probability distribution estimation task Estimating the (Joint) Probability Distribution. A set of data (of type T) is often assumed to be a sample taken from a population according to a probability distribution. A probability distribution/density function assigns a non-negative probability/density to each object of type T. Probably the most general data mining task (Hand et al. 2001) is the task of estimating the (joint) probability distribution D over type T from a set of data items or a sample drawn from that distribution. As mentioned above, in the most typical case we would have T = Tuple(T1, . . ., Tk), where each of T1, . . ., Tk is Boolean, Discrete(S) or Real. We talk about the joint probability distribution to emphasize the difference to the marginal distributions of each of the variables of type T1, . . ., Tk: the joint distribution captures the interactions among the variables. Representing multi-variate distributions is a non-trivial task. Two approaches are commonly used in data mining. In the density-based clustering paradigm, mixtures of multi-variate Gaussian distributions are typically considered (Hand et al. 2001). Probabilistic graphical models, most notably Bayesian networks, represent graphically the (in)dependencies between the variables: Learning their structure and parameters is an important approach to the problem of estimating the joint probability distribution. data mining task