Principles of Data Science - Notes

Data Science Terminology

• Data science is the process of acquiring knowledge through data to:
  • Make informed decisions
  • Predict the future
  • Understand the past/present
  • Create new industries/products

Basic Data Science Terminology

• Data: A collection of information in either a structured or unstructured format.
  • Structured Data: Data sorted into a row/column structure.
  • Unstructured Data: Data in a free form, like text or raw audio/signals.
• Semi-structured data: Data that doesn't conform entirely to a relational database but contains tags (e.g., XML and JSON files)

Why Data Science?

• Data science augments human capabilities by parsing large volumes of data and discovering relationships within the data.
• An example of data science is using machine learning to aid in the diagnosis, treatment, and prevention of illnesses such as COVID-19.
• Creating effective algorithms requires a combination of:
  • Math/statistics: Using equations and formulas to perform analysis.
  • Computer programming: The ability to use code to create outcomes on a computer.
  • Domain knowledge: Understanding the problem domain (e.g. medicine, finance).

The Data Science Venn Diagram

• Math/statistics: Using equations and formulas to perform analysis
• Computer programming: The ability to use code to create outcomes on a computer
• Domain knowledge: Understanding the problem domain (medicine, finance, social science, etc.)
• The intersection of math and coding is machine learning.

The Math

• Math is used to formalize relationships between variables and build data models.
• A data model refers to an organized and formal relationship between elements of data, usually meant to simulate a real-world phenomenon.
• Topics range from basic algebra to advanced probabilistic and statistical modeling.

Computer Programming

• Computer languages communicate with machines.
• Python, Julia, and R are some of the languages available; this book exclusively uses Python.
• Python is used because it is easy to read and write, is a common language, has a vast online community, and has prebuilt data science modules, such as pandas, PyTorch, Scikit-learn, Seaborn, NumPy/scipy, Requests, and BeautifulSoup.

Domain Knowledge

• Domain knowledge focuses on the particular topic you are working on.
• A big part of domain knowledge is presentation. Your results are only as good as your vehicle of communication.

Some More Terminology

• Machine learning: Giving computers the ability to learn from data without explicit rules
• Statistical model: Taking advantage of statistical theorems to formalize relationships between data elements in a (usually) simple mathematical formula.
• Exploratory data analysis (EDA): Preparing data to standardize results and gain quick insights. EDA is concerned with data visualization and preparation.
• Data mining: The process of finding relationships between elements of data

Data Science Case Studies

• An example of a data science case study is automating government paper pushing of social security claims.
• Another case study is scraping job descriptions for data scientists to find the most common keywords that people use in their job descriptions.

Types of Data

Structured vs. Unstructured Data

• Structured Data: Organized into rows and columns.
• Unstructured Data: Exists in a free form (e.g., text, images, videos).
• Semi-structured data contains element of both, examples are XML and JSON files, emails, and some types of NoSQL databases.

Quantitative vs. Qualitative Data

• Quantitative Data: Described using numbers, and basic mathematical procedures, including addition, are possible on the set.
• Qualitative Data: Cannot be described using numbers and basic mathematics
• Quantitative data can be broken down into:
  • Discrete counted data that only takes on certain values.
  • Continuous measured data that exists on an infinite range of values.

The Four Levels of Data

• Nominal: Data described purely by name or category (e.g., gender, nationality).
  • Measure of center: Mode
• Ordinal: Data with a rank order, but no relative differences between observations (e.g., Likert scales).
  • Measure of center: Median
• Interval: Data with meaningful subtraction between data points (e.g., temperature in Celsius).
  • Measure of center: arithmetic Mean
  • Measure of variation: Standard deviation
    1. Find the mean of the data.
    2. For each number in the dataset, subtract it from the mean and then square it.
    3. Find the average of each square difference.
    4. Take the square root of the number obtained in Step 3 – this is the standard deviation.
• Ratio: Data with meaningful multiplication and division (e.g., temperature in Kelvin, money).
  • Measure of center: Arithmetic mean still holds meaning at this level, as does a new type of mean called the geometric mean, which is the square root of the product of all the values.
  • geometric mean is the square root of the product of all the values.

The Five Steps of Data Science

• Data science follows a structured, step-by-step process that, when followed, preserves the integrity of the results and leads to a deeper understanding of the data and the environment the data comes from.
• The five steps of data science are:
  1. Asking an interesting question
  2. Obtaining the data
  3. Exploring the data
  4. Modeling the data
  5. Communicating and visualizing the results

Asking an Interesting Question

• The first and perhaps most important step in the data science process.

Obtaining the Data

• Sourcing and collecting the data that you will need to answer the question or solve the problem you have identified.

Exploring the Data

• Examining the characteristics and patterns in your data to gain a better understanding of it.
• Questions to guide data exploration:
  • Is the data structured or not?
  • What does each row represent?
  • What does each column represent?
  • Are there any missing data points?
  • Do we need to perform any transformations on the columns?
• pandas is a commonly used Python package for data manipulation and analysis.
• DataFrames are two-dimensional in nature. DataFrames are organized in a row/column structure just as spreadsheets are.
• The Series object is simply a DataFrame, but only with one dimension.

Modeling the Data

• Using statistical and ML techniques to build models that can be used to make predictions or inform decision-making.

Communicating and Visualizing the Results

• Effectively sharing your findings and insights with others.

Basic Mathematics

• Mathematics is one of the three crucial components of data science.
• The concepts presented in this chapter will not only be useful in later chapters but also in understanding probabilistic and statistical models.

Vectors and Matrices

• A vector is a one-dimensional array representing a series of numbers. Vectors give us a simple way of storing multiple dimensions of a single data point/observation.
  • Example: If → x = (3 6 8) then 𝓍 1 = 3
• A matrix is a two-dimensional representation of arrays of numbers.
  • The dimension of a matrix, denoted by n x m (n by m), tells us that the matrix has n rows and m columns.

Arithmetic Symbols

• The uppercase sigma, $\sum$, symbol is a universal symbol for addition. Whatever is to the right of the sigma symbol is usually something iterable, meaning that we can go over it one by one (for example, a vector).
  • Example: If we have a vector (x) of length n, the mean of the vector can be calculated as follows: $mean = \frac{1}{n} \sum{x_i}$
• The dot product is an operator such as addition and multiplication. It is used to combine two vectors.
  • Example: $(3, 7) \cdot (9, 5) = 3 * 9 + 7 * 5 = 62$

Logarithms/Exponents

• An exponent tells you how many times you have to multiply a number by itself.
• A logarithm is a number that answers the question “What exponent gets me from the base to this other number?”
• Exponents and logarithms are most important when dealing with growth.
  • Example: $A = Pert$
    • $A$ denotes the final amount
    • $P$ denotes the principal investment
    • $e$ denotes a constant (2.718)
    • $r$ denotes the rate of growth
    • $t$ denotes the time (in years)

Set Theory

• Set theory involves mathematical operations at the set level. It is sometimes thought of as a basic fundamental group of theorems that governs the rest of mathematics.
• A set is a collection of distinct objects. A set can be thought of as a list in Python but with no repeat objects.
• The magnitude of a set is the number of elements in the set and is represented as follows: $|A| = magnitude of A$
• If we wish to denote that an element is within a set, we can use the epsilon notation, as shown here: $2 \in {1,2, 3}$
• The intersection of two sets is a set whose elements appear in both sets. It is denoted using the ∩ symbol.
• The union of two sets is a set whose elements appear in either set. It is denoted using the ∪ symbol.
• The Jaccard measure (Jaccard similarity) between the two sets is defined as follows: $JS(A,B) = \frac{|A \cap B|}{|A \cup B|}$

Linear Algebra

• Linear algebra, an area of mathematics that deals with matrices and vectors, provides the necessary tools to perform these calculations efficiently.
• Matrix multiplication
  • To multiply matrices, their dimensions must match up. This means that the first matrix must have the same number of columns as the second matrix has rows.
  • The resulting matrix will always have dimensions equal to the outer numbers in the dimension pairs.
  • Each element is the result of a dot product between rows and columns of the original matrices.