GOBNILP

[News (including bugs)] [Stable version] [Development version] [Python version] [Version used for Liao et al, AAAI-19 paper] [Benchmarks] [Publications on the theory behind GOBNILP] [Publications using GOBNILP]

GOBNILP (Globally Optimal Bayesian Network learning using Integer Linear Programming) is a C program which learns Bayesian networks from complete discrete data or from local scores. GOBNILP uses the SCIP framework for Constraint Integer Programming. Detailed information on installing, running, licence etc can be found in the:

• GOBNILP manual

which is also contained in the GOBNILP distribution.

GOBNILP has been developed by James Cussens and Mark Bartlett. It was supported by MRC grant A graphical model approach to pedigree construction using constrained optimisation (G1002312) until Feb 2015. Goblin 'P' logo courtesy of Robby Higgins.

News (including bugs)

• 2020-01-30: pygobnilp 1.0 released.
• 2019-09-09: API documentation for latest version of the Pyhton version of GOBNILP is now available.
• 2019-09-08: Jupyter notebooks showing interactive use of the Python version of GOBNILP can now be viewed online. The notebooks themselves are available in this bitbucket git repo.
• 2018-04-20: The latest development version of GOBNILP can learn Gaussian networks using BGe scoring (using the OpenBLAS library).
• 2018-01-05: GOBNILP 1.6.3 is the latest stable version. It is identical to GOBNILP 1.6.2 except that one bug has been corrected which produced errors if you were effecting structural constraints (like enforcing/disallowing arrow/adjacencies). It cannot be used with recent versions of SCIP. Use SCIP 3.2.1 with it.

Stable version

Download GOBNILP (stable release).

The current stable version of GOBNILP does not work with recent versions of SCIP, use SCIP 3.2.1 instead.

Development version

The source code for the development version of GOBNILP is available at this bitbucket git repo. This version works with SCIP 6.0.1. Doxygen documentation for a recent development version (not always the latest) is available here. You can generate documentation for the latest development version by running 'make docs' once you have downloaded/cloned the development version. The development version is highly unstable and contains many undocumented features.

Python version

pygobnilp, a Python version of GOBNILP, is available. The stable Python version (currently pygobnilp 1.0) is described in the

• pygobnilp manual

pygobnilp can be installed using pip: pip install pygobnilp. pygobnilp relies on many Python packages and also the Gurobi MIP solver. Installing Gurobi and Anaconda Python together is a convenient way of getting most (not all) of what pygobnilp needs to function. pygobnilp is slower than the C development (or stable) version, but is useful for experimentation.

• The lastest version of pygobnilp is available from this bitbucket git repo.
• Jupyter notebooks showing interactive use of pygobnilp (both Python and R) can be viewed online.. (The notebooks are also available in the bitbucket git repo.)
• API documentation for pygobnilp is available.

Version used for Liao et al, AAAI-19 paper

Available here .

Benchmarks for the current version

GOBNILP has been developed using a set of local score files used originally in the paper Bayesian network learning with cutting planes. Most of these local score input files are in this gzipped tar file. The local score input files alarm, mirna, phen and wdbc were kindly sent to me by Tommi Jaakkola, the others I generated myself. More recently a local score input file (developed by Mark Bartlett) for learning pedigrees has been used as part of the Pedigree Reconstruction using Integer Linear Programming project. The current release can learn directly form data (as well as from local scores files). Some of the the original datasets and the local scores generated from them are available from this directory. However, these original datasets are in a format incompatible with the current GOBNILP release. (This directory also contain some local score files where the data from which they were generated is not available.)

The 'Mildew' local score files in the gzipped tar file contain errors. The correct local scores for 'Mildew' instances can be found in this this directory. For all other instances the same (correct) local scores can be found in either place. Thanks to Peter van Beek for spotting this problem.

The following table provides a summary of benchmarking results for GOBNILP 1.6 using default parameter setttings. (The current release is 1.6.1 but on the input used for these benchmarks 1.6 and 1.6.1 are identical.) All times are in seconds. The GOBNILP output for each of these runs is available in this single file. Both the summary and the full output were generated using SCIP's "make test" utility. (Benchmark results for older GOBNILP versions are available here.)

Benchmarks run on a single core of the following machine: Linux pc435h 3.13.0-49-generic #83-Ubuntu SMP Fri Apr 10 20:11:33 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux. Processor was: Intel(R) Core(TM) i5 CPU 650 @ 3.20GHz

GOBNILP can run into memory problems and immediately abort on sufficiently big problems. The 'Link' learning problems mentioned later are like this and are not included in the following table. Note that GOBNILP did not solve the Diabetes_10000_1_2 or the Pigs_10000_1_2 problem which are in the table. It did however make some progress towards a solution before aborting. Consult the full output for details.

------------------+------+--- Original --+-- Presolved --+----------------+----------------+------+---------+--------+-------+----------+---------+--------
Name              | Type | Conss |  Vars | Conss |  Vars |   Dual Bound   |  Primal Bound  | Gap% |  Iters  |  Nodes |  Time | To First | To Best |       
------------------+------+-------+-------+-------+-------+----------------+----------------+------+---------+--------+-------+----------+---------+--------
Diabetes_100_1_2      CIP    4809    7386    5089    7329      -47697.4126      -47697.4126    0.0      1251        1    50.4       14.2      50.4 ok
Diabetes_1000_1_2     CIP   15555   31406   17553   31368      -268847.008      -268847.008    0.0      5193        3   367.9       23.9     366.9 ok
Diabetes_10000_1_2     --       0       0       0       0           -1e+20            1e+20   --           0        0     0.0        0.0       0.0 abort
Mildew_100_1_3        CIP     854    3988     991    3974      -6380.72748      -6380.72748    0.0       107        1     2.2        1.3       2.2 ok
Mildew_1000_1_3       CIP     156     245     143     232      -52258.8572      -52258.8572    0.0       135        3     0.7        0.0       0.7 ok
Mildew_10000_1_3      CIP     461     744     478     737      -454894.404      -454894.404    0.0       310        1     1.1        0.1       1.1 ok
Pigs_100_1_2          CIP    2907    4368    2837    4288       -41017.047       -41017.047    0.0      1156        1    22.8       17.5      22.8 ok
Pigs_1000_1_2         CIP   13848   24383   14434   24383      -340449.646      -340449.646    0.0      6276        1    65.5       24.8      65.5 ok
Pigs_10000_1_2         --       0       0       0       0           -1e+20            1e+20   --           0        0     0.0        0.0       0.0 abort
Water_100_1_3         CIP     308     679     341     676      -1500.96839      -1500.96839    0.0      1668        3     3.9        0.5       3.8 ok
Water_1000_1_3        CIP     504     889     563     889      -13262.3418      -13262.3418    0.0      3532        3     3.2        0.1       3.2 ok
Water_10000_1_3       CIP     687    1391     772    1391       -128705.65       -128705.65    0.0     12733       89     7.7        0.2       5.2 ok
alarm_100_1_3         CIP     742    1330     782    1329      -1349.22742      -1349.22742    0.0       668        1     1.5        0.2       1.5 ok
alarm_1000_1_3        CIP    1010    2523    1157    2522      -11240.3471      -11240.3471    0.0      1913        1     2.6        0.3       2.6 ok
alarm_10000_1_3       CIP    1486    7356    2123    7355      -105226.512      -105226.512    0.0     31906       91    63.0        1.0      35.4 ok
asia_100_1_99         CIP      47      65      47      64      -245.644264      -245.644264    0.0        23        3     0.0        0.0       0.0 ok
asia_1000_1_99        CIP     115     175     126     175      -2317.41151      -2317.41151    0.0        70        1     0.1        0.0       0.1 ok
asia_10000_1_99       CIP     123     237     149     237      -22466.3965      -22466.3965    0.0       495        3     1.3        0.0       0.9 ok
carpo_100_1_3         CIP    3011    6830    3285    6819      -1829.30685      -1829.30685    0.0    173497      442   278.0        2.0     225.6 ok
carpo_1000_1_3        CIP    1899    4946    2166    4939       -17718.948       -17718.948    0.0     24307       19    46.2        1.1      45.2 ok
carpo_10000_1_3       CIP    2844   18086    4700   18085      -174130.564      -174130.564    0.0     94221      131   308.7        4.5     272.0 ok
hailfinder_100_1_3    CIP     237     357     223     322      -6019.46993      -6019.46993    0.0       207        1     0.4        0.0       0.4 ok
hailfinder_1000_1_    CIP     632    1136     679    1133      -52473.2456      -52473.2456    0.0      1382        3     3.2        0.2       3.2 ok
hailfinder_10000_1    CIP    1542    4693    1860    4693      -497631.796      -497631.796    0.0     20297       46    35.4        0.6      24.5 ok
insurance_100_1_3     CIP     288     448     285     441      -1686.22588      -1686.22588    0.0       131        1     0.3        0.1       0.3 ok
insurance_1000_1_3    CIP     592    1126     625    1125      -13887.3501      -13887.3501    0.0       708        1     1.1        0.2       1.1 ok
insurance_10000_1_    CIP    1117    4316    1442    4315      -132968.577      -132968.577    0.0      5334        2     9.1        0.9       9.1 ok
kredit_1000_1_3       CIP      67     104      62      98      -16695.6695      -16695.6695    0.0        28        3     0.1        0.0       0.1 ok
kredit_1000_1_99      CIP      67     104      62      98      -16695.6695      -16695.6695    0.0        28        3     0.1        0.0       0.1 ok
alarm                 CIP    1441    6484    1738    6483       -9944.3113       -9944.3113    0.0      3644        1     6.4        0.9       6.4 ok
mirna                 CIP     845    1789     900    1789       -2653.7505       -2653.7505    0.0       978        1     1.9        0.2       1.9 ok
phen                  CIP     648    2678     731    2677       -6070.7502       -6070.7502    0.0      1855        1     4.0        0.4       4.0 ok
wdbc                  CIP    1946    7079    2462    7078       -6804.2458       -6804.2458    0.0      6024        1    16.3        0.9      16.3 ok
pedigree1             CIP    1267    1954    1267    1954      -1466.59852      -1466.59852    0.0       599        1     4.0        0.6       4.0 ok
------------------+------+-------+-------+-------+-------+----------------+----------------+------+---------+--------+-------+----------+---------+--------

------------------------------[Nodes]---------------[Time]--------------[ToFirst]-----------[ToLast]-----
  Cnt  Pass  Time  Fail  total(k)     geom.     total     geom.     total     geom.     total     geom.
---------------------------------------------------------------------------------------------------------
   34    32     0     2         0       3.0    1309.1       5.6      96.9       1.5    1176.3       5.3
 shifted geom. [  100/ 10.0]           15.2                11.6                 1.9                10.8 
---------------------------------------------------------------------------------------------------------
@02 timelimit: 0
@01 SCIP(3.1.1)cpx(12.6.0.0):default [GitHash: bade511]

Peter van Beek has kindly made available the problem instances used in this paper. Here are the results of running GOBNILP 1.6.1 on these instances. (Same machine used as for above.)

------------------+------+--- Original --+-- Presolved --+----------------+----------------+------+---------+--------+-------+----------+---------+--------
Name              | Type | Conss |  Vars | Conss |  Vars |   Dual Bound   |  Primal Bound  | Gap% |  Iters  |  Nodes |  Time | To First | To Best |       
------------------+------+-------+-------+-------+-------+----------------+----------------+------+---------+--------+-------+----------+---------+--------
abalone_BIC           CIP     152     279     182     278      -16171.1923      -16171.1923    0.0       224        1     0.2        0.0       0.2 solved not verified
adult_BIC             CIP     290     719     360     718      -330559.759      -330559.759    0.0       402        1     0.5        0.1       0.5 solved not verified
alarm1000_BIC         CIP     807    1484     880    1482      -11783.0463      -11783.0463    0.0      1017        1     2.2        0.2       2.2 solved not verified
alarm100_BIC          CIP     195     342     188     335      -1594.60952      -1594.60952    0.0       189        1     0.5        0.0       0.5 solved not verified
alarm_BIC             CIP     483     950     524     942      -14390.7825      -14390.7825    0.0       485        3     0.5        0.1       0.5 solved not verified
aus_BIC               CIP      80     126      78     122      -5011.10158      -5011.10158    0.0        61        3     0.1        0.0       0.1 solved not verified
autos_BIC             CIP    1182    3091    1536    3090      -1577.15977      -1577.15977    0.0      6416       15    13.3        0.4      13.2 solved not verified
balance_BIC           CIP      12      18       8      13      -4521.01778      -4521.01778    0.0         0        1     0.0        0.0       0.0 solved not verified
bands_BIC             CIP     740    1333     808    1325      -5117.94929      -5117.94929    0.0      1663        1     5.2        0.3       4.7 solved not verified
barley1000_BIC        CIP     164     349     145     327      -67699.7393      -67699.7393    0.0       104        1     0.4        0.0       0.4 solved not verified
bc_BIC                CIP      31      47      22      34      -2785.97529      -2785.97529    0.0        17        3     0.0        0.0       0.0 solved not verified
bc-wisc_BIC           CIP     197     350     223     349      -3334.10035      -3334.10035    0.0       314        1     0.3        0.0       0.1 solved not verified
carpo1000_BIC         CIP     990    2052    1108    2046      -17976.7646      -17976.7646    0.0      3158        5     6.5        0.3       6.5 solved not verified
carpo100_BIC          CIP     353     639     339     622      -2000.21325      -2000.21325    0.0       366        1     0.7        0.1       0.7 solved not verified
carpo500_BIC          CIP     723    1272     753    1259      -9195.48572      -9195.48572    0.0      1376        3     2.8        0.2       2.8 solved not verified
credit_BIC            CIP      65     111      62     106      -6392.47961      -6392.47961    0.0        69        3     0.2        0.0       0.0 solved not verified
diabetes_BIC          CIP      31      53      27      49      -3692.79661      -3692.79661    0.0        34        7     0.1        0.0       0.1 solved not verified
ecoli_BIC             CIP      52      80      51      77      -1778.74275      -1778.74275    0.0        27        1     0.1        0.0       0.0 solved not verified
flag_BIC              CIP     650    1132     703    1132      -2748.10513      -2748.10513    0.0       698        1     1.9        0.2       1.9 solved not verified
glass_BIC             CIP      44      66      39      61       -1365.8638       -1365.8638    0.0        32        3     0.1        0.0       0.1 solved not verified
hailfinder100_BIC     CIP     130     228     101     194      -6414.53453      -6414.53453    0.0       104        1     0.6        0.0       0.6 solved not verified
hailfinder500_BIC     CIP     363     647     362     640      -27777.5516      -27777.5516    0.0       286        1     0.6        0.1       0.6 solved not verified
heart-cl_BIC          CIP      50      96      44      90      -3430.48929      -3430.48929    0.0        31        1     0.1        0.0       0.0 solved not verified
heart-hu_BIC          CIP      81     138      78     135      -2384.00702      -2384.00702    0.0        61        3     0.1        0.0       0.1 solved not verified
heart-st_BIC          CIP      59     105      55     101      -2860.86628      -2860.86628    0.0        82        3     0.2        0.0       0.1 solved not verified
hepatitis_BIC         CIP     234     413     238     412      -1647.96991      -1647.96991    0.0       340        1     0.9        0.0       0.9 solved not verified
horse_BIC             CIP     427     742     454     740      -4524.66273      -4524.66273    0.0       331        1     0.9        0.1       0.9 solved not verified
insurance1000_BIC     CIP     447     779     463     776      -14350.4705      -14350.4705    0.0       466        1     0.8        0.1       0.8 solved not verified
insurance100_BIC      CIP     124     253     119     247      -1782.71458      -1782.71458    0.0       144        1     0.3        0.0       0.3 solved not verified
iris_BIC              CIP      31      43      31      43       -465.43503       -465.43503    0.0        15        1     0.0        0.0       0.0 solved not verified
letter_BIC            CIP     691    4847    1430    4847      -209774.055      -209774.055    0.0      5288       26     6.4        0.8       5.5 solved not verified
liver_BIC             CIP      14      20      10      15      -1321.96265      -1321.96265    0.0         6        1     0.0        0.0       0.0 solved not verified
lung-cancer_BIC       CIP     195     418     178     396      -1379.28597      -1379.28597    0.0       290        1     1.0        0.0       1.0 solved not verified
lympho_BIC            CIP     118     218     116     216      -1972.63595      -1972.63595    0.0       100        1     0.3        0.0       0.3 solved not verified
mildew1000_BIC        CIP      97     177      81     160      -57238.0239      -57238.0239    0.0        72        3     0.4        0.0       0.4 solved not verified
mildew100_BIC         CIP      45      57      10      15       -6655.3931       -6655.3931    0.0         6        1     0.0        0.0       0.0 solved not verified
mushroom_BIC          CIP    1165   13711    3501   13710      -89683.4535      -89683.4535    0.0   2131157     4229  2654.8        3.5    1454.2 solved not verified
pg-block_BIC          CIP      74     120      75     119       -12711.762       -12711.762    0.0        51        3     0.1        0.0       0.0 solved not verified
post-op_BIC            --      11      10       2       0       -645.00339       -645.00339    0.0         0        1     0.0        0.0       0.0 solved not verified
promoters_BIC         CIP      71      89      14      31      -8552.14186      -8552.14186    0.0         0        1     0.0        0.0       0.0 solved not verified
segment_BIC           CIP     425    1306     603    1305      -15171.6049      -15171.6049    0.0      2251        1     6.0        0.2       5.8 solved not verified
shuttle_BIC           CIP     126     335     171     334      -98774.3553      -98774.3553    0.0      1324        7     3.5        0.0       3.5 solved not verified
soybean_BIC           CIP    1684    6930    2540    6927      -3122.06298      -3122.06298    0.0     30368       43    66.5        1.3      49.5 solved not verified
spectf_BIC            CIP     676    1033     692    1028      -8135.31187      -8135.31187    0.0       674        1     2.3        0.2       2.3 solved not verified
sponge_BIC            CIP     466     951     470     942      -2072.61151      -2072.61151    0.0       660        1     2.1        0.1       2.1 solved not verified
steel_BIC              --       0       0       0       0           -1e+20            1e+20   --           0        0     0.0        0.0       0.0 abort
thyroid_BIC           CIP      19      32      16      29       -602.06851       -602.06851    0.0        11        1     0.0        0.0       0.0 solved not verified
tic-tac_BIC           CIP     162     192     164     186      -9396.37586      -9396.37586    0.0       403        1     1.0        0.0       1.0 solved not verified
tumour_BIC            CIP     227     351     231     349      -3194.25203      -3194.25203    0.0       167        1     0.3        0.0       0.3 solved not verified
vehicle_BIC           CIP     508    1065     602    1065      -7965.40348      -7965.40348    0.0      1118        1     2.8        0.2       2.8 solved not verified
voting_BIC            CIP     597    2196     866    2195      -3205.78531      -3205.78531    0.0      2220        1     2.6        0.3       2.6 solved not verified
water1000_BIC         CIP     159     249     159     242      -13290.1069      -13290.1069    0.0       115        1     0.3        0.0       0.3 solved not verified
water100_BIC          CIP      88     138      76     124      -1465.27372      -1465.27372    0.0        48        3     0.2        0.0       0.2 solved not verified
wdbc_BIC              CIP    2259   15951    3538   15951      -6602.11732      -6602.11732    0.0     27710       20   158.3        3.2     155.6 solved not verified
wine_BIC              CIP     118     227     120     227      -1891.69481      -1891.69481    0.0        68        3     0.1        0.0       0.1 solved not verified
yeast_BIC             CIP      28      44      24      40      -8039.97506      -8039.97506    0.0        17        1     0.0        0.0       0.0 solved not verified
zoo_BIC               CIP     405     795     459     795       -773.48608       -773.48608    0.0       342        1     0.9        0.1       0.9 solved not verified
abalone_BDe           CIP     156     412     207     412      -15946.5748      -15946.5748    0.0       443        1     0.5        0.1       0.5 solved not verified
adult_BDe             CIP     356     977     443     977       -329373.73       -329373.73    0.0      1146       19     0.8        0.2       0.7 solved not verified
aus_BDe               CIP     132     204     132     201      -4997.83478      -4997.83478    0.0       110        3     0.2        0.0       0.2 solved not verified
autos_BDe             CIP    1437   26080    5189   26080      -1418.12127      -1418.12127    0.0    584969      951  1614.8       10.3    1251.3 solved not verified
balance_BDe           CIP      12      18       8      13      -4549.05536      -4549.05536    0.0         0        1     0.0        0.0       0.0 solved not verified
bc_BDe                CIP      31      47      22      34      -2781.62239      -2781.62239    0.0        14        3     0.0        0.0       0.0 solved not verified
bc-wisc_BDe           CIP     193     350     211     349      -3315.51218      -3315.51218    0.0       320        1     0.3        0.0       0.3 solved not verified
credit_BDe            CIP     129     198     128     194      -6185.72434      -6185.72434    0.0       149        9     0.2        0.0       0.2 solved not verified
diabetes_BDe          CIP      42      65      40      63      -3678.57293      -3678.57293    0.0        39        5     0.1        0.0       0.1 solved not verified
ecoli_BDe             CIP      74     115      77     115      -1715.92338      -1715.92338    0.0        51        3     0.1        0.0       0.0 solved not verified
flag_BDe              CIP     817    1811     927    1810      -2693.08869      -2693.08869    0.0      2419        2     7.2        0.3       7.1 solved not verified
glass_BDe             CIP     118     176     125     175      -1288.92632      -1288.92632    0.0        59        1     0.1        0.0       0.1 solved not verified
heart-cl_BDe          CIP      50      96      44      90      -3450.06475      -3450.06475    0.0        42        7     0.1        0.0       0.0 solved not verified
heart-hu_BDe          CIP      97     169      96     166      -2376.52921      -2376.52921    0.0       111        3     0.2        0.0       0.1 solved not verified
heart-st_BDe          CIP      63     119      59     115      -2867.53657      -2867.53657    0.0        65        3     0.1        0.0       0.0 solved not verified
hepatitis_BDe         CIP     377     724     381     720      -1615.68231      -1615.68231    0.0       334        1     1.2        0.1       1.2 solved not verified
horse_BDe             CIP     437     749     458     746      -4531.56021      -4531.56021    0.0       437        1     1.2        0.1       1.2 solved not verified
insurance1000_BDe     CIP     595    1147     628    1145      -13872.3332      -13872.3332    0.0       867        1     1.6        0.2       1.6 solved not verified
insurance100_BDe      CIP     315     487     317     484      -1669.43462      -1669.43462    0.0       167        1     0.3        0.1       0.3 solved not verified
iris_BDe              CIP      33      45      33      45       -452.21429       -452.21429    0.0        15        1     0.0        0.0       0.0 solved not verified
letter_BDe            CIP     695   19247    2881   19247      -200768.883      -200768.883    0.0     61485       56   201.8        9.5     149.7 solved not verified
liver_BDe             CIP      16      26      13      22      -1309.67331      -1309.67331    0.0         9        1     0.0        0.0       0.0 solved not verified
lympho_BDe            CIP     339     543     332     531      -1908.35311      -1908.35311    0.0       298        1     1.3        0.1       1.3 solved not verified
mildew1000_BDe        CIP     162     255     149     241      -51939.6265      -51939.6265    0.0       106        1     0.5        0.0       0.5 solved not verified
mildew100_BDe         CIP      55      88      21      43      -6423.33723      -6423.33723    0.0        13        1     0.0        0.0       0.0 solved not verified
mushroom_BDe           --       0       0       0       0           -1e+20            1e+20   --           0        0     0.0        0.0       0.0 abort
pg-block_BDe          CIP     184     388     207     388      -12455.5969      -12455.5969    0.0       272        3     0.5        0.2       0.5 solved not verified
post-op_BDe            --      11      10       2       0        -647.3529        -647.3529    0.0         0        1     0.0        0.0       0.0 solved not verified
segment_BDe           CIP     687    6892    1275    6891      -14281.7847      -14281.7847    0.0     43710       63    66.0        2.3      52.6 solved not verified
shuttle_BDe           CIP     190     920     307     919      -97635.7197      -97635.7197    0.0      7992       43     4.5        0.3       3.5 solved not verified
steel_BDe              --       0       0       0       0           -1e+20            1e+20   --           0        0     0.0        0.0       0.0 abort
thyroid_BDe           CIP      44      69      44      69       -577.52089       -577.52089    0.0        45        1     0.1        0.0       0.1 solved not verified
tic-tac_BDe           CIP      98     121      90     115      -9423.06831      -9423.06831    0.0        46        1     0.1        0.0       0.1 solved not verified
tumour_BDe            CIP     270     431     281     430      -3191.18567      -3191.18567    0.0       328        1     0.8        0.0       0.8 solved not verified
vehicle_BDe           CIP     716    3542    1126    3542      -7545.55964      -7545.55964    0.0      5727        1    15.1        0.6      14.6 solved not verified
voting_BDe            CIP     590    2284     863    2283      -3192.66656      -3192.66656    0.0      2324        1     2.6        0.4       2.6 solved not verified
wdbc_BDe              CIP    2224   14793    3351   14793      -6596.70042      -6596.70042    0.0     53778       46   250.4        2.9     238.2 solved not verified
wine_BDe              CIP     159     308     164     308      -1866.40612      -1866.40612    0.0       166        1     0.3        0.0       0.3 solved not verified
yeast_BDe             CIP      38      67      34      63      -7938.59791      -7938.59791    0.0        24        1     0.0        0.0       0.0 solved not verified
zoo_BDe               CIP     540    3168     797    3167       -642.25866       -642.25866    0.0     12399       40    22.4        1.1      21.8 solved not verified
------------------+------+-------+-------+-------+-------+----------------+----------------+------+---------+--------+-------+----------+---------+--------

------------------------------[Nodes]---------------[Time]--------------[ToFirst]-----------[ToLast]-----
  Cnt  Pass  Time  Fail  total(k)     geom.     total     geom.     total     geom.     total     geom.
---------------------------------------------------------------------------------------------------------
   97    94     0     3         5       2.3    5145.9       2.0      41.6       1.1    3478.9       2.0
 shifted geom. [  100/ 10.0]           11.7                 4.2                 0.4                 3.9 
---------------------------------------------------------------------------------------------------------
@02 timelimit: 0
@01 SCIP(3.1.1)cpx(12.6.0.0):default [GitHash: bade511]

The results in the above tables are for learning from precomputed local scores. These local scores were computed from synthetic data generated from various BNs. The following table gives information on those BNs in the first table, the synthetic data and the local scores. Importantly it gives the time taken to compute these local scores.

'BN' is the name of the BN from which the data was originally generated. 'p' is the number of variables in the original dataset (and thus in the optimal BN). 'n' is the number of datapoints in the data. 'palim' is the limit on the size of parent sets in any learned BN. '|PaSets|' is the number of candidate parent sets generated by GOBNILP's local scoring algorithm - this is the size of the input to the main GOBNILP learning algorithm. '1.4.1' is time in seconds to compute all the local scores using GOBNILP 1.4.1. '1.6' is the time taken using GOBNILP 1.6 (using default ADtree parameter settings). '1.6.1' is the time taken using GOBNILP 1.6.1 (using default ADtree parameter settings). The machines used for '1.4.1' and '1.6'/'1.6.1' were similar but not identical.

Parameter settings for the current release (1.6.1) are conservative to help avoid running out of memory on small machines. Faster computation is often possible with non-default values. For example, setting gobnilp/scoring/rmin to a non-default value of 100 allows GOBNILP 1.6.1 to compute local scores for Pigs_1000 and Link_1000 in 144s and 679s, respectively. However, such non-default values can sometimes slow down local score computation; with gobnilp/scoring/rmin set to 100 GOBNILP 1.6.1 takes 336s to compute local scores for kredit with no parent set limit, as opposed to 207s with its default value.

Publications on the theory behind GOBNILP

• Milan Studený and James Cussens. Towards using the chordal graph polytope in learning decomposable models. International Journal of Approximate Reasoning 88:259-281, 2017.
• James Cussens, David Haws and Milan Studený. Polyhedral aspects of score equivalence in Bayesian network structure learning. Mathematical Programming, 2016, doi:10.1007/s10107-016-1087-2. ( Full-text, view-only version ). (Arxiv version)
• James Cussens, Matti Järvisalo, Janne H. Korhonen and Mark Bartlett. Bayesian Network Structure Learning with Integer Programming: Polytopes, Facets, and Complexity. Journal of Artificial Intelligence Research, 58:185-229, 2017. May 2016.
• Milan Studený. How matroids occur in the context of learning Bayesian network structure. Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence (UAI-15) July 2015.

Publications using GOBNILP

• Draaisma et al. Molecular Evolution of IDH Wild-Type Glioblastomas Treated With Standard of Care Affects Survival and Design of Precision Medicine Trials: A Report From the {EORTC} 1542 Study, Journal of Clinical Oncology, on-line: Nov 19, 2019.
• Topi Talvitie, Ralf Eggeling and Mikko Koivisto. Learning Bayesian networks with local structure, mixed variables, and exact algorithms, International Journal of Approximate Reasoning, 115:69-95, 2019.
• Francesco Maura et al. Genomic landscape and chronological reconstruction of driver events in multiple myeloma, Nature Communications 10, Article number 3835, 2019.
• Ralf Eggeling, Jussi Viinikka, Aleksis Vuoksenmaa and Mikko Koivisto. On Structure Priors for Learning Bayesian Networks, Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019, Naha, Okinawa, Japan. PMLR: Volume 89
• Zhenyu A. Liao, Charupriya Sharma, James Cussens and Peter van Beek. Finding All Bayesian Network Structures within a Factor of Optimal, Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19), 2019.
• Jacob Grinfield et al. Classification and Personalized Prognosis in Myeloproliferative Neoplasms, New England Journal of Medicine 379:1416-1430, 2018.
• Jan Švorc and and Jiří Vomlel. Employing Bayesian Networks for Subjective Well-being Prediction, Proc WUPES-18, 2018.
• Lilia Costa, James Q. Smith and Thomas Nichols. A group analysis using the Multiregression Dynamic Models for fMRI networked time series, Journal of Statistical Planning and Inference, 198:43-61, January 2019.
• Xun Zheng, Bryon Aragam, Pradeep Ravikumar and Eric P. Xing. DAGs with NO TEARS: Continuous Optimization for Structure Learning, Proc. NeurIPS 2018
• Antti Hyttinen, Johan Pensar, Juha Kontinen and Jukka Corander. Structure Learning for Bayesian Networks over Labeled DAGs, Proc. PGM'18, PMLR 72:133-144, 2018
• Andrew Li and Peter van Beek. Bayesian Network Structure Learning with Side Constraints, Proc. PGM'18, PMLR 72:225-236, 2018
• Shahab Behjati and Hamid Beigy. An Order-based Algorithm for Learning Structure of Bayesian Networks, Proc. PGM'18, PMLR 72:25-36, 2018
• Jussi Viinikka, Ralf Eggeling and Mikko Koivisto. Intersection-Validation: A Method for Evaluating Structure Learning without Ground Truth , Proc. AISTATS, 2018
• Brandon Malone, Kustaa Kangas, Matti Järvisalo, Mikko Koivisto and Petri Myllymäki. Empirical hardness of finding optimal Bayesian network structures: algorithm selection and runtime prediction , Machine Learning 107(1):247-283, 2018
• Samuel Vozza. Extending GOBNILP to learn Gaussian Bayesian Networks, MEng Project Dissertation, Dept of Computer Science, University of York, May 2017
• Scott McGregor. Exact Bayesian Network Learning in R, MSc Computing Project Dissertation, Dept of Computer Science, University of York, 2017
• John W. Cook, David Danks and Sergey M. Plis. Learning Dynamic Structure from Undersampled Data , Causality Workshop, UAI 2017
• Colin Lee and Peter van Beek. An Experimental Analysis of Anytime Algorithms for Bayesian Network Structure Learning, Proceedings of Machine Learning Research, Volume 73: Advanced Methodologies for Bayesian Networks (AMBN-2017), Kyoto, Japan, September, 2017.
• Colin Lee and Peter van Beek. Metaheuristics for Score-and-Search Bayesian Network Structure Learning, Proceedings of the 30th Canadian Conference on Artificial Intelligence, Edmonton, Alberta, May, 2017.
• Lilia Costa, Thomas Nichols and Jim Q. Smith. Studying the Effective Brain Connectivity using the Multiregression Dynamic Models , Brazilian Journal of Probability and Statistics, 2017 (to appear).
• Tian Gao, Kshitij Fadnis and Murray Campbell. Local-to-Global Bayesian Network Structure Learning, Proc. ICML 2017, 2017.
• Siqi Nie, Cassio P. de Campos and Qiang Ji. Efficient learning of Bayesian networks with bounded tree-width, International Journal of Approximate Reasoning Volume 80, Pages 412-427, January 2017.
• Eunice Yuh-Jie Chen, Yujia Shen, Arthur Choi and Adnan Darwiche Learning Bayesian networks with ancestral constraints, Proc. NIPS 2016, 2016.
• Tameem Adel and Cassio P. de Campos. Learning Bayesian Networks with Incomplete Data by Augmentation, arXiv 1608.07734, Oct 2016
• Milan Studený and James Cussens. The Chordal Graph Polytope for Learning Decomposable Models. Proc. PGM 2016 (JMLR: Workshop and Conference Proceedings vol 52), 499-510, 2016.
• Chris. J. Oates and Jim Q. Smith and Sach Mukherjee. Estimating Causal Structure Using Conditional DAG Models, Journal of Machine Learning Research 17:54 1-23, 2016.
• Mauro Scanagatta, Giorgio Corani, Cassio P. de Campos and Marco Zaffalon. Learning Bounded Treewidth Bayesian Networks with Thousands of Variables, Arxiv 1605.03392, 2016.
• Giorgio Corani and Mauro Scanagatta. Air pollution prediction via multi-label classification, Environmental Modelling and Software, 80:259-264, 2016.
• Azmi Hafizha Rahman Z.A., M. Syahrul Mubarok and Adiwijaya. Learning Struktur Bayesian Networks menggunakan Novel Modified Binary Differential Evolution pada Klasifikasi Data, Ind. Symposium on Computing pp. 265-278, Sept 2016.
• Siqi Nie, Cassio P. de Campos, and Qiang Ji. Learning Bayesian Networks with Bounded Tree-width via Guided Search, In AAAI Conference on Artificial Intelligence (AAAI), 2016.
• Yonatan Halpern. Semi-Supervised Learning for Electronic Phenotyping in Support of Precision Medicine, PhD Thesis, New York University, 2016.
• Yuh-Jie Chen. Learning Bayesian Network Structures with Non-Decomposable Scores, PhD Thesis, UCLA, 2016.
• Meng Sun. Estimating relationships and relatedness from dense genome-wide data PhD thesis, University of Leicester, 2015.
• Brandon Malone. Empirical Behavior of Bayesian Network Structure Learning Algorithms, Proc. Advanced Methodologies for Bayesian Networks: Second International Workshop, AMBN 2015, Yokohama, Japan, November 16-18, Springer, 2015.
• Yoni Halpern, Steven Horng and David Sontag. Anchored Discrete Factor Analysis . Arxiv 1511.03299, Nov 2015.
• Paul Saikko. Re-implementing and Extending a Hybrid SAT-IP Approach to Maximum Satisfiability . MSc thesis, University of Helsinki, Nov 2015.
• Janne H. Korhonen and Pekka Parviainen. Tractable Bayesian Network Structure Learning with Bounded Vertex Cover Number . NIPS 2015: Proceedings of the 29th Annual Conference on Neural Information Processing Systems, 2015
• Mauro Scanagatta, Cassio P. de Campos, Giorgio Corani and Marco Zaffalon. Learning Bayesian networks with thousands of variables . NIPS 2015: Proceedings of the 29th Annual Conference on Neural Information Processing Systems, 2015
• Pekka Parviainen and Samuel Kaski. Bayesian Networks for Variable Groups. Arxiv 1508.07753, August, 2015
• Arnoud Pastink and Linda van der Gaag. Multi-classifiers of Small Treewidth. Proc. ECSQARU 2015, LNAI 9161, pp. 199-209, 2015.
• Peter van Beek and Hella-Franziska Hoffmann. Machine learning of Bayesian networks using constraint programming. Proceedings of CP 2015, Cork, Ireland, August, 2015.
• Vera Djordjilović, Monica Chiogna and Jirka Vomlel. An empirical comparison of popular algorithms for learning gene networks. Proc. CEB-EIB 2015, 2015
• Chris J. Oates, Lilia Carneiro da Costa and Tom Nichols. Towards a Multi-Subject Analysis of Neural Connectivity. Neural Computation, 27:151-170, 2015. (Also Arkiv 1404.1239, April 2014.)
• Waleed Alsanie and James Cussens. Learning Failure-free PRISM Programs. International Journal of Approximate Reasoning, 67:73-110, 2015.
• Brandon Malone, Matti Järvisalo and Petri Myllymäki. Impact of Learning Strategies on the Quality of Bayesian Networks: An Empirical Evaluation. Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence (UAI-15) July 2015.
• Mark Bartlett and James Cussens. Integer Linear Programming for the Bayesian Network Structure Learning Problem. Artificial Intelligence. Forthcoming. (Preprint)
• Chris J. Oates, Jim Q. Smith, Sach Mukherjee and James Cussens. Exact Estimation of Multiple Directed Acyclic Graphs. Statistics and Computing, Forthcoming. (Arkiv 1404.1238, April 2014.)
• Paul Saikko, Brandon Malone and Matti Järvisalo. MaxSAT-based Cutting Planes for Learning Graphical Models. Proc. CPAIOR 2015
• Kustaa Kangas, Teppo Niinimäki and Mikko Koivisto. Learning Chordal Markov Networks by Dynamic Programming. NIPS 2014.
• Chris J. Oates, Jim Q. Smith, Sach Mukherjee. Estimating causal structure using conditional DAG models. Arkiv 1411.2755, November 2014.
• Giorgio Corani, Alessandro Antonucci, Denis D. Maua and Sandra Gabaglio. Trading off Speed and Accuracy in Multilabel Classification Proc. PGM 2014, 145-159, LNAI 8754, Springer, 2014. (Proceedings).
• Mauro Scanagatta, Cassio P. de Campos and Marco Zaffalon. Min-BDeu and Max-BDeu Scores for Learning Bayesian Networks. Proc. PGM 2014, 426-441, LNAI 8754, Springer, 2014. (Preprint). (Proceedings).
• Ilya Korsunsky, Daniele Ramazzotti, Giulio Caravagna and Bud Mishra. Inference of Cancer Progression Models with Biological Noise. Arkiv 1408.6032, August 2014
• Lilia Costa, Jim Smith, Thomas Nichols and James Cussens. Searching Multiregression Dynamic Models of Resting-State fMRI Networks using Integer Programming. Bayesian Analysis. To appear.
• Nuala Sheehan, Mark Bartlett and James Cussens. Improved Maximum Likelihood Reconstruction of Complex Multi-generational Pedigrees. Theoretical Population Biology. 97:11-19, November 2014.
• Brandon Malone, Kustaa Kangas, Matti Järvisalo, Mikko Koivisto, and Petri Myllymäki. Predicting the Hardness of Learning Bayesian Networks. In Carla E. Brodley and Peter Stone, editors, Proceedings of the 28th AAAI Conference on Artificial Intelligence (AAAI 2014) AAAI Press, 2014.
• Alberto Franzin. An Integer Programming approach to Bayesian Network Structure Learning. Masters dissertation, University of Padua, April 2014.
• Milan Studený, David Haws Learning Bayesian network structure: Towards the essential graph by integer linear programming tools International Journal of Approximate Reasoning, 2013
• Changhe Yuan and Brandon Malone Learning Optimal Bayesian Networks: A Shortest Path Perspective, Journal of Artificial Intelligence Research, Volume 48, pages 23-65, 2013
• Pekka Parviainen and Mikko Koivisto. Finding Optimal Bayesian Networks Using Precedence Constraints. Journal of Machine Learning Resarch. vol 14. pp1387-1415, 2013.
• Eman Aljohani and James Cussens. Informative Priors For Learning Graphical Models. Proc. AIGM-13, Paris, 2013.
• Antonucci A., Corani G., Maua D., Gabaglio S., An Ensemble of Bayesian Networks for Multilabel Classification. Proc. 23rd Int. Joint Conference on Artificial Intelligence (IJCAI-13)
• Brandon Malone and Changhe Yuan. Evaluating Anytime Algorithms for Learning Optimal Bayesian Networks . Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI-13) July 2013.
• Eliot Brenner and David Sontag. SparsityBoost: A New Scoring Function for Learning Bayesian Network Structure. Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI-13) July 2013.
• Mark Bartlett and James Cussens. Advances in Bayesian Network Learning using Integer Programming. Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI-13) July 2013.
• Waleed Alsanie. Learning Failure-free PRISM Programs. PhD Thesis, University of York, September 2012.
• Zhenxing Wang and Laiwan Chan. Learning Bayesian Networks from Markov Random Fields: An Efficient Algorithm for Linear Models. ACM Transactions on Knowledge Discovery from Data (TKDD). 6(3) 2012 10:1-10:31.
• Robert G. Cowell. A simple greedy algorithm for reconstructing pedigrees. Theoretical Population Biology. 83 (2013) 55-63.
• James Cussens. Bayesian network learning with cutting planes. In Fabio G. Cozman and Avi Pfeffer, editors, Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011), pages 153-160, Barcelona, 2011. AUAI Press. This paper introduces the basic idea of the GOBNILP approach and uses a preliminary version of the software.

Last modified: Thu Jan 26 18:06:13 GMT 2017