 PORTALE DELLA DIDATTICA ### Introduction to belief propagation

01ROOKG

A.A. 2019/20

2019/20

Introduction to belief propagation

PERIOD: SEPTEMBER Belief propagation is a very powerful iterative algorithm (of the message-passing type), used for solving several statistical inference and combinatorial optimization problems (decoding of error-correcting codes, resourse allocation, data clustering, etcetera). The course aims at discussing the basic concepts of belief propagation, making use of a physical approach, that is, presenting the method as an algorithm for approximate computation of marginals of the Boltzmann distribution for a given kind of thermodynamic system, exploiting suitable formal analogies. Indeed two different approaches (which turn out to be equivalent) are presented, a variational one and a self-consistent one (the latter also known as cavity method). One of the aforementioned applications is also treated in some detail, according to main interests of students attending the course.

Introduction to belief propagation

PERIOD: SEPTEMBER Belief propagation is a very powerful iterative algorithm (of the message-passing type), used for solving several statistical inference and combinatorial optimization problems (decoding of error-correcting codes, resourse allocation, data clustering, etcetera). The course aims at discussing the basic concepts of belief propagation, making use of a physical approach, that is, presenting the method as an algorithm for approximate computation of marginals of the Boltzmann distribution for a given kind of thermodynamic system, exploiting suitable formal analogies. Indeed two different approaches (which turn out to be equivalent) are presented, a variational one and a self-consistent one (the latter also known as cavity method). One of the aforementioned applications is also treated in some detail, according to main interests of students attending the course.

Introduction to belief propagation

Introduction to belief propagation

Introduction to belief propagation

Introduction to belief propagation

Introduction to belief propagation

1. Recaps of statistical mechanics. Formal analogies with inference problems. 2. Old “belief propagation”: Bethe-Peierls approximation and quasi-chemical approximation. 3. Self-consistent approach and relationships with the cavity method. 4. Variational approach and relationships with the cluster-variation method. 5. Examples of application: statistical inference and combinatorial optimization.

Introduction to belief propagation

1. Recaps of statistical mechanics. Formal analogies with inference problems. 2. Old “belief propagation”: Bethe-Peierls approximation and quasi-chemical approximation. 3. Self-consistent approach and relationships with the cavity method. 4. Variational approach and relationships with the cluster-variation method. 5. Examples of application: statistical inference and combinatorial optimization.

Introduction to belief propagation

Introduction to belief propagation

Introduction to belief propagation

Introduction to belief propagation

Introduction to belief propagation

Introduction to belief propagation

Introduction to belief propagation

Modalitŕ di esame:

Introduction to belief propagation

Introduction to belief propagation

Exam:

Introduction to belief propagation