Means and covariance functions for geostatistical compositional data: an axiomatic approach

This work focuses on the characterization of the central tendency of a sample of compositional data. It provides new results about theoretical properties of means and covariance functions for compositional data, with an axiomatic perspective. Original results that shed new light on the geostatistical modeling of compositional data are presented. As a first result, it is shown that the weighted arithmetic mean is the only central tendency characteristic satisfying a small set of axioms, namely continuity, reflexivity and marginal stability. Moreover, this set of axioms also implies that the weights must be identical for all parts of the composition. This result has deep consequences on the spatial multivariate covariance modeling of compositional data. In a geostatistical setting, it is shown as a second result that the proportional model of covariance functions (i.e., the product of a covariance matrix and a single correlation function) is the only model that provides identical kriging weights for all components of the compositional data. As a consequence of these two results, the proportional model of covariance function is the only covariance model compatible with reflexivity and marginal stability

Improved Relation Extraction with Feature-Rich Compositional Embedding Models

Compositional embedding models build a representation (or embedding) for a linguistic structure based on its component word embeddings. We propose a Feature-rich Compositional Embedding Model (FCM) for relation extraction that is expressive, generalizes to new domains, and is easy-to-implement. The key idea is to combine both (unlexicalized) hand-crafted features with learned word embeddings. The model is able to directly tackle the difficulties met by traditional compositional embeddings models, such as handling arbitrary types of sentence annotations and utilizing global information for composition. We test the proposed model on two relation extraction tasks, and demonstrate that our model outperforms both previous compositional models and traditional feature rich models on the ACE 2005 relation extraction task, and the SemEval 2010 relation classification task. The combination of our model and a log-linear classifier with hand-crafted features gives state-of-the-art results.Comment: 12 pages for EMNLP 201

Compositional Model Repositories via Dynamic Constraint Satisfaction with Order-of-Magnitude Preferences

The predominant knowledge-based approach to automated model construction, compositional modelling, employs a set of models of particular functional components. Its inference mechanism takes a scenario describing the constituent interacting components of a system and translates it into a useful mathematical model. This paper presents a novel compositional modelling approach aimed at building model repositories. It furthers the field in two respects. Firstly, it expands the application domain of compositional modelling to systems that can not be easily described in terms of interacting functional components, such as ecological systems. Secondly, it enables the incorporation of user preferences into the model selection process. These features are achieved by casting the compositional modelling problem as an activity-based dynamic preference constraint satisfaction problem, where the dynamic constraints describe the restrictions imposed over the composition of partial models and the preferences correspond to those of the user of the automated modeller. In addition, the preference levels are represented through the use of symbolic values that differ in orders of magnitude

Semantic Part Segmentation using Compositional Model combining Shape and Appearance

In this paper, we study the problem of semantic part segmentation for animals. This is more challenging than standard object detection, object segmentation and pose estimation tasks because semantic parts of animals often have similar appearance and highly varying shapes. To tackle these challenges, we build a mixture of compositional models to represent the object boundary and the boundaries of semantic parts. And we incorporate edge, appearance, and semantic part cues into the compositional model. Given part-level segmentation annotation, we develop a novel algorithm to learn a mixture of compositional models under various poses and viewpoints for certain animal classes. Furthermore, a linear complexity algorithm is offered for efficient inference of the compositional model using dynamic programming. We evaluate our method for horse and cow using a newly annotated dataset on Pascal VOC 2010 which has pixelwise part labels. Experimental results demonstrate the effectiveness of our method

Iterated learning and grounding: from holistic to compositional languages

This paper presents a new computational model for studying the origins and evolution of compositional languages grounded through the interaction between agents and their environment. The model is based on previous work on adaptive grounding of lexicons and the iterated learning model. Although the model is still in a developmental phase, the first results show that a compositional language can emerge in which the structure reflects regularities present in the population's environment

Resolving Lexical Ambiguity in Tensor Regression Models of Meaning

This paper provides a method for improving tensor-based compositional distributional models of meaning by the addition of an explicit disambiguation step prior to composition. In contrast with previous research where this hypothesis has been successfully tested against relatively simple compositional models, in our work we use a robust model trained with linear regression. The results we get in two experiments show the superiority of the prior disambiguation method and suggest that the effectiveness of this approach is model-independent

A Generalised Quantifier Theory of Natural Language in Categorical Compositional Distributional Semantics with Bialgebras

Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, then instantiate the abstract setting to sets and relations and to finite dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalised quantifiers. The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases and sentences compositionally in distributional semantics