Department of Statistics

Permanent URI for this collectionhttp://197.255.125.131:4000/handle/123456789/34524

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    Coloured Random Graphs, Simple Random Allocation of Coloured Balls into Coloured Bins
    (2016-03-17) Doku-Amponsah, K.
    Simple coloured random allocation model is obtained when coloured balls are sequentially inserted at random into coloured bins. The empirical occupancy measure of the simple coloured random allocation model counts the number of bins of a given colour with a given number of balls of each colour. In this paper we show that, given the colours, both the empirical occupancy measure of simple coloured random allocation models and the empirical neighbourhood distribution of sparse coloured random graph models converge weakly to the product of independent Poisson distributions.
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    Exact Matrix Completion via Convex Optimization
    (2016-03-10) Lotsi, A.; Doku-Amponsah, K.
    We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys for some positive numerical constant C, then with very high probability, most n*n matrices of rank r can be perfectly recovered by solving a simple convex optimization problem. This program finds the matrix with minimum nuclear norm that fits the data. The condition above assumes that the rank is not too large. However, if one replaces the 1.2 exponent with 1.25, then the result holds for all values of the rank. Our results are connected with the recent literature on compressed sensing, and show that objects other than signals and images can be perfectly reconstructed from very limited information.