Topics

• Analytic sets

  Capacitability, a non-Borel witness, and the separation it settles.

• Auditing

  What an audit can learn from a learner it cannot see inside.

• Cardinal bounds

  On infinite ground sets, the exact bound on traces is Dedekind's ded.

• Compression

  Finite VC dimension is the same as compressibility with side information.

• Graphical models

  When local consistency forces a global structure, over acyclic bases both classical and quantum.

• Information theory

  Pinsker's inequality with the sharp constant, and the Gaussian divergence in closed form.

• Multiclass dimensions

  Pajor's inequality beyond two labels, and where Natarajan and DS dimension part ways.

• Online learning

  Littlestone dimension, the optimal mistake bound, and where online learning sits relative to PAC.

• PAC learnability

  The fundamental theorem of statistical learning, and what can be removed from a learner without losing it.

• Traces and shattering

  How many sets a family can cut out, and how many it shatters.

• VC dimension

  Computed exactly for halfspaces, and bounded in both directions for a dual class.