An Algorithm for Least-Squares Estimation of Nonlinear Parameters

By D. Marquardt. 1963

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In Optimization & Training

Citations in the corpus

Fast and Furious Convergence: Stochastic Second Order Methods under Interpolation (2019, methodology): “The subsampled gradient and the regularized subsampled Hessian are defined as ∇fGk(wk) = 1 bgk ∑ i∈Gk ∇fi(wk), (2) HSk(wk) = 1 bsk ∑ i∈Sk ∇2fi(wk) + τId (3) where τ ≥ 0 is the LM regularization (Levenberg, 1944; Marquardt, 1963).”
Deep learning in neural networks: An overview (2014, neutral): “Least-squares methods (Gauss– Newton, Levenberg–Marquardt) (Gauss, 1809; Levenberg, 1944; Marquardt, 1963; Newton, 1687; Schaback & Werner, 1992) and quasi-Newtonmethods (Broyden–Fletcher–Goldfarb–Shanno, BFGS) (Broyden et al., 1965; Fletcher & Powell, 1963; Goldfarb, 1970; Shanno, 1970) are…”
Pix3D: Dataset and Methods for Single-Image 3D Shape Modeling (2018, methodology): “To solve Equation 1, we first calculate a rough 3D pose using the Efficient PnP algorithm [35] and then refine it using the Levenberg-Marquardt algorithm [36, 39], as shown in Figure 2.”
New Insights and Perspectives on the Natural Gradient Method (2014, background): “And before that have had a long history of application in the context of practical non-linear regression procedures (Tikhonov, 1943; Levenberg, 1944; Marquardt, 1963; Moré, 1978).”
Generalizing to Unseen Domains via Adversarial Data Augmentation (2018, methodology): “We note that the transported point in the semantic space corresponds to a Tikhonov regularized Newton-step [21, 25] on the loss z 7→ `(θ; (z, y0)) at the current model θ.”
GPS Collar Sampling Frequency: Effects on Measures of Resource Use (2008, background): “If an animal randomly visited areas within its habitat, measures of resource use should mirror an exponential decay function as sampling intervals are progressively extended (Marquardt 1963).”
Proximal Algorithms (2013, background): “The step on the righthand side is very familiar: it is a Tikhonovregularized Newton update, also known as a Levenberg-Marquardt update [124, 134] or a modified Hessian Newton update [153].”
Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion (2001, unknown): “…sequence satisfies ma = given Presuming ii e to be nonsingular, this· necessary condition is also sufficient and we can write the Gauss-Newton iteration as Levenberg (1944) and Marquardt (1963) proposed a modification of the Gauss- Newton method in which the model increment at each step is damped.”
Audio Texture Synthesis with Scattering Moments (2013, methodology): “The Levenberg-Marquardt Algorithm (LMA) [12] sig-niﬁcantly accelerates the convergence.”
Cocaine and Chest Pain (1992, unknown): “Levenberg [109] and Marquardt [110] were the first to suggest this type of method in the context of nonlinear least-squares optimization.”
Reproductive biology and recruitment of the white sea bream in the Azores (2003, methodology): “Total length (LT50; n ¼ 1120) and age at first maturity (A50; n ¼ 753) were estimated for the pooled sexes by fitting the relative frequency of all mature individuals (stages 1–5) over 1 cm LT classes and by age to logistic curves, using the Levenberg– Marquardt algorithm ( Marquardt, 1963 ) for sol”
Back to the Feature: Learning Robust Camera Localization from Pixels to Pose (2021, methodology): “where λ, the damping factor, interpolates between the GaussNewton (λ=0) and gradient descent (λ→∞) formulations and is usually adjusted at each iteration using diverse heuristics [44, 55, 56].”