Related papers: An algebraic approach to revealed preferences
Principles of analogical reasoning have recently been applied in the context of machine learning, for example to develop new methods for classification and preference learning. In this paper, we argue that, while analogical reasoning is…
Richard Cox [1] set the axiomatic foundations of probable inference and the algebra of propositions. He showed that consistency within these axioms requires certain rules for updating belief. In this paper we use the analogy between…
Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…
We introduce a novel choice dataset, called joint choice, in which options and menus are multidimensional. In this general setting, we define a notion of choice separability, which requires that selections from some dimensions are never…
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 appear in imprecise-probabilistic decision…
We provide a generalized revealed preference test for quasilinear preferences. The test applies to nonlinear budget sets and non-convex preferences as those found in taxation and nonlinear pricing contexts. We study the prevalence of…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
An axiomatic approach is applied to the problem of extracting a ranking of the alternatives from a pairwise comparison ratio matrix. The ordering induced by row geometric mean method is proved to be uniquely determined by three independent…
We present a novel preference learning framework to capture participant preferences efficiently within limited interaction rounds. It involves three main contributions. First, we develop a variational Bayesian approach to infer the…
We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability…
We study identification in models of aggregate choice generated by unobserved behavioral types. An analyst observes only aggregate choice behavior, while the population distribution of types and their type-level choice patterns are latent.…
In this paper, we advocate the use of stratified logical theories for representing probabilistic models. We argue that such encodings can be more interpretable than those obtained in existing frameworks such as Markov logic networks. Among…
In this article algebraic constructions are introduced in order to study the variety defined by a radical parametrization (a tuple of functions involving complex numbers, $n$ variables, the four field operations and radical extractions). We…
A new method is presented, that can help a person become aware of his or her unconscious preferences, and convey them to others in the form of verbal explanation. The method combines the concepts of reflection, visualization, and…
There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…
That an agent's possible evidential states form a Boolean algebra (on which it is natural to define a probability measure) is an assertion that ideally should be proved, rather than assumed, in justifying rational choice as a representation…
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…
We study possibilities for algebraic closures, differences between definable and algebraic closures in first-order structures, and variations of these closures with respect to the bounds of cardinalities of definable sets and given sets of…
This paper focuses on preserving the privacy of sensitive patterns when inducing decision trees. We adopt a record augmentation approach for hiding sensitive classification rules in binary datasets. Such a hiding methodology is preferred…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…