Tractable approximations for probabilistic models: the adaptive Thouless-Anderson-Palmer mean field approach

Area of Science:

• Statistical physics
• Probabilistic machine learning
• Computational statistics

Background:

• Approximating averages in probabilistic models is computationally challenging.
• Traditional Thouless-Anderson-Palmer (TAP) methods require knowledge of coupling distributions.
• Existing methods struggle with adaptability to specific model parameters.

Purpose of the Study:

• To develop an advanced mean field method for approximating averages in probabilistic data models.
• To create a method that adapts to concrete couplings, unlike conventional TAP.
• To provide a more flexible and applicable approach for analyzing probabilistic systems.

Main Methods:

• The study develops an advanced mean field method.
• The method is based on the Thouless-Anderson-Palmer (TAP) approach from disorder physics.
• It is validated using replica calculations and simulations on a real data set.

Main Results:

• The proposed method successfully approximates averages in probabilistic data models.
• It adapts to concrete couplings, removing the need for distribution knowledge.
• The approach is validated for models exhibiting non-glassy behavior.

Conclusions:

• The advanced mean field method offers a novel and effective way to approximate averages in probabilistic models.
• This method provides greater flexibility by adapting to specific couplings.
• It shows promise for analyzing non-glassy probabilistic systems, supported by theoretical and empirical evidence.