Data Science =
Math (Fourier FFT) +
AI (Convoluted Neural Network) +
AI and Big Data are Twins, their Mother is Math.
“AI 3.0“ today, although impressive in “DeepLearning“, is still using “primitive” high school Math, namely:
AI has not taken advantage of the power of post-Modern Math invented since WW II, esp. IT related, ie :
- Category Theory (Functional Programming),
- Algebraic Topology : Homology (Big Data Analytics)
- Homotopy Type Theory ‘HoTT’ (Machine Proof Math Theorems) .
That is the argument of the Harvard Math Dean Prof ST Yau 丘城桐 (First Chinese Fields Medalist), who predicts the future “AI 4.0“ can be smarter and more powerful.
… Current AI deals with Big Data:
- Purely Statistical approach and experience-oriented, not from Big Data’s inherent Mathematical structures (eg. Homology or Homotopy).
- The Data analytical result is environment specific, lacks portability to other environments.
3. Lack effective Algorithms, esp. Algebraic Topology computes Homology or Co-homology using Linear Algebra (Matrices).
4. Limited by Hardware Speed (eg. GPU), reduced to layered-structure problem solving approach. It is a simple math analysis, not the REAL Boltzmann Machine which finds the most Optimum solution.
AI 1.0 : 1950s by Alan Turing, MIT John McCarthy (coined the term “AI”, Lisp Language inventor).
AI 2.0 : 1970s/80s. “Rule-Based Expert Systems” using Fuzzy Logic.
[AI Winter : 1990s / 2000s. Failed ambitious Japanese “5th Generation Computer” based on Prolog-based “Predicate” Logic]
AI 3.0 : 2010s – now. “DeepLearning” by Prof Geoffry Hinton using primitive Math (Statistics, Probability, Calculus Gradient Descent)
AI 4.0 : Future. Using “Propositional Type” Logic, Topology (Homology, Homotopy) , Linear Algebra, Category.
Microsoft 40+ series of FREE Python Tutorials on Youtube : AI / Machine Learning, Data Analytics, Automation Scripting.
“No, Machine Learning is not just glorified Statistics” by Joe Davison https://link.medium.com/fv3z50FDYY
Simplest explanation by Cheh Wu:
(4 Parts Video : auto-play after each part)
The Math Theory behind Gradient Descent: “Multi-Variable Calculus” invented by Augustin-Louis Cauchy (19 CE, France)
1. Revision: Dot Product of Vectors
2. Directional Derivative
3. Gradient Descent (opposite = Ascent)
Deeplearning with Gradient Descent: