spark-instrumented-optimizer/docs/mllib-guide.md

layout	title
global	Machine Learning Library (MLlib)

• Table of contents {:toc}

MLlib is a Spark implementation of some common machine learning (ML) functionality, as well associated tests and data generators. MLlib currently supports four common types of machine learning problem settings, namely, binary classification, regression, clustering and collaborative filtering, as well as an underlying gradient descent optimization primitive. This guide will outline the functionality supported in MLlib and also provides an example of invoking MLlib.

Dependencies

MLlib uses the jblas linear algebra library, which itself depends on native Fortran routines. You may need to install the gfortran runtime library if it is not already present on your nodes. MLlib will throw a linking error if it cannot detect these libraries automatically.

To use MLlib in Python, you will also need NumPy version 1.7 or newer.

Binary Classification

Binary classification is a supervised learning problem in which we want to classify entities into one of two distinct categories or labels, e.g., predicting whether or not emails are spam. This problem involves executing a learning Algorithm on a set of labeled examples, i.e., a set of entities represented via (numerical) features along with underlying category labels. The algorithm returns a trained Model that can predict the label for new entities for which the underlying label is unknown.

MLlib currently supports two standard model families for binary classification, namely Linear Support Vector Machines (SVMs) and Logistic Regression, along with L1 and L2 regularized variants of each model family. The training algorithms all leverage an underlying gradient descent primitive (described below), and take as input a regularization parameter (regParam) along with various parameters associated with gradient descent (stepSize, numIterations, miniBatchFraction).

Available algorithms for binary classification:

• SVMWithSGD
• LogisticRegressionWithSGD

Linear Regression

Linear regression is another classical supervised learning setting. In this problem, each entity is associated with a real-valued label (as opposed to a binary label as in binary classification), and we want to predict labels as closely as possible given numerical features representing entities. MLlib supports linear regression as well as L1 (lasso) and L2 (ridge) regularized variants. The regression algorithms in MLlib also leverage the underlying gradient descent primitive (described below), and have the same parameters as the binary classification algorithms described above.

Available algorithms for linear regression:

• LinearRegressionWithSGD
• RidgeRegressionWithSGD
• LassoWithSGD

Clustering

Clustering is an unsupervised learning problem whereby we aim to group subsets of entities with one another based on some notion of similarity. Clustering is often used for exploratory analysis and/or as a component of a hierarchical supervised learning pipeline (in which distinct classifiers or regression models are trained for each cluster). MLlib supports k-means clustering, one of the most commonly used clustering algorithms that clusters the data points into predfined number of clusters. The MLlib implementation includes a parallelized variant of the k-means++ method called kmeans||. The implementation in MLlib has the following parameters:

• k is the number of desired clusters.
• maxIterations is the maximum number of iterations to run.
• initializationMode specifies either random initialization or initialization via k-means||.
• runs is the number of times to run the k-means algorithm (k-means is not guaranteed to find a globally optimal solution, and when run multiple times on a given dataset, the algorithm returns the best clustering result).
• initializiationSteps determines the number of steps in the k-means|| algorithm.
• epsilon determines the distance threshold within which we consider k-means to have converged.

Available algorithms for clustering:

• KMeans

Collaborative Filtering

Collaborative filtering is commonly used for recommender systems. These techniques aim to fill in the missing entries of a user-item association matrix. MLlib currently supports model-based collaborative filtering, in which users and products are described by a small set of latent factors that can be used to predict missing entries. In particular, we implement the alternating least squares (ALS) algorithm to learn these latent factors. The implementation in MLlib has the following parameters:

• numBlocks is the number of blacks used to parallelize computation (set to -1 to auto-configure).
• rank is the number of latent factors in our model.
• iterations is the number of iterations to run.
• lambda specifies the regularization parameter in ALS.
• implicitPrefs specifies whether to use the explicit feedback ALS variant or one adapted for implicit feedback data
• alpha is a parameter applicable to the implicit feedback variant of ALS that governs the baseline confidence in preference observations

Explicit vs Implicit Feedback

The standard approach to matrix factorization based collaborative filtering treats the entries in the user-item matrix as explicit preferences given by the user to the item.

It is common in many real-world use cases to only have access to implicit feedback (e.g. views, clicks, purchases, likes, shares etc.). The approach used in MLlib to deal with such data is taken from Collaborative Filtering for Implicit Feedback Datasets. Essentially instead of trying to model the matrix of ratings directly, this approach treats the data as a combination of binary preferences and confidence values. The ratings are then related to the level of confidence in observed user preferences, rather than explicit ratings given to items. The model then tries to find latent factors that can be used to predict the expected preference of a user for an item.

Available algorithms for collaborative filtering:

• ALS

Gradient Descent Primitive

Gradient descent (along with stochastic variants thereof) are first-order optimization methods that are well-suited for large-scale and distributed computation. Gradient descent methods aim to find a local minimum of a function by iteratively taking steps in the direction of the negative gradient of the function at the current point, i.e., the current parameter value. Gradient descent is included as a low-level primitive in MLlib, upon which various ML algorithms are developed, and has the following parameters:

• gradient is a class that computes the stochastic gradient of the function being optimized, i.e., with respect to a single training example, at the current parameter value. MLlib includes gradient classes for common loss functions, e.g., hinge, logistic, least-squares. The gradient class takes as input a training example, its label, and the current parameter value.
• updater is a class that updates weights in each iteration of gradient descent. MLlib includes updaters for cases without regularization, as well as L1 and L2 regularizers.
• stepSize is a scalar value denoting the initial step size for gradient descent. All updaters in MLlib use a step size at the t-th step equal to stepSize / sqrt(t).
• numIterations is the number of iterations to run.
• regParam is the regularization parameter when using L1 or L2 regularization.
• miniBatchFraction is the fraction of the data used to compute the gradient at each iteration.

Available algorithms for gradient descent:

• GradientDescent

Using MLLib in Scala

Following code snippets can be executed in spark-shell.

Binary Classification

The following code snippet illustrates how to load a sample dataset, execute a training algorithm on this training data using a static method in the algorithm object, and make predictions with the resulting model to compute the training error.

{% highlight scala %} import org.apache.spark.SparkContext import org.apache.spark.mllib.classification.SVMWithSGD import org.apache.spark.mllib.regression.LabeledPoint

// Load and parse the data file val data = sc.textFile("mllib/data/sample_svm_data.txt") val parsedData = data.map { line => val parts = line.split(' ') LabeledPoint(parts(0).toDouble, parts.tail.map(x => x.toDouble).toArray) }

// Run training algorithm to build the model val numIterations = 20 val model = SVMWithSGD.train(parsedData, numIterations)

// Evaluate model on training examples and compute training error val labelAndPreds = parsedData.map { point => val prediction = model.predict(point.features) (point.label, prediction) } val trainErr = labelAndPreds.filter(r => r._1 != r._2).count.toDouble / parsedData.count println("Training Error = " + trainErr) {% endhighlight %}

The SVMWithSGD.train() method by default performs L2 regularization with the regularization parameter set to 1.0. If we want to configure this algorithm, we can customize SVMWithSGD further by creating a new object directly and calling setter methods. All other MLlib algorithms support customization in this way as well. For example, the following code produces an L1 regularized variant of SVMs with regularization parameter set to 0.1, and runs the training algorithm for 200 iterations.

{% highlight scala %} import org.apache.spark.mllib.optimization.L1Updater

val svmAlg = new SVMWithSGD() svmAlg.optimizer.setNumIterations(200) .setRegParam(0.1) .setUpdater(new L1Updater) val modelL1 = svmAlg.run(parsedData) {% endhighlight %}

Linear Regression

The following example demonstrate how to load training data, parse it as an RDD of LabeledPoint. The example then uses LinearRegressionWithSGD to build a simple linear model to predict label values. We compute the Mean Squared Error at the end to evaluate goodness of fit

{% highlight scala %} import org.apache.spark.mllib.regression.LinearRegressionWithSGD import org.apache.spark.mllib.regression.LabeledPoint

// Load and parse the data val data = sc.textFile("mllib/data/ridge-data/lpsa.data") val parsedData = data.map { line => val parts = line.split(',') LabeledPoint(parts(0).toDouble, parts(1).split(' ').map(x => x.toDouble).toArray) }

// Building the model val numIterations = 20 val model = LinearRegressionWithSGD.train(parsedData, numIterations)

// Evaluate model on training examples and compute training error val valuesAndPreds = parsedData.map { point => val prediction = model.predict(point.features) (point.label, prediction) } val MSE = valuesAndPreds.map{ case(v, p) => math.pow((v - p), 2)}.reduce(_ + _)/valuesAndPreds.count println("training Mean Squared Error = " + MSE) {% endhighlight %}

Similarly you can use RidgeRegressionWithSGD and LassoWithSGD and compare training Mean Squared Errors.

Clustering

In the following example after loading and parsing data, we use the KMeans object to cluster the data into two clusters. The number of desired clusters is passed to the algorithm. We then compute Within Set Sum of Squared Error (WSSSE). You can reduce this error measure by increasing k. In fact the optimal k is usually one where there is an "elbow" in the WSSSE graph.

{% highlight scala %} import org.apache.spark.mllib.clustering.KMeans

// Load and parse the data val data = sc.textFile("kmeans_data.txt") val parsedData = data.map( .split(' ').map(.toDouble))

// Cluster the data into two classes using KMeans val numIterations = 20 val numClusters = 2 val clusters = KMeans.train(parsedData, numClusters, numIterations)

// Evaluate clustering by computing Within Set Sum of Squared Errors val WSSSE = clusters.computeCost(parsedData) println("Within Set Sum of Squared Errors = " + WSSSE) {% endhighlight %}

Collaborative Filtering

In the following example we load rating data. Each row consists of a user, a product and a rating. We use the default ALS.train() method which assumes ratings are explicit. We evaluate the recommendation model by measuring the Mean Squared Error of rating prediction.

{% highlight scala %} import org.apache.spark.mllib.recommendation.ALS import org.apache.spark.mllib.recommendation.Rating

// Load and parse the data val data = sc.textFile("mllib/data/als/test.data") val ratings = data.map(_.split(',') match { case Array(user, item, rate) => Rating(user.toInt, item.toInt, rate.toDouble) })

// Build the recommendation model using ALS val numIterations = 20 val model = ALS.train(ratings, 1, 20, 0.01)

// Evaluate the model on rating data val usersProducts = ratings.map{ case Rating(user, product, rate) => (user, product)} val predictions = model.predict(usersProducts).map{ case Rating(user, product, rate) => ((user, product), rate) } val ratesAndPreds = ratings.map{ case Rating(user, product, rate) => ((user, product), rate) }.join(predictions) val MSE = ratesAndPreds.map{ case ((user, product), (r1, r2)) => math.pow((r1- r2), 2) }.reduce(_ + _)/ratesAndPreds.count println("Mean Squared Error = " + MSE) {% endhighlight %}

If the rating matrix is derived from other source of information (i.e., it is inferred from other signals), you can use the trainImplicit method to get better results.

{% highlight scala %} val model = ALS.trainImplicit(ratings, 1, 20, 0.01) {% endhighlight %}

Using MLLib in Java

All of MLlib's methods use Java-friendly types, so you can import and call them there the same way you do in Scala. The only caveat is that the methods take Scala RDD objects, while the Spark Java API uses a separate JavaRDD class. You can convert a Java RDD to a Scala one by calling .rdd() on your JavaRDD object.

Using MLLib in Python

Following examples can be tested in the PySpark shell.

Binary Classification

The following example shows how to load a sample dataset, build Logistic Regression model, and make predictions with the resulting model to compute the training error.

{% highlight python %} from pyspark.mllib.classification import LogisticRegressionWithSGD from numpy import array

Load and parse the data

data = sc.textFile("mllib/data/sample_svm_data.txt") parsedData = data.map(lambda line: array([float(x) for x in line.split(' ')])) model = LogisticRegressionWithSGD.train(parsedData)

Build the model

labelsAndPreds = parsedData.map(lambda point: (int(point.item(0)), model.predict(point.take(range(1, point.size)))))

Evaluating the model on training data

trainErr = labelsAndPreds.filter(lambda (v, p): v != p).count() / float(parsedData.count()) print("Training Error = " + str(trainErr)) {% endhighlight %}

Linear Regression

The following example demonstrate how to load training data, parse it as an RDD of LabeledPoint. The example then uses LinearRegressionWithSGD to build a simple linear model to predict label values. We compute the Mean Squared Error at the end to evaluate goodness of fit

{% highlight python %} from pyspark.mllib.regression import LinearRegressionWithSGD from numpy import array

Load and parse the data

data = sc.textFile("mllib/data/ridge-data/lpsa.data") parsedData = data.map(lambda line: array([float(x) for x in line.replace(',', ' ').split(' ')]))

Build the model

model = LinearRegressionWithSGD.train(parsedData)

Evaluate the model on training data

valuesAndPreds = parsedData.map(lambda point: (point.item(0), model.predict(point.take(range(1, point.size))))) MSE = valuesAndPreds.map(lambda (v, p): (v - p)**2).reduce(lambda x, y: x + y)/valuesAndPreds.count() print("Mean Squared Error = " + str(MSE)) {% endhighlight %}

Clustering

In the following example after loading and parsing data, we use the KMeans object to cluster the data into two clusters. The number of desired clusters is passed to the algorithm. We then compute Within Set Sum of Squared Error (WSSSE). You can reduce this error measure by increasing k. In fact the optimal k is usually one where there is an "elbow" in the WSSSE graph.

{% highlight python %} from pyspark.mllib.clustering import KMeans from numpy import array from math import sqrt

Load and parse the data

data = sc.textFile("kmeans_data.txt") parsedData = data.map(lambda line: array([float(x) for x in line.split(' ')]))

Build the model (cluster the data)

clusters = KMeans.train(parsedData, 2, maxIterations=10, runs=30, initialization_mode="random")

Evaluate clustering by computing Within Set Sum of Squared Errors

def error(point): center = clusters.centers[clusters.predict(point)] return sqrt(sum([x**2 for x in (point - center)]))

WSSSE = parsedData.map(lambda point: error(point)).reduce(lambda x, y: x + y) print("Within Set Sum of Squared Error = " + str(WSSSE)) {% endhighlight %}

Similarly you can use RidgeRegressionWithSGD and LassoWithSGD and compare training Mean Squared Errors.

Collaborative Filtering

In the following example we load rating data. Each row consists of a user, a product and a rating. We use the default ALS.train() method which assumes ratings are explicit. We evaluate the recommendation by measuring the Mean Squared Error of rating prediction.

{% highlight python %} from pyspark.mllib.recommendation import ALS from numpy import array

Load and parse the data

data = sc.textFile("mllib/data/als/test.data") ratings = data.map(lambda line: array([float(x) for x in line.split(',')]))

Build the recommendation model using Alternating Least Squares

model = ALS.train(ratings, 1, 20)

Evaluate the model on training data

testdata = ratings.map(lambda p: (int(p[0]), int(p[1]))) predictions = model.predictAll(testdata).map(lambda r: ((r[0], r[1]), r[2])) ratesAndPreds = ratings.map(lambda r: ((r[0], r[1]), r[2])).join(predictions) MSE = ratesAndPreds.map(lambda r: (r[1][0] - r[1][1])**2).reduce(lambda x, y: x + y)/ratesAndPreds.count() print("Mean Squared Error = " + str(MSE)) {% endhighlight %}

If the rating matrix is derived from other source of information (i.e., it is inferred from other signals), you can use the trainImplicit method to get better results.

{% highlight python %}

Build the recommendation model using Alternating Least Squares based on implicit ratings

model = ALS.trainImplicit(ratings, 1, 20) {% endhighlight %}