Simpson’s paradox, also known as amalgamation or aggregation paradox, appears when dealing with proportions. Proportions are by construction parts of a whole, which can be interpreted as compositions assuming they only carry relative information. The Aitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalg...

This paper is motivated by the recent interest in the analysis of high dimensional microbiome data. A key feature of this data is the presence of ‘structural zeros’ which are microbes missing from an observation vector due to an underlying biological process and not due to error in measurement. Typical notions of missingness are insufficient to model these structural zeros. We define a general ...

Compositional semantic aims at constructing the meaning of phrases or sentences according to the compositionality of word meanings. In this paper, we propose to synchronously learn the representations of individual words and extracted high-frequency phrases. Representations of extracted phrases are considered as gold standard for constructing more general operations to compose the representatio...

Many solutions to AI problems require the task to be represented in one of a multitude of rigorous mathematical formalisms. The construction of such mathematical models forms a difficult problem which is often left to the user of the problem-solver. This void between problem-solvers and their problems is studied by the eclectic field of automated modelling. Within this field, compositional mode...

In this report, we approach the problem of defining and analysing compositional hierarchical scheduling frameworks (HSF) upon uniform multiprocessor platforms. For this we propose the uniform multiprocessor periodic resource (UMPR) model for a component interface. We extend previous results (for dedicated uniform multiprocessors, and for compositional HSFs on identical multiprocessors), providi...

The central thesis explored in this paper is that parallel model checking is easily achieved through compositional methods. This may strike the reader as being self-evident. Nevertheless, it does not appear to have been considered before. The justification comes from the following observations: (1) the efficacy of a parallel program is inversely proportional to the amount of synchronization and...

This work studies constrained stochastic optimization problems where the objective and constraint functions are convex expressed as compositions of functions. The problem arises in context fair classification, regression, design queuing systems. Of particular interest is large-scale setting an oracle provides gradients constituent functions, goal to solve with a minimal number calls oracle. Owi...

An implementation of an out-of-order processing unit based on Tomasulo’s algorithm is formally verified using compositional model checking techniques. This demonstrates that finite-state methods can be applied to such algorithms, without recourse to higher-order proof systems. The paper introduces a novel compositional system that supports cyclic environment reasoning and multiple environment a...

Using large amounts of long genomic sequences, we studied the compositional patterns of eukaryotic genomes. We developed a simple measure, the compositional heterogeneity (or variability) index, to compare the differences in compositional heterogeneity between long genomic sequences. The index measures the average difference in GC content between two adjacent windows normalized by the standard ...

Neural networks are very powerful learning systems, but they do not readily generalize from one task to the other. This is partly due to the fact that they do not learn in a compositional way, that is, by discovering skills that are shared by different tasks, and recombining them to solve new problems. In this paper, we explore the compositional generalization capabilities of recurrent neural n...