A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines

By Michael F. Hutchinson. 1989

Subfields: Statistics and Probability, Numerical Methods & Scientific Computing

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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).”
Equivariant Flows: exact likelihood generative learning for symmetric densities (2020, methodology): “suggest an approximation via the Hutchinsonestimator (Hutchinson, 1989).”
Simple and Scalable Epistemic Uncertainty Estimation Using a Single Deep Deterministic Neural Network (2020, methodology): “To evaluate the two alternative candidates we turn to the Hutchinson’s Estimator (Hutchinson, 1990), which allows us to estimate the trace of the Jacobian by computing the derivative of random projections of the output.”
Invertible Residual Networks (2018, background): “The distribution p(v) needs to fulfill E[v] = 0 and Cov(v) = I , see (Hutchinson, 1990; Avron & Toledo, 2011).”
Neural Spline Flows (2019, methodology): “Deep diffeomorphic flow [49] is one such instance, where the model is trained by backpropagation through an Euler integrator, and the Jacobian is computed approximately using a truncated power series and the Hutchison trace estimator [22].”
Normalizing Flows for Probabilistic Modeling and Inference (2019, methodology): “The trace of J k gφ (z) can be efficiently estimated using the Hutchinson trace estimator (Hutchinson, 1990): Tr { Jkgφ(z) } ≈ v>Jkgφ(z) v, (60) where v can be any D-dimensional random vector with zero mean and unit covariance.”
Maximum Likelihood Training of Score-Based Diffusion Models (2021, positive): “Moreover, the divergences ∇ x ¨ s θ p x , t q and ∇ x ¨ f p x , t q in L SM θ p x q and L DSM θ p x q 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.”
Sliced Score Matching: A Scalable Approach to Density and Score Estimation (2019, background): “ˆ J vr is also closely related to Hutchinson’s trace estimator (Hutchinson, 1990), which we will analyze later in Section 4.3.”
Estimating the Spectral Density of Large Implicit Matrices (2018, methodology): “The classic randomized estimator described in Hutchinson (1989) and Skilling (1989), is the following, which we will call the Skilling-Hutchinson trace estimator : Proposition 4.1.”
A Variational Perspective on Diffusion-Based Generative Models and Score Matching (2021, methodology): “Computing the divergence term ∇ · µ directly can be expensive, but it can be efﬁciently estimated using the Hutchinson trace estimator (Hutchinson, 1989) along with reverse-mode automatic differentiation, similar to Grathwohl et al. (2018).”
Torsional Diffusion for Molecular Conformer Generation (2022, methodology): “[2021], the divergence term is approximated via Hutchinson’s method [Hutchinson, 1989], which gives an unbiased estimate of log p0(τ ).”
OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport (2020, methodology): “To alleviate the expensive training costs of CNFs, FFJORD (Grathwohl et al. 2019) sacriﬁces the exact but slow trace computation in (2) for a Hutchinson’s trace estimator with complexity O ( d ) (Hutchinson 1990”
Approximating Spectral Densities of Large Matrices (2013, unknown): “The stochastic sampling and averaging technique is based on the following key result [18, 36, 2].”
Comparing parameter choice methods for regularization of ill-posed problems (2011, unknown): “One can also estimate the trace efficiently using stochastic (Monte-Carlo) algorithms [48, 78, 52].”
WaveFFJORD: FFJORD-Based Vocoder for Statistical Parametric Speech Synthesis (2020, methodology): “Free-form Jacobian of Reversible Dynamics (FFJORD) improved CNFs by introducing the Hutchinson’s trace estimator [19] to the likelihood computing, i.”
Adjusted Plus-Minus for NHL Players using Ridge Regression with Goals, Shots, Fenwick, and Corsi (2012, methodology): “Regression-based versions of adjusted plus-minus (APM) statistics for NBA players can be found in Winston (2009), Rosenbaum (2004), Lewin (2007), Witus (2008), Ilardi and Barzilai (2008), Sill (2010), and Fearnhead and Taylor (2011).”
Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video (2020, methodology): “Instead, the authors of FFJORD [20] use Hutchinson’s trace estimator [26]: Here, e is Gaussian-distributed.”