Intuitive Meaning of Covariance

Ref: Sometimes we can "augment knowledge" with an unusual or different approach. I would like this reply to be accessible to kindergartners and also have some fun, so everybody get out your crayons! Given paired (x,y)(x,y) data, draw their scatterplot. (The younger students may need a teacher to produce this for them. 🙂 Each pair … Continue reading Intuitive Meaning of Covariance

CUDA 5.0 and VS2012 Integration

Ref: 1. Introduction Here I will share to you my first experience in creating a CUDA-based C++ program on Windows using Visual Studio 2012. CUDA is an acronym of Compute Unified Device Architecture, which is NVIDIA’s general purpose computing API for their graphics card hardware. This simple program is taken from the example code of … Continue reading CUDA 5.0 and VS2012 Integration

Standard Deviation: Why divided by (n-1) and not n?

Ref: Suppose that I am interested in the number of hours per day that high school students in North America spend doing their mathematics homework. The "population" of interest is all high school students in North America, a very large number of people. Lets call this number N. My real interest is the mean and … Continue reading Standard Deviation: Why divided by (n-1) and not n?

Sense of PCA, eigenvectors & eigenvalues

Ref: Imagine a big family dinner, where everybody starts asking you about PCA. First you explain it to your great-grandmother; then to you grandmother; then to your mother; then to your wife; finally, to your daughter (who is a mathematician). Each time the next person is less of a layman. Here is how the conversation … Continue reading Sense of PCA, eigenvectors & eigenvalues

Loss Functions: SVM vs. Softmax

Ref: A picture might help clarify the distinction between the Softmax and SVM classifiers: Example of the difference between the SVM and Softmax classifiers for one datapoint. In both cases we compute the same score vector f (e.g. by matrix multiplication in this section). The difference is in the interpretation of the scores in f: … Continue reading Loss Functions: SVM vs. Softmax