Programming, Math, and Statistics: Mastering the Foundations of Data Science and Machine Learning

Data science and machine learning are revolutionizing industries from healthcare to finance to technology. As companies scramble to hire data talent, aspiring practitioners are faced with a dizzying array of skills to learn – Python, R, SQL, statistics, linear algebra, machine learning algorithms, data visualization, and more.

As a full-stack developer and professional coder, I‘ve seen firsthand how data science and machine learning are transforming software development. Building intelligent, data-driven systems requires a unique blend of skills in programming, math, and statistics.

In this guide, we‘ll dive deep into each of these foundational areas. Whether you‘re a software engineer looking to break into data science or a budding data analyst aiming to level up your skills, by the end of this article you‘ll have a roadmap for mastering the core competencies of data science and machine learning.

The State of Data Science

Before we jump into the technical skills, let‘s set the stage with some data on the data science industry.

The demand for data science skills has exploded in recent years. According to LinkedIn‘s 2020 Emerging Jobs Report, "Data Scientist" topped the list for the third year in a row, with 37% annual growth. [1] And this growth shows no signs of slowing down – the U.S. Bureau of Labor Statistics predicts that jobs for data scientists and mathematical science occupations will grow 31% from 2019 to 2029, much faster than the average for all occupations. [2]

But it‘s not just the number of jobs that‘s increasing – the scope of industries hiring data scientists is also expanding. While tech giants like Google, Facebook, and Amazon were early adopters, data science is now being applied in healthcare, finance, retail, manufacturing, and more. Here‘s a breakdown of data scientist job postings by industry from Indeed.com:

Industry	% of Job Postings
Technology	29%
Healthcare	14%
Financial	13%
Gaming	8%
Retail	6%
Other	30%

Source: Indeed.com, Data Scientist Job Postings, March 2021

With this context in mind, let‘s dive into the skills you need to know to take advantage of this booming field.

Programming: The Toolkit of Data Science

At its core, data science is about using code to extract insights and knowledge from data. While drag-and-drop tools like Azure Machine Learning Designer or Orange exist for building models without code, any real-world data science project will require rolling up your sleeves and writing scripts.

The most popular programming language for data science is Python. In Stack Overflow‘s 2020 Developer Survey, 66.7% of data scientists and machine learning specialists reported using Python. [3] This is due to Python‘s simple syntax, powerful libraries for data manipulation and analysis, and rich ecosystem of tools for machine learning.

Here are some of the essential Python libraries you need to know for data science:

• NumPy: Introduces objects for multidimensional arrays and matrices, as well as routines that allow developers to perform advanced mathematical and statistical functions on those arrays with just a few lines of code. NumPy serves as the foundation upon which nearly all of Python‘s scientific computing and data analysis tools are built.

• Pandas: Provides high-performance, easy-to-use data structures and analysis tools. Pandas‘ primary objects are the Series (1-dimensional) and DataFrame (2-dimensional), which allow you to slice, dice, and manipulate datasets with ease. Pandas also provides read/write functionality for a wide variety of data formats, making it invaluable for data cleaning and preparation.

• Matplotlib: The foundational library for data visualization in Python. Matplotlib allows you to create a wide variety of static, animated, and interactive visualizations in Python. It can be used in Python scripts, the Python and IPython shell, web application servers, and various graphical user interface toolkits.

• Scikit-learn: The workhorse library for machine learning in Python. Scikit-learn provides a consistent interface for a wide range of supervised and unsupervised learning algorithms, making it simple to experiment with different models. It also provides essential tools for model evaluation and selection, like cross-validation and grid search.

As an example of how these libraries fit together, let‘s consider a basic machine learning workflow in Python. We‘ll use a dataset of housing prices to predict the price of a house based on features like the number of bedrooms, square footage, etc.

First, we can use Pandas to read in and explore the data:

import pandas as pd

data = pd.read_csv(‘housing.csv‘)
print(data.head())

      price  bedrooms  bathrooms  sqft_living  sqft_lot
0  221900.0         3       1.00         1180      5650  
1  538000.0         3       2.25         2570      7242  
2  180000.0         2       1.00          770     10000
3  604000.0         4       3.00         1960      5000
4  510000.0         3       2.00         1680      8080

Next, we can use Matplotlib to visualize the relationship between the features and the target variable:

import matplotlib.pyplot as plt

plt.scatter(data[‘sqft_living‘], data[‘price‘])
plt.xlabel(‘Square Footage‘)
plt.ylabel(‘Price‘)
plt.show()

Finally, we can use Scikit-learn to train a linear regression model and make predictions:

from sklearn.linear_model import LinearRegression

X = data[[‘bedrooms‘, ‘bathrooms‘, ‘sqft_living‘]]
y = data[‘price‘]

model = LinearRegression()
model.fit(X, y)

new_house = [[3, 2, 1500]]
prediction = model.predict(new_house)
print(f‘Predicted price: ${prediction[0]:,.0f}‘)

Predicted price: $356,923

This is just a taste of the power of Python for data science. With a solid understanding of these core libraries, you‘ll be well-equipped to tackle a wide range of data challenges.

Mathematics: The Language of Machine Learning

While it‘s possible to train machine learning models in Python without a deep understanding of the underlying math, a solid grasp of mathematical concepts is invaluable for data scientists. Three areas of math are especially important: linear algebra, calculus, and statistics.

Linear Algebra

At a high level, linear algebra is the study of vectors and matrices. Many machine learning models, including linear regression, logistic regression, and support vector machines, are based on linear algebra under the hood.

Some key linear algebra concepts in machine learning include:

• Vectors: Ordered lists of numbers. In machine learning, we often think of vectors as representing a single data point, with each element corresponding to a different feature.

• Matrices: 2-D arrays of numbers. A dataset of multiple vectors can be represented as a matrix, where each row is a vector.

• Matrix Multiplication: Multiplying two matrices is a key operation in many machine learning algorithms. For example, we can represent linear regression as a matrix multiplication: $y = Xw$, where $y$ is the vector of predictions, $X$ is the matrix of features, and $w$ is the vector of weights.

• Eigenvectors and Eigenvalues: Eigenvectors are vectors that, when a matrix is multiplied by them, yield a scaled version of themselves. Eigenvalues are the scale factors. These concepts are key to powerful techniques like Principal Component Analysis (PCA) for dimensionality reduction.

Calculus

Calculus is the study of continuous change. In machine learning, calculus comes into play primarily in the training of models, where we use optimization techniques to find the best set of model parameters.

The key calculus concept in machine learning is the derivative. The derivative of a function tells us the slope of the function at any given point. In machine learning, we use derivatives to understand how changing the model parameters will change the model‘s performance.

A common optimization algorithm is gradient descent. The basic idea is to start with random model parameters and iteratively update them in the direction that reduces the model‘s error. We can find this direction by taking the derivative of the model‘s error function with respect to each parameter. This process is repeated until the error is minimized.

Source: Siraj Raval on YouTube [4]

Statistics and Probability

Machine learning is inherently a statistical process. We‘re using data to estimate a function that maps inputs to outputs, and we need to understand the uncertainty in that estimate.

Some key statistical concepts in machine learning include:

• Probability Distributions: Many machine learning methods are based on probability distributions. For example, logistic regression predicts the probability of a binary outcome, which is modeled as a Bernoulli distribution. Gaussian Naive Bayes assumes that the features follow a Gaussian (normal) distribution.

• Bias-Variance Tradeoff: This is a key concept in model selection. Bias refers to the error introduced by approximating a real-world problem with a simplified model. Variance refers to the model‘s sensitivity to small fluctuations in the training set. Models with high bias tend to underfit, while models with high variance tend to overfit. The goal is to find a model with low bias and low variance.

• Hypothesis Testing: Hypothesis testing is the process of determining whether a result is statistically significant. This is important in machine learning for determining whether a model‘s performance is really better than chance. Common hypothesis tests include the t-test and chi-squared test.

• Bayesian Methods: Bayesian methods provide a principled way of incorporating prior knowledge into machine learning models. The basic idea is to treat the model parameters as random variables and update our beliefs about their values as we observe more data. Bayesian methods are particularly useful when data is limited.

Tying It All Together

We‘ve covered a lot of ground in this guide, from Python libraries to linear algebra to hypothesis testing. It can seem overwhelming, but remember that every expert was once a beginner.

To tackle these topics, I recommend a combination of theoretical learning and hands-on practice. Read textbooks and take online courses to build your conceptual understanding, but also dive into real datasets and build models yourself. Kaggle is a great resource for finding datasets and example projects.

It‘s also important to engage with the data science community. Attend meetups, join online forums, and follow data science blogs and influencers on social media. This will help you stay current with the latest techniques and tools, and provide inspiration for your own projects.

As a full-stack developer, I‘ve found that my software engineering skills have been invaluable in my data science journey. The ability to write clean, efficient, and well-tested code is just as important in data science as it is in web development or any other software field. Don‘t neglect your coding skills as you dive into math and statistics.

Finally, remember that data science is an incredibly broad and rapidly evolving field. Don‘t feel like you need to master every topic before you start applying your skills. Focus on building a solid foundation in programming, math, and statistics, and then start tackling real problems. The best way to learn is by doing.

Conclusion

Data science and machine learning are transforming industries and creating new opportunities for software professionals. By mastering the core skills of programming, math, and statistics, you‘ll be well-positioned to take advantage of this exciting field.

Keep learning, keep practicing, and keep pushing the boundaries of what‘s possible with data. The future belongs to those who can wrangle data, algorithms, and code to solve real-world problems. Will you be one of them?

References

[1] LinkedIn 2020 Emerging Jobs Report, https://business.linkedin.com/talent-solutions/emerging-jobs-report
[2] U.S. Bureau of Labor Statistics, Occupational Outlook Handbook, https://www.bls.gov/ooh/math/mathematicians-and-statisticians.htm
[3] Stack Overflow Developer Survey 2020, https://insights.stackoverflow.com/survey/2020
[4] Siraj Raval, "Gradient Descent, Step-by-Step" on YouTube, https://youtu.be/sDv4f4s2SB8