The geometry of uncertainty - The geometry of imprecise probabilities
Springer Nature, January 2021
Authors: Fabio Cuzzolin
The principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space, and manipulated in that space, for example, combined or conditioned.
In the chapters in Part I, Theories of Uncertainty, the author offers an extensive recapitulation of the state of the art in the mathematics of uncertainty. This part of the book contains the most comprehensive summary to date of the whole of belief theory, with Chap. 4 outlining for the first time, and in a logical order, all the steps of the reasoning chain associated with modelling uncertainty using belief functions, in an attempt to provide a self-contained manual for the working scientist. In addition, the book proposes in Chap. 5 what is possibly the most detailed compendium available of all theories of uncertainty.
Part II, The Geometry of Uncertainty, is the core of this book, as it introduces the author’s own geometric approach to uncertainty theory, starting with the geometry of belief functions: Chap. 7 studies the geometry of the space of belief functions, or belief space, both in terms of a simplex and in terms of its recursive bundle structure; Chap. 8 extends the analysis to Dempster’s rule of combination, introducing the notion of a conditional subspace and outlining a simple geometric construction for Dempster’s sum; Chap. 9 delves into the combinatorial properties of plausibility and commonality functions, as equivalent representations of the evidence carried by a belief function; then Chap. 10 starts extending the applicability of the geometric approach to other uncertainty measures, focusing in particular on possibility measures (consonant belief functions) and the related notion of a consistent belief function.
The chapters in Part III, Geometric Interplays, are concerned with the interplay of uncertainty measures of different kinds, and the geometry of their relationship, with a particular focus on the approximation problem.
Part IV, Geometric Reasoning, examines the application of the geometric approach to the various elements of the reasoning chain illustrated in Chap. 4, in particular conditioning and decision making.
Part V concludes the book by outlining a future, complete statistical theory of random sets, future extensions of the geometric approach, and identifying high-impact applications to climate change, machine learning and artificial intelligence.
Knowing Me, Knowing You: Theory of Mind in AI
Psychological Medicine, Volume 50, Issue 7, pages 1057-1061, May 2020
Authors: Fabio Cuzzolin, Andrea Morelli, Bogdan Cirstea and Barbara J. Sahakian
Despite the dramatic advances made in artificial intelligence (AI) and other fields of computer science towards implementing 'intelligent' systems expert in specific tasks, the goal of devising algorithms and machines able to interact with human beings just as naturally as other humans do is still elusive.
As this naturalness is arguably a consequence of the similarity of the underlying ‘hardware’ (the human brain), it is reasonable to claim that only artificial systems closely inspired by the actual functioning of the human brain and mind have the potential to render this possible.
More specifically, the aim of this paper is to propose a new, biologically inspired computational model able to mimic, in a more accurate way than existing ones, the set of functionalities know as Theory of Mind. This is a set of mental processes that allow an individual to attribute mental states to others. In human social interactions this mechanism is crucial, as it allows one to explain the observed behaviour of others, to guess their intentions and to effectively predict their future conduct. This happens by modelling and selecting the most likely (unobservable) mental states of the considered person, which are the primary causes of everyone's observed actions. The proposed model combines a number of concepts, including those of hierarchical structure, hypotheses pre-activation, and the notion of agent class or 'stereotype'. It rests on one of the main psychological approaches to Theory of Mind, termed Simulation Theory (ST), and is supported by significant neuroscientific evidence. Crucially, unlike previous efforts in AI, the proposed model puts the learning element at the forefront, in the belief that simulations of other intelligent being’'s reasoning processes need to be learned from experience.
In this perspective, a possible implementation of the model in terms of deep, reconfigurable neural networks, trained in a reinforcement learning setting, is outlined.
Spatio-Temporal Action Instance Segmentation and Localisation
Modelling Human Motion - From Human Perception to Robot Design, edited by Nicoletta Noceti, Alessandra Sciutti and Francesco Rea.
Authors: uman Saha, Gurkirt Singh, Michael Sapienza, Philip H. S. Torr and Fabio Cuzzolin
Current state-of-the-art human action recognition is focused on the classification of temporally trimmed videos in which only one action occurs per frame. In this work we address the problem of action localisation and instance segmentation in which multiple concurrent actions of the same class may be segmented out of an image sequence. We cast the action tube extraction as an energy maximisation problem in which configurations of region proposals in each frame are assigned a cost and the best action tubes are selected via two passes of dynamic programming. One pass associates region proposals in space and time for each action category, and another pass is used to solve for the tube’s temporal extent and to enforce a smooth label sequence through the video. In addition, by taking advantage of recent work on action foreground-background segmentation, we are able to associate each tube with class-specific segmentations. We demonstrate the performance of our algorithm on the challenging LIRIS-HARL dataset and achieve a new state-of-the-art result which is 14.3 times better than previous methods.
The chapter's entry can be found in the publisher's website here.