Related papers: Course-of-Value Induction in Cedille
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at…
Scott's graph model is a lambda-algebra based on the observation that continuous endofunctions on the lattice of sets of natural numbers can be represented via their graphs. A graph is a relation mapping finite sets of input values to…
Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…
Despite their ubiquitous use, Shapley value feature attributions can be misleading due to feature interaction in both model and data. We propose an alternative attribution approach, Shapley Sets, which awards value to sets of features.…
This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies.…
Inverse classification uses an induced classifier as a queryable oracle to guide test instances towards a preferred posterior class label. The result produced from the process is a set of instance-specific feature perturbations, or…
Conditional Random Fields (CRFs) are undirected graphical models, a special case of which correspond to conditionally-trained finite state machines. A key advantage of these models is their great flexibility to include a wide array of…
A cornerstone of the theory of lambda-calculus is that intersection types characterise termination properties. They are a flexible tool that can be adapted to various notions of termination, and that also induces adequate denotational…
In Programming by Example, a system attempts to infer a program from input and output examples, generally by searching for a composition of certain base functions. Performing a naive brute force search is infeasible for even mildly involved…
Sequence classification is the supervised learning task of building models that predict class labels of unseen sequences of symbols. Although accuracy is paramount, in certain scenarios interpretability is a must. Unfortunately, such…
This paper studies emulation of induction by coinduction in a call-by-name language with control operators. Since it is known that call-by-name programming languages with control operators cannot have general initial algebras, interaction…
We study polymorphic type assignment systems for untyped lambda-calculi with effects, based on Moggi's monadic approach. Moving from the abstract definition of monads, we introduce a version of the call-by-value computational…
Object-oriented programming languages such as Java and Objective C have become popular for implementing agent-based and other object-based simulations since objects in those languages can {\em reflect} (i.e. make runtime queries of an…
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
For an explanation of a deep learning model to be effective, it must provide both insight into a model and suggest a corresponding action in order to achieve some objective. Too often, the litany of proposed explainable deep learning…
Step-indexed semantic interpretations of types were proposed as an alternative to purely syntactic proofs of type safety using subject reduction. The types are interpreted as sets of values indexed by the number of computation steps for…
We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…
Dependently typed languages are well known for having a problem with code reuse. Traditional non-indexed algebraic datatypes (e.g. lists) appear alongside a plethora of indexed variations (e.g. vectors). Functions are often rewritten for…
In call-by-value languages, some mutually-recursive value definitions can be safely evaluated to build recursive functions or cyclic data structures, but some definitions (let rec x = x + 1) contain vicious circles and their evaluation…
We propose the conditional predictive impact (CPI), a consistent and unbiased estimator of the association between one or several features and a given outcome, conditional on a reduced feature set. Building on the knockoff framework of…