Data structures and algorithms in C for probabilistic modeling and inference in (discrete-time) finite-state Dynamic Bayesian Networks (DBNs).

Currently supported inference tasks:

• filtering.

Algorithms implemented in this version:

• Variable elimination in unrolled network
• Forward algorithm
• Forward algorithm with ADD (Algebraic Decision Diagrams)

The overall structure used for variable, factor and domain representation is highly inspired by the kpu-pp project.

Inputs are accepted in format .duai (uai extended model for dynamic nets). See below for more details.

Follow the instructions to install CUDD package in your platform and set the CUDD variable in Makefile to point to your library's installation location. Then enter the following comands in your prompt.

$ git clone https://github.com/thiagopbueno/dbn.git
$ make install
$ make
$ ./dbn

$ ./dbn
Usage: ./dbn /path/to/model.duai /path/to/observations.duai.evid [OPTIONS]

Filtering methods (-m option):
(1) variable elimination in unrolled network
(2) interface algorithm
(3) interface algorithm with ADDs

OPTIONS:
-m filtering method (1|2|3)
-v verbose

The extended uai model for DBNs is inspired by the specification of the UAI 2014 Inference Competition. The .duai model specification extends the .uai model format and the .duai.evid extends the .uai.evid evidence format.

Please note these formats are proposed by me for testing-only purposes and are still in development.

The syntax for the .duai model is the following:

# model file with extension .duai

DBAYES

<N> [list of variable sizes]

<T> [list of pairs (id_var_slice1, id_var_slice2)]

<S> [list of sensor variable ids]

<FACTOR_0_WIDTH> <ID_PARENT_VAR_FACTOR_0> [list of children variable ids for factor 0]
<FACTOR_1_WIDTH> <ID_PARENT_VAR_FACTOR_1> [list of children variable ids for factor 1]
...
<FACTOR_N_WIDTH> <ID_PARENT_VAR_FACTOR_1> [list of children variable ids for factor N]

<FACTOR_0_SIZE> [list probability values accordingly to the domain linearization of factor 0]
<FACTOR_1_SIZE> [list probability values accordingly to the domain linearization of factor 1]
...
<FACTOR_N_SIZE> [list probability values accordingly to the domain linearization of factor N]

where the constants are such that:

• N is the total number of variables
• T is the total number of variables in the 2TBN model
• S is the total number of variables in the sensor model

Please note that N >= T S. In case of internal nodes in the intra-slice model, N > T S; and in case of models with no internal nodes, N = T S.

The width of a factor refers to the cardinality of its scope/domain and its size is the number of possible instantiations of its scope/domain variables.

Comments are allowed anywhere and start with '#' sign and go until the end of the line. Whitespaces are ignored.

The syntax for the .duai.evid evidence format is the following:

# evidence file with extension .duai.evid
<E> <H>
<ID_VAR_1> [list of H evidence values for variable 1]
<ID_VAR_2> [list of H evidence values for variable 2]
...
<ID_VAR_E> [list of H evidence values for variable E]
<SV> [list of state variables to display filtering trajectory]

where the constants are such that:

• E is the total number of evidence variables
• H is the horizon size (number of timesteps) for filtering
• SV is the total number of state variables of interest (if this is less than T/2, variable elimination is performed)

Comments are allowed anywhere and start with '#' sign and go until the end of the line. Whitespaces are ignored.

The following example Enough Sleep Student Problem is extracted from exercices 15.13 and 15.14 of the textbook Artificial Intelligence: A Modern Approach - 3rd Edition, by Stuart Russel, Peter Norvig.

# data/models/enough-sleep.duai

DBAYES

# Variables
4
2 	#  id=0  name=S  domain={0,1}
2 	#  id=1  name=S' domain={0,1}
2 	#  id=2  name=R  domain={0,1}
2 	#  id=3  name=C  domain={0,1}

# 2TBN
2 0 1

# Sensor
2 2 3

# Domains
1 0
2 1 0
2 2 0
2 3 0

# Factors
2 0.3 0.7           # Pr(S)
4 0.7 0.2 0.3 0.8   # Pr(S'|S)
4 0.3 0.8 0.7 0.2   # Pr(R|S)
4 0.7 0.9 0.3 0.1   # Pr(C|S)

# data/models/enough-sleep.duai.evid
# Pr( S(4) | R(1)=0, R(2)=1, R(3)=1, C(1)=0, C(2)=0, C(3)=1 )
2 3
2 0 1 1
3 0 0 1
1 0

$ ./dbn data/models/HMMs/enough-sleep.duai data/evidence/enough-sleep.duai.evid -v -m 123

>> NETWORK: data/models/HMMs/enough-sleep.duai
number of interface variables   = 1
number of observation variables = 2
number of internal variables    = 0
total number of variables       = 4

>> OBSERVATIONS: data/evidence/enough-sleep.duai.evid
number of timeslices = 7

>> Unrolled filtering: total time = 0.985747 ms, time per slice = 0.140821 ms.
0
0 : 0.136 0.499 0.896 0.349 0.149 0.507 0.483
1 : 0.864 0.501 0.104 0.651 0.851 0.493 0.517


>> Forward filtering: total time = 0.266 ms, time per slice = 0.038 ms.
0
0 : 0.136 0.499 0.896 0.349 0.149 0.507 0.483
1 : 0.864 0.501 0.104 0.651 0.851 0.493 0.517


>> Forward ADD filtering: total time = 0.444 ms, time per slice = 0.063 ms.
0
0 : 0.136 0.499 0.896 0.349 0.149 0.507 0.483
1 : 0.864 0.501 0.104 0.651 0.851 0.493 0.517

Copyright (c) 2015-2016 Thiago Pereira Bueno All Rights Reserved.

DBN is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

DBN is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with DBN. If not, see http://www.gnu.org/licenses/.