The Eigenvalues of Mega-dimensional Matrices

By John Skilling. 1989

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Citations in the corpus

Score-Based Generative Modeling through Stochastic Differential Equations (2020, neutral): “In many cases computing ∇ ¨ ˜ f θ p x , t q is expensive, so we follow Grathwohl et al. (2018) to estimate it with the Skilling-Hutchinson trace estimator (Skilling, 1989; Hutchinson, 1990).”
Maximum Likelihood Training of Score-Based Diffusion Models (2021, positive): “Moreover, the divergences ∇x ̈ sθpx, tq and ∇x ̈ fpx, tq in LSM θ pxq and LDSM θ pxq have efficient unbiased estimators via the Skilling–Hutchinson trick [42, 22].”
Residual Flows for Invertible Generative Modeling (2019, methodology): “Furthermore, the Skilling-Hutchinson estimator (Skilling, 1989; Hutchinson, 1990) was used to estimate the trace in the power series.”
Estimating the Spectral Density of Large Implicit Matrices (2018, methodology): “…(see, e.g., Haydock et al. (1972), Tal-Ezer and Kosloﬀ (1984)), the combination of polynomial expansion and randomized trace estimation as in Skilling (1989) led to the kernel polynomial method for estimation the density of states in Silver and R¨oder (1994) and Silver et al. (1996), in…”
Bayesian Methods for Adaptive Models (2011, methodology): “For large–dimensional problems where this task is demanding, Skilling has developed methods for estimating TraceA statistically in k(2) time [72].”
A Practical Bayesian Framework for Backprop Networks (1991, methodology): “If this is the case, numerical methods are available to approximate the determinant or trace of a matrix in k 2 time (Skilling, 1989b).”
Bayesian Interpolation (1992, methodology): “(For problems where significant subjective priors do arise see Gull 1989b; Skilling 1989.)”
Skip Connections Eliminate Singularities (2017, methodology): “To estimate this eigenvalue density in our ∼ 1M -dimensional parameter spaces, we ﬁrst estimated the ﬁrst four moments of the spectral density using the method of Skilling (Skilling, 1989) and ﬁt the estimated moments with a ﬂexible mixture density model (see Supplementary Note 3 for details) consis”
Diffusion Models: A Comprehensive Survey of Methods and Applications (2022, methodology): “One can compute the one-dimensional integral above with numerical ODE solvers and the Skilling-Hutchinson trace estimator [100, 214].”
Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling (2021, methodology): “We highlight a few differences between our approach and the ones of Song and Ermon (2019); Ho et al.”
Neural Networks with Cheap Differential Operators (2019, methodology): “Due to requiring d AD calls to compute Ddimf for a blackbox neural network f , Grathwohl et al. (2019) adopted the stochastic trace estimator (Skilling, 1989; Hutchinson, 1990) to provide unbiased estimates for log p(t, h(t)).”
Relaxing Bijectivity Constraints with Continuously Indexed Normalising Flows (2019, methodology): “5 for the number of terms to compute in our Russian Roulette estimators; • We used the Skilling-Hutchinson trace estimator (Skilling, 1989; Hutchinson, 1990) to estimate the trace in the log Jacobian term; • At both training and test time, we used a single Monte Carlo sample of (n, v) to estimate (6”
Implicit Normalizing Flows (2021, methodology): “Instead, we propose the following unbiased estimator of ln p ( x ) using the same technique in Chen et al. (2019) with Skilling-Hutchinson trace estimator (Skilling, 1989; Hutchinson, 1989): where p ( N ) is a distribution supported over the positive integers.”
How to Train Your Energy-Based Models (2021, methodology): “(8)) with the Skilling-Hutchinson trace estimator (Skilling, 1989; Hutchinson, 1989).”
A Practical Bayesian Framework for Backpropagation Networks (1992, methodology): “If this is the case, numerical methods are available to approximate the determinant or trace of a matrix in k2 time ( Skilling, 1989 ).”