Previous discussion is all about supervised learning, meaning there is a labeled or known output data pairs (x, y) for the algorithm to be trained. However, in real world, there are circumstances when intellectual creatures like human beings who can tell patterns without known data or first time. This is realized by another kind of … Continue reading Machine Learning by Andrew Ng_8 K-Means and PCA

Another type of ML worth learning is SVM - support vector machine. The math behind is similar or derived from logistic regression with some mathematical substitution to get below: To be more concrete, it's main purpose is to achieve higher margin in terms of vector distance between data points and decision boundary Next, Kernel is … Continue reading Machine Learning by Andrew Ng_7 Support Vector Machine(SVM)

After a good grasp of theory of machine learning, we should delve into the application of it. Given my limited experience in using it, I won't go deeper but touch on general topic - evaluate ML hypothesis. It will take a bit significant amount of time before actual ML runnig, but definitely worthy to rigorously … Continue reading Machine Learning by Andrew Ng_6 Evaluate ML Hypothesis

The hot word "neuron network" is part of machine learning. It follows the same math logic described before except in a more convoluted manners. In essence, the neuron unit can be regarded as one regression unit: Convolution occurs in the sense that there is hidden layer composed of multiple neurons to take into features from … Continue reading Machine Learning by Andrew Ng_5 Neuron Network

The previous discussion is meant to solve predicting problem that is on continuous values. What if the value you try to predict is discretionary such as category A, B, or even just binary, positive or negative, yes or no etc. These are classification problems and the tool is not linear, or multivariate or polynomial regression … Continue reading Machine Learning by Andrew Ng_4 Logistic Regression

A prelude to get deeper into ML, I first like to point out why linear algebra is so important. It's a magic way to collapse tons of sample data and parameter data into a very short, flat, succinct one-line equation: prediction = data matrix * parameters, below uses single factor (size) for housing price prediction … Continue reading Machine Learning by Andrew Ng_3 Normal Equation

Systematic learning of professor Ng's machine learning course at youtube. First, repaste the major topics he covered in this 112-video series: Through out the whole course of machine learning, we need to grasp the essences of it. Cost of function is one the essences. to understand this concept from linear regression is a easy way. … Continue reading Machine Learning by Andrew Ng_2 Cost Function

It all starts from the leap jump accomplished by calculus in the attempt to calculate irregular shape. It does't take super smartness to go about by dividing the shape into infinitesimal small pieces, then sum up. But the sum-up is at most an approximation, not a finite, accurate value, what makes it accurate? That leap … Continue reading Multivariable Calculus_4 Integral of Vector Field and Multiple Integrals

It's exciting to apply multivariable calculus into solving real problems. First is to find the max/min points. It's largely required in optimization for instance, there are a number of factors in a financial model, tax, tracking error, turn over so on and so forth, you need to find the solution maximizing the performance while keeps … Continue reading Multivariable Calculus_3 Application on Optimization

Math is quite abstract but it has immense usage in our life. Multivariable calculus essentially helps solve complicated problems in practice such as simple needs to measure an irregular area, volume by approximating. To do a good job of approximating, first, introduce the concept of local linearilization by first dirivative for simple x, y function. … Continue reading Multivariable Calculus_2 Application of Multivariable Derivatives