Regression and the Moore-Penrose Pseudoinverse

By A. Albert. 2012

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In Artificial Intelligence

Citations in the corpus

Active learning of inverse models with intrinsically motivated goal exploration in robots (2013, neutral): “…θ i is drawn randomly in the vicinity of θ k ; Observe the resulting y i ; Update M and M − 1 with the resulting ( s t ,θ i , y i ) ; Reset the current context: pseudo-inverse of Moore–Penrose [108] to compute the pseudo-inverse J + (α) of the Jacobian J (α) in a vicinity ˙ α is thus sufficient.”
netmeta: An R Package for Network Meta-Analysis Using Frequentist Methods (2023, positive): “The first step to get network treatment estimates θ̂ is the calculation of the MoorePenrose pseudoinverse matrix (Albert 1972).”
Intrinsically motivated goal exploration for active motor learning in robots: A case study (2010, methodology): “Also, in the following, we use the pseudo-inverse of Moore-Penrose [16] to compute the pseudo-inverse J+(θ) of the Jacobian J(θ) in a vicinity ̂̇ θ and use this method to deduce the change ∆θ corresponding to a desired ∆x, for a given joint position θ : θ̇ = J+(θ)ẋ”
Deep Convolutional Networks are Hierarchical Kernel Machines (2015, background): “…kept ﬁxed, it can be shown [7] that the optimal coe ﬃ cients are given by c where we have deﬁned ( y If λ is let go to zero, the matrix on the right side of equation (18) converges to the pseudo-inverse of G [31] and if the Green’s function is radial the approximation method of [26] is recovered.”
Flexible Kernel Memory (2010, methodology): “…(cid:2) T ( X ) the memory loads by: and the association (recall) procedure is calculated by: y ~ Bx ~ YS { 1 z ; z ~ ½ ( X ) (cid:2) T ( x ) ; Remark 1 Linear independence of the vectors ( x i ) in the - space is required in order to use identity (3) for the Moore-Penrose pseudoinverse (see [44]).”