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In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how "embarrassing" it…
Dempster-Shafer's model aims at quantifying degrees of belief But there are so many interpretations of Dempster-Shafer's theory in the literature that it seems useful to present the various contenders in order to clarify their respective…
This paper extends the applications of belief-networks to include the revision of belief commitments, i.e., the categorical acceptance of a subset of hypotheses which, together, constitute the most satisfactory explanation of the evidence…
We define a new notion of conditional belief, which plays the same role for Dempster-Shafer belief functions as conditional probability does for probability functions. Our definition is different from the standard definition given by…
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…
Reinforcement learning (RL) has emerged as a transformative approach for financial trading, enabling dynamic strategy optimization in complex markets. This study explores the integration of sentiment analysis, derived from large language…
In decision problems under incomplete information, actions (identified to payoff vectors indexed by states of nature) and beliefs are naturally paired by bilinear duality. We exploit this duality to analyze the value of information, using…
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…
Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…
Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances…
Knowledge graphs are useful for many artificial intelligence tasks but often have missing data. Hence, a method for completing knowledge graphs is required. Existing approaches include embedding models, the Path Ranking Algorithm, and rule…
In this work, we propose an approach to generalize denoising diffusion probabilistic models for stock market predictions and portfolio management. Present works have demonstrated the efficacy of modeling interstock relations for market…
We present a methodology for representing probabilistic relationships in a general-equilibrium economic model. Specifically, we define a precise mapping from a Bayesian network with binary nodes to a market price system where consumers and…
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…
We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and…
This paper presents a general framework for studying diverse beliefs in dynamic economies. Within this general framework, the characterization of a central-planner general equilbrium turns out to be very easy to derive, and leads to a range…
Belief Propagation (BP) is a popular, distributed heuristic for performing MAP computations in Graphical Models. BP can be interpreted, from a variational perspective, as minimizing the Bethe Free Energy (BFE). BP can also be used to solve…
Two linearly uncorrelated binary variables must be also independent because non-linear dependence cannot manifest with only two possible states. This inherent linearity is the atom of dependency constituting any complex form of…
While linear mixed modeling methods are foundational concepts introduced in any statistical education, adequate general methods for interval estimation involving models with more than a few variance components are lacking, especially in the…
We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…