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module FunctionApproximation |
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//reduced example from https://github.com/tirthajyoti/Machine-Learning-with-Python/blob/master/Function%20Approximation%20by%20Neural%20Network/Function%20approximation%20by%20linear%20model%20and%20deep%20network.ipynb |
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open NumSharp |
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open Tensorflow |
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open System |
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let run()= |
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let N_points = 75 // Number of points for constructing function |
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let x_min = 1.0 // Min of the range of x (feature) |
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let x_max = 15.0 // Max of the range of x (feature) |
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let noise_mean = 0.0 // Mean of the Gaussian noise adder |
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let noise_sd = 10.0 // Std.Dev of the Gaussian noise adder |
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let linspace points = [| for i in 0 .. (points - 1) -> x_min + (x_max - x_min)/(float)points * (float)i |] |
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let func_trans(xAr:float []) = |
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xAr |
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|>Array.map (fun (x:float) -> (20.0 * x+3.0 * System.Math.Pow(x,2.0)+0.1 * System.Math.Pow(x,3.0))*sin(x)*exp(-0.1*x)) |
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let X_raw = linspace N_points |
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let Y_raw = func_trans(X_raw) |
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let X_mtr = Array2D.init X_raw.Length 1 (fun i j -> X_raw.[i]) |
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let X = np.array(X_mtr) |
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let noise_x = np.random.normal(noise_mean,noise_sd,N_points) |
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let y = np.array(Y_raw)+noise_x |
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let X_train = X |
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let y_train = y |
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let learning_rate = 0.00001 |
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let training_epochs = 35000 |
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let n_input = 1 // Number of features |
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let n_output = 1 // Regression output is a number only |
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let n_hidden_layer_1 = 25 // Hidden layer 1 |
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let n_hidden_layer_2 = 25 // Hidden layer 2 |
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let x = tf.placeholder(tf.float64, new TensorShape(N_points,n_input)) |
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let y = tf.placeholder(tf.float64, new TensorShape(n_output)) |
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let weights = dict[ |
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"hidden_layer_1", tf.Variable(tf.random_normal([|n_input; n_hidden_layer_1|],dtype=tf.float64)) |
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"hidden_layer_2", tf.Variable(tf.random_normal([|n_hidden_layer_1; n_hidden_layer_2|],dtype=tf.float64)) |
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"out", tf.Variable(tf.random_normal([|n_hidden_layer_2; n_output|],dtype=tf.float64)) |
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] |
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let biases = dict[ |
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"hidden_layer_1", tf.Variable(tf.random_normal([|n_hidden_layer_1|],dtype=tf.float64)) |
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"hidden_layer_2", tf.Variable(tf.random_normal([|n_hidden_layer_2|],dtype=tf.float64)) |
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"out", tf.Variable(tf.random_normal([|n_output|],dtype=tf.float64)) |
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] |
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// Hidden layer with RELU activation |
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let layer_1 = tf.add(tf.matmul(x, weights.["hidden_layer_1"]._AsTensor()),biases.["hidden_layer_1"]) |
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let layer_1 = tf.nn.relu(layer_1) |
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let layer_2 = tf.add(tf.matmul(layer_1, weights.["hidden_layer_2"]._AsTensor()),biases.["hidden_layer_2"]) |
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let layer_2 = tf.nn.relu(layer_2) |
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// Output layer with linear activation |
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let ops = tf.add(tf.matmul(layer_2, weights.["out"]._AsTensor()), biases.["out"]) |
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// Define loss and optimizer |
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let cost = tf.reduce_mean(tf.square(tf.squeeze(ops)-y)) |
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let gs = tf.Variable(1, trainable= false, name= "global_step") |
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let optimizer = tf.train.GradientDescentOptimizer(learning_rate=(float32)learning_rate).minimize(cost,global_step = gs) |
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let init = tf.global_variables_initializer() |
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Tensorflow.Python.``with``(tf.Session(), fun (sess:Session) -> |
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sess.run(init) |> ignore |
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// Loop over epochs |
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for epoch in [0..training_epochs] do |
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// Run optimization process (backprop) and cost function (to get loss value) |
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let result=sess.run([|optimizer:>ITensorOrOperation; gs._AsTensor():>ITensorOrOperation; cost:>ITensorOrOperation|], new FeedItem(x, X_train), new FeedItem(y, y_train)) |
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let loss_value = (double) result.[2]; |
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let step = (int) result.[1]; |
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if epoch % 1000 = 0 then |
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sprintf "Step %d loss: %f" step loss_value |> Console.WriteLine |
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let w=sess.run(weights |> Array.ofSeq |> Array.map (fun pair -> pair.Value)) |
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let b = sess.run(biases |> Array.ofSeq |> Array.map (fun pair -> pair.Value)) |
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let yhat=sess.run([|ops:>ITensorOrOperation|],new FeedItem(x,X_train)) |
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for i in [0..(N_points-1)] do |
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sprintf "pred %f real: %f" ((double)(yhat.[0].[i].[0])) ((double)Y_raw.[i]) |> Console.WriteLine |
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) |
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