In this paper, we propose an unsupervised method to identify noun sense changes based on rigorous analysis of time-varying text data available in the form of millions of digitized books. We construct distributional thesauri based networks from data at different time points and cluster each of them separately to obtain word-centric sense clusters corresponding to the different time points. Subsequently, we compare these sense clusters of two different time points to find if (i) there is birth of a new sense or (ii) if an older sense has got split into more than one sense or (iii) if a newer sense has been formed from the joining of older senses or (iv) if a particular sense has died. We conduct a thorough evaluation of the proposed methodology both manually as well as through comparison with WordNet. Manual evaluation indicates that the algorithm could correctly identify 60.4% birth cases from a set of 48 randomly picked samples and 57% split/join cases from a set of 21 randomly picked samples. Remarkably, in 44% cases the birth of a novel sense is attested by WordNet, while in 46% cases and 43% cases split and join are respectively confirmed by WordNet. Our approach can be applied for lexicography, as well as for applications like word sense disambiguation or semantic search.

We study confidence regions and approximate chi-squared tests for variable groups in high-dimensional linear regression. When the size of the group is small, low-dimensional projection estimators for individual coefficients can be directly used to construct efficient confidence regions and p-values for the group. However, the existing analyses of low-dimensional projection estimators do not directly carry through for chisquared-based inference of a large group of variables without inflating the sample size by a factor of the group size. We propose to de-bias a scaled group Lasso for chi-squaredbased statistical inference for potentially very large groups of variables. We prove that the proposed methods capture the benefit of group sparsity under proper conditions, for statistical inference of the noise level and variable groups, large and small. Such benefit is especially strong when the group size is large.

In this paper, we propose an unsupervised and automated method to identify noun sense changes based on rigorous analysis of time-varying text data available in the form of millions of digitized books and millions of tweets posted per day. We construct distributional-thesauri-based networks from data at different time points and cluster each of them separately to obtain word-centric sense clusters corresponding to the different time points. Subsequently, we propose a split/join based approach to compare the sense clusters at two different time points to find if there is ‘birth’ of a new sense. The approach also helps us to find if an older sense was ‘split’ into more than one sense or a newer sense has been formed from the ‘join’ of older senses or a particular sense has undergone ‘death’. We use this completely unsupervised approach (a) within the Google books data to identify word sense differences within a media, and (b) across Google books and Twitter data to identify differences in word sense distribution across different media. We conduct a thorough evaluation of the proposed methodology both manually as well as through comparison with WordNet.

Supplementary data are available at Bioinformatics online.

We study concentration in spectral norm of nonparametric estimates of correlation matrices. We work within the confine of a Gaussian copula model. Two nonparametric estimators of the correlation matrix, the sine transformations of the Kendall's tau and Spearman's rho correlation coefficient, are studied. Expected spectrum error bound is obtained for both the estimators. A general large deviation bound for the maximum spectral error of a collection of submatrices of a given dimension is also established. These results prove that when both the number of variables and sample size are large, the spectral error of the nonparametric estimators is of no greater order than that of the latent sample covariance matrix, at least when compared with some of the sharpest known error bounds for the later. As an application, we establish the minimax optimal convergence rate in the estimation of high-dimensional bandable correlation matrices via tapering off of these nonparametric estimators. An optimal convergence rate for sparse principal component analysis is also established as another example of possible applications of the main results.

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Model selection strategies have been routinely employed to determine a model for data analysis in statistic, and further study and inference then often proceed as though the selected model were the true model that were known a priori. This practice does not account for the uncertainty introduced by the selection process and the fact that the selected model can possibly be a wrong one. Model averaging approaches try to remedy this issue by combining estimators for a set of candidate models. Specifically, instead of deciding which model is the 'right' one, a model averaging approach suggests to fit a set of candidate models and average over the estimators using certain data adaptive weights. In this paper we establish a general frequentist model averaging framework that does not set any restrictions on the set of candidate models. It greatly broadens the scope of the existing methodologies under the frequentist model averaging development. Assuming the data is from an unknown model, we derive the model averaging estimator and study its limiting distributions and related predictions while taking possible modeling biases into account. We propose a set of optimal weights to combine the individual estimators so that the expected mean squared error of the average estimator is minimized. Simulation studies are conducted to compare the performance of the estimator with that of the existing methods. The results show the benefits of the proposed approach over traditional model selection approaches as well as existing model averaging methods.