Update regression-example.jl (#148)

adds batch size, selection of optimizers, possibility for initialization

examples/regression-example.jl

@@ -3,60 +3,61 @@ This script shows how a simple MLP net may be used
 for regression. It shows how data in memory may be
 used for training and evaluation, and how to obtain
 the predictions from the trained net.
-
-TO DO:
-    * specify batch size, and allow different sizes
-      for the training and evaluation sets
-    * tanh activation does not seem to work properly,
-      investigate
 =#
 using MXNet
 using Distributions
 using PyPlot
 
-# data generating process for exogenous inputs
-generate_inputs(media, var, tam) = rand(MvNormal(media, var), tam)
-
-# function that maps inputs to outputs
-f1(data) = sin(data[1,:]).*sin(data[2,:])./(data[1,:].*data[2,:])
+# data generating process
+generate_inputs(mean, var, size) = rand(MvNormal(mean, var), size)
+output(data) = sin(data[1,:]).*sin(data[2,:])./(data[1,:].*data[2,:])
 
-# parameters for input d.g.p.
+# create training and evaluation data sets
 mean=[0.0;0.0]
 var=[1.0 0.0;0.0 1.0]
-
-# create training and evaluation data sets
-TrainInput = generate_inputs(mean, var, 5000)
-TrainOutput = f1(TrainInput)
-ValidationInput = generate_inputs(mean, var, 5000)
-ValidationOutput = f1(ValidationInput)
+samplesize  = 5000
+TrainInput = generate_inputs(mean, var, samplesize)
+TrainOutput = output(TrainInput)
+ValidationInput = generate_inputs(mean, var, samplesize)
+ValidationOutput = output(ValidationInput)
 
 # how to set up data providers using data in memory
-trainprovider = mx.ArrayDataProvider(:data => TrainInput, :label => TrainOutput)
-evalprovider = mx.ArrayDataProvider(:data => ValidationInput, :label => ValidationOutput)
+batchsize = 100 # can adjust this later, but must be defined now for next line
+trainprovider = mx.ArrayDataProvider(:data => TrainInput, batch_size=batchsize, shuffle=true, :label => TrainOutput)
+evalprovider = mx.ArrayDataProvider(:data => ValidationInput, batch_size=batchsize, shuffle=true, :label => ValidationOutput)
 
-# create a single hidden layer MPL
+# create a two hidden layer MPL: try varying num_hidden, and change tanh to relu,
+# or add/remove a layer
 data = mx.Variable(:data)
 label = mx.Variable(:label)
-fc1  = mx.FullyConnected(data = data, name=:fc1, num_hidden=20)
-act1 = mx.Activation(data = fc1, name=:relu, act_type=:relu)
-fc2  = mx.FullyConnected(data = act1, name=:fc2, num_hidden=1)
+net  = @mx.chain    mx.FullyConnected(data = data, num_hidden=10) =>
+                    mx.Activation(act_type=:tanh) =>
+                    mx.FullyConnected(num_hidden=3) =>
+                    mx.Activation(act_type=:tanh) =>
+                    mx.FullyConnected(num_hidden=1)        
 
-# cost is squared error loss
-cost = mx.LinearRegressionOutput(data=fc2, label=label, name = :loss)
+# squared error loss is appropriate for regression, don't change
+cost = mx.LinearRegressionOutput(data = net, label=label)
 
-# final model definition
+# final model definition, don't change, except if using gpu
 model = mx.FeedForward(cost, context=mx.cpu())
 
-# set up the optimizer
-optimizer = mx.SGD(lr=0.1, momentum=0.9, weight_decay=0.00001)
+# set up the optimizer: select one, explore parameters, if desired
+#optimizer = mx.SGD(lr=0.01, momentum=0.9, weight_decay=0.00001)
+optimizer = mx.ADAM()
 
 # train, reporting loss for training and evaluation sets
-mx.fit(model, optimizer, eval_metric=mx.MSE(), trainprovider, eval_data=evalprovider, n_epoch = 1000)
+# initial training with small batch size, to get to a good neighborhood
+batchsize = 100
+mx.fit(model, optimizer, initializer=mx.NormalInitializer(0.0,0.1), eval_metric=mx.MSE(), trainprovider, eval_data=evalprovider, n_epoch = 500)
+# more training with the full sample
+batchsize = samplesize
+mx.fit(model, optimizer, eval_metric=mx.MSE(), trainprovider, eval_data=evalprovider, n_epoch = 500)
 
 # obtain predictions
-fit = mx.predict(model, evalprovider)
+plotprovider = mx.ArrayDataProvider(:data => ValidationInput, :label => ValidationOutput)
+fit = mx.predict(model, plotprovider)
 plot(ValidationOutput,fit',".")
 xlabel("true")
 ylabel("predicted")
 title("outputs: true versus predicted. 45º line is what we hope for")
-