Aston Recent Activities

1
Aston - Recent Activities

• David Saad

2
Inference in Sparse/Dense Graphs

• Task infer variables S from interactions Z
• MPM / MAP- Both computationally difficult
• Message passing highly successful for inference
  in sparse systems with discrete variables
• Densely connected graphs?

3
Inference by Replication

• Inference by replication over a large number of
  systems
• Applications CDMA signal detection, learning in
  Ising linear perceptron

4
CDMA Signal Detection
5
Ising Linear Perceptron
6
Resource Allocation

• A system of nodes (computers?) on a graph
• Each node with its own capability and task
• How can we redistribute sub-tasks such that
• All tasks are carried out
• The flow is minimise
• Quadratic cost

7
Inference with Real Variables

• Message passing with real variables passing
  functions
• Cavity and replica based analyses
• Message passing algorithm

8
Resource Allocation - Results

• c3, N1,000, Gaussian capacities, average 0.1,
  0.2, 0.4, 0.6, 0.8, and 1.0 (top to bottom

9
Colourful Neighbourhoods

• Linked to distributed storage SP3
• Simple BP based algorithm and WSAT
• Linear/Poisson graphs
• Similar performance
• WSAT required tweaking
• Worse scaling

10
Colourful Neighbourhoods

• For larger systems BP is likely to be better
• Cluster variation, for a better solution and
  larger neighbourhoods
• Worse scaling with the number of segments

11
Phase Diagram LDPC Codes

• Phase diagram under RS and 1step RSB for LDPC
  codes
• For both BEC and BSC
• Extending previous results using an alternative
  computational method

12
Current and Future Work

• Using the replicated inference approach for LDPC
  decoding and compression
• Extending the inference method for networks with
  real variables and a range of channel constraints
  (RSB?)
• Cluster variation for multi-stage neighbourhoods

13
Input from Andrea Montanari

• Area theorem for various channels, coding systems
  (LDPC, turbo)
• matching condition - constraint on capacity
  achieving codes
• upper bound on the MAP threshold coincides with
  statistical physics calculations
• prove convergence and correctness of BP for LDPC
  codes above the ML threshold
• Proved convergence of belief propagation for
  multi-user detection with Gaussian/BPSK signals
  and Tanaka's capacity formula

14
Unpublished/ In Progress

• Information capacity of a tree like network
• Use complexity to derive bounds on the threshold
  for reliable communication along such networks
• Phase transitions and algorithms in network
  tomography.
• Algorithm for finite length code optimization