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Machine learning algorithms with dart

Table of contents

What is the ml_algo for?

The main purpose of the library - to give developers, interested both in Dart language and data science, native Dart implementation of machine learning algorithms. This library targeted to dart vm, so, to get smoothest experience with the lib, please, do not use it in a browser.

Following algorithms are implemented:

  • Linear regression:

    • Gradient descent based linear regression
    • Coordinate descent based linear regression
  • Linear classifier:

    • Logistic regression
    • Softmax regression
  • Non-parametric regression:

    • KNN regression

The library's structure

  • Model selection

    • CrossValidator. Factory, that creates instances of a cross validator. Cross validation allows researchers to fit different hyperparameters of machine learning algorithms, assessing prediction quality on different parts of a dataset.
  • Classification algorithms

    • Linear classification
      • Logistic regression

        An algorithm, that performs linear binary classification.

        • LogisticRegressor.gradient. Logistic regression with gradient ascent optimization of log-likelihood cost function. To use this kind of classifier your data have to be linearly separable.

        • LogisticRegressor.coordinate. Not implemented yet. Logistic regression with coordinate descent optimization of negated log-likelihood cost function. Coordinate descent allows to do feature selection (aka L1 regularization) To use this kind of classifier your data have to be linearly separable.

      • Softmax regression

        An algorithm, that performs linear multiclass classification.

        • SoftmaxRegressor.gradient. Softmax regression with gradient ascent optimization of log-likelihood cost function. To use this kind of classifier your data have to be linearly separable.

        • SoftmaxRegressor.coordinate. Not implemented yet. Softmax regression with coordinate descent optimization of negated log-likelihood cost function. As in case of logistic regression, coordinate descent allows to do feature selection (aka L1 regularization) To use this kind of classifier your data have to be linearly separable.

  • Regression algorithms

    • Linear regression
      • LinearRegressor.gradient. A well-known algorithm, that performs linear regression using gradient vector of a cost function.

      • LinearRegressor.coordinate An algorithm, that uses coordinate descent in order to find optimal value of a cost function. Coordinate descent allows to perform feature selection along with regression process (This technique often calls Lasso regression).

    • Nonlinear regression
      • ParameterlessRegressor.knn An algorithm, that makes prediction for each new observation based on first k closest observations from training data. It has quite high computational complexity, but in the same time it may easily catch non-linear pattern of the data.

Examples

Logistic regression

Let's classify records from well-known dataset - Pima Indians Diabets Database via Logistic regressor

Import all necessary packages. First, it's needed to ensure, if you have ml_preprocessing package in your dependencies:

dependencies:
  ml_preprocessing: ^3.2.0

We need this repo to parse raw data in order to use it farther. For more details, please, visit ml_preprocessing repository page.

import 'dart:async';

import 'package:ml_algo/ml_algo.dart';
import 'package:ml_preprocessing/ml_preprocessing.dart';

Download dataset from Pima Indians Diabets Database and read it (of course, you should provide a proper path to your downloaded file):

final data = DataFrame.fromCsv('datasets/pima_indians_diabetes_database.csv', 
  labelName: 'class variable (0 or 1)');
final features = (await data.features)
      .mapColumns((column) => column.normalize()); // it's needed to normalize the matrix column-wise to reach 
                                                   // computational stability and provide uniform scale for all 
                                                   // the values in the column
final labels = await data.labels;

Data in this file is represented by 768 records and 8 features. 9th column is a label column, it contains either 0 or 1 on each row. This column is our target - we should predict a class label for each observation. Therefore, we should point, where to get label values. Let's use labelName parameter for that (labels column name, 'class variable (0 or 1)' in our case).

Processed features and labels are contained in data structures of Matrix type. To get more information about Matrix type, please, visit ml_linal repo

Then, we should create an instance of CrossValidator class for fitting hyperparameters of our model

final validator = CrossValidator.KFold(numberOfFolds: 5);

All are set, so, we can do our classification.

Evaluate our model via accuracy metric:

final accuracy = validator.evaluate((trainFeatures, trainLabels) => 
    LogisticRegressor.gradient(
        trainFeatures, trainLabels,
        initialLearningRate: .8,
        iterationsLimit: 500,
        batchSize: 768,
        fitIntercept: true,
        interceptScale: .1,
        learningRateType: LearningRateType.constant), 
    features, labels, MetricType.accuracy);

Let's print score:

print('accuracy on classification: ${accuracy.toStringAsFixed(2)}');

We will see something like this:

acuracy on classification: 0.77

All the code above all together:

import 'dart:async';

import 'package:ml_algo/ml_algo.dart';
import 'package:ml_preprocessing/ml_preprocessing.dart';

Future main() async {
  final data = DataFrame.fromCsv('datasets/pima_indians_diabetes_database.csv', 
     labelName: 'class variable (0 or 1)');
  final features = (await data.features).mapColumns((column) => column.normalize());
  final labels = await data.labels;
  final validator = CrossValidator.kFold(numberOfFolds: 5);
  final accuracy = validator.evaluate((trainFeatures, trainLabels) => 
    LogisticRegressor.gradient(
        trainFeatures, trainLabels,
        initialLearningRate: .8,
        iterationsLimit: 500,
        batchSize: 768,
        fitIntercept: true,
        interceptScale: .1,
        learningRateType: LearningRateType.constant), 
    features, labels, MetricType.accuracy);

  print('accuracy on classification: ${accuracy.toStringFixed(2)}');
}

Softmax regression

Let's classify another famous dataset - Iris dataset. Data in this csv is separated into 3 classes - therefore we need to use different approach to data classification - Softmax regression.

As usual, start with data preparation. Before we start, we should update our pubspec's dependencies with xrange` library:

dependencies:
    ...
    xrange: ^0.0.5
    ...

Download the file and read it:

final data = DataFrame.fromCsv('datasets/iris.csv',
    labelName: 'Species',
    columns: [ZRange.closed(1, 5)],
    categories: {
      'Species': CategoricalDataEncoderType.oneHot,
    },
);

final features = await data.features;
final labels = await data.labels;

The csv database has 6 columns, but we need to get rid of the first column, because it contains just ID of every observation - it's absolutely useless data. So, as you may notice, we provided a columns range to exclude ID-column:

columns: [ZRange.closed(1, 5)]

Also, since the label column 'Species' has categorical data, we encoded it to numerical format:

categories: {
  'Species': CategoricalDataEncoderType.oneHot,
},

Next step - create a cross validator instance:

final validator = CrossValidator.kFold(numberOfFolds: 5);

Evaluate quality of prediction:

final accuracy = validator.evaluate((trainFeatures, trainLabels) => 
      LinearClassifier.softmaxRegressor(
          trainFeatures, trainLabels,
          initialLearningRate: 0.03,
          iterationsLimit: null,
          minWeightsUpdate: 1e-6,
          randomSeed: 46,
          learningRateType: LearningRateType.constant
      ), features, labels, MetricType.accuracy);

print('Iris dataset, softmax regression: accuracy is '
  '${accuracy.toStringAsFixed(2)}'); // It yields 0.93

Gather all the code above all together:

import 'dart:async';

import 'package:ml_algo/ml_algo.dart';
import 'package:ml_preprocessing/ml_preprocessing.dart';
import 'package:xrange/zrange.dart';

Future main() async {
  final data = DataFrame.fromCsv('datasets/iris.csv',
    labelName: 'Species',
    columns: [ZRange.closed(1, 5)],
    categories: {
      'Species': CategoricalDataEncoderType.oneHot,
    },
  );

  final features = await data.features;
  final labels = await data.labels;
  final validator = CrossValidator.kFold(numberOfFolds: 5);
  final accuracy = validator.evaluate((trainFeatures, trainLabels) => 
      LinearClassifier.softmaxRegressor(
          trainFeatures, trainLabels,
          initialLearningRate: 0.03,
          iterationsLimit: null,
          minWeightsUpdate: 1e-6,
          randomSeed: 46,
          learningRateType: LearningRateType.constant
      ), features, labels, MetricType.accuracy);

  print('Iris dataset, softmax regression: accuracy is '
      '${accuracy.toStringAsFixed(2)}');
}

K nearest neighbour regression

Let's do some prediction with a well-known non-parametric regression algorithm - k nearest neighbours. Let's take a state of the art dataset - boston housing.

As usual, import all necessary packages

import 'dart:async';

import 'package:ml_algo/ml_algo.dart';
import 'package:ml_preprocessing/ml_preprocessing.dart';
import 'package:xrange/zrange.dart';

and download and read the data

final data = DataFrame.fromCsv('lib/_datasets/housing.csv',
    headerExists: false,
    fieldDelimiter: ' ',
    labelIdx: 13,
);

As you can see, the dataset is headless, that means, that there is no a descriptive line in the beginning of the file, hence we can just use the index-based approach to point, where the outcomes column resides (13 index in our case)

Extract features and labels

// As in example above, it's needed to normalize the matrix column-wise to reach computational stability and provide 
// uniform scale for all the values in the column
final features = (await data.features).mapColumns((column) => column.normalize());
final labels = await data.labels;

Create a cross-validator instance

final validator = CrossValidator.kFold(numberOfFolds: 5);

Let the k parameter be equal to 4.

Assess a knn regressor with the chosen k value using MAPE metric

final error = validator.evaluate((trainFeatures, trainLabels) => 
  ParameterlessRegressor.knn(trainFeatures, trainLabels, k: 4), features, labels, MetricType.mape);

Let's print our error

print('MAPE error on k-fold validation: ${error.toStringAsFixed(2)}%'); // it yields approx. 6.18

Contacts

If you have questions, feel free to write me on

Libraries

ml_algo