Related papers: Rectification of Composition Tableaux
Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
In this paper we explore a class of belief update operators, in which the definition of the operator is compositional with respect to the sentence to be added. The goal is to provide an update operator that is intuitive, in that its…
We consider the problem of reconstructing a low rank matrix from noisy observations of a subset of its entries. This task has applications in statistical learning, computer vision, and signal processing. In these contexts, "noise"…
We study four operations defined on pairs of tableaux. Algorithms for the first three involve the familiar procedures of jeu de taquin, row insertion, and column insertion. The fourth operation, hopscotch, is new, although specialised…
In this paper we introduce a framework for option model composition. Option models are temporal abstractions that, like macro-operators in classical planning, jump directly from a start state to an end state. Prior work has focused on…
Originating from Allen's Interval Algebra, composition-based reasoning has been widely acknowledged as the most popular reasoning technique in qualitative spatial and temporal reasoning. Given a qualitative calculus (i.e. a relation model),…
This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…
Inference is a fundamental reasoning technique in probability theory. When applied to a large joint distribution, it involves updating with evidence (conditioning) in one or more components (variables) and computing the outcome in other…
In this paper we study a worst case to average case reduction for the problem of matrix multiplication over finite fields. Suppose we have an efficient average case algorithm, that given two random matrices $A,B$ outputs a matrix that has a…
The matrix completion problem has been studied broadly under many underlying conditions. The problem has been explored under adaptive or non-adaptive, exact or estimation, single-phase or multi-phase, and many other categories. In most of…
The well-known conditions for a simplicial set to be the nerve of a small category generalize with respect to two parameters: the dimension n of the things which compose, and the position i of the thing which is the result of the…
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…
A unified approach to parametrization of the mixing matrix for $N$ generations is developed. This approach not only has a clear geometrical underpinning but also has the advantage of being economical and recursive and leads in a natural way…
A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need to be related back to matrix polynomials. In this paper we…
Gaussian graphical models represent the underlying graph structure of conditional dependence between random variables which can be determined using their partial correlation or precision matrix. In a high-dimensional setting, the precision…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
We introduce notions of linear reduction and linear equivalence of bijections for the purposes of study bijections between Young tableaux. Originating in Theoretical Computer Science, these notions allow us to give a unified view of a…