Locally Weighted Projection Regression : An O(n) Algorithm for Incremental Real Time Learning in High Dimensional Space

By Sethu Vijayakumar, Stefan Schaal. 2000

401 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/749c81cc86c3a946424332f3866474b4a1e8014f

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Citations in the corpus

Online Sparse Multi-Output Gaussian Process Regression and Learning (2019, background): “However, in practice, multi-output functions arise widely in geostatistics [16], robotics [17], sensor networks [18], chemometrics [19], traffic flow forecasting [20] and computational physics [21], [22], just to name a few.”
Learning Movement Primitives (2005, methodology): “For solving the function approximation problem, we chose a nonparametric regression technique from locally weighted learning (LWPR) [17] as it allows us to determine the necessary number of basis functions N, their centers c i , and bandwidth h i automatically.”
Model learning for robot control: a survey (2011, methodology): “Locally weighted projection regression (Vijayakumar and Schaal 2000) Local Incremental Yes OðnÞ Inverse dynamics (Schaal et al.”
Control Functionals for Quasi-Monte Carlo Integration (2015, unknown): “Schematic reproduced from [32].”
A Developmental Roadmap for Learning by Imitation in Robots (2007, methodology): “To learn this map we use the Locally Weighted Projection Regression method, [32].”
Scalable Inference for Gaussian Process Models with Black-Box Likelihoods (2015, methodology): “This also corroborates previous findings that, on this problem, having more data does help [16].”
Model Learning with Local Gaussian Process Regression (2009, methodology): “Locally-weighted projection regression is currently the standard real-time learning method in robot control applications and has been shown to scale into very high-dimensional domains [1, 2, 15].”
BM: An iterative algorithm to learn stable non-linear dynamical systems with Gaussian mixture models (2010, methodology): “Existing approaches to the statistical estimation of f̂ use either Gaussian Process Regression (GPR) [10], Gaussian Mixture Regression (GMR) [4] or Locally Weighted Projection Regression (LWPR) [11].”
Adaptive Neural Trees (2018, methodology): “We evaluate ANTs using the MNIST (LeCun et al., 1998) and CIFAR-10 (Krizhevsky & Hinton, 2009) object classiﬁcation datasets, and the SARCOS multivariate regression dataset (Vijayakumar & Schaal, 2000) (see Supp.”
Learning from observation using primitives (2001, methodology): “We use a locally weighted learning technique, Locally Weighted Projection Regression (LWPR) [129], to represent these learned models.”
Remarks on multi-output Gaussian process regression (2018, methodology): “This example is an inverse dynamic model of a 7-degree-of-freedom anthropomorphic robot arm [96].”
A Review of Robot Learning for Manipulation: Challenges, Representations, and Algorithms (2019, methodology): “This representational paradigm has been successful in manipulation tasks in which very little task knowledge is given a priori to the robot, such as an 88dimensional octopus arm control problem in which Gaussian Process Temporal Difference learning is used [100], and 50-dimensional control of a SARC”
Imitation learning of globally stable non-linear point-to-point robot motions using nonlinear programming (2010, background): “…ξ t,n } T n ,N t =0 ,n =1 , each recorded point in the trajectories [ ξ t,n , _ ξ t,n ] is associated with a probability density function P ( ξ t,n , _ ξ t,n ) : where N ( ξ t,n , _ ξ t,n ; θ k ) is given by: Taking the posterior mean estimate of P ( _ ξ | ξ ) yields (see [14]): The resulting…”
A survey of robot learning from demonstration (2009, unknown): “Locally Weighted Projection Regression (LWPR) [72] extends this approach to scale with input data dimensionality and redundancy.”
Interference and Generalization in Temporal Difference Learning (2020, methodology): “Regression has similar but less consistent results; SARCOS has a high correlation peak when there starts being enough data, albeit shows no correlation at all when all 44k training examples are given (the generalization gap is then almost 0 for all hyperparameters); on the other hand the California ”
Learning Forward Models for the Operational Space Control of Redundant Robots (2010, methodology): “…linear and non-linear functions: perceptrons, multi-layer perceptrons, radial basis function networks, gaussian processes, support-vector regression, gaussian process regression, learning classiﬁers systems and locally weighted regression methods such as lwpr Vijayakumar and Schaal (2000).”