CNTK on .NET platform – my session at ATD 14

Advanced Technology Days 14, ATD14, is a two days conference organized by the Microsoft and MS Community in Zagreb the Capital of Croatia. My session about Microsoft Cognitive Toolkit, CNTK on .NET platform held on second day, and I was very happy to talk about this, since only two months ago .NET Core support has finally implemented in the library.

There were more demos that I had time to preset them, so at the end of this blog you can find link for all demos and presentation file. Also the information about data sets need to be downloaded prior to run examples are placed in the code.
The last demo about ANNdotNET you can find on https://bhrnjica.net/anndotnet
The demos and presentation file can be found at this location: https://1drv.ms/f/s!AgPZDj-_uxGLhY1pCCODeT03qK_T3A

See you next time,

How to visualize CNTK network in C#

When building deep learning models, it is often required to check the model for consistency and proper parameters definition. In ANNdotNET, ml network models are designed using Visual Network Designer (VND), so it is easy to see the network configuration. Beside VND, in ANNdotNET there are several visualization features on different level: network preparation, model training phase, post training evaluation, performance analysis, and export results. In this blog post we will learn how to use those features when working with deep learning models

Visualization during network preparation and model training

When preparing network and training parameters, we need information about data sets, input format and output type. This information is relevant for selecting what type of network model to configure, what types of layers we will use, and what learner to select. For example the flowing image shows  network configuration containing of 2 embedding layers, 3 dense layers and 2 dropout layers. This network configuration is used to train CNTK model for mushroom data set. As can be seen network layers are arranged as listbox items, and the user has possibility to see, on the highest level, how neural networks looks like, which layers are included in the network, and how many dimensions each layer is defined. This is very helpful, since it provides the way of building network very quickly and accurately, and it requires much less times in comparisons to use traditional way of coding the network in python, or other programming language.

ANNdotNET Network Settings page provides pretty much information about the network, input and output layers, what data set are defined, as well as whole network configuration arranged in layers. Beside network related information, the Network Settings tab page also provides the learning parameters for the network training. More about Visual Network Designer the ready can find on one of the previous blog post.

Since ANNdotNET implements MLEngine which is based on CNTK, so all CNTK related visualization features could be used. The CNTK  library provides rich set of visualizations. For example you can use Tensorboard in CNTK  for visualization not just computational graph, but also training history, model evaluation etc. Beside Tensorboard, CNTK provides logger module which uses Graphviz tool for visualizing network graph. The bad news of this is that all above features cannot be run on C#, since those implementation are available only in python.

This is one of the main reason why ANNdotNET provides rich set of visualizations for .NET platform. This includes: training history, model evaluation for training and validation data set, as well as model performance analysis. The following image show some of the visualization features: the training history (loss and evaluation) of minibatches during training of mushroom model:

Moreover, the following image shows evaluation of training and validation set for each iteration during training:

Those graphs are generated during training phase, so the user can see what is happening with the model.  This is of tremendous help, when deciding when to stop the training process, or are training parameters produce good model at all, or this can be helpful in case when can stop and change parameters values. In case we need to stop the training process immediately, ANNdotNET provides Stop command which stops training process at any time.

Model performance visualization

Once the model is trained, ANNdotNET provides performance analysis tool for all three types of ML problems: regression, binary and multi class classification.

Since the mushrooms project is binary ML problem the following image shows the performance of the trained model:

Using Graphviz to visualize CNTK network graph in C#

We have seen that ANNdotNET provides all types of visualizations CNTK models, and those features are provided by mouse click through the GUI interfaces. One more feature are coming to ANNdotNET v1.1 which uses Grpahviz to visualize CNTK network graph. The feature is implemented based on original CNTK python implementation with some modification and style.

In order to use Graphviz to visualize network computation graph the following requirements must be met:

• Install Graphviz on you machine.
• Register Graphviz path as system variable. (See image below)

Now that you have install Graphviz tool, you can generate nice image of your network model directly in ANNdotNET just by click on Graph button above the Visual Network Designer (see image 1).

Here is some of nice graphs which can be generate from ANNdotNET preclaculated models.

In case you like this nice visualization features go to http://github.com/bhrnjica/anndotnet, download the latest version from release section or just download the source code and try it with Visual Studio, but don’t forget to give a star.

In the next blog post I will show you how visualization of CNTK computational graph is implemented, so you will be able to use it in your custom solutions.

Export options in ANNdotNET

ANNdotNET v1.0 has been release a few weeks ago, and the feedback is very positive. Also up to now there is no any blocking or serious bug in the release which makes me very happy. For this blog post we are going through Export options in ANNdotNET.

The ANNdotNET supposed to be an application which can offer whole life-cycle for  machine learning project: from the defining raw data set, cleaning and features engineering, to training and evaluation of the model. Also with different mlconfig files within the same project, the user has ability to create as many ml configurations as wants. Once the user select the best ml configuration, and the training and evaluation process completes, the next step in ML project life-cycle is the model deployment/export.

Currently, ANNdotNET defines three export options:

• Export model result to CSV file,
• Export model and model result to Excel, and
• Export model in CNTK file format.

With those three export option, we can achieve many ML scenarios.

Export to CSV

Export to CSV provides exporting actual and predicted values of testing data set to comma separated txt file. In case the testing data set is not provided, the result of validation data set will exported. In case nor testing nor validation dataset are not provided the export process is terminated.

The export process starts by selecting appropriate mlconfig file. The network model must be trained prior to be exported.

Once the export process completes, the csv file is created on disk. We can import the exported result in Excel, and similar content will be shows as image below:

Exported result is shows in two columns. The actual and predicted values. In case the classification result is exported, in the header the information about class values are exported.

Export to Excel

Export to Excel option is more than just exporting the result. In fact, it is deployment of the model into Excel environment. Beside exporting all defined data sets (training, Validation, and Test) the model is also exported. Predicted values are calculated by using ANNdotNET Excel Add-in, which the model evaluation looks like calling ordinary Excel formula.  More information how it works can be found here.

Exported xlsx file can be opened, and the further analysis for the model and related data sets can be continued. The following image shows exported model for Concrete Slum Test example. Since only two data sets are defined (training and validation) those data sets are exported. As can be seen the predicted column is not filled, only the row is filled with the formula that must be evaluated by inserting equal sign “=” in front of the formula.

Once the formula is evaluated for the first row, we can use Excel trick to copy it on other rows.

The same situation is for other data sets separated in Excel Worksheets.

Export to CNTK

The last option allows to export CNTK trained model in CNTK format. Also ONNX format will be supported as soon as being available on CNTK for C# library. This option is handy in situation where trained CNTK model being evaluated in other solutions.

For this blog post, there is a short video which the reader can see all three options in actions.

Sentiment Analysis using ANNdotNET

The October 2018 issue of MSDN magazine brings the article “Sentiment Analysis Using CNTK” written by James McCaffrey. I was wondering if I can implement this solution in ANNdotNET as Dr. McCaffrey written in the magazine. Indeed I have implemented complete solution in less than 5 minutes.

In this blog post I am going to walk you through this very good and well written MSDN article example. I am not going to repeat the text written in the MSDN article, so it is recommendation to read the article first, and back here and implement the example in ANNdotNET. Since the ANNdotNET is GUI tool, it is interesting to see all great visualizations during the model training and evaluation. Also the ANNdotNET provides complete binary model evaluation by providing the confusion matrix, ROC Curve, and other binary performance parameters, this example makes more interesting and valuable to read.

Whole example is implemented in five steps.

Step 1: Prepare files and folder structure

First we need to create several folders and files in order to create empty annproject. This manual creation of folders are necessary because ANNdotNET v1.0 has not option to create Empty project. This will be added in the next version.

So first, create the following set of hierarchically ordered folders:

• SentimentAnalysis
• MoveReview
• data

The following figure shows this set of folder.

Only thing we need from the MSDN article is train and test data sets. The data can be downloaded from the MSDN sample: Code_McCaffreyTestRun1018.zip. Once the zip file is downloaded unzip the sample, and copy files: imdb_sparse_train_50w.txt and indb_sparse_test_50w.txt to data folder as image above shows.

Step 3: Create MoviewReview.ann and LSTM-Net.mlconfig files

• Open Notepad and create file with the following content:
```project:|Name:MovieReview |Type:NoRawData |MLConfigs:LSTM-Net
data:|RawData:MovieReview_rawdata.txt
```

Save file in SentimenAnalysis folder as MovieReview.ann. The following picture shows saved annproject file on disk.

Now open Notepad again, create a new empty file. The empty file is supposed to be  mlconfig file with the content shown below. Don’t worry about the content of the file, since all those details will be visible once we open it with ANNdotNET. If you want to know more about structure of the mlconfig file, please refer to this wiki page of the ANNdotNET project.

```configid:msdn-oct-2018-issue-sentiment-analysis-article
features:|x 129892 1
labels:|y 2 0
network:|Layer:Embedding 50 0 0 None 0 0 |Layer:LSTM 25 25 0 TanH 1 1 |Layer:Dense 2 0 0 Softmax 0 0
learning:|Type:AdamLearner |LRate:0.01 |Momentum:0.85 |Loss:CrossEntropyWithSoftmax |Eval:ClassificationAccuracy |L1:0 |L2:0
training:|Type:Default |BatchSize:250 |Epochs:400 |Normalization:0 |RandomizeBatch:0 |SaveWhileTraining:0 |FullTrainingSetEval:1 |ProgressFrequency:1 |ContinueTraining:0 |TrainedModel:
paths:|Training:data\imdb_sparse_train_50w.txt |Validation:data\imdb_sparse_test_50w.txt |Test:data\imdb_sparse_test_50w.txt |TempModels:temp_models |Models:models |Result:LSTM-Net_result.csv |Logs:log<span id="mce_SELREST_end" style="overflow:hidden;line-height:0;"></span>
```

The file should be saved in the MovieReview folder with LSTM-Net.mlconfig file name. The next image shows where mlconfig file is stored.

Step 4. Open annproject file with ANNdotNET GUI tool

Now we have setup everything in order to open and train sentiment analysis example with ANNdotNET. Since ANNdotNET implements MLEngine which is based on CNTK, data sets are compatible and can be read by the trainer. In order to get better result we have changed learning parameter a little bit. Instead of SGD we used AdamLearner.

In case you don’t have ANNdotNET tool installed on your machine, just go to release section and download the latest version. Or clone the GitHub repository and run it within the Visual Studio. All information about how to run ANNdotNET as standalone application or as the Visual Studio solution can be found at GitHub page https://github.com/bhrnjica/anndotnet.

After simple unzipping binaries of the ANNdotNET on your machine, run it by simply selecting anndotnet.wnd.exe file. Once the ANNdotNET is running, click the Open application command and select the MoveReview.ann file. In a second the application loads the project with corresponded mlconfig file. From the project explorer, click on LSTM-NET three item, and similar content as image below should be appeared.

Everything we have written into mlconfig file are now shown in the Network settings tab page.

1. Input layer with 129892 dimensions
2. Output layer with 2 dimension (binary problem)
3. Learning parameters:
1. AdamLearner, with 0.01 lr and 0.85 momentum,
2. Loss Function is CrossEntropywithSoftmax
3. Evaluation function is ClassificationAccuracy
4. NNetwork Designer shows typical LSTM recurrent network

Step 5. Training and Evaluation of the Example

Now that we reviewed the network settings, we can switch to the train tab page, and review the training parameters. Since we already setup training parameters in the mlconfig file, we don’t need to change anything.

Start training process by click on the Run application command. After some time we should see the following result:

If we switch to Evaluation page we can perform some statistics analysis in order to evaluate if the model is good or not. Once the evaluation tab page is shown, click on Refresh button to evaluate the model against training and validation data stets.

The left statistics are for the training dataset, and the left side is for the validation data set. As can be seen, the model perfectly predicted all data from the training data set, and about 70% of accuracy described the validation data set. Off cource, the model is not good as we expected for the production, but for this demonstration is good enough. There are also two buttons to show ROC curve, and other binary performance parameters, for both data sets, which the reader my taste.

That’s all needed in order to have complete Sentiment Analysis exemple setup and running. In case you want complete ANNdotNET project, it can be downloaded from here.

ANNdotNET v1.0 has been released

Half year ago, in this post announced the new open source project ANNdotNET, which was ANN part of the GPdotNET v4 – artificial intelligence tool. On that day I finished my new book about machine learning and genetic programming when also released the new version of GPdotNET V5.0 genetic programming tool, without ANN and other non GP related modules. Now my second big open source project achieved the first stable released.

ANNdotNET (http://github.com/bhrnjica/anndotnet) is deep learning tool on .NET platform, which has similar workflow as GPdotNET. Both projects share several modules, mostly for data preparation, and model evaluation since all that stuff are same.

ANNdotNET is project which is more than GUI tool, since it contains CMD tool, which can be part of bigger cloud solution. There are several key concepts of the project which is worth to mention here:

1. Machine Learning Configuration mlconfig file

The ANNdotNET is based on so called machine learning configuration file, where everything about data, training and learning parameters, as well as neural network layers are store in the file so called mlconfig file. Along mlconfig file, there are several other file types generated during development of the ml solution. The mlconfig file can be shared between cloud services in order to prepare and transform data, train, evaluate or export ml models. If you want to see more information about files in ANNdotNET you can look at the wiki page of the project. Since the mlconfig file is independent of the tool, it can be executed with GUI or CMD tool, or any other custom tool, implemented on anndotnet API.

2. Machine Learning Project Explorer

In order to start developing ml solution with ANNdotNET, the first thing you do is create annproject file, by selecting New option from the Application command. Under annproject the user can create as many mlconfig files as he/she want. The annproject and related mlconfig files are presented in the ML Project Explorer, where the user can manage them as ordinary list items.

3. ANNdotNET MLEngine – Machine Learning Engine

ANNdotNET introduces the ANNdotNET Machine Learning Engine (MLEngine) which is responsible for training and evaluation models defined in the mlconfig files.The ML Engine relies on Microsoft Cognitive Toolkit, CNTK open source library which is proved to be one of the best open source library for deep learning. Through all application’s components ML Engine exposed all great features of the CNTK e.g. GPU support for training and evaluation, different kind of learners, but also extends CNTK features with more Evaluation functions (RMSE, MSE, Classification Accuracy, Coefficient of Determination, etc.), Extended Mini-batch Sources, Trainer and Evaluation models.

MLEngine is build on top of CNTK and .NET, with ability to provide backed component for any cloud/on-premise  ML solution.

4. Visual Neural Network Designer

ML Engine also contains the implementation of neural network layers which supposed to be high level CNTK API very similar as layer implementation in Keras and other python based deep learning APIs. With this implementation the ANNdotNET implements the Visual Neural Network Designer called ANNdotNET NNDesigner which allows the user to design neural network configuration of any size with any type of the layers. In the first release the following layers are implemented:

• Normalization Layer – takes the numerical features and normalizes its values before getting to the network. More information can be found here.
• Dense – classic neural network layer with activation function,
• LSTM – LSTM layer with option for peephole and self-stabilization.
• Embedding – Embedding layer.
• Drop – drop layer.

More layer types will be added in the future release. More information about Visual Network Designer can be found on previous blog post.

5. Data Transformation

Along the ml related stuff, ANNdotNET implement set of components for data transformation from raw dataset into mlready datasets. The user doesn’t worry about complex CNTK file format, one-hot encoding, and other data and variable transformation e.g handling missing values, data normalization etc. Data transformation starts loading raw data file into ANNdotNET, then with set of GUI related options the data can be completely prepared to mlready dataset. There are set of short videos about how to quickly transform raw dataset into mlready dataset.

5. Model Evaluation, Saving Good Models & Retraining Trained Models

Once the model is trained, ANNdotNET provides basic evaluation tool for evaluating trained models. The MLEvaluator contains set of basic options in order to evaluate regression, binary or multi-class classification models. Without leaving ANNdotNET the user has ability to decide if the model is good or not by performing set of statistics measures agains model and related datasets (training, validation and test). Beside evaluation, ANNdotNET offers instantly evaluation during training phase, by providing an option for saving good models during training phase. On this way ANNdotNET has ability to select best trained model regardless of the number of iterations. Different strategy for selecting the best model among set of saved models will be implemented in the future. Also any previous trained models can be trained again from the last check point. This is important option in various scenario. For example to change some parameters and continue training. Also this option has ability to start training model on one machine or environment, and then continue with training on different machine or environment.

Summary

ANNdotNET – is an open source project for deep learning on .NET Platform. This is complete GUI solution for data preparation, training, evaluation and deployment ml models. ANNdotNET introduces the ANNdotNET Machine Learning Engine ( `MLEngine`) which is responsible for training and evaluation models defined in the mlconfig files. The `MLEngine` relies on Microsoft Cognitive Toolkit, CNTK open source library which is proved to be one of the best open source library for deep learning. Through all application’s components `MLEngine` exposed all great features of the CNTK e.g. GPU support for training and evaluation, different kind of learners. `MLEngine` also extends CNTK features with more evaluation functions (RMSE, MSE, Classification Accuracy, Coefficient of Determination, etc.), Extended Mini-batch Sources, Trainer and Evaluation models.
The process of creating, training, evaluating and exporting models is provided from the GUI Application and does not require knowledge for supported programming languages.

The ANNdotNET is ideal in several scenarios:

• more focus on network development and training process using classic desktop approach, instead of focusing on coding,
• less time spending on debugging source code, more focusing on different configuration and parameter variants,
• ideal for engineers/users who are not familiar with programming languages,
• in case the problem requires coding custom models, or training process, ANNdotNET CMD provides high level of API for such implementation,
• all ml configurations developed with GUI tool,can be handled with CMD tool and vice versa.

In case you like this project star it on GitHub at http://github.com/bhrnjica/anndotnet. In case you want to use it in you academic paper, please cite it appropriate as specified at this link: https://doi.org/10.5281/zenodo.1461722

Brief Introduction to ANNdotNET

ANNdotNET – is an open source project for deep learning on .NET platform (.NET Framework and .NET Core). The project is hosted at http://github.com/bhrnjica/anndotnet with more information at the https://bhrnjica.net/anndotnet.

The project comes in two versions: GUI and CMD tool. The main purpose of the project is focus on building deep learning models without to be distracted with debugging the source code and installing/updating missing packages and environments. The user should no worry which version of ML Engine the application is using. In other words, the ANNdotNET is ideal in several scenarios:

1. more focus on network development and training process using classic desktop approach, instead of focusing on coding,
2. less time spending on debugging source code, more focusing on different configuration and parameter variants,
3. ideal for engineers/users who are not familiar with supported programming languages,
4. in case the problem requires coding more advanced custom models, or training process, ANNdotNET CMD provides high level of API for such implementation,
5. all ml configurations files generated with GUI tool, can be handled with CMD tool and vice versa.

With ANNdotNET GUI Tool the user can prepare data for training, by performing several actions: data cleaning, feature selection, category encoding, missing values handling, and create training and validation dataset prior to start building deep neural network. Once the data is prepared, the user can create Machine Learning Configuration (mlconfig) file in order to start building and training deep neural network. All previous actions user can handle using GUI tool implemented in the application.

For persisting information about data preparation and transformation actions, the application uses annproject file type which consists information about raw dataset, metadata information and information about mlconfig files.

The machine learning configurations are stored in separated files with mlconfig file extension. For more information about files in ANNdotNET the reader may open this link. The following image shows how ANNdotNET handles annproject and corresponded machine learning configurations within the annproject:

As can be seen the annproject can be consisted of arbitrary number of mlconfigs, which is typical scenario when working on ML Project. User can switch between mlconfigs any time except when the application is in training or evaluation mode.

ANNdotNET ML Engine

ANNdotNET introduces the ANNdotNET Machine Learning Engine (MLEngine) which is responsible for training and evaluation models defined in the mlconfig files.The ML Engine relies on Microsoft Cognitive Toolkit, CNTK open source library which is proved to be one of the best open source library for deep learning. Through all application ML Engine exposed all great features of the CNTK e.g. GPU support for training and evaluation, different kind of learners, but also extends CNTK features with more Evaluation functions (RMSE, MSE, Classification Accuracy, Coefficient of Determination, etc.), Extended Mini-batch Sources, Trainer and Evaluaton models.

ML Engine also contains the implementation of neural network layers which supposed to be high level CNTK API very similar as layer implementation in Keras and other python based deep learning APIs. With this implementation the ANNdotNET implements the Visual Neural Network Designer called ANNdotNET NNDesigner which allows the user to design neural network configuration of any size with any type of the layers. In the first release the following layers are implemented:

• Normalization Layer – takes the numerical features and normalizes its values before getting to the network. More information can be found here.
• Dense – classic neural network layer with activation function
• LSTM – LSTM layer with option for peephole and self-stabilization.
• Embedding – Embedding layer,
• Drop – drop layer.

More layer types will be added in the future release.

Designing the neural network can be simplify by using pre-defined layer. So on this way we can implement almost any network we usually implement through the source code.

How to use ANNdotNET NNDesigner

Once the MLConfig is created user can open it and start building neural network. NNDesigner is placed in the Network Setting tab page. The following image shows the Network Setting tab page.

NNetwork Designer contains combo box with supported NN layers, and two action buttons for adding and removing layers in/from the network. Adding and removing layers is simple as adding and removing items in/from the list box. In order to add a layer, select the item from the combo box, and press Add button. In order to remove the layer form the network, click the layer in the listbox and press Remove button, then confirm deletion. In order to successfully create the network, the last layer in the list must be created with the same output dimension as the Output layer shown on the left side of the window, otherwise the warning messages will appear about this information once the training is stared.

Once the layer is added to the list it must be configured. The layer configuration depends of its type . The main parameter for each layer is output dimension and activation function, except the drop and normalization layer. The following text explains parameters for all supported layers:

Normalization layer – does not require any parameter. The following image shows the normalization item in the NNDesigner. You can insert only one normalization layer, and it is positioned at the first place.

Drop layer – requires percentage drop value which is integer value. The following image shows how drop layer looks in the NNDesigner. There is no any constrains for this layer.

Embedding layer – requires only output dimension to be configured. There is no any constrains for the layer. The following image shows how it looks in the NNDesigner:

Dense layer – requires output dimension and activation function to be configured. There is no any constrains for the layer.

LSTM layer – requires: output and cell dimension, activation function, and two Boolean parameters to enable peephole and self-stabilization variant in the layer. The following image shows how LSTM item looks in the NNDesigner.

The LSTM layer has some constrains which is already implemented in the code. In case two LSTM layers are added in the network, the network becomes the Stacked LSTM which should be treated differently. Also all LSTM layers are inserted as stack, and they cannot be inserted on different places in the list. The implementation of the Stacked LSTM layer will be shown later.

Different network configurations

In this section, various network configuration will be listed, in order to show how easy is to use NNDesigner to create very complex neural network configurations. Network examples are implemented in pre-calculated examples which come with default ANNdotNET installation package.

Feed Forward network

This example shows how to implement Feed Forward network, with one hidden and one output layer which is the last layer in the NNDesinger. The example is part of the ANNdotNET installation package.

Feed Forward with Normalization layer

This example shows feed forward network with normalization layer as the first layer. The example of this configuration can be found in the installation package of the ANNdotNET.

Feed Forward Network with Embedding layers

In this example embedding layers are used in order to reduce the dimensions of the input layer. Network is configured with 3 embedding layers, one hidden and output layer. The example is part of the ANNdotNET installation package.

Deep Neural Network

This example shows deep neural network with three kind of layers: Embedding, Drop and Dense layers. The project is part of the ANNdotNET installation package.

LSTM Deep Neural Network

This example shows how to configure LSTM based network. The network consist of normalization, embedding, drop, dense and LSTM layers. The project is part of the ANNdotNET installation package.

Stacked LSTM Neural Network

This is example of Stacked LSTM network, consist of multiple LSTM layers connected into stack. The example is part of the installation package.

The complete list of examples can be seen at the ANNdotNET Start Page. In order to open the example, the user just need to click the link. Hope this project will be useful for many ml scenarios.

Linear Regression with CNTK and C#

CNTK is Microsoft’s deep learning tool for training very large and complex neural network models. However, you can use CNTK for various other purposes. In some of the previous posts we have seen how to use CNTK to perform matrix multiplication, in order to calculate descriptive statistics parameters on data set.
In this blog post we are going to implement simple linear regression model, LR. The model contains only one neuron. The model also contains bias parameters, so in total the linear regression has only two parameters: w and b.
The image below shows LR model:

The reason why we use the CNTK to solve such a simple task is very straightforward. Learning on simple models like this one, we can see how the CNTK library works, and see some of not-so-trivial actions in CNTK.
The model shown above can be easily extend to logistic regression model, by adding activation function. Besides the linear regression which represent the neural network configuration without activation function, the Logistic Regression is the simplest neural network configuration which includes activation function.

The following image shows logistic regression model:
In case you want to see more info about how to create Logistic Regression with CNTK, you can see this official demo example.
Now that we made some introduction to the neural network models, we can start by defining the data set. Assume we have simple data set which represent the simple linear function $y=2x+1$. The generated data set is shown in the following table:

We already know that the linear regression parameters for presented data set are: $b_0=1$ and $b_1=2$, so we want to engage the CNTK library in order to get those values, or at least parameter values which are very close to them.

All task about how the develop LR model by using CNTK can be described in several steps:

Step 1: Create C# Console application in Visual Studio, change the current architecture to $x64$, and add the latest “CNTK.GPU “ NuGet package in the solution. The following image shows those action performed in Visual Studio.

Step 2: Start writing code by adding two variables: $X$ – feature, and label $Y$. Once the variables are defined, start with defining the training data set by creating batch. The following code snippet shows how to create variables and batch, as well as how to start writing CNTK based C# code.

First we need to add some using statements, and define the device where computation will be happen. Usually, we can defined CPU or GPU in case the machine contains NVIDIA compatible graphics card. So the demo starts with the following cod snippet:

```using System;
using System.Linq;
using System.Collections.Generic;
using CNTK;
namespace LR_CNTK_Demo
{
class Program
{
static void Main(string[] args)
{
//Step 1: Create some Demo helpers
Console.Title = "Linear Regression with CNTK!";
Console.WriteLine("#### Linear Regression with CNTK! ####");
Console.WriteLine("");
//define device
var device = DeviceDescriptor.UseDefaultDevice();
```

Now define two variables, and data set presented in the previous table:

```//Step 2: define values, and variables
Variable x = Variable.InputVariable(new int[] { 1 }, DataType.Float, "input");
Variable y = Variable.InputVariable(new int[] { 1 }, DataType.Float, "output");

//Step 2: define training data set from table above
var xValues = Value.CreateBatch(new NDShape(1, 1), new float[] { 1f, 2f, 3f, 4f, 5f }, device);
var yValues = Value.CreateBatch(new NDShape(1, 1), new float[] { 3f, 5f, 7f, 9f, 11f }, device);
```

Step 3: Create linear regression network model, by passing input variable and device for computation. As we already discussed, the model consists of one neuron and one bias parameter. The following method implements LR network model:

```private static Function createLRModel(Variable x, DeviceDescriptor device)
{
//initializer for parameters
var initV = CNTKLib.GlorotUniformInitializer(1.0, 1, 0, 1);

//bias
var b = new Parameter(new NDShape(1,1), DataType.Float, initV, device, "b"); ;

//weights
var W = new Parameter(new NDShape(2, 1), DataType.Float, initV, device, "w");

//matrix product
var Wx = CNTKLib.Times(W, x, "wx");

//layer
var l = CNTKLib.Plus(b, Wx, "wx_b");

return l;
}
```

First, we create initializer, which will initialize startup values of network parameters. Then we defined bias and weight parameters, and join them in form of linear model “$wx+b$”, and returned as Function type. The createModel function is called in the main method. Once the model is created, we can exam it, and prove there are only two parameters in the model. The following code create the Linear Regression model, and print model parameters:

```//Step 3: create linear regression model
var lr = createLRModel(x, device);
//Network model contains only two parameters b and w, so we query
//the model in order to get parameter values
var paramValues = lr.Inputs.Where(z => z.IsParameter).ToList();
var totalParameters = paramValues.Sum(c => c.Shape.TotalSize);
Console.WriteLine(\$"LRM has {totalParameters} params, {paramValues[0].Name} and {paramValues[1].Name}.");
```

In the previous code, we have seen how to extract parameters from the model. Once we have parameters, we can change its values, or just print those values for the further analysis.

Step 4: Create Trainer, which will be used to train network parameters w and b. The following code snippet shows implementation of Trainer method.

```public Trainer createTrainer(Function network, Variable target)
{
//learning rate
var lrate = 0.082;
var lr = new TrainingParameterScheduleDouble(lrate);
//network parameters
var zParams = new ParameterVector(network.Parameters().ToList());

//create loss and eval
Function loss = CNTKLib.SquaredError(network, target);
Function eval = CNTKLib.SquaredError(network, target);

//learners
//
var llr = new List();
var msgd = Learner.SGDLearner(network.Parameters(), lr);

//trainer
var trainer = Trainer.CreateTrainer(network, loss, eval, llr);
//
return trainer;
}
```

First we defined learning rate the main neural network parameter. Then we create Loss and Evaluation functions. With those parameters we can create SGD learner. Once the SGD learner object is instantiated, the trainer is created by calling CreateTrainer static CNTK method, and passed it further as function return. The method createTrainer is called in the main method:

```//Step 4: create trainer
var trainer = createTrainer(lr, y);
```

Step 5: Training process: Once the variables, data set, network model and trainer are defined, the training process can be started.

```//Ştep 5: training
for (int i = 1; i <= 200; i++)
{
var d = new Dictionary();
//
trainer.TrainMinibatch(d, true, device);
//
var loss = trainer.PreviousMinibatchLossAverage();
var eval = trainer.PreviousMinibatchEvaluationAverage();
//
if (i % 20 == 0)
Console.WriteLine(\$"It={i}, Loss={loss}, Eval={eval}");

if(i==200)
{
//print weights
var b0_name = paramValues[0].Name;
var b0 = new Value(paramValues[0].GetValue()).GetDenseData(paramValues[0]);
var b1_name = paramValues[1].Name;
var b1 = new Value(paramValues[1].GetValue()).GetDenseData(paramValues[1]);
Console.WriteLine(\$" ");
Console.WriteLine(\$"Training process finished with the following regression parameters:");
Console.WriteLine(\$"b={b0[0][0]}, w={b1[0][0]}");
Console.WriteLine(\$" ");
}
}
}
```

As can be seen, in just 200 iterations, regression parameters got the values we almost expected $b_0=0.995$, and $w=2.005$. Since the training process is different than classic regression parameter determination, we cannot get exact values. In order to estimate regression parameters, the neural network uses iteration methods called Stochastic Gradient Decadent, SGD. On the other hand, classic regression uses regression analysis procedures by minimizing the least square error, and solve system equations where unknowns are b and w.
Once we implement all code above, we can start LR demo by pressing F5. Similar output window should be shown:

Hope this blog post can provide enough information to start with CNTK C# and Machine Learning. Source code for this blog post can be downloaded here.