The Fundamentals of Data Science

 

Two of the biggest buzzwords in our industry is “big data” and “data science”. Big Data seems to have a lot of interest right now, but Data Science is fast becoming a very hot topic.

I think there’s room to really define the science of data science – what are those fundamentals that are needed to make data science truly a science we can build upon?

Below are my thoughts for an outline for such a set of fundamentals:

Fundamentals of Data Science

Introduction

The easiest thing for people within the big data / analytics / data science disciplines is to say “I do data science”. However, when it comes to data science fundamentals, we need to ask the following critical questions: What really is “data”, what are we trying to do with data, and how do we apply scientific principles to achieve our goals with data?

– What is Data?
– The Goal of Data Science
– The Scientific Method

Probability and Statistics

The world is a probabilistic one, so we work with data that is probabilistic – meaning that, given a certain set of preconditions, data will appear to you in a specific way only part of the time.  To apply data science properly, one must become familiar and comfortable with probability and statistics.

– The Two Characteristics of Data
– Examples of Statistical Data
– Introduction to Probability
– Probability Distributions
– Connection with Statistical Distributions
– Statistical Properties (Mean, Mode, Median, Moments, Standard Deviation, etc.)
– Common Probability Distributions (Discrete, Binomial, Normal)
– Other Probability Distributions (Chi-Square, Poisson)
– Joint and Conditional Probabilities
– Bayes’ Rules
– Bayesian Inference

Decision Theory

This section is one of the key fundamentals of data science.  Whether applied in scientific, engineering, or business fields, we are trying to make decisions using data.  Data itself isn’t useful unless it’s telling us something, which we’re making a decision about what it is telling us.  How do we come up with those decisions? What are the factors that go into this decision making process?  What is the best method for making decisions with data?  This section tell us…

– Hypothesis Testing
– Binary Hypothesis Test
– Likelihood Ratio and Log Likelihood Ratio
– Bayes Risk
– Neyman-Pearson Criterion
– Receiver Operating Characteristic (ROC) Curve
– M-ary Hypothesis Test
– Optimal Decision Making

Estimation Theory

Sometimes we make characterizations of data – averages, parameter estimates, etc.  Estimation from data is essentially an extension of decision making, a natural next section from Decision Theory.

– Estimation as Extension of M-ary Hypothesis Test
– Unbiased Estimation
– Minimum Mean Square Error (MMSE)
– Maximum Likelihood Estimation (MLE)
– Maximum A Posteriori Estimation (MAP)
– Kalman Filter

Coordinate Systems

To bring various data elements together into a common decision making framework, we need to know how to align the data.  Knowledge of coordinate systems and how they are used becomes important to lay a solid foundation for bringing disparate data together.

– Introduction to Coordinate Systems
– Euclidian Spaces
– Orthogonal Coordinate Systems
– Properties of Orthogonal Coordinate Systems (angle, dot product, coordinate transformations,
etc.)
– Cartesian Coordinate System
– Polar Coordinate System
– Cylindrical Coordinate System
– Spherical Coordinate System
– Transformations Between Coordinate Systems

Linear Transformations

Once we understand coordinate systems, we can learn why to transform the data to get at the underlying information.  This section describe how we can transform our data into other useful data products through various types of transformations, including the popular Fourier transform.

– Introduction to Linear Transformations
– Properties of Linear Transformations
– Matrix Multiplication
– Fourier Transform
– Properties of Fourier Transforms (time-frequency relationship, shift invariance, spectral
properties, Perseval’s Theorem, Convolution Theorem, etc.)
– Discrete and Continuous Fourier Transforms
– Uncertainty Principle and Aliasing
– Wavelet and Other Transforms

Effects of Computation on Data

An often overlooked aspect of data science is the impact the algorithms we apply have on the information we are seeking to find. Merely applying algorithms and computations to create analytics and other data products has an impact on the effectiveness data-driven decision making ability.  This section take us on a journey of advanced aspects of data science.

– Mathematical Representation of Computation
– Reversible Computations (Bijective Mapping)
– Irreversible Computations
– Impulse Response Functions
– Transformation of Probability Distributions (due to addition, subtraction, multiplication,
division, arbitrary computations, etc.)
– Impacts on Decision Making

Prototype Coding / Programming

One of the key elements to data science is the willingness of practitioners to “get their hands dirty” with data.  This means being able to write programs that access, process, and visualize data in important languages in science and industry. This section takes us on a tour of these important elements.

– Introduction to Programming
– Data Types, Variables, and Functions
– Data Structures (Arrays, etc.)
– Loops, Comparisons, If-Then-Else
– Functions
– Scripting Languages vs. Compilable Langugages
– SQL
– SAS
– R
– Python
– C++

Graph Theory

Graphs are ways to illustrate connections between different data elements, and they are important in today’s interconnected world.

– Introduction to Graph Theory
– Undirected Graphs
– Directed Graphs
– Various Graph Data Structures
– Route and Network Problems

Algorithms

Key to data science is understanding the use of algorithms to compute important data-derived metrics.  Popular data manipulation algorithms are included in this section.

– Introduction to Algorithms
– Recursive Algorithms
– Serial, Parallel, and Distributed Algorithms
– Exhaustive Search
– Divide-and-Conquer (Binary Search)
– Gradient Search
– Sorting Algorithms
– Linear Programming
– Greedy Algorithms
– Heuristic Algorithms
– Randomized Algorithms
– Shortest Path Algorithms for Graphs

Machine Learning

No data science fundamentals course would be complete without exposure to machine learning.  However, it’s important to know that these techniques build upon the fundamentals described in previous sections.  This section gives practitioners an understanding of useful and popular machine learning techniques and why they are applied.

– Introduction to Machine Learning
– Linear Classifiers (Logistic Regression, Naive Bayes Classifier, Support Vector Machines)
– Decision Trees (Random Forests)
– Bayesian Networks
– Hidden Markov Models
– Expectation-Maximization
– Artificial Neural Networks and Deep Learning
– Vector Quantization
– K-Means Clustering

Question:  Do you have any thoughts on the fundamentals of data science? You can leave a comment below.

A Data Science Lesson from Richard Feynman

Richard Feynman

Richard Feynman

Richard Feynman is one of the greatest scientific minds, and what I love about him, aside from his brilliance, is his perspective on why we perform science.   I’ve been reading the compilation of short works of Feynman titled The Pleasure of Finding Things Out, and I recently came across a section that really hit home with me.

In the world of data science, much is made about the algorithms used to work with data, such as random forests or k-mean clustering.  However, I believe there is a missing component – one that deals the fundamentals underlying data science, and that is the real science of data science.

10 Things To Know When Hiring Data Scientists

I’ve been performing data science before there was a field called “data science“, so I’ve had the opportunity to work with and hire a lot of great people.  But if you’re trying to hire a data scientist, how do you know what to look for, and what should you consider in the interview process?

Data Science Word Cloud

I’ve been doing what is now called “data science” since the early 1990s and have helped to hire numerous scientists and engineers over the years.  The teams I’ve had the opportunity to work with are some of the best in the world, tackling some of the most challenging problems facing our country.  These folks are also some of the smartest people I’ve ever had the opportunity to work with.

That said, not everyone is a good fit, and the discipline of data science requires important key elements.  Hiring someone into your team is incredibly important to your business, especially if you’re a small startup or building a critical internal data science team; mistakes can be expensive in both time and money.  This can be even more intimidating if you don’t have the background or experience in hiring scientists, especially someone responsible for this new discipline of working with data.

Beating Cancer and Favoritism with Data

Fortune-Startup RisingI read a couple of items in this month’s Fortune magazine that I thought it was worth passing along.

The first was a small article by Brian Dumaine about the work being done at Applied Proteomics to identify cancer before it develops.  At Applied Proteomics, they use mass spectroscopy to capture and catalog 360,000 different pieces of protein found in blood plasma, and then let supercomputers crunch on the data to identify anomalies associated with cancer.  The company has raised $57 million in venture capital and is backed by Microsoft co-founder Paul Allen.  You can read the first bit of the article here.

The second is from the Word Check callout, showing how access to information is making the word a better place:

wasa: Pronounced [wah-SUH]

(noun) Arabic slang:  A display of partiality toward a favored person or group without regard for their qualifications.  A system that drives much of life in the Middle East — from getting into a good school to landing a good job.

But on the Internet, there is no wasa.

– Adapted from Startup Rising: The Entrepreneurial Revolution Remaking the Middle East by Christopher M. Schroeder

A Review of The Signal and The Noise, A New Book by Nate Silver

Imagine a guy with glasses who used to model baseball stats and play online poker nailing the outcome of the 2012 elections. And when I say “nailing”, I mean that he correctly predicted the U.S. Presidential contest in every one of the 50 states (and nearly every U.S. Senate race, too). He even performed better than some of the most widely-used polling firms. Now imagine that he gives his thoughts on making these types of predictions. That’s exactly what Nate Silver does in his new book The Signal and the Noise.

Nate-Silver-book
I’ve worked in what’s now being called “data science” for nearly twenty years. The title of Silver’s book – The Signal and the Noise – presents an important and sometimes overlooked part of this science. The “signal” is what we’re looking for in the data, and the “noise” is all the stuff in the data that gets in the way of what we’re looking for.