We present a new perspective on the subspace compensation techniques that currently dominate the field of speaker recognition using Gaussian Mixture Models (GMMs). Rather than the traditional factor analysis approach, we use Gaussian modeling in the sufficient statistic supervector space combined with Probabilistic Principal Component Analysis (PPCA) within-class and shared across class covariance matrices to derive a family of training and testing algorithms. Key to this analysis is the use of two noise terms for each speech cut: a random channel offset and a length dependent observation noise. Using the Wiener filtering perspective, formulas for optimal train and test algorithms for Joint Factor Analysis (JFA) are simple to derive. In addition, we can show that an alternative form of Wiener filtering results in the i-vector approach, thus tying together these two disparate techniques.