Related papers: Universal Relationships in Measures of Unpredictab…

Although a system is described by a well-known set of equations leading to a deterministic behavior, in the real world the value of a measurand obtained by an experiment will mostly scatter. Accordingly, an uncertainty is associated with…

For Hilbert, the consistency of a formal theory T is an infinite series of statements "D is free of contradictions" for each derivation D and a consistency proof is i) an operation that, given D, yields a proof that D is free of…

A distinction is sometimes made between "statistical" and "subjective" probabilities. This is based on a distinction between "unique" events and "repeatable" events. We argue that this distinction is untenable, since all events are "unique"…

The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…

Estimating the unknown number of classes in a population has numerous important applications. In a Poisson mixture model, the problem is reduced to estimating the odds that a class is undetected in a sample. The discontinuity of the odds…

We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or…

Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. We discuss in breadth how and in which sense universal (non-i.i.d.) sequence prediction solves…

The paper demonstrates that falsifiability is fundamental to learning. We prove the following theorem for statistical learning and sequential prediction: If a theory is falsifiable then it is learnable -- i.e. admits a strategy that…

There are many randomness notions. On the classical account, many of them are about whether a given infinite binary sequence is random for some given probability. If so, this probability turns out to be the same for all these notions, so…

In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.

We exhibit a one to one correspondence between some universal probabilistic properties of the ordering coordinate of one-dimensional Ising-like models and a class of continuous time random walks. This correspondence provides an new…

This paper presents a simple generalization of causal consistency suited to any object defined by a sequential specification. As causality is captured by a partial order on the set of operations issued by the processes on shared objects…

We analyze identifiability as a possible explanation for the ubiquity of linear properties across language models, such as the vector difference between the representations of "easy" and "easiest" being parallel to that between "lucky" and…

Event prediction is the ability of anticipating future events, i.e., future real-world occurrences, and aims to support the user in deciding on actions that change future events towards a desired state. An event prediction method learns the…

In continual learning, understanding the properties of task sequences and their relationships to model performance is important for developing advanced algorithms with better accuracy. However, efforts in this direction remain…

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…

A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational…

Abstract Contextuality is a property of systems of random variables. The identity of a random variable in a system is determined by its joint distribution with all other random variables in the same context. When context changes, a variable…

The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…

In the classic problem of sequence prediction, a predictor receives a sequence of values from an emitter and tries to guess the next value before it appears. The predictor masters the emitter if there is a point after which all of the…