Publication: Memoirs of the American Mathematical Society Publication Year: 2019; Volume 261, Number 1262ISBNs: 978-1-4704-3685-8 (print); 978-1-4704-5416-6 (online) DOI: Published electronically: November 6, 2019 Keywords: Stochastic processes indexed by graphs,graphical models,time-like graphs,martingales indexed by directed sets,stochastic heat equationMSC: Primary 60G20, 60G60, 60H15, 60J65, 60J80, 62H05; Secondary 05C99$.ajax(async: true, format: 'json', success: bkstore_link_success, error: bkstore_link_error, dataType: 'json', data: product_code: 'MEMO/261/1262', check_stripped: '1', method: 'GET', url: '/cgi-bin/tizra/tizra_id_from_product_code', );function bkstore_link_success(result, status, xhr) if (result.tizra_id && result.base_product_code) // alert(result.tizra_id); var buyBookDiv = document.getElementById('buy_in_amsbookstore_div'); var pars = buyBookDiv.getElementsByTagName('p'); var p; var customUrl = result.base_product_code.toLowerCase(); customUrl = customUrl.replace(/\/ else if (result.error) // Do nothing. This means we shouldn't display the link.// In development, we might want to display the error: if (false) alert('Error: '+result.error); else // do nothing? function bkstore_link_error(xhr, textStatus, errorThrown) // We just do nothing if the ajax call fails.// If we want to test in development, can do something like: if (false) alert('status: '+textStatus+'\nerror: '+errorThrown); View full volume PDF
probabilistic graphical models koller ebook 12
In this course, we will study a class of inference models known as Probabilistic Graphical Models (PGMs). PGMs are a great example of how Computer Science and Statistics can work together. PGMs use graph data structures to represent domains with large amounts of variables and specialised algorithms for efficient inference over these graphical models. Therefore, PGMs have pushed the limits of probability theory to the scale and rate necessary to provide automated reasoning in modern AI systems.
During this course, we will cover several graphical models, including Bayesian networks, Markov networks, Conditional Random Fields, Markov chains, Hidden Markov Models and Markov decision processes. We will have a clear understanding of how these models work as well as their main algorithms for inference and learning. We will also cover several algorithms used to learn parameters and make inference such as Monte Carlo Markov Chains (MCMC), Gibbs Sampling, Viterbi and the Baum-Welch algorithms, among others.
This course presents an in-depth study of statistical machine learning approaches. It aims to provide the student with a solid understanding of methods for learning and inference in structured probabilistic models, with a healthy balance of theory and practice.
In the recent years, machine learning has been able to solve difficult pattern recognition problems. Such developments have put the notions of backpropagation, using large data sets and probabilistic inference with classical decision-making theory (Von Neumann and Morgenstern, 2007) at the heart of many contemporary AI models. Together with increasing computational power and data set availability have led for AI successes in the recent years. Speech and natural language understanding, self-driving cars, automated assistants, and mastering complex games like Go are some examples of the success of these approaches (Gershman et al., 2015; Schrittwieser et al., 2020; Bengio et al., 2021; He et al., 2021). Although these AI-applications have reached human-level performance on several challenging benchmarks, they are still far from matching human-level behavior in other ways. Deep neural networks typically need much more data than people do to solve the same types of problems, whether it is learning to recognize a new type of object or learning to play a new game. For example, while humans can learn to drive with few dozen hours of practice, self-driving cars need millions of (simulated or real) hours and still lack behind human performance in handling surprising situations (Lake et al., 2017). Or when learning the meanings of words in their native language, children easily make meaningful generalizations from very sparse data. In contrast, AI based deep reinforcement learning systems still have not come close to learning to play new games like Atari as quickly as humans can (Lake et al., 2017).
Abstract:Probabilistic graphical models allow us to encode a large probability distribution as a composition of smaller ones. It is oftentimes the case that we are interested in incorporating in the model the idea that some of these smaller distributions are likely to be similar to one another. In this paper we provide an information geometric approach on how to incorporate this information and see that it allows us to reinterpret some already existing models. Our proposal relies on providing a formal definition of what it means to be close. We provide an example on how this definition can be actioned for multinomial distributions. We use the results on multinomial distributions to reinterpret two already existing hierarchical models in terms of closeness distributions.Keywords: probabilistic modeling; distance; KL divergence; closeness; Beta distribution; multinomial distribution 2ff7e9595c