Original: Introductory Machine Learning for Non-Major Students
Revised: Introductory Machine Learning for Non STEM Students

Original: Anonymous Authors

Original: Abstract
Revised: Abstract

Original: Data Science in general, and Machine Learning in particular, is a powerful tool for decision-makers across non-STEM  ﬁelds like Human Resources
Revised: Data Science in general, and Machine Learning in particular, is a powerful tool for decision-makers across non-STEM (Sience, Techonology, Engineering and Maths) ﬁelds like Human Resources

Original: Management, Law or Marketing.
Revised: Management, Law or Marketing.

Original: Introductory
Revised: Introductory

Original: Machine Learning, for non-majors that lack a strong background in Statistics and Computer Science, is a challenge for both teacher and students.
Revised: Machine Learning, for non-majors that lack a strong background in Statistics and Computer Science, is a challenge for both teacher and students.

Original: The use of similes and games is a soft way to deal with deﬁnitions of concepts and procedures that are essential for further advanced courses on these subjects.
Revised: The use of similes and games is a soft way to deal with deﬁnitions of concepts and procedures that are essential for further advanced courses on these subjects.

Original: 1. Introduction
Revised: 1. Introduction

Original: Machine Learning (ML) is a ﬁeld underpinned by Statistics,
Revised: Machine Learning (ML) is a ﬁeld underpinned by Statistics,

Original: Calculus, Algebra and Computer Science, with a long history in STEM curricula.
Revised: Calculus, Algebra and Computer Science, with a long history in STEM curricula.

Original: During the last decade, its practical applications made it quite popular outside academia.
Revised: During the last decade, its practical applications made it quite popular outside academia.

Original: Fostered by the explosive growth of digital data and availability of cheap and ubiquitous computing power, Machine Learning is now a common subject in non-STEM graduate and undergraduate programs (Plasek, 2016; O’Neil, 2014).
Revised: Fostered by the explosive growth of digital data and availability of cheap and ubiquitous computing power, Machine Learning is now a common subject in non-STEM graduate and undergraduate programs (Plasek, 2016; O’Neil, 2014).

Original: Research about teaching ML to non-majors is a developing ﬁeld (Way et al., 2017; Long & Magerko, 2020).
Revised: Research about teaching ML to non-majors is a developing ﬁeld (Way et al., 2017; Long & Magerko, 2020).

Original: A recent survey showed that maths and programming are the two main barriers for these students (Sulmont et al., 2019).
Revised: A recent survey showed that maths and programming are the two main barriers for these students (Sulmont et al., 2019).

Original: There are three possible choices to deal with these obstacles.
Revised: There are three possible choices to deal with these obstacles.

Original: First one is ignoring the students’ background and lecturing them as if they were following the STEM path.
Revised: First one is ignoring the students’ background and lecturing them as if they were following the STEM path.

Original: The second one is pure story-telling, just providing some application examples without a long-term strategy to teach effective Machine Learning skills.
Revised: The second one is pure story-telling, just providing some application examples without a long-term strategy to teach effective Machine Learning skills.

Original: The last one is a middle way, where concepts and deﬁnitions are taught using analogies and games (Opel et al., 2019) as a preliminary step to introduce abstract concepts as information entropy or ROC.
Revised: The last one is a middle way, where concepts and deﬁnitions are taught using analogies and games (Opel et al., 2019) as a preliminary step to introduce abstract concepts as information entropy or ROC.

Original: This approach may be misleading, as Edsger Dijkstra noted (Dijkstra, 1989), if they are not related to the mathematics and technology that are the basis of ML.
Revised: This approach may be misleading, as Edsger Dijkstra noted (Dijkstra, 1989), if they are not related to the mathematics and technology that are the basis of ML.

Original: In this communication I describe the instructional design of an introductory Machine Learning course initially intended for undergraduate Law students.
Revised: In this communication I describe the instructional design of an introductory Machine Learning course initially intended for undergraduate Law students.

Original: Comillas is a Private Catholic University, with a centurylong history and a main campus in the heart of Madrid, where it offers undergraduate and graduate courses in Engineering, Law and Business Managament.
Revised: Comillas is a Private Catholic University, with a centurylong history and a main campus in the heart of Madrid, where it offers undergraduate and graduate courses in Engineering, Law and Business Managament.

Original: By mid 2010’s the governing bodies made a strategic move to offer what are called Doubles Degrees in the context of the European Higher Education Area (Klebes-Pelissier, 2007), a ten semester program.
Revised: By mid 2010’s the governing bodies made a strategic move to offer what are called Doubles Degrees in the context of the European Higher Education Area (Klebes-Pelissier, 2007), a ten semester program.

Original: The ﬁrst one was Law and Business
Revised: The ﬁrst one was Law and Business

Original: Analytics set to start by September 2017, followed by Business Management and Business Analytics and Engineering and Business Analytics .
Revised: Analytics set to start by September 2017, followed by Business Management and Business Analytics and Engineering and Business Analytics .

Original: Students that get a Double Degree in Law and Business Analytics may follow a Master in Laws that is mandatory for the State Examination for Access to the Legal Profession, but they may also choose to build a career in the booming Legal-tech industry.
Revised: Students that get a Double Degree in Law and Business Analytics may follow a Master in Laws that is mandatory for the State Examination for Access to the Legal Profession, but they may also choose to build a career in the booming Legal-tech industry.

Revised: A high percentage of Comillas graduates begin their professional life in the consulting industry and a sound technical background is a competitive advantage.

Revised: Requests to enroll this Double Degree are high and average students’ performance is remarkable.

Original: First contact of these students with Business Analytics is a 30 hours introductory course during the third semester.
Revised: First contact of these students with Business Analytics is the 30 hours introductory course during the third semester.

Original: By the end of the ﬁve years they become very proﬁcient in programming and building models, but at that moment they haven’t written a line of code and have just followed the basic Calculus course. On the other hand, requests to enroll this Double Degree are high, so the selection process is quite competitive and average students’ performance is remarkable.
Revised: They haven’t had any prior experience with programming languages or data science. This course is a gentle introduction to both ﬁelds. There are three learning goals: to write simple R scripts, to know the very basics of predictive models and to have an overview of their applications in ﬁnance, marketing and human resources management.

Original: The syllabus of the course starts with fundamentals of programming and statistics with the R language and Exploratory
Revised: The syllabus of the course starts with fundamentals of programming and statistics with the R language and Exploratory

Original: Data Analysis, 8 hours in total.
Revised: Data Analysis, 8 hours in total.

Original: They have to master both
Revised: They have to master both

Original: R and Python by the end of the ten semesters, but this is the ﬁrst contact with a programming tool, so we decided to start with R because of the simplicity of the environment.
Revised: R and Python by the end of the ten semesters, but this is the ﬁrst contact with a programming tool, so we decided to start with R because of the simplicity of the environment.

Original: Anyway, it is a challenge to install and conﬁgure R and
Revised: Anyway, it is a challenge to install and conﬁgure R and

Original: RStudio with a variety of devices, and as a consequence installation of additional packages is hard.
Revised: RStudio with a variety of devices, and as a consequence installation of additional packages is hard.

Original: 2. Explaining ML Principles
Revised: 2. Explaining ML Principles

Original:  Lessons 4 to 7 cover Machine Learning fundamentals.
Revised: The syllabus comprises ten lessons. Lessons 1 to 3 are an introduction to programming with R and Exploratory Data Analysis. Lessons 4 to 6 cover Machine Learning fundamentals and Lessons 7 to 10 business applications of

Revised: ML.

Revised: In this paper I focus my description of lessons 4 andthat deal with supervised predictive models.

Original: One of the problems when teaching Data Science is the misuse of vocabulary in mass media and the hype about its unlim- ited applications to solve business problems.
Revised: One of the problems when teaching Data Science is the misuse of vocabulary in mass media and the hype about its unlimited applications to solve business problems.

Original: Students have heard of read about Big Data, Machine Learning, Algorithms and Business Intelligence almost as synonyms.
Revised: Students have heard or read about Big Data, Machine Learning, Algorithms and Business Intelligence almost as synonyms.

Original: The goal of the ﬁrst lecture (2 hours) is to make clear what learning and prediction mean in this context, what are the steps to train, evaluate and deploy a model and when you should and shouldn’t use predictive models.
Revised: The goal of the ﬁrst session on Machine Learning (lesson 4, 2 hours) is to make clear what learning and prediction mean in this context, what are the steps to train, evaluate and deploy a model and when you should and shouldn’t use predictive models.

Original: Non-major students, without a prior contact with Data Science, may have heard some kind of buzzword-ﬁlled discourses about the almost-magical powers of machines.
Revised: Non-major students, without a prior contact with Data Science, may have heard some kind of buzzword-ﬁlled discourses about the almost-magical powers of machines.

Original: To spoil this idea I start the lesson with a powerful citation: ”Let’s start by telling the truth: machines don’t learn.
Revised: To spoil this idea I start the lesson with a powerful citation: ”Let’s start by telling the truth: machines don’t learn.

Original: What a typical learning machine does, is ﬁnding a mathematical formula” (Burkov, 2019).
Revised: What a typical learning machine does, is ﬁnding a mathematical formula” (Burkov, 2019).

Original: This theatrical introduction sets the stage to explain how learning works (Fig. 1), following the steps described in (Abu-Mostafa et al., 2012).
Revised: This theatrical introduction sets the stage to explain how learning works (Fig. 1), following the steps described in (Abu-Mostafa et al., 2012).

Original: Although the book is excellent, its level of abstraction is hard for the group at that moment.
Revised: Although the book is excellent, its level of abstraction is hard for the group at that moment.

Original: To make it simpler, I have found that linear regression, is a quite convenient example to understand it step-by-step.
Revised: To make it simpler, I have found that linear regression, is a quite convenient example to understand it step-by-step.

Original: Students know what linear regression is and how it works despite they do not identify it as a predictive model yet.
Revised: Students know what linear regression is and how it works despite they do not identify it as a predictive model yet.

Original: So, I propose an hypothetical project to predict the weight ofan undergraduate student just knowing its height and gender.
Revised: So, I propose a hypothetical project to predict the weight of undergraduate students just knowing their height and gender.

Original: This example is simple enough to explain some fundamental ideas of Machine Learning:
Revised: This example is simple enough to explain some fundamental ideas of Machine Learning:

Revised: • We have a set of vectors X k

Revised: =

Revised: ( x 1 k , x 2 k , .., x nk , where each X k is a discrete sample of a n − dimensional universe.

Original: • We have  a set
Revised: We have as well a set

Original: of vectors
Revised: of outcomes y k

Original: X that tell a story about some function  f ( X ) that we will never know in detail.
Revised: that tell a story about some function Y = f ( X ) that we will never know in detail.

Original: This ﬁrst statement is critical to understand that ML always work under uncertainty.
Revised: This ﬁrst statement is critical to understand that ML always work under uncertainty.

Original: If we had an analytical expression of f ( X ) ML is pointless.
Revised: If we had an analytical expression of f ( X ) ML is pointless.

Original: Law and Business Management students understand it quickly as uncertainty is a natural element of their world view.
Revised: Law and Business Management students understand it quickly as uncertainty is a natural element of their world view.

Original: Engineering undergrads have a much more difﬁcult time to accept this fact.
Revised: In my particular experience, engineering undergrads have a much more difﬁcult time to accept this fact.

Original: • If the samples are a good representation of the population, we may make some educated guess about a function g ( X ) that is close enough to f  for predictive purposes.
Revised: • If the samples are a good representation of the population, we may make some educated guess about a function g ( X ) that is close enough to f ( X ) for predictive purposes.

Original: • We choose a possible family of functions to search for that potential g ( X ) , that we call model , and an algorithm selects, among all possible g
Revised: • We choose a possible family of functions to search for that potential g ( X ) , that we call model , and an algorithm selects, among all possible g

Original: i ( x ) , the best one according to a mathematical rule called loss function .
Revised: i ( X ) , the best one according to a mathematical rule called loss function .

Original: Finally , students identify least squares as the algorithm and the regression line 
Revised: Finally, students identify least squares as the algorithm and the regression line as the model.

Original: as the model. We sample the height values of ﬁve students of the same gender and build a regression model with R and, in general, results of guesses are accurate because they all are healthy teenagers.
Revised: We sample the height values of ﬁve students of the same gender and build a regression model with R and, in general, results of guesses are accurate because they all are healthy teenagers.

Original: Then, we check that it doesn’t work as well if we try to predict values of individuals of the opposite gender.
Revised: Then, we check that it doesn’t work as well if we try to predict values of individuals of the opposite gender.

Original: We start a short discussion on the possible origin of this mismatch and they identify that we haven’t included the feature gender , so we rebuild it and things go more smoothly.
Revised: We start a short discussion on the possible origin of this mismatch and they identify that we haven’t included the feature gender , so we rebuild it and things go more smoothly.

Original: When they are happy enough I tell we are going to play theevil overﬁtting game .
Revised: When they are happy enough I tell we are going to play the overﬁtting game .

Original: I build a black box model that returns the exact weight of the individual if it was one of the building samples, and a random value otherwise, and that is a bit of a shock.
Revised: I build a black box model that returns the exact weight of the individual if it was one of the building samples, and a random value otherwise, and that is a bit of a shock.

Original: The example may sound a bit absurd from a business point of view.
Revised: The example may sound a bit useless from a business point of view.

Original: I translate it into an environment management agency that needs to know the biomass of salmons that return a given year through a ladder with a trap and a camera that measures the length of a percentage of individuals.
Revised: I translate it into an environment management agency that needs to know the biomass of salmons that return a given year through a ladder with a trap and a camera that measures the length of a percentage of individuals.

Original: After the introduction to regression, dangers of classiﬁcation are illustrated with Fisher’s Iris dataset.
Revised: After the introduction to regression, dangers of classiﬁcation are illustrated with Fisher’s Iris dataset(Bezdek et al., 1999).

Original: Despite criticism about its goodness to teach ML concepts, the dataset has the nice property that provides two classiﬁcation problems that are visually quite evident.
Revised: Despite criticism about its goodness to teach ML concepts, the dataset has the nice property that provides two classiﬁcation problems that are visually quite evident.

Original: First, I draw a straight line to divide setosa and versicolor samples.
Revised: First, I draw a straight line to divide setosa and versicolor samples.

Original: I make the pun that I used L’Or´eal’s
Revised: I make the pun that I used L’Or ´ eal’s

Original: Rule to choose the optimal slope ( Because
Revised: Rule to choose the optimal slope.

Original:  I’m worth it ),  and  show how changing it misclassiﬁcation happens (Fig. 2).
Revised: As the French cosmetics company slogan says ( Because I’m worth it ), I made a choice at random and this helps me to show how changing the slope misclassiﬁcation happens (Fig. 2).

Original: Then we attack the non-linear separable classiﬁcation of virginica versus versicolor to stress the idea that uncertainty is an inevitable fact for ML models and a visual example on how you can get a zero training error and a weak classiﬁer.
Revised: Then we discuss the non-linear separable classiﬁcation of virginica versus versicolor to stress the idea that uncertainty is an inevitable fact for ML models and a visual example on how you can get a zero training error but a weak classiﬁer.

Original: The confusion matrix is well understood with theboy who cried wolf example of Type-I error.
Revised: The confusion matrix is well understood with the example of the doctor that diagnoses a middle-age gentleman that is pregnant (Type-I error).

Original: The ROC  and AUC  concepts are not easy to grasp, so I try to put it simple, AUC is just an ordinal index for a given prediction problem and a given dataset in order to compare results.
Revised: The ROC (Receiver Operating Curve) and AUC (Area Under the Curve) concepts are not easy to grasp, so I try to put it simple, AUC is just an ordinal index for a given prediction problem and a given dataset in order to compare results.

Original: Lesson 5 deals with mainstream ML models: decision trees and their families, logistic regression, neural networks and
Revised: Lesson 5 deals with mainstream ML models: decision trees and their families, logistic regression, neural networks and

Original: SVMs.
Revised: SVMs (Support Vector Machines).

Original: This is tough stuff for beginners.
Revised: This is tough stuff for beginners.

Original: We play another game to discover what information entropy is and how a decision tree works by reducing it, the classical Guess Who .
Revised: We play another game to discover what information entropy is and how a decision tree works by reducing it, the classical Guess Who .

Original: A student thinks of another one and the group has to guess who is he/she with Yes/No questions.
Revised: A student thinks of another one and the group has to guess who is he/she with Yes/No questions.

Original: As these groups are quite well gender-balanced, the obvious ﬁrst question is ”Is a girl (or boy)?”.
Revised: As these groups are quite well gender-balanced, the obvious ﬁrst question is ”Is a girl (or boy)?”.

Original: Decision trees are very intuitive because our brain works the principle of entropy reduction but
Revised: Decision trees are very intuitive because our brain works the principle of entropy reduction but

Original: each round I give this lecture
Revised: each round I give this lecture

Original: I ﬁnd that entropy formula is the worst nightmare for students.
Revised: I ﬁnd that entropy formula is a nightmare for students.

Original: The minus sign and log 2 ( p i ) are the most feared beasts.
Revised: The minus sign and log 2 ( p i ) are rather hard at a ﬁrst glance, but we overcome this problem developing a full classiﬁcation example (Fig. 3).

Original: The basic idea of merging the results of several trees using a Random Forest or a Decision Jungle is easy to teach, as the use of a regression (logistic) to classify setting a simple boundary.
Revised: The basic idea of merging the results of several trees using a Random Forest or a Decision Jungle is easy to teach, as the use of a regression (logistic) to classify setting a simple boundary.

Original: Neural networks are a hard mathematical topic, so I just show an animation of how the Perceptron training algorithm works (remembering the L’Or´eal pun).
Revised: Neural networks are a hard mathematical topic, so I just show an animation of how the Perceptron training algorithm works (remembering the L’Or ´ eal pun).

Original: As the backpropagation algorithm is out of reach at this level, I explain the concepts of black box and interpretability of models .
Revised: As the backpropagation algorithm is out of reach at this level, I explain the concepts of black box and interpretability of models .

Original: The second lesson ends with Support Vector Machines and an explanation on how a kernel transforms a linear nonseparable problem into a separable one, using a visual example from one to two dimensions.
Revised: Lesson 5 ends with Support Vector Machines and an explanation on how a kernel transforms a linear non-separable problem into a separable one, using a visual example from one to two dimensions.

Original: After these 4 hours of theory we have a 2 hours handson session.
Revised: After these 4 hours of theory we have a 2 hours handson session.

Original: Despite students have got a basic knowledge of the R language I feared that trying to build a toy model would be a painful experience.
Revised: Despite students have got a basic knowledge of the R language I feared that trying to build a toy model would be a painful experience.

Original: Instead, we use a user-friendly graphical environment, Azure Machine
Revised: Instead, we use a user-friendly graphical environment, Azure Machine

Original: Learning Suite .
Revised: Learning Suite .

Original: There are similar tools like KNIME or BigML , the choice was driven by reasons of convenience, as the agreement between the University and Microsoft includes a basic license.
Revised: There are similar tools like KNIME or BigML , the choice was driven by reasons of convenience, as the agreement between the University and Microsoft includes a basic license.

Original: With a visual environment like that, we build a classiﬁer from scratch in 45 minutes, identifying each machine learning step.
Revised: With a visual environment like that, we build a classiﬁer from scratch in 45 minutes, identifying each machine learning step.

Original: Students love the ability to test different models just adding components with a drag and drop order.
Revised: Students love the ability to test different models just adding components with a drag and drop operation.

Original: Comparing AUCs awakes their competitive instinct, the basis of the ﬁnal act.
Revised: Comparing AUCs awakes their competitive instinct, the basis of the ﬁnal act.

Original: We also build a regression model although RMSEs are not as exciting as AUCs.
Revised: We also build a regression model although RMSEs are not as exciting as AUCs.

Original: This part of the course ends with a Kaggle-like competition.
Revised: This part of the course ends with a Kaggle-like competition (Fig. 4).

Original: I provide a synthetic dataset, a user case and the rules of competition.
Revised: I provide a synthetic dataset, a user case and the rules of competition.

Original: Students work in groups of six chosen at random, to teach them an important lesson, in real life you have to collaborate with people that are not part of your circle of friends.
Revised: Students work in groups of six chosen at random, to teach them an important lesson, in real life you have to collaborate with people that are not part of your circle of friends.

Original: After three weeks they send a report, with the best AUC they got and publish their model.
Revised: After three weeks they send a report, with the best AUC they got and publish their model.

Original: This exercise worths a 10% of the ﬁnal grade, the winner team earns an extra 10% , so they put a lot of effort in this assignment.
Revised: This exercise worths a 10% of the ﬁnal grade, the winner team earns an extra 10% , so they put a lot of effort in this assignment.

Original: I give some hints on features engineering and transformations and they apply all their knowledge with enthusiasm.
Revised: I give some hints on feature engineering and transformations and they apply all their knowledge with enthusiasm.

Original: Usually, some clever team discovers how to balance the samples with a SMOTE  procedure, and even try ensemble methods that we did not see during the hands-on session.
Revised: Usually, some clever team discovers how to balance the samples with a SMOTE (Synthetic Minority Over-sampling Technique) procedure, and even try ensemble methods that we did not see during the hands-on session.

Original: Next lesson is an introduction to non-supervised models, in two hours and working with R .

Original: After the supervised experience, nothing is so exciting for them.