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transactions for a day, and there are no fraudulent transactions. The ML
estimate tells us that the probability of credit card fraud is zero. The MAP
estimate would allow us to incorporate our prior knowledge that there is some
probability of fraud, we just haven’t seen it yet.
2.3 Point estimation and probabilistic linear regression We will now apply point estimation to a slightly more interesting problem,
linear regression, and on the way will discover some very elegant connections
between some of the machine learning algorithms we have already seen and
our new probabilistic approach. Suppose now that we have m data points
(x1 , y1 ), . . . , (xm , ym ), where xi ∈ Jd are the independent variables and yi ∈ J
7 are the dependent variables. We will use a likelihood model under which yi
depends linearly on xi , and the yi ’s are all independent. Speciﬁcally, we
yi ∼ θT xi + E, where θ ∈ Jd are the parameters we are interested in, and E represents noise.
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This note was uploaded on 03/24/2014 for the course MIT 15.097 taught by Professor Cynthiarudin during the Spring '12 term at MIT.
- Spring '12