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While previous sentiment analysis research has concentrated on the interpretation of explicitly stated opinions and attitudes, this work initiates the computational study of a type of opinion implicature (i.e., opinion-oriented inference)…
Transparency, user trust, and human comprehension are popular ethical motivations for interpretable machine learning. In support of these goals, researchers evaluate model explanation performance using humans and real world applications.…
Judgmental forecasting employs human opinions to make predictions about future events, rather than exclusively historical data as in quantitative forecasting. When these opinions form an argumentative structure around forecasts, it is…
Causal inference can be formalized as Bayesian inference that combines a prior distribution over causal models and likelihoods that account for both observations and interventions. We show that it is possible to implement this approach…
A wide variety of model explanation approaches have been proposed in recent years, all guided by very different rationales and heuristics. In this paper, we take a new route and cast interpretability as a statistical inference problem. We…
We study `definable' subsets of Baire space $\mathcal{N}$. The logic of our arguments is intuitionistic and we use L.E.J.~Brouwer's Thesis on bars in $\mathcal{N}$ and his continuity axioms. We avoid the operation of taking the complement…
Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…
Due to their great flexibility, nonparametric Bayes methods have proven to be a valuable tool for discovering complicated patterns in data. The term "nonparametric Bayes" suggests that these methods inherit model-free operating…
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 typically arise from applying decision rules…
We present a prescriptive type system with parametric polymorphism and subtyping for constraint logic programs. The aim of this type system is to detect programming errors statically. It introduces a type discipline for constraint logic…
Understanding the predictions made by deep learning models remains a central challenge, especially in high-stakes applications. A promising approach is to equip models with the ability to answer counterfactual questions -- hypothetical…
Reynold's parametricity theory captures the property that parametrically polymorphic functions behave uniformly: they produce related results on related instantiations. In dependently-typed programming languages, such relations and…
Although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors, time and other factors, relatively little has been done in the multivariate case. Our focus is on developing…
This work introduces a framework for quantifying the information content of logical propositions through the use of implication hypergraphs. We posit that a proposition's informativeness is primarily determined by its relationships with…
This paper is motivated by the questions of how to give the concept of probability an adequate real-world meaning, and how to explain a certain type of phenomenon that can be found, for instance, in Ellsberg's paradox. It attempts to answer…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
The ubiquity of machine learning based predictive models in modern society naturally leads people to ask how trustworthy those models are? In predictive modeling, it is quite common to induce a trade-off between accuracy and…
The intuitive notion of the Gromov invariant for maps from a Riemann surface to a Grassmannian is shown to agree with the definition in \cite{BDW}. Also, an induction on the genus is proved, which extends the results of \cite{BDW} to a…
This article continues study of the prequential framework for evaluating a probability forecaster. Testing the hypothesis that the sequence of forecasts issued by the forecaster is in agreement with the observed outcomes can be done using…