126: Probability and Random Processes

By Uc Berkeley, Midterm. 2004

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Bayesian Structure Learning with Generative Flow Networks (2022, methodology): “Bengio et al. (2021b) proposed an alternative characterization of GFlowNets inspired by the detailed-balance equations from the literature on Markov chains (Grimmett and Stirzaker, 2020 ) is a distribution over the parents of s t +1 in the structure of the GFlowNet.”
On the O(1=k) convergence of asynchronous distributed alternating Direction Method of Multipliers (2013, methodology): “Our analysis uses results related to supermartingales (interested readers are referred to [18] and [48] for a comprehensive treatment of the subject).”
Dimension Reduction: A Guided Tour (2010, background): “A sequence Xn of random variables is said to converge in probability to a random variable X if limn→∞P (|Xn − X| > ) = 0 for all > 0 [45].”
Theoretical advances in artificial immune systems (2008, background): “For more details on the theory of Markov chains, the reader is referred to chapter 6 of [67].”
Exploiting the Block Structure of the Web for Computing (2003, background): “By the Ergodic Theorem for Markov chains [7], the Markov chain defined by has a unique stationary probability distribution if is aperiodic and irreducible; the former holds for the Markov chain induced by the Web graph.”
Probability on Trees and Networks (2017, background): “In this case, is infS grS Γ > 1? This question was posed by Gromov (1981b) (see also Gromov (1999) for a revised version in English) and for a long time, it remained open. It is known to hold for certain classes of groups, but finally a counterexample was found by Wilson (2004b); see also Bartholdi ”
Monte Carlo Gradient Estimation in Machine Learning (2019, methodology): “…a process of limits, the validity of the interchange will relate to the conditions for which it is possible to exchange limits and integrals, in such cases most often relying on the use of the dominated convergence theorem or the Leibniz integral rule (Flanders, 1973; Grimmett and Stirzaker, 2001).”
Reinforcement Learning Optimized Look-Ahead Energy Management of a Parallel Hybrid Electric Vehicle (2017, methodology): “In this paper, these functions are taken as a Gaussian membership function [43] with the standard deviation σ=1 as follows: 2”
Limit theorems for discrete-time metapopulation models (2010, background): “1 of [24]), which can be interpreted as a Markov branching process with binary splitting.”
Assessing the Potential of Predictive Control for Hybrid Vehicle Powertrains Using Stochastic Dynamic Programming (2005, background): “As indicated already in the Introduction, the basis for the assessment of different predictive-control strategies is stochastic modeling of a specific transport mission in urban traffic.”
Incremental Learning-to-Learn with Statistical Guarantees (2018, methodology): “The previous theorem relies on the theory of Martingales [15] and the analysis of the first term 1 T ∑T t=1 ft(h (t)) of the regret ([13]), in fact this term is a data-dependent statistics evaluating the average cumulative error of the prediction h(t) of the algorithm on the next point Zt, therefore”
Face recognition with image sets using manifold density divergence (2005, methodology): “According to the law of large numbers [16], this expectation can be evaluated by a Monte-Carlo simulation.”
MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOS (2017, background): “2014 [7] G. R. Grimmett, D. R. Stirzaker.”
Size bias for one and all (2013, background): “1], and [45], where notation Vi refers to the sum, with ith term omitted, size biased by the ith term.”