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Get Complete Project Material File(s) Now! » Bregman divergences and exponential families Although K-means provides a simple and eﬀective clustering algorithm, it lacks the flexibility of a probabilistic model and the ability to have soft-assignments of a data point to...

Get Complete Project Material File(s) Now! » The full-space problem For the rest of this Chapter, let us introduce and discuss some initial conditions of the Kardar-Parisi-Zhang equation. In this Section we shall focus on the full-space problem and after...

Get Complete Project Material File(s) Now! » Sampling and acquisition Two days after MRI measurements, samples were taken from each fruit for macrovision imaging. The sampling protocol consisted of cutting a 1 cm slice, corresponding to twice the MRI virtual...

Get Complete Project Material File(s) Now! » From Counterfactual Reasoning to Counterfactual Explanations in Machine Learning Counterfactual reasoning. The term counterfactual originally comes from psychology (see e.g. Roese, 1997; Byrne, 2008), and Artificial Intelligence literatures (Lewis, 1973; Ginsberg, 1986). In...

Get Complete Project Material File(s) Now! » Reference priors for multiparametric models Previously, we dealt with the case of one-parameter models. Naturally, in the case of multiparameter models, it is always possible to view the list of parameters as one...

Get Complete Project Material File(s) Now! » Dual representations of the divergence under L-moment constraints The minimization of ϕ-divergences under linear equality constraint is performed using Fenchel-Legendre duality. It transforms the constrained problems into an unconstrained one in the space...

Get Complete Project Material File(s) Now! » Contributions using the Empirical Bayes method for the Spike and Slab prior The following work, which is treated in more details in Chapters 2 and 3, was motivated by pursuing the work seen...

Get Complete Project Material File(s) Now! » The “anthropocene”: an extinction era At present, human beings are considered the dominant species on Earth (Vitousek et al. 1997). Anthropogenic actions can modify entire ecosystems and lead to the disappearance of the...

Get Complete Project Material File(s) Now! » Chapter 2 Generalised multivariate beta type II distributions Introduction In this chapter the generalised multivariate beta type II distribution is derived; this distribution stems from monitoring the variance of a normal random variable...