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object --+ | properties.Function --+ | properties.CompositeFunction --+ | object --+ | | | properties.Gradient --+ | | | object --+ | | | | | properties.LipschitzContinuousGradient --+ | | | object --+ | | | | | properties.Eigenvalues --+ | | | object --+ | | | | | properties.ProximalOperator --+ | | | properties.NesterovFunction --+ | object --+ | | | properties.ProximalOperator --+ | object --+ | | | properties.Continuation --+ | object --+ | | | properties.DualFunction --+ | object --+ | | | properties.StronglyConvex --+ | object --+ | | | properties.StepSize --+ | LinearRegressionL1L2TV --+ | LinearRegressionL1L2GL
Combination (sum) of RidgeRegression, L1 and Overlapping Group Lasso.
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Inherited from Inherited from Inherited from Inherited from Inherited from Inherited from Inherited from |
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Inherited from Inherited from Inherited from |
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Inherited from |
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Parameters: ---------- X : Numpy array (n-by-p). The X matrix for the linear regression. y : Numpy array (n-by-1). The y vector for the linear regression. l1 : Non-negative float. The Lagrange multiplier, or regularisation constant, for the L1 penalty. l2 : Non-negative float. The Lagrange multiplier, or regularisation constant, for the ridge penalty. gl : Non-negative float. The Lagrange multiplier, or regularisation constant, of the overlapping group L1-L2 function. A : Numpy array (usually sparse). The linear operator for the Nesterov formulation for group L1-L2. May not be None! mu : Non-negative float. The regularisation constant for the smoothing of the overlapping group L1-L2 function. penalty_start : Non-negative integer. The number of columns, variables etc., to except from penalisation. Equivalently, the first index to be penalised. Default is 0, all columns are included. mean : Boolean. Whether to compute the squared loss or the mean squared loss. Default is True, the mean squared loss.
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Free any cached computations from previous use of this Function.
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Returns the regularisation constant for the smoothing. From the interface "NesterovFunction".
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Sets the regularisation constant for the smoothing. From the interface "NesterovFunction". Parameters: ---------- mu : Non-negative float. The regularisation constant for the smoothing to use from now on. Returns: ------- old_mu : Non-negative float. The old regularisation constant for the smoothing that was overwritten and is no longer used.
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Function value.
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Function value.
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Function value with known alpha.
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Gradient of the differentiable part of the function. From the interface "Gradient".
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Lipschitz constant of the gradient. From the interface "LipschitzContinuousGradient".
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The proximal operator of the non-differentiable part of the function. From the interface "ProximalOperator".
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Computes a "good" value of mu with respect to the given beta. From the interface "NesterovFunction".
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The maximum value of the regularisation of the dual variable. We have M = max_{alpha in K} 0.5*|alpha|²_2. From the interface "NesterovFunction".
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The optimal value of mu given epsilon. From the interface "Continuation".
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The optimal value of epsilon given mu. From the interface "Continuation".
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The maximum value of epsilon. From the interface "Continuation". Parameters ---------- mu : Positive float. The regularisation constant of the smoothing. Returns ------- eps : Positive float. The upper limit, the maximum, precision.
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The maximum value of mu. From the interface "Continuation". Parameters ---------- eps : Positive float. The maximum precision of the smoothing. Returns ------- mu : Positive float. The upper limit, the maximum, of the regularisation constant of the smoothing.
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Returns the beta that minimises the dual function. Used when we compute the gap. From the interface "DualFunction".
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Compute the duality gap. From the interface "DualFunction".
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Linear operator of the Nesterov function. From the interface "NesterovFunction".
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Computes A^T.alpha. From the interface "NesterovFunction".
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Projection onto the compact space of the Nesterov function. From the interface "NesterovFunction".
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The step size to use in descent methods. From the interface "StepSize". Parameters ---------- x : Numpy array. The point at which to evaluate the step size.
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