Gaussian process regression

Resources:

http://kingfengji.com/?p=44 Talk about the return of the Gaussian process .

http://www.cnblogs.com/tornadomeet/archive/2013/06/15/3137239.html Machine learning & Data Mining note _11(Gaussian process regression)

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On the internet for a long time, finally found a few articles on the introduction of this aspect, in the first article of the link, we can go to download some demo

But did not understand, the program has not been transferred. Great gods, you can try.

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What is the Gaussian process regression:

Actually divided into two processes, Gaussian process + regression.

Gaussian process: Actually is the normal distribution on the function. It is a linear set consisting of multiple Gaussian functions.

Tip: The Gaussian distribution is actually a normal distribution, and the Gaussian we're talking about is actually a model. Gaussian model.

Gaussian model specifically what, you can imagine the Gaussian function distribution, is the middle width, both sides of the narrow east.

Described as:

Regression: Regression is a relationship. The relationship between Xi and Yi. For example, linear regression analysis, which refers to the existence of X and y linear relationship, that is, a functional relationship.

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Take a look at the following formula:

Instance:

How to calculate k? Need a kernel function, in the Gaussian process regression, our most common kernel is the Gaussian kernel inside the SVM, in order to avoid naming confusion, we generally call the square exponential kernel function.

Squared exponential kernel.

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Now we continue to analyze the above example, if we pass the Gaussian kernel function, calculate the k11-k33, then x* out of mischief, it corresponds to the f* is how much?

We can predict the x* based on the F and K calculated above, because it is a function, a function, and we know that x must be able to calculate Y. At this point, we can base the joint distribution

All the parameters, the corresponding P (f*), that is, this method gives the predicted value of the entire posterior probability distribution, we get the entire distribution of f*, not point estimation.

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In the road edge detection algorithm, when we do GPR (), you will find that we calculate the model, we need to evaluate it, the point of not meet the conditions to kill.

(For each area) the seed points are obtained by the HT Hough Transform, and then the relationship between the seed points, such as covariance K, is used to predict whether other points are satisfying the model. (understood as a straight model), the second step, go to eval, for each of these points, X belongs to test, calculates K (x*,x*) and K (x,x*), unknown point, test point. It is then compared to our own definition of the tmodel (the threshold of the variance of the test point x*) and the Tdata (the test point x* to its predicted mean f*). When satisfied, we consider it to be satisfied and remain in the SP, starting from the set SP of the seed point of the initial selection, each iteration from SC, select Snew, meet on accumulate until SC is empty. That is, this area has been found so far.

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In fact, this algorithm, like the regional growth algorithm, is to define the point of each detection and then increase its length.

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Gaussian process regression