Related papers: Separable joint choices
The main aim of the article is to show, in the absence of the Axiom of Choice, relationships between the following, independent of $\mathbf{ZF}$, statements: "Every countable product of compact metrizable spaces is separable (respectively,…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…
We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to…
The use of separable approximations is proposed to mitigate the curse of dimensionality related to the approximation of high-dimensional value functions in optimal control. The separable approximation exploits intrinsic decaying sensitivity…
Many online shops offer functionality that help their customers navigate the available alternatives. For instance, options to filter and to sort goods are wide-spread. In this paper we show that sorting and filtering can be used by rational…
Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of…
A new family of $n$-dimensional solutions of the Jacobi identities is characterized. Such a family is very general, thus unifying in a common framework many different well-known Poisson systems seemingly unrelated. This unification is not…
Previous studies have used a specific success metric within an algorithmic search framework to prove machine learning impossibility results. However, this specific success metric prevents us from applying these results on other forms of…
The concept of sequential choice functions is introduced and studied. This concept applies to the reduction of the problem of stable matchings with sequential workers to a situation where the workers are linear.
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
We give a new proof of the decidability of reachability in alternating pushdown systems, showing that it is a simple consequence of a cut-elimination theorem for some natural-deduction style inference systems. Then, we show how this result…
Consideration sets play a crucial role in discrete choice modeling, where customers often form consideration sets in the first stage and then use a second-stage choice mechanism to select the product with the highest utility. While many…
The notions of $k$-separability and $k$-producibility are useful and expressive tools for the characterization of entanglement in multipartite quantum systems, when a more detailed analysis would be infeasible or simply needless. In this…
For analysis of a high-dimensional dataset, a common approach is to test a null hypothesis of statistical independence on all variable pairs using a non-parametric measure of dependence. However, because this approach attempts to identify…
Differential privacy is a de facto standard for statistical computations over databases that contain private data. The strength of differential privacy lies in a rigorous mathematical definition that guarantees individual privacy and yet…
We study Differential Privacy in the abstract setting of Probability on metric spaces. Numerical, categorical and functional data can be handled in a uniform manner in this setting. We demonstrate how mechanisms based on data sanitisation…
The main aim of decision support systems is to find solutions that satisfy user requirements. Often, this leads to predictability of those solutions, in the sense that having the input data and the model, an adversary or enemy can predict…
Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
In this paper, we consider the problem of testing properties of joint distributions under the Conditional Sampling framework. In the standard sampling model, the sample complexity of testing properties of joint distributions is exponential…