Random Fields and Geometry

By Robert J. Adler, Jonathan E. Taylor. 2007

1,677 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/48caa22bd6d406d5826be014b031093c112d853b

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Citations in the corpus

On the Diffusion of Shape (2007, methodology): “In stochastic processes, the tube formula is used to evaluate the maximal distributions of Gaussian processes (cf [1]).”
Exponential Regret Bounds for Gaussian Process Bandits with Deterministic Observations (2012, background): “In either case, the sample f is twice differentiable almost surely, in the former case by (Adler & Taylor, 2007, Theorem 1.4.2) and (Stein, 1999, §2.6)) and in the latter situation by (Ghosal & Roy, 2006, Theorem 5).”
Bayesian Multi-Scale Optimistic Optimization (2014, background): “The first case was shown by (Adler & Taylor, 2007, Theorem 1.4.2) and (Stein, 1999, §2.6), while the second result was shown by (Ghosal & Roy, 2006, Theorem 5).”
Topological complexity of smooth random functions (2011, background): “Also related to the structure of these notes is the fact that in 2007 we published a 450 page Springer monograph [8] Random Fields and Geometry (hereafter RFG) which more or less covers the theoretical aspects of these notes.”
Statistical thresholds for tensor PCA (2018, background): “Let C denote the subset of C([0, 1]) of functions that are positive, nonincreasing and concave.”
Comparison and anti-concentration bounds for maxima of Gaussian random vectors (2013, background): “48 07 v3 [ m at h. PR ] 1 9 Fe b 20”
Random Fields Simplified: Preserving Marginal Distributions, Correlations, and Intermittency, With Applications From Rainfall to Humidity (2020, neutral): “…with a Gaussian process or another tractable process (Chilès & Delfiner, 2009; Wackernagel, 2003) and (2) methods assuming that the random field follows specific processes, such as χ2 or t‐Student (e.g., Adler & Taylor, 2007), Gamma (Wolpert & Ickstadt, 1998), or skew normal (Allard, 2012).”
An experimental methodology for response surface optimization methods (2011, background): “5) are related to counting connected components of excursion sets (Adler and Taylor 2007).”
The topology of probability distributions on manifolds (2013, result): “Our results are also related to ideas in the statistics and statistical physics of random fields, see [3, 7, 14, 53, 54], a random process on a manifold can be thought of as an approximation of excursion sets of Gaussian random fields or energy landscapes.”
Replica Symmetry Breaking Condition Exposed by Random Matrix Calculation of Landscape Complexity (2007, methodology): “in [35] and [36], and [ 37 ] contains further extensions and a proof in general setting.”
Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization (2016, methodology): “The coeﬃcients L j (Θ) on the RHS of (35) are known as the Lipschitz-Killing curvatures of the domain Θ, which measure the “intrinsic volumes” of the domain Θ using the Riemannian metric induced by the Gaussian process G n (Adler and Taylor (2009), equation (12.2.2)).”
NIRS-SPM: statistical parametric mapping for near infrared spectroscopy (2008, positive): “The expected EC approach has been extensively studied by Adler (Adler, 1981, 2000; Adler and Taylor, 2007), Worsley (Worsley, 1994, 1995; Cao and Worsley, 1999b) and more recently by Taylor et al.”
Spatio-temporal exceedance locations and confidence regions (2013, background): “The mean structure µ(s, t) is assumed to follow the linear model µ(s, t) = x(s, t)Tβ, where x(s, t) is a k × 1 vector of known space–time covariates for location s at time t, β is a vector of space–time trend parameters, and W (s, t) is assumed to be a Gaussian process having continuous sample paths”
Linear regression with sparsely permuted data (2017, neutral): “3 in [4]) and the fact that ‖PX‖2 ≤ 1.”