Stat841f09 - Wiki Course Notes

# tells us how likely this hence we have found a

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Unformatted text preview: that would be one, i.e. the probability is 1. If the point is far from the center, then the probability ( function value) will be close to zero, that is, it’s less likely. Therefore, we can treat as the probability of a particular feature given data. When we have those features, then is the linear combination of the features. Hence, any of the weights , which is equal to particular will appear given those features. Therefore, the weight shows the probability of class membership given feature. , tells us how likely this Hence, we have found a probabilistic point of view to look at RBF Network! Note There are some inconsistencies with this probabilistic point of view. There are no restrictions that force and 1. So if least squares is used to solve this, to be between 0 cannot be interpreted as a probability. As ide Feature Space: One way to produce a feature space is LDA Suppose, we have n data points to . Each data point has d features. And these n data points consist of the X matrix, wikicour senote.com/w/index.php?title= Stat841&amp;pr intable= yes 51/74 10/09/2013 Stat841 - Wiki Cour se Notes Also, we have feature space, If we want to solve a regression problem for the input data, we don’t perform Least Square on this matrix, we do Least Square on the feature space, i.e. on the matrix. The dimensionality of is M by n. We can add which is not any function of Now, we still have n data points, but we define these n data points in terms of a new set of features. So, originally, we define our data points by d features, but now, we define them by M features. And what are those M features telling us? Let us look at the first column of matrix. The first entry is applied to , and so on, until the last entry is applied to . Suppose each of these is defined by . Then, each checks the similarity of the data point with its center. Hence, the new set of features are actually representing M centers in our data set, and for each data point, its new features check how this point is similar to the first c...
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