Contents
Table 1: Table shows the Spearman correlation coefficient and associated p-value for pairs of observable lists.
['Observables Compared', 'Spearman  [ITALIC] ρ', 'p-value']
One possibility is that certain justifiable improvements in the algorithms for constructing the matrices can increase these ratios. For example, in the present construction of the noun vectors ( which are fed into a linear regression method to produce adjective matrices), it can happen that the list of nouns has some overlap with the list of context words. When this happens, there is an issue of how to count the frequency of proximity of a word with itself. The present algorithm uses a reasonable, but perhaps non-unique, choice for handling these cases. A modification of the algorithm would exclude these cases from the construction of word vectors, and investigate the resulting matrices. Perturbations of the Gaussian model by adding these specific observables as perturbations would be a natural guess. Can we get comparable or higher levels of success in predicting expectation values when using different matrix constructions? How universal are the statistical characteristics we are finding? Different constructions have been used in the computational side to produce the linguistic matrices, e.g. algorithms such as linear regression The main ideas behind these constructions is the same: they all explore the original intuitions of Firth and Harris, that we can use the context of the words and the degrees of similarities between them to build matrices for words with functional types. As the methods behind these constructions advance, the matrices become denser and learn to perform better in tasks that they are trained on. It will be interesting to compute the matrix model characteristics - the μ,Λ parameters, the theory/experiment ratios for higher order observables, and their standard deviations - for other linguistic corpora, e.g. specialising to particular genres of literature, different domains (e.g. news articles) and modes (e.g audio and video) of content, or using other languages than English. This will be a way to identify which of the matrix model characteristics are universal and which are corpus-dependent. This reflects the similarity in the matrix model characteristics between these pairs (theory/expt ratios for expectation values and standard deviations) which are visible in Sections 3,4,5.