Learning and Unlearning with Mixture Models

Interactive and online learning is becoming important in cognitive computer vision and cognitive robotics, where the primary goal is to study and develop cognitive agents – systems which could continually learn and interact within natural environments. Since most of the real-world environments are ever-changing, and all the information which they provide cannot be available (nor processed) at once, an agent or a system interacting within such an environment has to fulfill some general requirements in the way it builds the models of its environment:

  • The learning algorithm should be able to create and update the models as new data arrives.
  • The models should be updated without explicitly requiring access to the old data.
  • The computational effort needed for a single update should not depend on the amount of data observed sofar.
  • The models should be compact and should not grow significantly with the number of training instances.

Furthermore, in real-life scenarios, an erroneus information will typically get incorporatedinto the models. In such situations, the models should allow for error-recovery without the need of complete relearning. This is especially important in the user-agent interaction settings, in which the user can provide not only positive but negative examples as well to improve the agents knowledge about its environment. Therefore, another requirement (5) is that:

  • the models should support the process of unlearning, i.e., they have to allow online adaptation using the negative examples as well.

Gaussian mixture models (GMM) are powerful tools for estimating probability density functions (generative reconstructive models) from observed data. We are particularly interested in ways of developing the methods for estimating GMMs, for which the five requirements in the previous paragraph apply. We have therefore proposed a method which is based on Kernel Density Estimators and builds GMMs incrementally from positive as well as negative examples and maintains low complexity of the models.

Example of generating a negative KDE:

Example of unlearning using the negative KDE:

A journal paper discussing a method which contains these qualities:

See also: The supplementary page for the paper

An Example of online updating: