Related papers: Inclusion with repetitions and Boolean constants -…
Conventional word embeddings represent words with fixed vectors, which are usually trained based on co-occurrence patterns among words. In doing so, however, the power of such representations is limited, where the same word might be…
Probabilities of causation (PoCs) are fundamental quantities for counterfactual analysis and personalized decision making. However, existing analytical results are largely confined to binary settings. This paper extends PoCs to multi-valued…
We study the complexity of various fundamental counting problems that arise in the context of incomplete databases, i.e., relational databases that can contain unknown values in the form of labeled nulls. Specifically, we assume that the…
While explainability is a desirable characteristic of increasingly complex black-box models, modern explanation methods have been shown to be inconsistent and contradictory. The semantics of explanations is not always fully understood - to…
Learning product representations that reflect complementary relationship plays a central role in e-commerce recommender system. In the absence of the product relationships graph, which existing methods rely on, there is a need to detect the…
Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its complexity. One way to do so is through compositional…
We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…
The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions…
Boolean satisfiability ({\SAT}) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the…
We show that every finite Boolean combination of polynomial equalities and inequalities in C^n admits two uniform normal forms: an $\exists\forall$ form and a $\forall\exists$ form, each using a single polynomial equation. Both forms use…
This paper studies axioms for nonmonotonic consequences from a semantics-based point of view, focusing on a class of mathematical structures for reasoning about partial information without a predefined syntax/logic. This structure is called…
We generalise the problem of inverse reinforcement learning to multiple tasks, from multiple demonstrations. Each one may represent one expert trying to solve a different task, or as different experts trying to solve the same task. Our main…
It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…
Cyclic proof theory breaks tradition by allowing certain infinite proofs: those that can be represented by a finite graph, while satisfying a soundness condition. We reconcile cyclic proofs with traditional finite proofs: we extend abstract…
In broad applications, it is routinely of interest to assess whether there is evidence in the data to refute the assumption of conditional independence of $Y$ and $X$ conditionally on $Z$. Such tests are well developed in parametric models…
Scientific claims gain credibility by replicability, especially if replication under different circumstances and varying designs yields equivalent results. Aggregating results over multiple studies is, however, not straightforward, and when…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
It is known that exactly eight varieties of Heyting algebras have a model-completion, but no concrete axiomatisation of these model-completions were known by now except for the trivial variety (reduced to the one-point algebra) and the…
In this paper we present a method ofcomputing the posterior probability ofconditional independence of two or morecontinuous variables from data,examined at several resolutions. Ourapproach is motivated by theobservation that the appearance…
To estimate causal effects from observational data, an applied researcher must impose beliefs. The instrumental variables exclusion restriction, for example, represents the belief that the instrument has no direct effect on the outcome of…