity. Notably, this phase transition implies an area-law for the entropy of emerging geometric space. Certain vacua of the theory can be interpreted as baby universes; we find that these configurations appear as stable vacua in a mean field approximation of our model, but are excluded dynamically whenever the action is exact indicating the dynamical stability of geometric space. The model is intended as a setting for subsequent studies of emergent time mechanisms.Comment: 26 pages, 9 figures, 2 appendice

A closed-form approach to Bayesian inference in tree-structured graphical models

We consider the inference of the structure of an undirected graphical model in an exact Bayesian framework. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. This task would be intractable without any restriction on the considered graphs, so we limit our exploration to mixtures of spanning trees. We consider the inference of the structure of an undirected graphical model in a Bayesian framework. To avoid convergence issues and highly demanding Monte Carlo sampling, we focus on exact inference. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. To this aim, we restrict the set of considered graphs to mixtures of spanning trees. We investigate under which conditions on the priors - on both tree structures and parameters - exact Bayesian inference can be achieved. Under these conditions, we derive a fast an exact algorithm to compute the posterior probability for an edge to belong to {the tree model} using an algebraic result called the Matrix-Tree theorem. We show that the assumption we have made does not prevent our approach to perform well on synthetic and flow cytometry data

Information-theoretic Reasoning in Distributed and Autonomous Systems

The increasing prevalence of distributed and autonomous systems is transforming decision making in industries as diverse as agriculture, environmental monitoring, and healthcare. Despite significant efforts, challenges remain in robustly planning under uncertainty. In this thesis, we present a number of information-theoretic decision rules for improving the analysis and control of complex adaptive systems. We begin with the problem of quantifying the data storage (memory) and transfer (communication) within information processing systems. We develop an information-theoretic framework to study nonlinear interactions within cooperative and adversarial scenarios, solely from observations of each agent's dynamics. This framework is applied to simulations of robotic soccer games, where the measures reveal insights into team performance, including correlations of the information dynamics to the scoreline. We then study the communication between processes with latent nonlinear dynamics that are observed only through a filter. By using methods from differential topology, we show that the information-theoretic measures commonly used to infer communication in observed systems can also be used in certain partially observed systems. For robotic environmental monitoring, the quality of data depends on the placement of sensors. These locations can be improved by either better estimating the quality of future viewpoints or by a team of robots operating concurrently. By robustly handling the uncertainty of sensor model measurements, we are able to present the first end-to-end robotic system for autonomously tracking small dynamic animals, with a performance comparable to human trackers. We then solve the issue of coordinating multi-robot systems through distributed optimisation techniques. These allow us to develop non-myopic robot trajectories for these tasks and, importantly, show that these algorithms provide guarantees for convergence rates to the optimal payoff sequence

Disentanglement of Latent Representations via Sparse Causal Interventions

The process of generating data such as images is controlled by independent and unknown factors of variation. The retrieval of these variables has been studied extensively in the disentanglement, causal representation learning, and independent component analysis fields. Recently, approaches merging these domains together have shown great success. Instead of directly representing the factors of variation, the problem of disentanglement can be seen as finding the interventions on one image that yield a change to a single factor. Following this assumption, we introduce a new method for disentanglement inspired by causal dynamics that combines causality theory with vector-quantized variational autoencoders. Our model considers the quantized vectors as causal variables and links them in a causal graph. It performs causal interventions on the graph and generates atomic transitions affecting a unique factor of variation in the image. We also introduce a new task of action retrieval that consists of finding the action responsible for the transition between two images. We test our method on standard synthetic and real-world disentanglement datasets. We show that it can effectively disentangle the factors of variation and perform precise interventions on high-level semantic attributes of an image without affecting its quality, even with imbalanced data distributions.Comment: 16 pages, 10 pages for the main paper and 6 pages for the supplement, 14 figures, submitted to IJCAI 2023. V2: added link to repositor

Strategies for selecting and evaluating information

Within the domain of psychology, Optimal Experimental Design (OED) principles have been used to model how people seek and evaluate information. Despite proving valuable as computational-level methods to account for people's behaviour, their descriptive and explanatory powers remain largely unexplored. In a series of experiments, we used a naturalistic crime investigation scenario to examine how people evaluate queries, as well as outcomes, in probabilistic contexts. We aimed to uncover the psychological strategies that people use, not just to assess whether they deviated from OED principles. In addition, we explored the adaptiveness of the identified strategies across both one-shot and stepwise information search tasks. We found that people do not always evaluate queries strictly in OED terms and use distinct strategies, such as by identifying a leading contender at the outset. Moreover, we identified aspects of zero-sum thinking and risk aversion that interact with people's information search strategies. Our findings have implications for building a descriptive account of information seeking and evaluation, accounting for factors that currently lie outside the realm of information-theoretic OED measures, such as context and the learner's own preferences

Active inference on discrete state-spaces: A synthesis

Active inference is a normative principle underwriting perception, action, planning, decision-making and learning in biological or artificial agents. From its inception, its associated process theory has grown to incorporate complex generative models, enabling simulation of a wide range of complex behaviours. Due to successive developments in active inference, it is often difficult to see how its underlying principle relates to process theories and practical implementation. In this paper, we try to bridge this gap by providing a complete mathematical synthesis of active inference on discrete state-space models. This technical summary provides an overview of the theory, derives neuronal dynamics from first principles and relates this dynamics to biological processes. Furthermore, this paper provides a fundamental building block needed to understand active inference for mixed generative models; allowing continuous sensations to inform discrete representations. This paper may be used as follows: to guide research towards outstanding challenges, a practical guide on how to implement active inference to simulate experimental behaviour, or a pointer towards various in-silico neurophysiological responses that may be used to make empirical predictions

Stochastic processes for graphs, extreme values and their causality: inference, asymptotic theory and applications

This thesis provides some theoretical and practical statistical inference tools for multivariate stochastic processes to better understand the behaviours and properties present in the data. In particular, we focus on the modelling of graphs, that is a family of nodes linked together by a collection of edges, and extreme values, that are values above a high threshold to have their own dynamics compared to the typical behaviour of the process. We develop an ensemble of statistical models, statistical inference methods and their asymptotic study to ensure the good behaviour of estimation schemes in a wide variety of settings. We also devote a chapter to the formulation of a methodology based on pre-existing theory to unveil the causal dependency structure behind high-impact events.Open Acces

Influence modelling and learning between dynamic bayesian networks using score-based structure learning

A Ph.D. thesis submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment of the requirements for the degree of Doctor of Philosophy in Computer Science May 2018Although partially observable stochastic processes are ubiquitous in many fields of science, little work has been devoted to discovering and analysing the means by which several such processes may interact to influence each other. In this thesis we extend probabilistic structure learning between random variables to the context of temporal models which represent partially observable stochastic processes. Learning an influence structure and distribution between processes can be useful for density estimation and knowledge discovery. A common approach to structure learning, in observable data, is score-based structure learning, where we search for the most suitable structure by using a scoring metric to value structural configurations relative to the data. Most popular structure scores are variations on the likelihood score which calculates the probability of the data given a potential structure. In observable data, the decomposability of the likelihood score, which is the ability to represent the score as a sum of family scores, allows for efficient learning procedures and significant computational saving. However, in incomplete data (either by latent variables or missing samples), the likelihood score is not decomposable and we have to perform inference to evaluate it. This forces us to use non-linear optimisation techniques to optimise the likelihood function. Furthermore, local changes to the network can affect other parts of the network, which makes learning with incomplete data all the more difficult. We define two general types of influence scenarios: direct influence and delayed influence which can be used to define influence around richly structured spaces; consisting of multiple processes that are interrelated in various ways. We will see that although it is possible to capture both types of influence in a single complex model by using a setting of the parameters, complex representations run into fragmentation issues. This is handled by extending the language of dynamic Bayesian networks to allow us to construct single compact models that capture the properties of a system’s dynamics, and produce influence distributions dynamically. The novelty and intuition of our approach is to learn the optimal influence structure in layers. We firstly learn a set of independent temporal models, and thereafter, optimise a structure score over possible structural configurations between these temporal models. Since the search for the optimal structure is done using complete data we can take advantage of efficient learning procedures from the structure learning literature. We provide the following contributions: we (a) introduce the notion of influence between temporal models; (b) extend traditional structure scores for random variables to structure scores for temporal models; (c) provide a complete algorithm to recover the influence structure between temporal models; (d) provide a notion of structural assembles to relate temporal models for types of influence; and finally, (e) provide empirical evidence for the effectiveness of our method with respect to generative ground-truth distributions. The presented results emphasise the trade-off between likelihood of an influence structure to the ground-truth and the computational complexity to express it. Depending on the availability of samples we might choose different learning methods to express influence relations between processes. On one hand, when given too few samples, we may choose to learn a sparse structure using tree-based structure learning or even using no influence structure at all. On the other hand, when given an abundant number of samples, we can use penalty-based procedures that achieve rich meaningful representations using local search techniques. Once we consider high-level representations of dynamic influence between temporal models, we open the door to very rich and expressive representations which emphasise the importance of knowledge discovery and density estimation in the temporal setting.MT 201