150 Machine Learning, Statistics, and Maths Articles

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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.

Orbit of one instance of the sine map

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

1. Core Articles


  1. Machine Learning Inference for Point Processes: A General, Simple Introduction with Simulations
  2. Simple Machine Learning Approach to Testing for Independence
  3. An Easy Way to Solve Complex Optimization Problems in Machine Learning
  4. Introducing an All-purpose, Robust, Fast, Simple Non-linear Regression
  5. Variance, Attractors and Behavior of Chaotic Statistical Systems
  6. New Family of Generalized Gaussian Distributions
  7. Gentle Approach to Linear Algebra, with Machine Learning Applications
  8. Confidence Intervals Without Pain
  9. Re-sampling: Amazing Results and Applications
  10. How to Automatically Determine the Number of Clusters in your Data - and more
  11. New Perspectives on Statistical Distributions and Deep Learning
  12. A Plethora of Original, Not Well-Known Statistical Tests
  13. New Decimal Systems - Great Sandbox for Data Scientists and Mathematicians
  14. Are the Digits of Pi Truly Random?
  15. Data Science and Machine Learning Without Mathematics
  16. Advanced Machine Learning with Basic Excel
  17. State-of-the-Art Machine Learning Automation with HDT
  18. Tutorial: Neutralizing Outliers in Any Dimension
  19. The Fundamental Statistics Theorem Revisited
  20. Variance, Clustering, and Density Estimation Revisited
  21. The Death of the Statistical Tests of Hypotheses
  22. 4 Easy Steps to Structure Highly Unstructured Big Data, via Automated Indexation 
  23. The best kept secret about linear and logistic regression
  24. Black-box Confidence Intervals: Excel and Perl Implementation
  25. Jackknife and linear regression in Excel: implementation and comparison
  26. Jackknife logistic and linear regression for clustering and predictions


  1. The Machine Learning Process in 7 Steps
  2. New Stock Trading and Lottery Game Rooted in Deep Math
  3. Time series, Growth Modeling and Data Science Wizardy 
  4. How to Stabilize Data Systems, to Avoid Decay in Model Performance
  5. 22 Differences Between Junior and Senior Data Scientists
  6. The First Things you Should Learn as a Data Scientist - Not what you Think
  7. Difference between Machine Learning, Data Science, AI, Deep Learning, and Statistics
  8. 21 data science systems used by Amazon to operate its business
  9. Life Cycle of Data Science Projects
  10. 40 Techniques Used by Data Scientists
  11. Designing better algorithms: 5 case studies
  12. Architecture of Data Science Projects
  13. 24 Uses of Statistical Modeling (Part II)  | (Part I)
  14. The ABCD's of Business Optimization
  15. What you won't learn in stats classes
  16. Biased vs Unbiased: Debunking Statistical Myths

2. Blog Posts About Data Science


  1. A Gentle, Original Approach to Stochastic Point Processes
  2. A New Class of Non-standard Probability Distributions
  3. A New Machine Learning Optimization Technique - Part I
  4. Machine Learning Perspective on the Twin Prime Conjecture
  5. The Inverse Problem in Random Dynamical Systems
  6. Central Limit Theorem for Non-Independent Random Variables
  7. Defining and Measuring Chaos in Data Sets: Why and How, in Simple Words
  8. Hurwitz-Riemann Zeta And Other Special Probability Distributions
  9. Maximum runs in Bernoulli trials: simulations and results
  10. Moving Averages: Natural Weights, Iterated Convolutions, and Central Limit Theorem
  11. Amazing Things You Did Not Know You Could Do in Excel
  12. New Tests of Randomness and Independence for Sequences of Observations
  13. Interesting Application of the Poisson-Binomial Distribution
  14. Alternative to the Arithmetic, Geometric, and Harmonic Means
  15. Bernouilli Lattice Models - Connection to Poisson Processes
  16. Simulating Distributions with One-Line Formulas, even in Excel
  17. Simplified Logistic Regression
  18. Simple Trick to Normalize Correlations, R-squared, and so on
  19. Simple Trick to Remove Serial Correlation in Regression Models
  20. A Beautiful Result in Probability Theory
  21. Long-range Correlations in Time Series: Modeling, Testing, Case Study
  22. Difference Between Correlation and Regression in Statistics
  23. One Trillion Random Digits
  24. New Perspective on the Central Limit Theorem and Statistical Testing
  25. Simple Solution to Feature Selection Problems
  26. Scale-Invariant Clustering and Regression
  27. Deep Dive into Polynomial Regression and Overfitting
  28. Stochastic Processes and New Tests of Randomness - Application to Cool Number Theory Problem
  29. A Simple Introduction to Complex Stochastic Processes - Part 2
  30. A Simple Introduction to Complex Stochastic Processes
  31. High Precision Computing: Benchmark, Examples, and Tutorial
  32. Logistic Map, Chaos, Randomness and Quantum Algorithms
  33. 9 Off-the-beaten-path Statistical Science Topics with Interesting Applications
  34. Data Science Method to Discover Large Prime Numbers
  35. Nice Generalization of the K-NN Clustering Algorithm -  Also Useful for Data Reduction
  36. How and Why: Decorrelate Time Series
  37. Distribution of Arrival Times of Extreme Events
  38. Why Zipf's law explains so many big data and physics phenomenons


  1. Interesting Problem: Random Triangles
  2. A Simple Regression Problem
  3. Some Irresistible Integrals, Computed Using Statistical Concepts
  4. Another Off-the-beaten-path Data Science Problem
  5. Two More Math Problems: Continued Fractions, Nested Square Roots, Digits of Pi
  6. Difficult Probability Problem: Distribution of Digits in Rogue Systems
  7. Little Stochastic Geometry Problem: Random Circles
  8. Question: Correlation Coefficient in Flat Line Model
  9. Paradox Regarding Random (Normal) Numbers
  10. 88 percent of all integers have a factor under 100

Business and General

  1. Lessons to be Learned from the Facebook Outage
  2. Simple Introduction to Public-Key Cryptography and Cryptanalysis
  3. What I Learned From 25 Years of Machine Learning
  4. Common Errors in Machine Learning due to Poor Statistics Knowledge
  5. How to Lie with P-values
  6. Growth Modeling for Business Managers and Executives
  7. Unexpected Use of AI: Solving Complex Mathematical Problems 
  8. 8 Tips to Leverage Analytics: Advice for Small (and Big) Businesses
  9. Four Types of Data Scientist
  10. New Directions in Cryptography
  11. From Petabytes to Nanobits, with Application to Blockchain
  12. Preventing Cambridge Analytica and Others to Hack into Facebook Data
  13. Interesting Application of the Zipf Distribution: Data Purging
  14. 22 tips for better data science
  15. Machine Learning Algorithm to Trade Bitcoin
  16. How Mathematical Discoveries are Made
  17. How to Solve the New $1 Million Kaggle Problem - Home Value Estimates
  18. Detecting Fake News, Fake Reviews, Fake Accounts, Fake Pictures
  19. 10 Data Science, Machine Learning and IoT Predictions for 2017
  20. Modern Computational Advertising on Social Networks: The Basics
  21. Building an Algorithm to Break Strong Encryption
  22. Why so many Machine Learning Implementations Fail?

3. Other Blog Posts


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


  1. Could we Live in a Universe with Fewer than Three Dimensions?
  2. Covid: Predictions for the Next Ten Years
  3. Is Machine Learning an Art, a Science or Something Else?
  4. Machine Learning Career: Pros and Cons of Having a PhD
  5. Are Data Scientists Becoming Obsolete?
  6. Covid-19: Fundamental Statistics that are Ignored
  7. Could Machine Learning Practitioners Prove Deep Math Conjectures?
  8. Why You Should be a Data Science Generalist - and How to Become One
  9. Is a PhD helpful for a data science career?
  10. Full Stack Data Scientist: The Elusive Unicorn and Data Hacker
  11. Are data science or stats curricula in US too specialized?
  12. How do you identify an actual data scientist?
  13. Is it still possible today to become a self-taught data scientist?
  14. Why Logistic Regression should be the last thing you learn when becoming a Data Scientist
  15. 5 Myths About PhD Data Scientists
  16. Can you be sued for using the wrong data?


  1. Six Degrees of Separation Between Any Two Data Sets
  2. 7 Simple Tricks to Handle Complex Machine Learning Issues
  3. From Machine Learning to Machine Unlearning
  4. First Doctorship in Data Science
  5. Python Overtakes R for Data Science and Machine Learning
  6. Mars Craters: An Interesting Stochastic Geometry Problem
  7. Sample Projects for Data Scientists in Training
  8. Number Representation Systems Explained in One Picture
  9. Data Science Cheat Sheet
  10. Hitchhiker's Guide to Data Science, Machine Learning, R, Python
  11. Answers to dozens of data science job interview questions
  12. Advanced Machine Learning with Basic Excel
  13. Difference between ML, Data Science, AI, Deep Learning, and Statistics
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