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We introduce and motivate generative modeling as a central task for machine learning and provide a critical view of the algorithms which have been proposed for solving this task. We overview how generative modeling can be defined mathematically as trying to make an estimating distribution the same as an unknown ground truth distribution. This can then be quantified in terms of the value of a statistical divergence between the two distributions. We outline the maximum likelihood approach and how it can be interpreted as minimizing KL-divergence. We explore a number of approaches in the maximum likelihood family, while discussing their limitations. Finally, we explore the alternative adversarial approach which involves studying the differences between an estimating distribution and a real data distribution. We discuss how this approach can give rise to new divergences and methods that are necessary to make adversarial learning successful. We also discuss new evaluation metrics which are required by the adversarial approach.
A concise introduction to quantum entanglement in multipartite systems is presented. We review entanglement of pure quantum states of three--partite systems analyzing the classes of GHZ and W states and discussing the monogamy relations. Special atte
These are lecture notes of a mini-course given by the first author in Moscow in July 2019, taken by the second author and then edited and expanded by the first author. They were also a basis of the lectures given by the first author at the CMSA Math
In the past several years, observational entropy has been developed as both a (time-dependent) quantum generalization of Boltzmann entropy, and as a rather general framework to encompass classical and quantum equilibrium and non-equilibrium coarse-gr
This article serves as a brief introduction to the Shannon information theory. Concepts of information, Shannon entropy and channel capacity are mainly covered. All these concepts are developed in a totally combinatorial flavor. Some issues usually n
This mini review is to introduce the readers of Plasma to the field of plasma medicine. This is a multidisciplinary field of research at the intersection of physics, engineering, biology and medicine. Plasma medicine is only about two decades old, bu