Related papers: Equational Axioms for Expected Value Operators
After a brief introduction to Probability Bracket Notation (PBN), indicator operator and conditional density operator (CDO), we investigate probability spaces associated with various quantum systems: system with one observable (discrete or…
The desirable gambles framework provides a rigorous foundation for imprecise probability theory but relies heavily on linear utility via its coherence axioms. In our related work, we introduced function-coherent gambles to accommodate…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
The new axiomatic system for the quantum field theory is proposed. The new axioms are the description of the distributions. For the finite series these distributions satisfy the linear Wightman axioms.
Conditional forecasts, i.e. projections of a set of variables of interest on the future paths of some other variables, are used routinely by empirical macroeconomists in a number of applied settings. In spite of this, the existing…
We show that the correct mathematical foundation of quantum decision theory, dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of the projection-valued measure. The latter is…
Classic decision-theory is based on the maximum expected utility (MEU) principle, but crucially ignores the resource costs incurred when determining optimal decisions. Here we propose an axiomatic framework for bounded decision-making that…
We investigate to which extent the relevant features of (static) Systemic Risk Measures can be extended to a conditional setting. After providing a general dual representation result, we analyze in greater detail Conditional Shortfall…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
This paper shows how we can combine logical representations of actions and decision theory in such a manner that seems natural for both. In particular we assume an axiomatization of the domain in terms of situation calculus, using what is…
Changes in input distribution can induce shifts in the average predictions of machine learning models. Such prediction shifts may impact downstream business outcomes (e.g. a bank's loan approval rate), so understanding their causes can be…
This article establishes a complete approximate axiomatization for the real-closed field $\mathbb{R}$ expanded with all differentially-defined functions, including special functions such as $\sin(x), \cos(x), e^x, \dots$. Every true…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
The concept of conditional expectation is important in applications of probability and statistics in many areas such as reliability engineering, economy, finance, and actuarial sciences due to its property of being the best predictor of a…
Shapley values originated in cooperative game theory but are extensively used today as a model-agnostic explanation framework to explain predictions made by complex machine learning models in the industry and academia. There are several…
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…
Conformal predictors are machine learning algorithms that output prediction sets that have a guarantee of marginal validity for finite samples with minimal distributional assumptions. This is a property that makes conformal predictors…
Considering a minimal number of assumptions and in the context of the timeless formalism, conditional probabilities are derived for subsequent measurements in the non-relativistic regime. Only unitary transformations are considered with…
We consider an agent interacting with an unknown environment. The environment is a function which maps natural numbers to natural numbers; the agent's set of hypotheses about the environment contains all such functions which are computable…
Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a…