In recent years, there has been a growing interest in learning tractable graphical models in which exact inference is efficient. Two main approaches are to restrict the inference complexity directly, as done by low-treewidth graphical models and arithmetic circuits (ACs), or introduce latent variables, as done by mixtures of trees, latent tree models, and sum-product networks (SPNs). In this paper, we combine these approaches to learn a mixtures of ACs (MAC). A mixture can represent many distributions exponentially more compactly than a single AC. By using ACs as mixture components, MAC can represent complex distributions using many fewer components than required by other mixture models. MAC generalizes ACs, mixtures of trees, latent class models, and thin junction trees, and can be seen as a special case of an SPN. Compared to state-of-the-art algorithms for learning SPNs and other tractable models, MAC is consistently more accurate while maintaining tractable inference.
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Probabilistic graphical models have been successfully applied in a lot of different fields, e.g., medical diagnosis and bio-statistics. Multiple specific extensions have been developed to handle, e.g., time-series data or Gaussian distributed random variables. In the case that handles both Gaussian variables and time-series data, downsides are that the models still have a discrete time-scale, evidence needs to be propagated through the graph and the conditional relationships between the variables are bound to be linear. This paper converts two probabilistic graphical models (the Markov chain and the hidden Markov model) into Gaussian processes by constructing covariance and mean functions, that encode the characteristics of the probabilistic graphical models. Our developed Gaussian process based formalism has the advantage of supporting a continuous time scale, direct inference from any time point to the other without propagation of evidence and flexibility to modify the covariance function if needed.
There are plenty of nerdy things to love about using Linux, but one of the nerdiest things has to be the use of the text-mode web browser. I can feel you backing away slowly. Others might be thinking, "Alex, it's 2017. Why on earth would I use a text-mode browser? What are you, stuck in 1985?" Hear me out: The text-mode web browser is one of those super-useful tools that can really save your bacon.
Considering that the Nintendo Switch is almost upon us with its focus on functional variety, can console gaming really support another graphical powerhouse like Microsoft's Scorpio? Set for release this summer, Microsoft's Scorpio is already being touted as a big step up in terms of graphical potency for console gaming. When it was covered by Microsoft back in June of last year, the main emphasis on this new console was the increase in its graphical prowess. The two problems with this are that games are something you play rather than simply watch and that we are already at capacity when it comes to big budget games. This is because the real limitation on gaming is no longer technical but budgetary.