Machine Learning

Jean-LucCAUT-2016
Help Banks to detect Suspicious Transaction & Fraud

Jean-LucCAUT-2016
Introduction
Supervised learning models
Confusion matrix
Unsupervised models

Jean-LucCAUT-2016
Introduction
Supervised learning models
Confusion Matrix
Unsupervised models

Jean-LucCAUT-2016
Machine Learning
is a subfield of Computer Science that evolved from the study of pattern
recognition and computational learning theory in artificial intelligence.
In 1959 Arthur Samuel, defined machine learning as a:
"Field of study that gives computers the ability to learn without being
explicitly programmed.”
Let’s go further and have look on what is hidden behind the scenes.

Jean-LucCAUT-2016
Machine Learning is often used to build predictive models by extracting patterns
from large datasets.
These models are used in predictive data analytics applications including price
prediction, risk assessment, predicting customer behavior, and document
classification.
This presentation offers a detailed and focused treatment of one the most
important machine learning approach used in predictive data analytics,
covering both theoretical concepts and practical applications.
Technical and mathematical material is augmented with explanatory worked
example developed in Python in order to illustrate the application of these
models in the financial business context.

Jean-LucCAUT-2016
Machine Learning tasks are typically classified into three broad categories,
depending on the nature of the learning "signal" or "feedback" available to a
learning system. These are:
Supervised learning: The computer is presented with example inputs and their
desired outputs, given by a "teacher", and the goal is to learn a general rule that
maps inputs to outputs.
Unsupervised learning: No labels are given to the learning algorithm, leaving it on its
own to find structure in its input. Unsupervised learning can be a goal in itself
(discovering hidden patterns in data) or a means towards an end (feature learning).
Reinforcement learning: A computer program interacts with a dynamic environment
in which it must perform a certain goal (such as driving a vehicle), without a teacher
explicitly telling it whether it has come close to its goal. Another example is learning
to play a game by playing against an opponent.

Jean-LucCAUT-2016
Visualizing the important characteristics of a dataset
Exploratory Data Analysis (EDA) is an important and recommended first step prior to the
training of a machine learning model.
First, we will create a scatterplot matrix that allows us to visualize the pair-wise
correlations between the different features in this dataset in one place.

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Correlation Matrix
To quantify the linear relationship between the features, we will now create a correlation
matrix.
The correlation matrix is a square matrix that contains the Pearson product-
moment correlation coefficients (often abbreviated as Pearson's r), which measure
the linear dependence between pairs of features.
For example, we can see that
there is a linear relationship
between RM and the
housing prices MEDV.
Or between NOX emission
and the surface of industries
INDUS.

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Supervised learning is the machine learning task of inferring a function from
labeled training data. The computer is presented with example inputs and their
desired outputs, given by a "teacher", and the goal is to learn a general rule
that maps inputs to outputs.
The training data consist of a set of training examples. In supervised learning, each
example is a pair consisting of an input object (typically a vector) and a desired
output value (also called the supervisory signal).
A supervised learning algorithm analyzes the training data and produces an inferred
function, which can be used for mapping new examples. An optimal scenario will
allow for the algorithm to correctly determine the class labels for unseen instances.
This requires the learning algorithm to generalize from the training data to unseen
situations in a "reasonable" way .

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Determine the type of training
examples
Gather a training set.
Determine the input feature
representation of the learned
function.
Determine the structure of the
learned function and corresponding
learning algorithm.
Run the learning algorithm on the
gathered training set.
Evaluate the accuracy of the
learned function.
Learning Process

Jean-LucCAUT-2016
A quick look at our dataset allows us
to notice that Petal length and width
could be good candidates for our
classification.
This step called dimensionality
reduction of our feature space. The
main advantage is that the learning
algorithm will run much faster.
A potential use of supervised learning model is classification.
The Iris dataset is a classic example in the field of machine learning, it contains the
measurements of 150 iris flowers from three different species: Setosa, Versicolor, and
Viriginica.
Here, each flower Sample represents one row in our data set, and the flower
measurements in centimeters are stored as columns, which we also call the Features of the
dataset.
Data set is available at: https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data

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Many different machine learning algorithms have been developed to solve different
problem tasks.
An important point that can be summarized from David Wolpert's famous No Free Lunch
Theorems is that we can't get learning "for free" (The Lack of A Priori Distinctions Between Learning
Algorithms, D.H. Wolpert 1996; No Free Lunch Theorems for Optimization, D.H. Wolpert and W.G. Macready, 1997).
For example, each classification algorithm has its inherent biases, and no single
classification model enjoys superiority if we don't make any assumptions about the task.
In practice, it is therefore essential to compare at least a handful of different algorithms in
order to train and select the best performing model.
“Would you tell me, please,
which way I ought to go from here?” Said Alice
“That depends a good deal on where you want to get to,” said the Cat.
Alice in Wonderland, Lewis Carroll

Jean-LucCAUT-2016
Linear classification model
the Logistic Regression and the conditional probabilities
Logistic regression is the most widely used algorithms for classification in industry. It is very
easy to implement but performs very well on linearly separable classes.
To explain the idea behind logistic regression as a probabilistic model, let's first introduce
the odds ratio, which is the odds in favor of a particular event.
The term positive event does refers to the event that we want to predict, e.g. the
probability that a patient has a certain disease. We can then further define he logit
function, which is simply the logarithm of the odds ratio where p stands for the probability
of the positive event.
The logit function takes input values in the range 0 to 1 and transforms them to values over
the entire real number range, which we can use to express a linear relationship between
feature values and the log-odds:

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Then we are interested in predicting the probability that a certain sample belongs to a
particular class, which is the inverse form of the logit function. It is also called the logistic
function, sometimes simply abbreviated as sigmoid function due to its characteristic S-
shape.
Here, z is the net input, that is, the linear combination of weights and sample features and
can be calculated as:
The output of the sigmoid function is then interpreted as the probability of particular
sample belonging to class 1, given its features x parameterized by the
weights w.
Z

Jean-LucCAUT-2016
If we compute for a particular flower sample, it means that the chance that this
sample is an Iris-Versicolor flower is 80 percent.
Similarly, the probability that this flower is an Iris-Setosa flower can be calculated as
or 20 percent.
The predicted probability can then simply be
converted into a binary outcome via a quantizer.

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Code developed in Python in order to use the Sigmoid function:

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What is a good classifier?
Well calibrated classifiers are probabilistic classifiers for which the output of the
predict_proba method can be directly interpreted as a confidence level.
Well calibrated (binary) classifier should classify the samples such that among the samples
to which it gave a predict_proba value close to 0.8, approx. 80% actually belong to the
positive class.
LogisticRegression returns well calibrated predictions as it directly optimizes log-loss.
GaussianNaiveBayes tends to push probabilties to 0 or 1. This is mainly because it
makes the assumption that features are conditionally independent given the class,
which is not the case in this dataset which contains 2 redundant features.
RandomForestClassifier shows the opposite behavior: Errors caused by variance tend
to be one-sided near zero and one. We observe this effect most strongly with random
forests because the base-level trees trained have relatively high variance due to feature
subseting.
Support Vector Classification (SVC) shows an even more sigmoid curve as the
RandomForestClassifier, which is typical for maximum-margin methods, which focus on
hard samples that are close to the decision boundary (the support vectors).

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Classifier comparison

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Example with a Logistic Regression Classifier:
Logistic regression, despite its name, is a linear
model for classification rather than regression.
Logistic regression is also known in the
literature as logit regression, maximum-entropy
classification or the log-linear classifier.
In this model, the probabilities describing the
possible outcomes of a single trial are modeled
using a logistic function.

Jean-LucCAUT-2016
Python code for parsing and classifying data with a logistic regression model:

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Simple Least Square model
As we can see in the following plot,
the linear regression line reflects the
general trend that house prices tend
to increase with the number of rooms:
Data set is available at: https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data
To see our Linear Regression model in action, let's use the RM (number of rooms)
variable from the Housing Data Set as the explanatory variable to train a model that
can predict MEDV (the housing prices).

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Regression model wrapped in RANSAC algorithm
Linear regression models can be heavily impacted by the presence of outliers. In certain
situations, a very small subset of our data can have a big effect on the estimated model
coefficients.
As an alternative to throwing out
outliers, we will look at a robust method
of regression using the RANdom
SAmple Consensus (RANSAC) algorithm,
which fits a regression model to a subset
of the data, the so-called inliers.
Using RANSAC, we don't know if this
approach has a positive effect on the
predictive performance for unseen data.
Thus, in the next section we will discuss
how to evaluate a model for different
approaches.

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Python Code for RANSAC regression algorithm:

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Non Linear classification model
Using a Kernel SVM
SVMs enjoy high popularity among machine learning practitioners because they can be
easily kernelized to solve nonlinear classification problems.
The basic idea behind kernel methods to deal with such linearly inseparable data is to
create nonlinear combinations of the original features to project them onto a higher
dimensional space via a mapping function Ø() where it becomes linearly separable.
To solve a nonlinear problem using an SVM,
we transform the training data onto a higher
dimensional feature space via the mapping
function Ø() and train a linear SVM model to
classify the data in this new feature space.
Then we can use the same mapping function
Ø() to transform new, unseen data to classify
it using the linear SVM model.

Jean-LucCAUT-2016
As we can see in the resulting plot, the kernel SVM separates the data relatively well:
The g parameter, which we set to gamma=0.1, can be understood as a cut-off parameter
for the Gaussian sphere. If we increase the value for , we increase the influence or reach of
the training samples, which leads to a softer decision boundary.
To get a better intuition for , let's apply RBF kernel SVM to our Iris flower dataset:

Jean-LucCAUT-2016
To get a better intuition for g parameter, let's apply RBF kernel SVM to our Iris flower
dataset:
In the resulting plot, we can now see that
the decision boundary around the classes
0 and 1 is much tighter using a relatively
large value of g (100.0) :

Jean-LucCAUT-2016
Python code for Kernel SVM part 1:

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Python code for Kernel SVM part 2:

Jean-LucCAUT-2016
Decision Tree and non linear relationships
To use a decision tree for regression, we will replace entropy as the impurity measure of a
node t by the MSE.
In the context of decision tree regression, the MSE is often also referred to as within-node
variance, which is why the splitting criterion is also better known as variance reduction.
To see what the line fit of a
decision tree looks like, let's
use the DecisionTreeRegressor
implemented in scikit-learn to
model the nonlinear
relationship between the
MEDV and LSTAT variables:

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Python code for a decision tree for regression.

Jean-LucCAUT-2016
When it comes to select among different machine learning algorithms, a recommended
approach is nested cross-validation. Varma and Simon concluded that the true error of
the estimate is almost unbiased relative to the test set when nested cross-validation is
used (S. Varma and R. Simon. Bias in Error Estimation When Using Cross-validation for Model Selection. BMC
bioinformatics, 2006).
Cross-Validation process
Description:

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In the field of Machine learning and specifically the problem of statistical classification,
a confusion matrix, also known as an error matrix, is a specific table layout that allows
visualization of the performance of an algorithm.
Exemple with a cross-validation training model:
Assuming that class 1 (malignant) is the positive class in
this example, our model correctly classified 71 of the
samples that belong to class 0 (True Negatives) and 40
samples that belong to class 1 (True Positives),
respectively.
However, our model also incorrectly misclassified 2
samples from class 0 as class 1 (False Positives) which is
a false alarm, and it predicted that 1 sample is benign
although it is a malignant tumor (False Negatives).

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The error can be understood as the sum of all false predictions divided by the number of
total predictions:
The Accuracy is calculated as the sum of correct predictions divided by the number of total
predictions:
The true positive rate (TPR), false positive rate (FPR) and precision (PRE) are
performance metrics that are especially useful for imbalanced class problems:

Jean-LucCAUT-2016
Receiver operator characteristic (ROC) graphs are useful tools for selecting models for
classification based on their performance with respect to the false positive and true
positive rates, which are computed by shifting the decision threshold of the classifier.
The diagonal of an ROC graph can be interpreted as random guessing, and classification
models that fall below the diagonal are considered as worse than random guessing.
A perfect classifier would fall into the top-left corner of the graph with a true positive rate
of 1 and a false positive rate of 0.
Next slide is a plot of a ROC curve of a classifier that only uses two features from the
Breast Cancer Wisconsin dataset to predict whether a tumor is benign or malignant.
Based on the ROC curve, we can also compute the area under the curve (AUC) to
characterize the performance of a classification model.

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The resulting ROC curve indicates that there is a certain degree of variance between the
different folds, and the average ROC AUC (0.75) falls between a perfect score (1.0) and
random guessing (0.5):

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In this example we are going to use a Decision Tree then Random Forest model in order
to detect fraudulent use of Credit Card.
A non linear model will better resolve our problem, we assume that the effect of the
amount is not linear, because the impact of amount could depend on another variable
such as card use in 24h, or maybe small and large charges are most likely to be fraudulent
than charges with moderate amounts…
Let us import a .csv file with 89,393 transactions

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In the following example, we have trained a Decision Tree with a sample of the training
data, starting with a node and pick the split that maximizes the decrease in Gini:
2.p.(1 – p)

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Random forests have gained huge popularity in applications of machine learning during
the last decade due to their good classification performance, scalability, and ease of use.
Intuitively, a random forest can be considered as an ensemble of decision trees.
The idea behind ensemble learning is to combine weak learners to build a more robust
model, a strong learner, that has a better generalization error and is less susceptible to
overfitting. The random forest algorithm can be summarized in four simple steps:
Draw a random bootstrap sample of size n (randomly choose n samples from the
training set with replacement).
Grow a decision tree from the bootstrap sample. At each node:
Randomly select d features without replacement.
Split the node using the feature that provides the best split according to the
objective function, for instance, by maximizing the information gain.
Repeat the steps 1 to 2 k times.
Aggregate the prediction by each tree to assign the class label by majority vote.

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In the following example we have trained N trees, each on a (bootstrapped) sample of
the training data
At each split, we only consider a subset of the available features, say total # of features
of them. Thus reducing correlation among the trees. The final score is the average of the
score produced by each tree.

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Python code for RandomForestClassifier

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In this part we will discuss one of the most popular clustering algorithms, k-means, which
is widely used in academia as well as in industry.
Clustering (or cluster analysis) is a technique that allows us to find groups of similar
objects, objects that are more related to each other than to objects in other groups.
Examples of business-oriented applications of clustering include the grouping of
documents, music, and movies by different topics, or finding customers that share similar
interests based on common purchase behaviors as a basis for recommendation engines.
.
In the following scatterplot,
we can see that k-means
placed the three centroids
at the center of each
sphere, which looks like a
reasonable grouping given
this dataset:

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Python code for k-means algorithm.

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Hard clustering describes a family of algorithms where each sample in a dataset is
assigned to exactly one cluster, as in the k-means algorithm that we discussed in the
previous slide.
In contrast, algorithms for soft clustering (sometimes also called fuzzy clustering) assign a
sample to one or more clusters. A popular example of soft clustering is the fuzzy C-means
(FCM) algorithm (also called soft k-means or fuzzy k-means).
As we can see in the
following scatterplot, one
of the centroids falls
between two of the three
spherical groupings of the
sample points. Although
the clustering does not
look completely terrible, it
is suboptimal.

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Although we can't cover the vast number of different clustering algorithms in this
chapter, let's at least introduce one more approach to clustering: Density-based Spatial
Clustering of Applications with Noise (DBSCAN). The notion of density in DBSCAN is
defined as the number of points within a specified radius e .
In DBSCAN, a special label is assigned to each sample (point) using the following criteria:
A point is considered as core point if at least a specified number (MinPts) of
neighboring points fall within the specified radius e
A border point is a point that has fewer neighbors than MinPts within , but lies within
the e radius of a core point
All other points that are neither core nor border points are considered as noise points

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For a more illustrative example, let's create a new dataset of half-moon-shaped
structures to compare k-means clustering, hierarchical clustering, and DBSCAN:
We will start by using the k-means algorithm and complete linkage clustering to see
whether one of those previously discussed clustering algorithms can successfully identify
the half-moon shapes as separate clusters.
Based on the visualized clustering results, we can see that the k-means algorithm is
unable to separate the two clusters, and the hierarchical clustering algorithm was
challenged by those complex shapes:

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The DBSCAN algorithm can successfully detect the half-moon shapes, which highlights
one of the strengths of DBSCAN (clustering data of arbitrary shapes)
However, we should also note some of the disadvantages of DBSCAN. With an increasing
number of features in dataset, given a fixed size training set, the negative effect of the
curse of dimensionality increases. This is especially a problem if we are using the
Euclidean distance metric.
However, the problem of the
curse of dimensionality is
not unique to DBSCAN; it
also affects other clustering
algorithms that use the
Euclidean distance metric,
for example, the k-means
and hierarchical clustering
algorithms

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The DBSCAN algorithm:

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