Related papers: Algorithmic Randomness, Exchangeability, and the P…
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments…
We introduce the notion of a reproducible algorithm in the context of learning. A reproducible learning algorithm is resilient to variations in its samples -- with high probability, it returns the exact same output when run on two samples…
We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting…
A long sequence of tosses of a classical coin produces an apparently random bit string, but classical randomness is an illusion: the algorithmic information content of a classically-generated bit string lies almost entirely in the…
Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation…
Basic principles of statistical inference are commonly violated in network data analysis. Under the current approach, it is often impossible to identify a model that accommodates known empirical behaviors, possesses crucial inferential…
A variety of problems in distributed control involve a networked system of autonomous agents cooperating to carry out some complex task in a decentralized fashion, e.g., orienting a flock of drones, or aggregating data from a network of…
In a prequential approach to algorithmic randomness, probabilities for the next outcome can be forecast `on the fly' without the need for fully specifying a probability measure on all possible sequences of outcomes, as is the case in the…
This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…
A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti's Theorem. In its original form it applies to infinite 0-1 valued exchangeable sequences. Later it was extended and…
Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than…
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical…
We present a flexible framework for learning predictive models that approximately satisfy the equalized odds notion of fairness. This is achieved by introducing a general discrepancy functional that rigorously quantifies violations of this…
Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other.…
In this study, we explore the inherent trade-off between accuracy and robustness in neural networks, drawing an analogy to the uncertainty principle in quantum mechanics. We propose that neural networks are subject to an uncertainty…
Ensuring fairness in computational problems has emerged as a $key$ topic during recent years, buoyed by considerations for equitable resource distributions and social justice. It $is$ possible to incorporate fairness in computational…
The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…
We develop necessary and sufficient conditions and a novel provably consistent and efficient algorithm for discovering topics (latent factors) from observations (documents) that are realized from a probabilistic mixture of shared latent…