In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a sequence of random variables in a probability space, where the index of the sequence often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.
In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it – that is, the Markov chain's equilibrium distribution matches the target distribution. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution.
Zohar Manna was an Israeli-American computer scientist who was a professor of computer science at Stanford University.
Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that operates by constructing a multitude of decision trees at training time. For classification tasks, the output of the random forest is the class selected by most trees. For regression tasks, the mean or average prediction of the individual trees is returned. Random decision forests correct for decision trees' habit of overfitting to their training set.
Yves F. Meyer is a French mathematician. He is among the progenitors of wavelet theory, having proposed the Meyer wavelet. Meyer was awarded the Abel Prize in 2017.
Wendelin Werner is a German-born French mathematician working on random processes such as self-avoiding random walks, Brownian motion, Schramm–Loewner evolution, and related theories in probability theory and mathematical physics. In 2006, at the 25th International Congress of Mathematicians in Madrid, Spain he received the Fields Medal "for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory". He is currently Rouse Ball professor of Mathematics at the University of Cambridge.
Marie-Elisabeth Lucienne Paté-Cornell,, is a Stanford University Professor in the Department of Management Science and Engineering and was the Founding Chair of the Department.
Charles "Chip" Lawrence is an American bioinformatician and mathematician, who is the pioneer in developing novel statistical approaches to biological sequence analysis.
Stuart Alan Geman is an American mathematician, known for influential contributions to computer vision, statistics, probability theory, machine learning, and the neurosciences. He and his brother, Donald Geman, are well known for proposing the Gibbs sampler, and for the first proof of convergence of the simulated annealing algorithm.
Raphael Douady is a French mathematician and economist. He holds the Robert Frey Endowed Chair for Quantitative Finance at Stony Brook, New York. He is a fellow of the Centre d’Economie de la Sorbonne, Paris 1 Pantheon-Sorbonne University, and academic director of the Laboratory of Excellence on Financial Regulation.
Grégory Miermont is a French mathematician working on probability, random trees and random maps.
The École normale supérieure de Rennes, also called ENS Rennes is a French scientific grande école, belonging to the network of écoles normales supérieures established according to the model of the École normale supérieure in Paris. Like its sister universities, its mandate lies in training students with a view to careers in academia, engineering and government.
Gérard Ben Arous is a French mathematician, specializing in stochastic analysis and its applications to mathematical physics. He served as the director of the Courant Institute of Mathematical Sciences at New York University from 2011 to 2016.
Sandrine Péché is a French mathematician who works as a professor in the Laboratoire de Probabilités, Statistique et Modélisation of Paris Diderot University. Her research concerns probability theory, mathematical physics, and the theory and applications of random matrices.
Michael Ira Miller is an American-born biomedical engineer and data scientist, and the Bessie Darling Massey Professor and Director of the Johns Hopkins University Department of Biomedical Engineering. He worked with Ulf Grenander in the field of Computational Anatomy as it pertains to neuroscience, specializing in mapping the brain under various states of health and disease by applying data derived from medical imaging. Miller is the director of the Johns Hopkins Center for Imaging Science, Whiting School of Engineering and codirector of Johns Hopkins Kavli Neuroscience Discovery Institute. Miller is also a Johns Hopkins University Gilman Scholar.
Alan Enoch Gelfand is an American statistician, and is currently the James B. Duke Professor of Statistics and Decision Sciences at Duke University. Gelfand’s research includes substantial contributions to the fields of Bayesian statistics, spatial statistics and hierarchical modeling.
The following outline is provided as an overview of and topical guide to machine learning:
In network theory, collective classification is the simultaneous prediction of the labels for multiple objects, where each label is predicted using information about the object's observed features, the observed features and labels of its neighbors, and the unobserved labels of its neighbors. Collective classification problems are defined in terms of networks of random variables, where the network structure determines the relationship between the random variables. Inference is performed on multiple random variables simultaneously, typically by propagating information between nodes in the network to perform approximate inference. Approaches that use collective classification can make use of relational information when performing inference. Examples of collective classification include predicting attributes of individuals in a social network, classifying webpages in the World Wide Web, and inferring the research area of a paper in a scientific publication dataset.
In the domain of physics and probability, the filters, random fields, and maximum entropy (FRAME) model is a Markov random field model of stationary spatial processes, in which the energy function is the sum of translation-invariant potential functions that are one-dimensional non-linear transformations of linear filter responses. The FRAME model was originally developed by Song-Chun Zhu, Ying Nian Wu, and David Mumford for modeling stochastic texture patterns, such as grasses, tree leaves, brick walls, water waves, etc. This model is the maximum entropy distribution that reproduces the observed marginal histograms of responses from a bank of filters, where for each filter tuned to a specific scale and orientation, the marginal histogram is pooled over all the pixels in the image domain. The FRAME model is also proved to be equivalent to the micro-canonical ensemble, which was named the Julesz ensemble. Gibbs sampler is adopted to synthesize texture images by drawing samples from the FRAME model.
Florent Krzakala is a French physicist and applied mathematician, currently a professor at EPFL. His research focuses on the resolution of theoretical problems in physics, computer science, machine learning, statistics and signal processing using mathematical tools inspired by the field of statistical physics.
