Lecture 15 Factor Analysis Factor Analysis Like clustering is classification without knowing the labels we have that Factor Analysis is like regression without the targets Attributes are noisy linear functions of factors Noise model p x y is Gaussian and prior p y is gaussian All factors can cooperate to generate output unlike MoG We use fewer factors than attributes dimensionality reduction Its like a sphere of data that gets warped into an ellipse after which we add independent noise to each attribute Final model is Gaussian so we can remove the mean first centering EM E step We compute the posteriors using algebra for Gaussians Since we know that the posteriors must Gaussian we only need to consider the quadratic form in the exponent There are also some tricks to replace dxd inverses by smaller kxk inverses k factors d attributes M step take derivatives and set to zero analytic updates We can change A y together using a rotation and the model will not change
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