Sunday, January 18, 2015

Algorithms and Music

               MATHEMATICAL MODELS

  Regression is a method by which a functional relationship in the real world may be described by a mathematical model which may then, like all models, may be used to explore, describe or predict the relationship.
  The method of least squares, published in 1805, showed the orbits of astrological bodies about the sun. The observations of planets and comets,using regression techniques, began to further the science. The term regression was coined in the 19th century to describe a biological phenomenon. The heights of descendants of tall ancestors would regress downward toward a normal average would become known as regression toward the mean.
  Linear regression
Linear regression The degrees of freedom number in the Regression line is the number of predictors used. Here that number is 1, and the regression has a single predictor.

 Multiple regression analysis models can be used to observe the algebraic formula :           (y = a + bc)

When using these math techniques, Using multi-tier tests to bring the model into balance, always seems to me like a symphony of music. Turns out it is allot like music, but in the form of algorithms.  
  Machine learning  is a scientific discipline that explores the construction and study of algorithms that can learn from data. Such algorithms operate by building a model based on inputs and using that to make predictions or decisions, rather than following only explicitly programmed instructions.Machine learning can be considered a subfield of computer science and statistics. It has strong ties to artificial intelligence and optimization, which deliver methods, theory and application domains to the field. Machine learning is employed in a range of computing tasks where designing and programming explicit, rule-based algorithms is infeasible. Example applications include spam filtering, optical character recognition  search engines and computer vision. Machine learning is sometimes conflated with data mining, although that focuses more on exploratory data analysis.Machine learning and pattern recognition "can be viewed as two facets of the same field.
  Finally, the foundations of this science, have the constant balance necessary to allow observations to be made. Observing such discoveries as the golden ratio,the zero,PHI +, phi -,irrational numbers, Solfeggio scale of music,and the Fibonacci sequence in nature and more. The multiple layers of perfection of this science have been unfolding since the Egyptians and the Greeks,Hindu sanskriti, I Ching Hexagrams,started to unfold into human knowledge and allow the meta- knowledge that we see today.