Related papers: Exchangeable lower previsions
We introduce the notion of a restricted exchangeable partition of $\mathbb{N}$. We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In…
We propose a new paradigm for Belief Change in which the new information is represented as sets of models, while the agent's body of knowledge is represented as a finite set of formulae, that is, a finite base. The focus on finiteness is…
Let A be a standard Borel space, and consider the space A^{\bbN^{(k)}} of A-valued arrays indexed by all size-k subsets of \bbN. This paper concerns random measures on such a space whose laws are invariant under the natural action of…
A notion of conditionally identically distributed (c.i.d.) sequences has been studied as a form of stochastic dependence that is weaker than exchangeability, but is equivalent to exchangeability for stationary sequences. In this article we…
Statistical inference from data is a foundational task in science. Recently, it has received growing attention for its central role in inference systems of primary interest in data sciences and machine learning. However, the understanding…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
We introduce a framework uniting algorithmic randomness with exchangeable credences to address foundational questions in philosophy of probability and philosophy of science. To demonstrate its power, we show how one might use the framework…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
A sequence of random variables is called \textit{exchangeable} if its joint distribution is invariant under permutations of indices. The original formulation of de Finetti's theorem roughly says that any exchangeable sequence of…
Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to…
The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a…
We present distributions of countable models and correspondent structural characteristics of complete theories with continuum many types: for prime models over finite sets relative to Rudin-Keisler preorders, for limit models over types and…
In this paper, we consider iterative propositional calculi, which are finite sets of propositional formulas together with the rules of modus ponens and weak substitution (when formula being substituted must be already inferred). We…
Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the component labels are arbitrary…
For positive $q\neq1$, the $q$-exchangeability of an infinite random word is introduced as quasi-invariance under permutations of letters, with a special cocycle which accounts for inversions in the word. This framework allows us to extend…
The law of maturity is the belief that less-observed events are becoming mature and, therefore, more likely to occur in the future. Previous studies have shown that the assumption of infinite exchangeability contradicts the law of maturity.…
We provide a numerical refutation of the developments of Fiorini et al. (2015)* for models with disjoint sets of descriptive variables. We also provide an insight into the meaning of the existence of a one-to-one linear map between…
We propose a learning framework for calibrating predictive models to make loss-controlling prediction for exchangeable data, which extends our recently proposed conformal loss-controlling prediction for more general cases. By comparison,…
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 advance a general theory of coherent preference that surrenders restrictions embodied in orthodox doctrine. This theory enjoys the property that any preference system admits extension to a complete system of preferences, provided it…