Representational models: A common framework for understanding encoding, pattern-component, and representational-similarity analysis
Fig 3
Adjudicating between encoding models with and without regularization.
The axes of the three-dimensional space are formed by the response to three experimental conditions. The activity profile of each unit defines a point in this space. Models are defined by their features (blue arrows) and (when using regularization) a prior distribution of the weights for these features. The features and the prior, together, define a distribution of activity profiles (ellipsoids indicate an iso-probability-density contours of the Gaussian distributions). To predict the activity profile of a single measurement channel, the model is fitted to the training data set (cross). Simple regression finds the shortest projection (black dot) onto the subspace defined by the features, whereas regression with regularization (red dot) biases the prediction towards the predicted distribution. Two models (A, B) with features that span different model subspaces are distinguishable using regression without regularization. (C) This model spans the same subspace as model A. Unregularized regression results in the same projection as for model A, whereas regression with regularization leads to a different projection. (D) A saturated model with as many features as conditions. Unregularized regression can perfectly fit any data point (cross and black dot coincide). With regularization, the prediction is biased towards the predicted distribution (iso-probability-density ellipsoid).