CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size

Let $\mathbf{A}=\frac{1}{\sqrt{np}}(\mathbf{X}^T\mathbf{X}-p\mathbf {I}_n)$ where $\mathbf{X}$ is a $p\times n$ matrix, consisting of independent and identically distributed (i.i.d.) real random variables $X_{ij}$ with mean zero and variance one. When $p/n\to\infty$, under fourth moment conditions a central limit theorem (CLT) for linear spectral statistics (LSS) of $\mathbf{A}$ defined by the eigenvalues is established. We also explore its applications in testing whether a population covariance matrix is an identity matrix.Comment: Published at http://dx.doi.org/10.3150/14-BEJ599 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Learning from Ontology Streams with Semantic Concept Drift

Data stream learning has been largely studied for extracting knowledge structures from continuous and rapid data records. In the semantic Web, data is interpreted in ontologies and its ordered sequence is represented as an ontology stream. Our work exploits the semantics of such streams to tackle the problem of concept drift i.e., unexpected changes in data distribution, causing most of models to be less accurate as time passes. To this end we revisited (i) semantic inference in the context of supervised stream learning, and (ii) models with semantic embeddings. The experiments show accurate prediction with data from Dublin and Beijing