a python implementation of various versions of the information bottleneck, including automated parameter searching
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…ped zeroes, added make_bins, improved plotting, added query_coord, fixed other bugs
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README.md

This project implements the generalized information bottleneck (Strouse, Schwab 2016), which includes the information bottleneck (IB) (Tishby, Pereira, Bialek 1999) and the deterministic information bottleneck (DIB) (Strouse, Schwab 2016) as special cases.

The generalized IB operates on an input distribution p(X,Y) and clusters/compresses X into T such that T has/retains maximal information about Y. Its output is a cluster mapping / compressive encoder q(t|x). The cost function the generalized IB minimizes is:

L[q(t|x)] = H(T) - alpha × H(T|X) - beta × I(T;Y)

alpha=0 is the DIB case, alpha=1 is the IB case, and intermediate values interpolate between the two. beta is a tradeoff parameter between compression and informativeness. For more, see the paper links above.

FILES

  1. IB.py includes the core functionality to run the generalized IB on data. This is the primary file most will be interested in.
  2. data_generation.py includes some example functions to generate synthetic data for the IB. This is just to help you get off the ground quickly, but you probably want to run the IB on your own data.
  3. example_experiments.py includes some example files written to run IB experiments, for illustrative purposes.

DIRECTIONS

If all you want to do is run IB with a specific alpha and beta, then see the first example in example_experiments.py. This task uses the model and dataset classes defined in IB.py.

If instead you are interested in tracing out an IB curve across multiple beta, or want to run a set of experiments with different parameters (alpha, convergence parameters, etc), then see the second example in example_experiments.py. This task uses the IB function in IB.py.

The IB function accepts as input a pandas dataframe, where rows indicate separate experiments (i.e. settings of the fit parameters) and columns indicate fit parameters. This design choice was made to: 1) facilitate experimentation, and 2) so that the input format matched the output format. It is inspired by the "tidy data" paradigm (Wickham 2014). For each combination of fit parameters, the refine_beta function helps to select the appropriate beta to try out, and the output dataframe will include all such runs. (Note that if you want to hand choose your beta, you should use IB_single.)

In the simplest case, one might wish to run just one version of the generalized IB, say the DIB, on a dataset with the default parameters. To do that, one could create a dataframe with a single column, "alpha", and a single row, with the value of alpha in that row equal to 0. That may sound like an overly complicated way to call a single experiment, but its very helpful when running dozens, such as: testing out many versions of the generalized IB (alpha) over different initializations (p0) with different convergence conditions (ctol_abs, ctol_rel, zeroLtol).

See documentation within each file for more details.