Related papers: Infinite Choice and Probability Distributions. An …
Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…
Mathematical psychology has a long tradition of modeling probabilistic choice via distribution-free random utility models and associated random preference models. For such models, the predicted choice probabilities often form a bounded and…
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…
Probabilistic reasoning systems combine different probabilistic rules and probabilistic facts to arrive at the desired probability values of consequences. In this paper we describe the MESA-algorithm (Maximum Entropy by Simulated Annealing)…
Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…
Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional…
In problems involving the allocation of a single non-disposable commodity, we study rules defined on a general domain of preferences requiring only that each preference exhibit a unique global maximum. Our focus is on rules that satisfy a…
This work proposes a complete algebraic model for classical information theory. As a precursor the essential probabilistic concepts have been defined and analyzed in the algebraic setting. Examples from probability and information theory…
Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
A large branch of explainable machine learning is grounded in cooperative game theory. However, research indicates that game-theoretic explanations may mislead or be hard to interpret. We argue that often there is a critical mismatch…
There are different approaches to qualitative probability, which includes subjective probability. We developed a representation of qualitative probability based on relational systems, which allows modeling uncertainty by probability…
I discuss the design of the method of entropic inference as a general framework for reasoning under conditions of uncertainty. The main contribution of this discussion is to emphasize the pragmatic elements in the derivation. More…
Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…
Can stated preferences help in counterfactual analyses of actual choice? This research proposes a novel approach to researchers who have access to both stated choices in hypothetical scenarios and actual choices. The key idea is to use…
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…
The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…