CNTK 106 Tutorial – Time Series prediction with LSTM using C#


In this post will show how to implement CNTK 106 Tutorial in C#. This tutorial lecture is written in Python and there is no related example in C#. For this reason I decided to translate this very good tutorial into C#. The tutorial can be found at: CNTK 106: Part A – Time series prediction with LSTM (Basics)  and uses sin wave function in order to predict time series data. For this problem the Long Short Term Memory, LSTM, Recurrent Neural Network is used.

Goal

The goal of this tutorial is prediction the simulated data of a continuous function ( sin wave). From N previous values of the y=sin(t) function where y is the observed amplitude signal at time t, prediction of  M values of y is going to predict for the corresponding future time points.

The excitement of this tutorial is using the LSTM recurrent neural network which is nicely suited for this kind of problems. As you probably know LSTM is special recurrent neural network which has ability to learn from its experience during the training. More information about this fantastic version of recurrent neural network can be found here.

The blog post is divided into several sub-sections:

  1. Simulated data part
  2. LSTM Network
  3. Model training and evaluation

Since the simulated data set is huge, the original tutorial has two running mode which is described by the variable isFast. In case of fast mode, the variable is set to True, and this mode will be used in this tutorial. Later, the reader may change the value to False in order to see much better training model, but the training time will be much longer. The Demo for this this blog post exposes variables of the batch size and iteration number to the user, so the user may defined those numbers as he/she want.

Data generation

In order to generate simulated sin wave data, we are going to implement several helper methods. Let N and M  be a ordered set of past values and future (desired predicted values) of the sine wave, respectively. The two methods are implemented:

  1. generateWaveDataset()

The generateWaveDataset takes the periodic function,set of independent values (which is corresponded the time for this case) and generate the wave function, by providing the time steps and time shift. The method is related to the generate_data() python methods from the original tutorial.

static Dictionary<string, (float[][] train, float[][] valid, float[][] test)> loadWaveDataset(Func<double, double> fun, float[] x0, int timeSteps, int timeShift)
{
    ////fill data
    float[] xsin = new float[x0.Length];//all data
    for (int l = 0; l < x0.Length; l++)
        xsin[l] = (float)fun(x0[l]);


    //split data on training and testing part
    var a = new float[xsin.Length - timeShift];
    var b = new float[xsin.Length - timeShift];

    for (int l = 0; l < xsin.Length; l++)
    {
        //
        if (l < xsin.Length - timeShift) a[l] = xsin[l]; // if (l >= timeShift)
            b[l - timeShift] = xsin[l];
    }

    //make arrays of data
    var a1 = new List<float[]>();
    var b1 = new List<float[]>();
    for (int i = 0; i < a.Length - timeSteps + 1; i++)
    {
        //features
        var row = new float[timeSteps];
        for (int j = 0; j < timeSteps; j++)
            row[j] = a[i + j];
        //create features row
        a1.Add(row);
        //label row
        b1.Add(new float[] { b[i + timeSteps - 1] });
    }

    //split data into train, validation and test data set
    var xxx = splitData(a1.ToArray(), 0.1f, 0.1f);
    var yyy = splitData(b1.ToArray(), 0.1f, 0.1f);


    var retVal = new Dictionary<string, (float[][] train, float[][] valid, float[][] test)>();
    retVal.Add("features", xxx);
    retVal.Add("label", yyy);
    return retVal;
}

Once the data is generated, three datasets should be created: train, validate and test dataset, which are generated by splitting the dataset generated by the above method. The following splitData method splits the original sin wave dataset into three datasets,

static (float[][] train, float[][] valid, float[][] test) splitData(float[][] data, float valSize = 0.1f, float testSize = 0.1f)
{
    //calculate
    var posTest = (int)(data.Length * (1 - testSize));
    var posVal = (int)(posTest * (1 - valSize));

    return (data.Skip(0).Take(posVal).ToArray(), data.Skip(posVal).Take(posTest - posVal).ToArray(), data.Skip(posTest).ToArray());
}

In order to visualize the data, the Windows Forms project is created. Moreover, the ZedGraph .NET class library is used in order to visualize the data. The following picture shows the generated data.

Network modeling

As mentioned on the beginning of the blog post, we are going to create LSTM recurrent neural network, with 1 LSTM cell for each input. We have N inputs and each input is a value in our continuous function. The N outputs from the LSTM are the input into a dense layer that produces a single output. Between LSTM and dense layer we insert a dropout layer that randomly drops 20% of the values coming from the LSTM to prevent overfitting the model to the training dataset. We want use use the dropout layer during training but when using the model to make predictions we don’t want to drop values.

The description above can be illustrated on the following picture:

The implementation of the LSTM can be sumarize in one method, but the real implementation can be viewed in the demo sample which is attached with this blog post.
The following methods implements LSTM network depicted on the image above. The arguments for the method are already defined.

public static Function CreateModel(Variable input, int outDim, int LSTMDim, int cellDim, DeviceDescriptor device, string outputName)
{

    Func<Variable, Function> pastValueRecurrenceHook = (x) => CNTKLib.PastValue(x);

    //creating LSTM cell for each input variable
    Function LSTMFunction = LSTMPComponentWithSelfStabilization<float>(
        input,
        new int[] { LSTMDim },
        new int[] { cellDim },
        pastValueRecurrenceHook,
        pastValueRecurrenceHook,
        device).Item1;

    //after the LSTM sequence is created return the last cell in order to continue generating the network
    Function lastCell = CNTKLib.SequenceLast(LSTMFunction);

    //implement drop out for 10%
    var dropOut = CNTKLib.Dropout(lastCell,0.2, 1);

    //create last dense layer before output
    var outputLayer =  FullyConnectedLinearLayer(dropOut, outDim, device, outputName);

    return outputLayer;
}

Training the network

In order to train the model, the nextBatch() method is implemented that produces batches to feed the training function. Note that because CNTK supports variable sequence length, we must feed the batches as list of sequences. This is a convenience function to generate small batches of data often referred to as minibatch.

private static IEnumerable<(float[] X, float[] Y)> nextBatch(float[][] X, float[][] Y, int mMSize)
{

    float[] asBatch(float[][] data, int start, int count)
    {
        var lst = new List<float>();
        for (int i = start; i < start + count; i++) { if (i >= data.Length)
                break;

            lst.AddRange(data[i]);
        }
        return lst.ToArray();
    }

    for (int i = 0; i <= X.Length - 1; i += mMSize) { var size = X.Length - i; if (size > 0 && size > mMSize)
            size = mMSize;

        var x = asBatch(X, i, size);
        var y = asBatch(Y, i, size);

        yield return (x, y);
    }
}

Note: Since the this tutorial is implemented as WinForms C# project which can visualize training and testing datasets, as well as it  can show the best found model during the training process, there are lot of other implemented methods which are not mentioned here, but can be found in the demo source code attached in this blog post.

Key Insight

When working with LSTM the user should pay attention on the following:

Since LSTM must work with axes with unknown dimensions, the variables should be defined on different way as we could saw in the previous blog posts. So the input and the output variable are initialized with the following code listing:

// build the model
var feature = Variable.InputVariable(new int[] { inDim }, DataType.Float, featuresName, null, false /*isSparse*/);
var label = Variable.InputVariable(new int[] { ouDim }, DataType.Float, labelsName, new List<CNTK.Axis>() { CNTK.Axis.DefaultBatchAxis() }, false);

As specified in the original tutorial: “Specifying the dynamic axes enables the recurrence engine handle the time sequence data in the expected order. Please take time to understand how to work with both static and dynamic axes in CNTK as described here, the dynamic axes is key point in LSTM.
Now the implementation is continue with the defining learning rate, momentum, the learner and the trainer.

 
var lstmModel = LSTMHelper.CreateModel(feature, ouDim, hiDim, cellDim, device, "timeSeriesOutput");

Function trainingLoss = CNTKLib.SquaredError(lstmModel, label, "squarederrorLoss");
Function prediction = CNTKLib.SquaredError(lstmModel, label, "squarederrorEval");


// prepare for training
TrainingParameterScheduleDouble learningRatePerSample = new TrainingParameterScheduleDouble(0.0005, 1);
TrainingParameterScheduleDouble momentumTimeConstant = CNTKLib.MomentumAsTimeConstantSchedule(256);

IList<Learner> parameterLearners = new List<Learner>() {
    Learner.MomentumSGDLearner(lstmModel.Parameters(), learningRatePerSample, momentumTimeConstant, /*unitGainMomentum = */true)  };

//create trainer
var trainer = Trainer.CreateTrainer(lstmModel, trainingLoss, prediction, parameterLearners);

Now the code is ready, and the 10 epochs should return acceptable result:

 
// train the model
for (int i = 1; i <= iteration; i++)
{
    //get the next minibatch amount of data
    foreach (var miniBatchData in nextBatch(featureSet.train, labelSet.train, batchSize))
    {
        var xValues = Value.CreateBatch<float>(new NDShape(1, inDim), miniBatchData.X, device);
        var yValues = Value.CreateBatch<float>(new NDShape(1, ouDim), miniBatchData.Y, device);

        //Combine variables and data in to Dictionary for the training
        var batchData = new Dictionary<Variable, Value>();
        batchData.Add(feature, xValues);
        batchData.Add(label, yValues);

        //train minibarch data
        trainer.TrainMinibatch(batchData, device);
    }

    if (this.InvokeRequired)
    {
        // Execute the same method, but this time on the GUI thread
        this.Invoke(
            new Action(() =>
            {
                //output training process
                progressReport(trainer, lstmModel.Clone(), i, device);
            }
            ));
    }
    else
    {
        //output training process
        progressReport(trainer, lstmModel.Clone(), i, device);

    }             
}

Model Evaluation

Model evaluation is implemented during the training process. In this way we can see the learning process and how the model is getting better and better.

Fore each minibatch the progress method is called which updates the charts for the training and testing data set.

void progressReport(Trainer trainer, Function model, int iteration, DeviceDescriptor device)
{
    textBox3.Text = iteration.ToString();
    textBox4.Text = trainer.PreviousMinibatchLossAverage().ToString();
    progressBar1.Value = iteration;

    reportOnGraphs(trainer, model, iteration, device);
}

private void reportOnGraphs(Trainer trainer, Function model, int i, DeviceDescriptor device)
{
    currentModelEvaluation(trainer, model, i, device);
    currentModelTest(trainer, model, i, device);
}

The following picture shows the training process, where the model evaluation is shown simultaneously, for the training and testing data set.
Also the simulation of the Loss value during the training is simulated as well.

As can be see the blog post extends the original Tutorial with some handy tricks during the training process. Also this demo is good strarting point for development bether tool for LSTM Time Series training. The full source code of this blog post, which shows much more implementation than presented in the blog post can be found here.

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Deploy CNTK model to Excel using C#


In the last blog post, we saw how to save model state (checkpoint) in order to load it and train again. Also we have seen how to save model for the evaluation and testing. In fact we have seen how to prepare the model to be production ready.

Once we finish with the modelling process, we enter in to production phase, to install the model on place where we can use it for solving real world problems. This blog post is going to describe the process how deployed CNTK model can be exported to Excel like as AddIn and be used like ordinary Excel formula.

Preparing and deploying CNTK model

From the previous posts we saw how to train and save the model. This will be our starting point for this post.

Assume we trained and saved the model for evaluation from the previous blog post with file name as “IrisModel.model”. The model calculates Iris flower based on 4 input parameters, as we saw earlier.

  1. The first step is to create  .NET Class Library and install the following Nugget packages
    1. CNTK CPU Only ver. 2.3
    2. Excel Dna Addin
    3. Include saved IrisModel.model file in the project as Content and should be copied in Debug folder of the application.

As we can see, for this export we need Excel Dna Addin, fantastic library for making anything as Excel Addin. It can be install as Nuget package, and more information can be found at http://excel-dna.net/.

The following picture shows above 3 actions.

Once we prepare everything, we can start with the implementation of the Excel Addin.

  1. Change the Class.cs name into IrisModel.cs, and implement two methods:
    1. public static string IrisEval(object arg) and
    2. private static float EvaluateModel(float[] vector).

The first method is direct Excel function which will be called in the excel, and the second method is similar from the previous blog post for model evaluation. The following code snippet shows the implementation for the methods:

[ExcelFunction(Description = "IrisEval - Prediction for the Iris flower based on 4 input values.")]
public static string IrisEval(object arg)
{
    try
    {
        //First convert object in to array
        object[,] obj = (object[,])arg;

        //create list to convert values
        List<float> calculatedOutput = new List<float>();
        //
        foreach (var s in obj)
        {
            var ss = float.Parse(s.ToString(), CultureInfo.InvariantCulture);
            calculatedOutput.Add(ss);
        }
        if (calculatedOutput.Count != 4)
            throw new Exception("Incorrect number of input variables. It must be 4!");
        return EvaluateModel(calculatedOutput.ToArray());
    }
    catch (Exception ex)
    {
        return ex.Message;
    }

}
private static string EvaluateModel(float[] vector)
{
    //load the model from disk
    var ffnn_model = Function.Load(@"IrisModel.model", DeviceDescriptor.CPUDevice);

    //extract features and label from the model
    Variable feature = ffnn_model.Arguments[0];
    Variable label = ffnn_model.Output;

    Value xValues = Value.CreateBatch<float>(new int[] { feature.Shape[0] }, vector, DeviceDescriptor.CPUDevice);
    //Value yValues = - we don't need it, because we are going to calculate it

    //map the variables and values
    var inputDataMap = new Dictionary<Variable, Value>();
    inputDataMap.Add(feature, xValues);
    var outputDataMap = new Dictionary<Variable, Value>();
    outputDataMap.Add(label, null);

    //evaluate the model
    ffnn_model.Evaluate(inputDataMap, outputDataMap, DeviceDescriptor.CPUDevice);
    //extract the result  as one hot vector
    var outputData = outputDataMap[label].GetDenseData<float>(label);
    var actualLabels = outputData.Select(l => l.IndexOf(l.Max())).ToList();
    var flower = actualLabels.FirstOrDefault();
    var strFlower = flower == 0 ? "setosa" : flower == 1 ? "versicolor" : "virginica";
    return strFlower;
}<span style="display: inline-block; width: 0px; overflow: hidden; line-height: 0;" data-mce-type="bookmark" class="mce_SELRES_start"></span>

That is all we need for model evaluation in Excel.

Notice that the project must be build with the x64 architecture, and also installed Excel must be in x64 version.  This demo will not work in Excel 32 bits.

Rebuild the project and open Excel file with Iris Data set. You can use the file included in the demo project,  specially prepared for this blog post.

  • Got to Excel – > Options -> Addins,
    • Install the ExportCNTKToExcel-AddIn64-packed addin file.

  • Start typing the Excel  formula :
    • IrisEval(A1:D1) and press Enter. And the magic happen.

 

Complete source code for this blog post can be found here.

 

How to save CNTK model to file in C#


Final process of training is the model which should be used in the production as safe, reliable and accurate. Usually model training is frustrating and time consuming process, and it is not like we can see as demo to introduce with the library. Once the model is built with right combination of parameter values and network architecture, the process of modelling turn in to interesting and funny task, since it calculates the values just as we expect.

In most of the time, we have to save the current state of the model, and continue with training due to various reasons:

  • to change the parameters of the learner
  • to switch from one to another machine,
  • or to share the state of the model with your team mate,
  • to switch from CPU to GPU,
  • etc

In all above cases the current state of the model should be saved, and continue the training process from the last stage of the model. Because, the training from the beginning is not a solution, since we already invest time and knowledge to achieve progress of the model building.

The CNTK supports two kind of persisting the model.

  • production/ready or evaluation ready state, and
  • saving the checkpoint of the model for later training.

In the first case, the model is prepare for the evaluation and production but cannot be trained again, because it is freed from all other information but for the evaluation. During the saving process, only one files is generated.

In the second case, beside a model file, another file is generated with the name “modelname.ckp”. The file contains all information needed for the continuation of training.  Once the trainer  checkpoint is persisted we can continue with model training even if we changed the following:

  • the training data set with the same dimensions and data types
  • the parameters of the learner,
  • the learner

What we cannot change in order to continue with training is the the network model. In other words, the model must remain with the same number of layers, input and output dimensions.

Saving, loading and evaluating the model

Once the model is trained it can be persisted as separated file. As separate file, it can be loaded and evaluated with different dataset, but the number of the features and the label must remain the same as in case when was trained. Use this method when you want to share the model with someone else, or when you want to deploy the model in the production.

The model is saved simply by calling the CNTK method  Save:

public void SaveTrainedModel(Function model, string fileName)
{
    model.Save(fileName);
}

The model evaluation requires several steps:

  • load the model from the file,
  • extract the features and label from the model
  • call evaluate method from the model, by passing the batch created from the features, label and the evaluation dataset.

The model is loaded by calling Load method.

public Function LoadTrainedModel(string fileName, DeviceDescriptor device)
{
   return Function.Load(fileName, device, ModelFormat.CNTKv2);
}

Once the model is loaded, features and label are extracted from the model on the following way:

//load the mdoel from file
Function model = Function.Load(modelFile, device);
//extract features and label from the model
Variable feature = ffnn_model.Arguments[0];
Variable label = ffnn_model.Output;

The next step is creating the minibatch in order to pass the data to the evaluation.In this case we are going to create only one row for the Iris example of:

//Example: 5.0f, 3.5f, 1.3f, 0.3f, setosa
float[] xVal = new float[4] { 5.0f, 3.5f, 1.3f, 0.3f };
Value xValues = Value.CreateBatch<float>(new int[] {feature.Shape[0] }, xVal, device);
//Value yValues = - we don't need it, because we are going to calculate it

Once we created the variable and values we can map them and pass to the model evaluation, and calculate the result:

//map the variables and values
var inputDataMap = new Dictionary<Variable, Value>();
inputDataMap.Add(feature,xValues);
var outputDataMap = new Dictionary<Variable, Value>();
outputDataMap.Add(label, null);
//evaluate the model
ffnn_model.Evaluate(inputDataMap, outputDataMap, device);
//extract the result  as one hot vector
var outputData = outputDataMap[label].GetDenseData<float>(label);

The evaluation result should be transformed to proper format, and compared with expected result:

//transforms into class value
var actualLabels = outputData.Select(l => l.IndexOf(l.Max())).ToList();
var flower = actualLabels.FirstOrDefault();
var strFlower = flower == 0 ? "setosa" : flower == 1 ? "versicolor" : "versicolor";
Console.WriteLine($"Model Prediction: Input({xVal[0]},{xVal[1]},{xVal[2]},{xVal[3]}), Iris Flower={strFlower}");
Console.WriteLine($"Model Expectation: Input({xVal[0]},{xVal[1]},{xVal[2]},{xVal[3]}), Iris Flower= setosa");

Training previous saved model

Training previously saved model is very simple, since it requires no special coding. Right after the trainer is created with all necessary stuff (network, learning rate, momentum and other),
you just need to call

 trainer.RestoreFromCheckpoint(strIrisFilePath);

No additional code should be added.
The above method is called, after you successfully saved the model state by calling

trainer.SaveCheckpoint(strIrisFilePath);

The method is usually called at the end of the training process.
Complete source code from this blog post can be found here.

How to setup learning rate per iteration in CTNK using C#


So far we have seen how to train and validate models in CNTK using C#. Also there many more details which should be revealed in order to better understand the CNTK library. One of the important feature not only in the CNTK but also in every DNN (deep neural networks) is the learning rate.

In ANN the learning rate is the number by which the derivative is multiply before it is subtracted by the weight. If the weight is decreased to much the loss function will be increased and the network will diverge. On the other hand if the weight is decreased to little the loss function will be changed little and the diverge progress will be to slow. So selecting the right value of the parameter is important. During the training process, the learning rate is usually defined as constant value. In CNTK the learning rate is defined as follow:

// set learning rate for the network
var learningRate = new TrainingParameterScheduleDouble(0.2, 1);

From the code above the learning rate is assign to 0.2 value per sample. This means whole training process will be done with the learning rate of 0.2.
The CNTK support dynamic changing of the learning rate.
Assume we want to setup different the learning rates so that from the fist to the 100 iterations the learning rate would be 0.2. From the 100 to 500 iterations we want the learning rate would be 0.1. Moreover, after the 500 iterations are completed and to he end of the iteration process, we want to setup the learning rate to 0.05.

Above said can be expressed:

lr1=0.2 , from 1 to 100 iterations

lr2= 0.1 from 100 to 500 iterations

lr3= 0.05 from 500 to the end of the searching process.

In case we want to setup the learning rate dynamically we need to use the PairSizeTDouble class in order to defined the learning rate. So for the above requirements the flowing code should be implemented:

PairSizeTDouble p1 = new PairSizeTDouble(2, 0.2);
PairSizeTDouble p2 = new PairSizeTDouble(10, 0.1);
PairSizeTDouble p3 = new PairSizeTDouble(1, 0.05);

var vp = new VectorPairSizeTDouble() { p1, p2, p3 };
var learningRatePerSample = new CNTK.TrainingParameterScheduleDouble(vp, 50);

First we need to defined PairSizeTDouble object for every learning rate value, with the integer number which will be multiply.
Once we define the rates, make a array of rate values by creating the VectorPairSizeTDouble object. Then the array is passed as the first argument in the TrainingParameterScheduleDouble method. The second argument of the method is multiplication number. So in the first rate value, the 2 is multiple with 50 which is 100, and denotes the iteration number. Similar multiplication are done in the other rate values.

Testing and Validation CNTK models using C#


…continue from the previous post.
Once the model is build and Loss and Validation functions are satisfied our expectation, we need to validate and test the model using the data which was not part of the training data set (unseen data). The model validation is very important because we want to see if our model is trained well,so that can evaluates unseen data approximately same as the training data. Otherwise the model which cannot predict the output is called overfitted model. Overfitting can happen when the model was trained long enough that shows very high performance for the training data set, but for the testing data evaluate bad results.
We will continue with the implementation from the prevision two posts, and implement model validation. After the model is trained, the model and the trainer are passed to the Evaluation method. The evaluation method loads the testing data and calculated the output using passed model. Then it compares calculated (predicted) values with the output from the testing data set and calculated the accuracy. The following source code shows the evaluation implementation.

private static void EvaluateIrisModel(Function ffnn_model, Trainer trainer, DeviceDescriptor device)
{
    var dataFolder = "Data";//files must be on the same folder as program
    var trainPath = Path.Combine(dataFolder, "testIris_cntk.txt");
    var featureStreamName = "features";
    var labelsStreamName = "label";

    //extract features and label from the model
    var feature = ffnn_model.Arguments[0];
    var label = ffnn_model.Output;

    //stream configuration to distinct features and labels in the file
    var streamConfig = new StreamConfiguration[]
        {
            new StreamConfiguration(featureStreamName, feature.Shape[0]),
            new StreamConfiguration(labelsStreamName, label.Shape[0])
        };

    // prepare testing data
    var testMinibatchSource = MinibatchSource.TextFormatMinibatchSource(
        trainPath, streamConfig, MinibatchSource.InfinitelyRepeat, true);
    var featureStreamInfo = testMinibatchSource.StreamInfo(featureStreamName);
    var labelStreamInfo = testMinibatchSource.StreamInfo(labelsStreamName);

    int batchSize = 20;
    int miscountTotal = 0, totalCount = 20;
    while (true)
    {
        var minibatchData = testMinibatchSource.GetNextMinibatch((uint)batchSize, device);
        if (minibatchData == null || minibatchData.Count == 0)
            break;
        totalCount += (int)minibatchData[featureStreamInfo].numberOfSamples;

        // expected labels are in the mini batch data.
        var labelData = minibatchData[labelStreamInfo].data.GetDenseData<float>(label);
        var expectedLabels = labelData.Select(l => l.IndexOf(l.Max())).ToList();

        var inputDataMap = new Dictionary<Variable, Value>() {
            { feature, minibatchData[featureStreamInfo].data }
        };

        var outputDataMap = new Dictionary<Variable, Value>() {
            { label, null }
        };

        ffnn_model.Evaluate(inputDataMap, outputDataMap, device);
        var outputData = outputDataMap[label].GetDenseData<float>(label);
        var actualLabels = outputData.Select(l => l.IndexOf(l.Max())).ToList();

        int misMatches = actualLabels.Zip(expectedLabels, (a, b) => a.Equals(b) ? 0 : 1).Sum();

        miscountTotal += misMatches;
        Console.WriteLine($"Validating Model: Total Samples = {totalCount}, Mis-classify Count = {miscountTotal}");

        if (totalCount >= 20)
            break;
    }
    Console.WriteLine($"---------------");
    Console.WriteLine($"------TESTING SUMMARY--------");
    float accuracy = (1.0F - miscountTotal / totalCount);
    Console.WriteLine($"Model Accuracy = {accuracy}");
    return;

}

The implemented method is called in the previous Training method.

 EvaluateIrisModel(ffnn_model, trainer, device);

As can be seen the model validation has shown that the model predicts the data with high accuracy, which is shown on the following picture.

This was the latest post in series of blog posts about using Feed forward neural networks to train the Iris data using CNTK and C#.

The full source code for all three samples can be found here.

Train Iris data by Batch using CNTK and C#


In the previous post we have seen how to train NN model by using MinibatchSource. Usually we should use it when we have large amount of data. In case of small amount of the data, all data can be loaded in memory, and all can be passed to each iteration in order to train the model. This blog post will implement this kind of feeding the trainer.
We will reused the previous implementation, so the starting point can be previous source code. For data loading we have to define a new method. The Iris data is stored in text format like the following:

sepal_length,sepal_width,petal_length,petal_width,species
5.1,3.5,1.4,0.2,setosa(1 0 0)
7.0,3.2,4.7,1.4,versicolor(0 1 0)
7.6,3.0,6.6,2.1,virginica(0 0 1)
...

The output column is encoded to 1-N-1 encoding rule we have seen previously.
The method will read all the data from the file, parse the data and create two float arrays:

  • float[] feature, and
  • float[] label.

As can be seen both arrays are 1D, which means all data will be inserted in 1D, because the CNTK requires so.  Since the data is in 1D array, we should also provide the dimensionality of the data so te CNTK can resolve what values for each features. The following listing shows the loading Iris data in two 1D array returned as tuple.

static (float[], float[]) loadIrisDataset(string filePath, int featureDim, int numClasses)
{
    var rows = File.ReadAllLines(filePath);
    var features = new List<float>();
    var label = new List<float>();
    for (int i = 1; i < rows.Length; i++)
    {
        var row = rows[i].Split(',');
        var input = new float[featureDim];
        for (int j = 0; j < featureDim; j++)
        {
            input[j] = float.Parse(row[j], CultureInfo.InvariantCulture);
        }
        var output = new float[numClasses];
        for (int k = 0; k < numClasses; k++)
        {
            int oIndex = featureDim + k;
            output[k] = float.Parse(row[oIndex], CultureInfo.InvariantCulture);
        }

        features.AddRange(input);
        label.AddRange(output);
    }

    return (features.ToArray(), label.ToArray());
}

Once the data is loaded we should change very little amount of the previous code in order to implement batching instead of using minibatchSource. At the beginning we provides several variable to define the NN model structure. Then we call the loadIrisDataset, and define xValues and yValues, which we use in order to create feature and label input variables. Then we create dictionary which connect the feature and labels with data values which we will pass to the trainer later.
The next code is the same as in the previous version in order to create NN model, Loss and Evaluation functions, and learning rate.

Then we create loop, for 800 iteration. Once the iteration reaches the maximum value the program outputs the model properties and terminates.
Above said it implemented in the following code.

public static void TrainIriswithBatch(DeviceDescriptor device)
{
    //data file path
    var iris_data_file = "Data/iris_with_hot_vector.csv";

    //Network definition
    int inputDim = 4;
    int numOutputClasses = 3;
    int numHiddenLayers = 1;
    int hidenLayerDim = 6;
    int sampleSize = 130;

    //load data in to memory
    var dataSet = loadIrisDataset(iris_data_file, inputDim, numOutputClasses);

    // build a NN model
    //define input and output variable
    var xValues = Value.CreateBatch<float>(new NDShape(1, inputDim), dataSet.Item1, device);
    var yValues    = Value.CreateBatch<float>(new NDShape(1, numOutputClasses), dataSet.Item2, device);

    // build a NN model
    //define input and output variable and connecting to the stream configuration
    var feature = Variable.InputVariable(new NDShape(1, inputDim), DataType.Float);
    var label = Variable.InputVariable(new NDShape(1, numOutputClasses), DataType.Float);

    //Combine variables and data in to Dictionary for the training
    var dic = new Dictionary<Variable, Value>();
    dic.Add(feature, xValues);
    dic.Add(label, yValues);

    //Build simple Feed Froward Neural Network model
    // var ffnn_model = CreateMLPClassifier(device, numOutputClasses, hidenLayerDim, feature, classifierName);
    var ffnn_model = createFFNN(feature, numHiddenLayers, hidenLayerDim, numOutputClasses, Activation.Tanh, "IrisNNModel", device);

    //Loss and error functions definition
    var trainingLoss = CNTKLib.CrossEntropyWithSoftmax(new Variable(ffnn_model), label, "lossFunction");
    var classError = CNTKLib.ClassificationError(new Variable(ffnn_model), label, "classificationError");

    // set learning rate for the network
    var learningRatePerSample = new TrainingParameterScheduleDouble(0.001125, 1);

    //define learners for the NN model
    var ll = Learner.SGDLearner(ffnn_model.Parameters(), learningRatePerSample);

    //define trainer based on ffnn_model, loss and error functions , and SGD learner
    var trainer = Trainer.CreateTrainer(ffnn_model, trainingLoss, classError, new Learner[] { ll });

    //Preparation for the iterative learning process
    //used 800 epochs/iterations. Batch size will be the same as sample size since the data set is small
    int epochs = 800;
    int i = 0;
    while (epochs > -1)
    {
        trainer.TrainMinibatch(dic, device);

        //print progress
        printTrainingProgress(trainer, i++, 50);

        //
        epochs--;
    }
    //Summary of training
    double acc = Math.Round((1.0 - trainer.PreviousMinibatchEvaluationAverage()) * 100, 2);
    Console.WriteLine($"------TRAINING SUMMARY--------");
    Console.WriteLine($"The model trained with the accuracy {acc}%");
}

If we run the code, the output will be the same as we got from the previous blog post example:

The full source code with training data can be downloaded
here.

Using CNTK 2.2 and Python to learn from Iris data


Now that we have setup CNTK 2.2 and Python we can start with first example. For the first time, we can take the Iris data. The data set has categorical output value which contains three classes : Sentosa, Virglica and Versicolor. The features consist of the 4 real value inputs. The Iris data set can be easily found on  the internet. One of the places is on http://kaggle.com

Usually, the Iris data is given in the flowing format:

Since we are going to use CNTK we should prepare the data in cntk file format, which is far from the format we can see on the previous image. This format has different structure and looks like on the flowing image:

The difference is obvious. To transform the previous file format in to the cntk format it tooks me several minutes and now we can continue with the implementation.

First, lets implement simple python function to read the cntk format. For the implementation we are going to use CNTK MinibatchSource, which is specially developed to handle file data. The flowing python code reads the file and return the MinibatchSource.

import cntk

# The data in the file must satisfied the following format:
# |labels 0 0 1 |features 2.1 7.0 2.2 - the format consist of 4 features and one 3 component hot vector
#represents the iris flowers
def create_reader(path, is_training, input_dim, num_label_classes):

#create the streams separately for the label and for the features
labelStream = cntk.io.StreamDef(field='label', shape=num_label_classes, is_sparse=False)
featureStream = cntk.io.StreamDef(field='features', shape=input_dim, is_sparse=False)

#create deserializer by providing the file path, and related streams
deserailizer = cntk.io.CTFDeserializer(path, cntk.io.StreamDefs(labels = labelStream, features = featureStream))

#create mini batch source as function return
mb = cntk.io.MinibatchSource(deserailizer, randomize = is_training, max_sweeps = cntk.io.INFINITELY_REPEAT if is_training else 1)
return mb

The code above take several arguments:

-path – the file path where the data is stored,

-is_training – Boolean variable which indicates if the data is for training or testing. In case of training the data will be randomized.

– input_dim, num_label_classes are the numbers of the input features and the output hot vector size. Those two arguments are important in order to properly parse the file.

The first method creates the two streams , which are passed as argument in order to create deserializer, and then for minibatchsource creation. The function returns minibatchsource object which the trainer uses for data handling.

Once that we implemented the data reader, we need the python function for model creation. For the Iris data set we are going to create 4-50-3 feed forward neural network, which consist of one input layer with 4 neurons, one hidden layer with 50 neurons and the output layer with 4 neurons. The hidden layer will contain tanh- activation function.

The function which creates the NN model will looks like on the flowing code snippet:

#model creation
# FFNN with one input, one hidden and one output layer 
def create_model(features, hid_dim, out_dim):
    #perform some initialization 
    with cntk.layers.default_options(init = cntk.glorot_uniform()):
        #hidden layer with hid_def number of neurons and tanh activation function
        h1=cntk.layers.Dense(hid_dim, activation= cntk.ops.tanh, name='hidLayer')(features)
        #output layer with out_dim neurons
        o = cntk.layers.Dense(out_dim, activation = None)(h1)
        return o

As can be seen Dense function creates the layer where the user has to specify the dimension of the layer, activation function and the input variable. When the hidden layer is created, input variable is set to the input data. The output layer is created for the hidden layer as input.

The one more helper function would be showing the progress of the learner. The flowing function takes the three arguments and prints the current status of the trainer.

# Function that prints the training progress
def print_training_progress(trainer, mb, frequency):
    training_loss = "NA"
    eval_error = "NA"

    if mb%frequency == 0:
        training_loss = trainer.previous_minibatch_loss_average
        eval_error = trainer.previous_minibatch_evaluation_average
        print ("Minibatch: {0}, Loss: {1:.4f}, Error: {2:.2f}%".format(mb, training_loss, eval_error*100))   
    return mb, training_loss, eval_error

Once we implemented all three functions we can start with CNTK learning on the Iris data.

At the beginning,  we have to specify some helper variable which we will use later.

#setting up the NN type
input_dim=4
hidden_dim = 50
num_output_classes=3
input = cntk.input_variable(input_dim)
label = cntk.input_variable(num_output_classes)

Create the reader for data batching.

# Create the reader to training data set
reader_train= create_reader("C:/sc/Offline/trainData_cntk.txt",True,input_dim, num_output_classes)

Then create the NN model, with Loss and Error functions:

#Create model and Loss and Error function
z= create_model(input, hidden_dim,num_output_classes);
loss = cntk.cross_entropy_with_softmax(z, label)
label_error = cntk.classification_error(z, label)

Then we defined how look like the trainer. The trainer will be with Stochastic Gradient Decadent learner, with learning rate of 0.2

# Instantiate the trainer object to drive the model training
learning_rate = 0.2
lr_schedule = cntk.learning_parameter_schedule(learning_rate)
learner = cntk.sgd(z.parameters, lr_schedule)
trainer = cntk.Trainer(z, (loss, label_error), [learner])

Now we need to defined parameters for learning, and showing results.

# Initialize the parameters for the trainer
minibatch_size = 120 #mini batch size will be full data set
num_iterations = 20 #number of iterations 

# Map the data streams to the input and labels.
input_map = {
label  : reader_train.streams.labels,
input  : reader_train.streams.features
} 
# Run the trainer on and perform model training
training_progress_output_freq = 1

plotdata = {"batchsize":[], "loss":[], "error":[]}

As can be seen the batchsize is set to dataset size which is typical for small data sets.  Since we defined minibach to dataset size, the iteration should be very small value since Iris data is very simple and the learner will find good result very fast.

Running the trainer looks very simple. For each iteration, the reader load the batch size amount of the data, and pass to the trainer. The trainer performs the learning process using SGD learner, and returns the Loss and the error value for the current iteration. Then we call print function to show the progress of the trainer.

for i in range(0, int(num_iterations)):
        # Read a mini batch from the training data file
        data=reader_train.next_minibatch(minibatch_size, input_map=input_map) 
        trainer.train_minibatch(data)
        batchsize, loss, error = print_training_progress(trainer, i, training_progress_output_freq)
        if not (loss == "NA" or error =="NA"):
            plotdata["batchsize"].append(batchsize)
            plotdata["loss"].append(loss)
            plotdata["error"].append(error)

Once the learning process completes, we can perform some result presentation.

# Plot the training loss and the training error
import matplotlib.pyplot as plt

plt.figure(1)
plt.subplot(211)
plt.plot(plotdata["batchsize"], plotdata["loss"], 'b--')
plt.xlabel('Minibatch number')
plt.ylabel('Loss')
plt.title('Minibatch run vs. Training loss')

plt.show()

plt.subplot(212)
plt.plot(plotdata["batchsize"], plotdata["error"], 'r--')
plt.xlabel('Minibatch number')
plt.ylabel('Label Prediction Error')
plt.title('Minibatch run vs. Label Prediction Error')
plt.show()

We plot the Loss and Error function converted in to total accuracy of the classifier. The folowing pictures shows those graphs.

The last part of the ML procedure is the testing or validating the model. FOr the Iris data set we prepare 20 samples which will be used for the testing. The code i similar to the previous, except we call create_reader with different file name. Then we try to evaluate the model and grab the Loss and error values, and print out.

# Read the training data
reader_test = create_reader("C:/sc/Offline/testData_cntk.txt",False, input_dim, num_output_classes)

test_input_map = {
    label  : reader_test.streams.labels,
    input  : reader_test.streams.features,
}

# Test data for trained model
test_minibatch_size = 20
num_samples = 20
num_minibatches_to_test = num_samples // test_minibatch_size
test_result = 0.0

for i in range(num_minibatches_to_test):
    
    data = reader_test.next_minibatch(test_minibatch_size,input_map = test_input_map)
    eval_error = trainer.test_minibatch(data)
    test_result = test_result + eval_error

# Average of evaluation errors of all test minibatches
print("Average test error: {0:.2f}%".format(test_result*100 / num_minibatches_to_test))

Full sample with python code and data set can be found here.