Exploration of a continuous minimax entropy framework with parameterized features

Investigate the continuous formulation of the minimax entropy problem in which features are parameterized by continuous weights f_w(x), develop methods to optimize the parameters w to minimize the entropy S(P_w) of the associated maximum entropy model, and characterize the complementary insights this continuous framework provides relative to discrete feature selection.

Background

Beyond selecting among discrete features (e.g., averages or pairwise correlations), the authors propose optimizing over a parameterized family of feature functions f_w(x). They illustrate this idea and suggest gradient‑based optimization via ∇_w S(P_w), indicating a potential continuous analogue of the minimax entropy problem.

They emphasize that this direction has not yet been explored, and could yield complementary insights compared to the discrete setting, motivating the development of algorithms and theory for continuous feature optimization in minimax entropy models.