object Optimizer_SGD extends Error
The Optimizer object provides functions to optimize the parameters (weights
and biases) of Neural Networks with various numbers of layers.
This optimizer used Stochastic Gradient Descent
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def
optimize(x: MatriD, y: VectoD, b: VectoD, eta_: Double = hp.default ("eta"), bSize: Int = hp.default ("bSize").toInt, maxEpochs: Int = hp.default ("maxEpochs").toInt, f1: AFF = f_sigmoid): (Double, Int)
Given training data 'x' and 'y' for a 2-layer, single output Neural Network, fit the parameter/weight vector 'b'.
Given training data 'x' and 'y' for a 2-layer, single output Neural Network, fit the parameter/weight vector 'b'. Iterate over several epochs, where each epoch divides the training set into 'nB' batches. Each batch is used to update the weights.
- x
the m-by-nx input matrix (training data consisting of m input vectors)
- y
the m output vector (training data consisting of m output vectors)
- b
the nx parameter/weight vector for layer 1->2 (input to output)
- eta_
the initial learning/convergence rate
- bSize
the batch size
- maxEpochs
the maximum number of training epochs/iterations
- f1
the activation function family for layers 1->2 (input to output)
-
def
optimize2(x: MatriD, y: MatriD, b: NetParam, eta_: Double = hp.default ("eta"), bSize: Int = hp.default ("bSize").toInt, maxEpochs: Int = hp.default ("maxEpochs").toInt, f1: AFF = f_sigmoid): (Double, Int)
Given training data 'x' and 'y' for a 2-layer, multi-output Neural Network, fit the parameter/weight matrix 'b'.
Given training data 'x' and 'y' for a 2-layer, multi-output Neural Network, fit the parameter/weight matrix 'b'. Iterate over several epochs, where each epoch divides the training set into 'nB' batches. Each batch is used to update the parameter's weights.
- x
the m-by-nx input matrix (training data consisting of m input vectors)
- y
the m-by-ny output matrix (training data consisting of m output vectors)
- b
the parameters with an nx-by-ny weight matrix for layer 1->2 (input to output)
- eta_
the initial learning/convergence rate
- bSize
the batch size
- maxEpochs
the maximum number of training epochs/iterations
- f1
the activation function family for layers 1->2 (input to output)
-
def
optimize2I(x: MatriD, y: MatriD, b: NetParam, etaI: PairD, bSize: Int = hp.default ("bSize").toInt, maxEpochs: Int = hp.default ("maxEpochs").toInt, f1: AFF = f_sigmoid): (Double, Int)
Given training data 'x' and 'y' for a 2-layer, multi-output Neural Network, fit the parameter/weight vector 'b'.
Given training data 'x' and 'y' for a 2-layer, multi-output Neural Network, fit the parameter/weight vector 'b'. Select the best learning rate within the interval 'etaI'.
- x
the m-by-nx input matrix (training data consisting of m input vectors)
- y
the m-by-ny output matrix (training data consisting of m output vectors)
- b
the parameter with nx-by-ny weight matrix for layer 1->2 (input to output)
- etaI
the learning/convergence rate interval
- bSize
the batch size
- maxEpochs
the maximum number of training epochs/iterations
- f1
the activation function family for layers 1->2 (input to output)
-
def
optimize3(x: MatriD, y: MatriD, a: NetParam, b: NetParam, eta_: Double = hp.default ("eta"), bSize: Int = hp.default ("bSize").toInt, maxEpochs: Int = hp.default ("maxEpochs").toInt, f1: AFF = f_sigmoid, f2: AFF = f_lreLU): (Double, Int)
Given training data 'x' and 'y' for a 3-layer Neural Network, fit the parameters (weights and biases) 'a' & 'b'.
Given training data 'x' and 'y' for a 3-layer Neural Network, fit the parameters (weights and biases) 'a' & 'b'. Iterate over several epochs, where each epoch divides the training set into 'nB' batches. Each batch is used to update the weights.
- x
the m-by-nx input matrix (training data consisting of m input vectors)
- y
the m-by-ny output matrix (training data consisting of m output vectors)
- a
the parameters with nx-by-nz weight matrix & nz bias vector for layer 0->1
- b
the parameters with nz-by-ny weight matrix & ny bias vector for layer 1->2
- eta_
the initial learning/convergence rate
- bSize
the batch size
- maxEpochs
the maximum number of training epochs/iterations
- f1
the activation function family for layers 0->1 (input to hidden)
- f2
the activation function family for layers 1->2 (hidden to output)
-
def
optimize3I(x: MatriD, y: MatriD, a: NetParam, b: NetParam, etaI: PairD, bSize: Int = hp.default ("bSize").toInt, maxEpochs: Int = hp.default ("maxEpochs").toInt, f1: AFF = f_sigmoid, f2: AFF = f_lreLU): (Double, Int)
Given training data 'x' and 'y' for a 3-layer Neural Network, fit the parameters (weights and biases) 'a' & 'b'.
Given training data 'x' and 'y' for a 3-layer Neural Network, fit the parameters (weights and biases) 'a' & 'b'. Select the best learning rate within the interval 'etaI'.
- x
the m-by-nx input matrix (training data consisting of m input vectors)
- y
the m-by-ny output matrix (training data consisting of m output vectors)
- a
the paramters with nx-by-nz weight matrix & nz bias vector for layer 0->1
- b
the paramters with nz-by-ny weight matrix & ny bias vector for layer 1->2
- etaI
the learning/convergence rate interval
- bSize
the batch size
- maxEpochs
the maximum number of training epochs/iterations
- f1
the activation function family for layers 0->1 (input to hidden)
- f2
the activation function family for layers 1->2 (hidden to output
-
def
optimizeI(x: MatriD, y: VectoD, b: VectoD, etaI: PairD, bSize: Int = hp.default ("bSize").toInt, maxEpochs: Int = hp.default ("maxEpochs").toInt, f1: AFF = f_sigmoid): (Double, Int)
Given training data 'x' and 'y' for a 2-layer, single output Neural Network, fit the parameter/weight vector 'b'.
Given training data 'x' and 'y' for a 2-layer, single output Neural Network, fit the parameter/weight vector 'b'. Select the best learning rate within the interval 'etaI'.
- x
the m-by-nx input matrix (training data consisting of m input vectors)
- y
the m output vector (training data consisting of m output vectors)
- b
the nx parameter/weight vector for layer 1->2 (input to output)
- etaI
the learning/convergence rate interval
- bSize
the batch size
- maxEpochs
the maximum number of training epochs/iterations
- f1
the activation function family for layers 1->2 (input to output)
-
def
optimizeX(x: MatriD, y: MatriD, b: NetParams, eta_: Double = hp.default ("eta"), bSize: Int = hp.default ("bSize").toInt, maxEpochs: Int = hp.default ("maxEpochs").toInt, lambda: Double = 0.0, f: Array[AFF] = ...): (Double, Int)
Given training data 'x' and 'y' for a multi-hidden layer Neural Network, fit the parameter array 'b', where each 'b(l)' contains a weight matrix and bias vector.
Given training data 'x' and 'y' for a multi-hidden layer Neural Network, fit the parameter array 'b', where each 'b(l)' contains a weight matrix and bias vector. Iterate over several epochs, where each epoch divides the training set into 'nB' batches. Each batch is used to update the weights.
- x
the m-by-nx input matrix (training data consisting of m input vectors)
- y
the m-by-ny output matrix (training data consisting of m output vectors)
- b
the array of parameters (weights & biases) between every two adjacent layers
- eta_
the initial learning/convergence rate
- bSize
the batch size
- maxEpochs
the maximum number of training epochs/iterations
- f
the array of activation function family for every two adjacent layers
-
def
optimizeXI(x: MatriD, y: MatriD, b: NetParams, etaI: PairD, bSize: Int = hp.default ("bSize").toInt, maxEpochs: Int = hp.default ("maxEpochs").toInt, lambda: Double = 0.0, f: Array[AFF] = ...): (Double, Int)
Given training data 'x' and 'y' for a multi-hidden layer Neural Network, fit the parameter array 'b', where each 'b(l)' contains a weight matrix and bias vector.
Given training data 'x' and 'y' for a multi-hidden layer Neural Network, fit the parameter array 'b', where each 'b(l)' contains a weight matrix and bias vector. Select the best learning rate within the interval 'etaI'.
- x
the m-by-nx input matrix (training data consisting of m input vectors)
- y
the m-by-ny output matrix (training data consisting of m output vectors)
- b
the array of parameters (weights & biases) between every two adjacent layers
- etaI
the lower and upper bounds of learning/convergence rate
- bSize
the batch size
- maxEpochs
the maximum number of training epochs/iterations
- f
the array of activation function family for every two adjacent layers
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