You will find here articles and tutorials that I published between 2017 and 2021, covering original, off-the-beaten-path content in machine learning, operations research, statistics, dynamical systems, mathematics and related topics. The emphasis is on applications, the style is compact, and many illustrations are provided. Concepts are explained in simple English, avoiding jargon and arcane theories.

To receive updates about new articles and eBooks, sign up for our newsletter, here. The most recent material is available here. Two of my eBooks, available for free, can be accessed here. See my bio, here. Besides my Data Science Central articles listed below, I also invite you to read my posts on MathOverflow, StackExchange, and CrossValidated.

Here is the list, broken down by category, and in reverse chronological order.

Technical

- Machine Learning Inference for Point Processes: A General, Simple Introduction with Simulations
- Simple Machine Learning Approach to Testing for Independence
- An Easy Way to Solve Complex Optimization Problems in Machine Learning
- Introducing an All-purpose, Robust, Fast, Simple Non-linear Regression
- Variance, Attractors and Behavior of Chaotic Statistical Systems
- New Family of Generalized Gaussian Distributions
- Gentle Approach to Linear Algebra, with Machine Learning Applications
- Confidence Intervals Without Pain
- Re-sampling: Amazing Results and Applications
- How to Automatically Determine the Number of Clusters in your Data - and more
- New Perspectives on Statistical Distributions and Deep Learning
- A Plethora of Original, Not Well-Known Statistical Tests
- New Decimal Systems - Great Sandbox for Data Scientists and Mathematicians
- Are the Digits of Pi Truly Random?
- Data Science and Machine Learning Without Mathematics
- Advanced Machine Learning with Basic Excel
- State-of-the-Art Machine Learning Automation with HDT
- Tutorial: Neutralizing Outliers in Any Dimension
- The Fundamental Statistics Theorem Revisited
- Variance, Clustering, and Density Estimation Revisited
- The Death of the Statistical Tests of Hypotheses
- 4 Easy Steps to Structure Highly Unstructured Big Data, via Automated Indexation
- The best kept secret about linear and logistic regression
- Black-box Confidence Intervals: Excel and Perl Implementation
- Jackknife and linear regression in Excel: implementation and comparison
- Jackknife logistic and linear regression for clustering and predictions

Business

- The Machine Learning Process in 7 Steps
- New Stock Trading and Lottery Game Rooted in Deep Math
- Time series, Growth Modeling and Data Science Wizardy
- How to Stabilize Data Systems, to Avoid Decay in Model Performance
- 22 Differences Between Junior and Senior Data Scientists
- The First Things you Should Learn as a Data Scientist - Not what you Think
- Difference between Machine Learning, Data Science, AI, Deep Learning, and Statistics
- 21 data science systems used by Amazon to operate its business
- Life Cycle of Data Science Projects
- 40 Techniques Used by Data Scientists
- Designing better algorithms: 5 case studies
- Architecture of Data Science Projects
- 24 Uses of Statistical Modeling (Part II) | (Part I)
- The ABCD's of Business Optimization
- What you won't learn in stats classes
- Biased vs Unbiased: Debunking Statistical Myths

Technical

- A Gentle, Original Approach to Stochastic Point Processes
- A New Class of Non-standard Probability Distributions
- A New Machine Learning Optimization Technique - Part I
- Machine Learning Perspective on the Twin Prime Conjecture
- The Inverse Problem in Random Dynamical Systems
- Central Limit Theorem for Non-Independent Random Variables
- Defining and Measuring Chaos in Data Sets: Why and How, in Simple Words
- Hurwitz-Riemann Zeta And Other Special Probability Distributions
- Maximum runs in Bernoulli trials: simulations and results
- Moving Averages: Natural Weights, Iterated Convolutions, and Central Limit Theorem
- Amazing Things You Did Not Know You Could Do in Excel
- New Tests of Randomness and Independence for Sequences of Observations
- Interesting Application of the Poisson-Binomial Distribution
- Alternative to the Arithmetic, Geometric, and Harmonic Means
- Bernouilli Lattice Models - Connection to Poisson Processes
- Simulating Distributions with One-Line Formulas, even in Excel
- Simplified Logistic Regression
- Simple Trick to Normalize Correlations, R-squared, and so on
- Simple Trick to Remove Serial Correlation in Regression Models
- A Beautiful Result in Probability Theory
- Long-range Correlations in Time Series: Modeling, Testing, Case Study
- Difference Between Correlation and Regression in Statistics
- One Trillion Random Digits
- New Perspective on the Central Limit Theorem and Statistical Testing
- Simple Solution to Feature Selection Problems
- Scale-Invariant Clustering and Regression
- Deep Dive into Polynomial Regression and Overfitting
- Stochastic Processes and New Tests of Randomness - Application to Cool Number Theory Problem
- A Simple Introduction to Complex Stochastic Processes - Part 2
- A Simple Introduction to Complex Stochastic Processes
- High Precision Computing: Benchmark, Examples, and Tutorial
- Logistic Map, Chaos, Randomness and Quantum Algorithms
- 9 Off-the-beaten-path Statistical Science Topics with Interesting Applications
- Data Science Method to Discover Large Prime Numbers
- Nice Generalization of the K-NN Clustering Algorithm - Also Useful for Data Reduction
- How and Why: Decorrelate Time Series
- Distribution of Arrival Times of Extreme Events
- Why Zipf's law explains so many big data and physics phenomenons

Problems

- Interesting Problem: Random Triangles
- A Simple Regression Problem
- Some Irresistible Integrals, Computed Using Statistical Concepts
- Another Off-the-beaten-path Data Science Problem
- Two More Math Problems: Continued Fractions, Nested Square Roots, Digits of Pi
- Difficult Probability Problem: Distribution of Digits in Rogue Systems
- Little Stochastic Geometry Problem: Random Circles
- Question: Correlation Coefficient in Flat Line Model
- Paradox Regarding Random (Normal) Numbers
- 88 percent of all integers have a factor under 100

Business and General

- Lessons to be Learned from the Facebook Outage
- Simple Introduction to Public-Key Cryptography and Cryptanalysis
- What I Learned From 25 Years of Machine Learning
- Common Errors in Machine Learning due to Poor Statistics Knowledge
- How to Lie with P-values
- Growth Modeling for Business Managers and Executives
- Unexpected Use of AI: Solving Complex Mathematical Problems
- 8 Tips to Leverage Analytics: Advice for Small (and Big) Businesses
- Four Types of Data Scientist
- New Directions in Cryptography
- From Petabytes to Nanobits, with Application to Blockchain
- Preventing Cambridge Analytica and Others to Hack into Facebook Data
- Interesting Application of the Zipf Distribution: Data Purging
- 22 tips for better data science
- Machine Learning Algorithm to Trade Bitcoin
- How Mathematical Discoveries are Made
- How to Solve the New $1 Million Kaggle Problem - Home Value Estimates
- Detecting Fake News, Fake Reviews, Fake Accounts, Fake Pictures
- 10 Data Science, Machine Learning and IoT Predictions for 2017
- Modern Computational Advertising on Social Networks: The Basics
- Building an Algorithm to Break Strong Encryption
- Why so many Machine Learning Implementations Fail?

Mathematics

- The Fascinating World of Non-Periodic Orbits
- Fascinating Facts About Complex Random Variables and the Riemann Hypothesis
- More Surprising Math Images
- Beautiful Mathematical Images
- Deep visualizations to Help Solve Riemann's Conjecture
- Spectacular Visualization: The Eye of the Riemann Zeta Function
- New Probabilistic Approach to Factoring Big Numbers
- Simple Trick to Dramatically Improve Speed of Convergence
- State-of-the-Art Statistical Science to Tackle Famous Number Theory Conjectures
- New Perspective on Fermat's Last Theorem
- Fun Math: Infinite Nested Radicals of Random Variables - Connection with Fractals and Brownian Motions
- Surprising Uses of Synthetic Random Data Sets
- Two New Deep Conjectures in Probabilistic Number Theory
- Extreme Events Modeling Using Continued Fractions
- A Strange Family of Statistical Distributions
- Some Fun with Gentle Chaos, the Golden Ratio, and Stochastic Number Theory
- Fascinating New Results in the Theory of Randomness
- New Mathematical Conjecture?
- Cool Problems in Probabilistic Number Theory and Set Theory
- Fractional Exponentials - Dataset to Benchmark Statistical Tests
- Two Beautiful Mathematical Results - Part 2
- Two Beautiful Mathematical Results
- Four Interesting Math Problems
- Number Theory: Nice Generalization of the Waring Conjecture
- Fascinating Chaotic Sequences with Cool Applications
- Representation of Numbers with Incredibly Fast Converging Fractions
- Simple Proof of the Prime Number Theorem
- Factoring Massive Numbers: Machine Learning Approach
- Representation of Numbers as Infinite Products
- A Beautiful Probability Theorem
- Fascinating Facts and Conjectures about Primes and Other Special Nu...
- Three Original Math and Proba Challenges, with Tutorial
- Challenges of the week

Opinion

- Could we Live in a Universe with Fewer than Three Dimensions?
- Covid: Predictions for the Next Ten Years
- Is Machine Learning an Art, a Science or Something Else?
- Machine Learning Career: Pros and Cons of Having a PhD
- Are Data Scientists Becoming Obsolete?
- Covid-19: Fundamental Statistics that are Ignored
- Could Machine Learning Practitioners Prove Deep Math Conjectures?
- Why You Should be a Data Science Generalist - and How to Become One
- Is a PhD helpful for a data science career?
- Full Stack Data Scientist: The Elusive Unicorn and Data Hacker
- Are data science or stats curricula in US too specialized?
- How do you identify an actual data scientist?
- Is it still possible today to become a self-taught data scientist?
- Why Logistic Regression should be the last thing you learn when becoming a Data Scientist
- 5 Myths About PhD Data Scientists
- Can you be sued for using the wrong data?

General

- Six Degrees of Separation Between Any Two Data Sets
- 7 Simple Tricks to Handle Complex Machine Learning Issues
- From Machine Learning to Machine Unlearning
- First Doctorship in Data Science
- Python Overtakes R for Data Science and Machine Learning
- Mars Craters: An Interesting Stochastic Geometry Problem
- Sample Projects for Data Scientists in Training
- Number Representation Systems Explained in One Picture
- Data Science Cheat Sheet
- Hitchhiker's Guide to Data Science, Machine Learning, R, Python
- Answers to dozens of data science job interview questions
- Advanced Machine Learning with Basic Excel
- Difference between ML, Data Science, AI, Deep Learning, and Statistics