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This paper deals with computing the smallest enclosing ball of a set of points subject to probabilistic data. In our setting, any of the n points may not or may occur at one of finitely many locations, following its own discrete probability distribution. The objective is therefore considered to be a random variable and we aim at finding a center minimizing… (More)

This article deals with random projections applied as a data reduction technique for Bayesian regression analysis. We show sufficient conditions under which the entire d-dimensional distribution is approximately preserved under random projections by reducing the number of data points from n to k ∈ O(poly(d/ε)) in the case n d. Under mild assumptions, we… (More)

- Alexander Munteanu, Max Wornowizki, Katharina Morik
- 2014

We consider the two-sample homogeneity problem where the information contained in two samples is used to test the equality of the underlying distributions. For instance, in cases where one sample stems from a simulation procedure modelling the data generating process of the other sample consisting of observed data, a mere rejection of the null hypothesis is… (More)

We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the algorithm is restricted to polylog(n) size. Thus, the output of the algorithm is optimal in the limit. We show positive… (More)

- Leo Geppert, Katja Ickstadt, Alexander Munteanu, Christian Sohler, Katharina Morik
- 2014

This article introduces random projections applied as a data reduction technique for Bayesian regression analysis. We show sufficient conditions under which the entire d-dimensional distribution is preserved under random projections by reducing the number of data points from n to k ∈ O(poly(d/ε)) in the case n d. Under mild assumptions, we prove that… (More)

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