Related papers: Symmetry of models versus models of symmetry
A discussion is presented, within a simple unifying scheme, about different types of symmetry of PDE's, with the introduction and a precise characterization of the notions of "standard" and "weak" conditional symmetries, together with their…
In the theory of belief functions, many measures of uncertainty have been introduced. However, it is not always easy to understand what these measures really try to represent. In this paper, we re-interpret some measures of uncertainty in…
The Rasch model is the most prominent member of the class of latent trait models that are in common use. The main reason is that it can be considered as a measurement model that allows to separate person and item parameters, a feature that…
Unfair predictions of machine learning (ML) models impede their broad acceptance in real-world settings. Tackling this arduous challenge first necessitates defining what it means for an ML model to be fair. This has been addressed by the ML…
In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit conditions and the implicit conditions of probability assignments `me properly distinguished,…
This is the introductive paper to the volume "Symmetries in Physics: Philosophical Reflections", Cambridge University Press, 2003. We begin with a brief description of the historical roots and emergence of the concept of symmetry that is at…
Probability measures by themselves, are known to be inappropriate for modeling the dynamics of plain belief and their excessively strong measurability constraints make them unsuitable for some representational tasks, e.g. in the context of…
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
In this paper, we consider the problem of social learning, where a group of agents embedded in a social network are interested in learning an underlying state of the world. Agents have incomplete, noisy, and heterogeneous sources of…
In this paper, we analyze the viewpoint stability of foundational models - specifically, their sensitivity to changes in viewpoint- and define instability as significant feature variations resulting from minor changes in viewing angle,…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
In the absence of empirical confirmation, scientists may judge a theory's chances of being viable based on a wide range of arguments. The paper argues that such arguments can differ substantially with regard to their structural similarly to…
Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle…
A probability model exhibits instability if small changes in a data outcome result in large, and often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a…
Supervised machine learning models boast remarkable predictive capabilities. But can you trust your model? Will it work in deployment? What else can it tell you about the world? We want models to be not only good, but interpretable. And yet…
We characterize a notion of confidence that arises in learning or updating beliefs: the amount of trust one has in incoming information and its impact on the belief state. This learner's confidence can be used alongside (and is easily…
Bell's theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum…
Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…
Motivated by recently emerging problems in machine learning and statistics, we propose data models which relax the familiar i.i.d. assumption. In essence, we seek to understand what it means for data to come from a set of probability…
A frequently confused point in studies of symmetry violation is the distinction between observer and particle transformations. In this work, we consider a model in which a coefficient in the Standard-Model Extension leads to violations of…