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We can schedule messages in a way that accounts for their potential usefulness; for example, we can pass a message between clusters where the beliefs disagree most strongly on the sepset. This approach, called residual belief propagation is convenient, since it is fully general and does not require a deep understanding of the properties of the network.
- Probabilistic Graphical Models, Box 11.B
Each line outputs the error and the system time in milliseconds
Guillermos-MacBook-Air:gmX guillermoblascojimenez$ $SPARK_HOME/bin/spark-submit --class "com.blackbox.gmx.example.Student" --master local[4] target/scala-2.10/gmx_2.10-1.0.jar
14/10/06 11:30:00 WARN SparkConf:
SPARK_JAVA_OPTS was detected (set to '
-Dspark.serializer=org.apache.spark.serializer.KryoSerializer
-Dspark.kryo.registrator=org.apache.spark.graphx.GraphKryoRegistrator ').
This is deprecated in Spark 1.0+.
Please instead use:
14/10/06 11:30:00 WARN SparkConf: Setting 'spark.executor.extraJavaOptions' to '
-Dspark.serializer=org.apache.spark.serializer.KryoSerializer
-Dspark.kryo.registrator=org.apache.spark.graphx.GraphKryoRegistrator ' as a work-around.
14/10/06 11:30:00 WARN SparkConf: Setting 'spark.driver.extraJavaOptions' to '
-Dspark.serializer=org.apache.spark.serializer.KryoSerializer
-Dspark.kryo.registrator=org.apache.spark.graphx.GraphKryoRegistrator ' as a work-around.
Cluster Graph built
Cluster with 8 clusters
error: 0.12519177621599598 at 1412587808098
error: 0.0372313362941709 at 1412587809062
error: 0.06300571554158453 at 1412587809978
error: 0.00161212143632129 at 1412587810791
error: 0.030923425188297375 at 1412587811548
error: 0.054924511754993896 at 1412587812446
error: 0.00179216227496699 at 1412587813092
error: 0.026453902880653097 at 1412587813676
error: 0.04633838053832956 at 1412587814227
error: 0.0019397498390229576 at 1412587814756
error: 0.021979344335079948 at 1412587815193
error: 0.037895937786007076 at 1412587815570
error: 0.0020447103515861204 at 1412587815960
error: 0.017800920542429398 at 1412587816370
error: 0.030117038195337953 at 1412587816803
error: 0.0021008989559054185 at 1412587817336
error: 0.014122736707891216 at 1412587817809
error: 0.023341273358217927 at 1412587818336
error: 0.0021067342348015045 at 1412587818805
error: 0.011044122733230993 at 1412587819282
error: 0.017722184448606144 at 1412587819783
error: 0.002064930329880744 at 1412587820272
error: 0.008574193904316924 at 1412587820734
error: 0.013257235603442087 at 1412587821255
error: 0.001981613649191978 at 1412587821748
error: 0.006658818172795672 at 1412587822271
error: 0.009836377066600989 at 1412587822832
error: 0.0018651133405955605 at 1412587823427
error: 0.005209808956860952 at 1412587824059
error: 0.007292594390134931 at 1412587824722
error: 0.001724712954617012 at 1412587825355
error: 0.004129219619470362 at 1412587826043
error: 0.00544330835573178 at 1412587826734
error: 0.0015695776468153963 at 1412587827453
error: 0.0033256497207461593 at 1412587828197
error: 0.004118071455019422 at 1412587828965
error: 0.001407971738427338 at 1412587829776
error: 0.0027226952114126094 at 1412587830663
error: 0.003173069003239549 at 1412587831625
error: 0.001246791472562367 at 1412587832493
error: 0.002261411859234501 at 1412587833425
error: 0.002495589621008917 at 1412587834445
error: 0.0010913759412709664 at 1412587835472
error: 0.0018990935164854544 at 1412587836638
error: 0.0020022487072031683 at 1412587837774
error: 9.455283197521791E-4 at 1412587838964
error: 0.0016063215660626236 at 1412587840208
error: 0.0016341730447027739 at 1412587841567
error: 8.116733361830232E-4 at 1412587842921
error: 0.0013636151992905824 at 1412587844582
error: 0.0013513514689513575 at 1412587846075
error: 6.9108589586185E-4 at 1412587847592
error: 0.0011584153631472333 at 1412587849197
error: 0.0011274015433960385 at 1412587850789
error: 5.841414925669533E-4 at 1412587852685
error: 9.826983437212836E-4 at 1412587854452
error: 9.452949549260945E-4 at 1412587856312
error: 4.905556028834128E-4 at 1412587858777
error: 8.312518158165064E-4 at 1412587860722
error: 7.941479333414236E-4 at 1412587862791
error: 4.0959345835718075E-4 at 1412587865178
error: 7.005185711507701E-4 at 1412587867307
error: 6.66960775445E-4 at 1412587869639
error: 3.402422239565994E-4 at 1412587872412
error: 5.878721798916212E-4 at 1412587875131
error: 5.591084200205985E-4 at 1412587877876
error: 2.8134470297948023E-4 at 1412587880482
error: 4.911941301720584E-4 at 1412587883528
error: 4.673795723369543E-4 at 1412587886294
error: 2.316978488437011E-4 at 1412587889442
error: 4.08646498442017E-4 at 1412587892523
error: 3.8939242588711693E-4 at 1412587895810
error: 1.9012137346270506E-4 at 1412587898961
error: 3.3856260888576244E-4 at 1412587902726
error: 3.2325556409674224E-4 at 1412587906439
error: 1.5550232517912334E-4 at 1412587910030
error: 2.7940323852191685E-4 at 1412587913892
error: 2.673806875499431E-4 at 1412587917908
error: 1.2682124391892125E-4 at 1412587921811
error: 2.2974531031923326E-4 at 1412587926020
error: 2.203845929616536E-4 at 1412587931047
error: 1.0316480149530829E-4 at 1412587936686
error: 1.8828371244058144E-4 at 1412587943826
error: 1.810405714242484E-4 at 1412587949923
error: 8.372897270365223E-5 at 1412587955998
error: 1.5383589335611405E-4 at 1412587962615
error: 1.4825513370506739E-4 at 1412587970265
error: 6.78159206745734E-5 at 1412587976948
error: 1.2534443071747666E-4 at 1412587983611
error: 1.210562958977216E-4 at 1412587990095
error: 5.482700395990345E-5 at 1412587997221
error: 1.0187594691457726E-4 at 1412588004837
error: 9.858610511237596E-5 at 1412588012438
error: 4.425365933934775E-5 at 1412588020448
error: 8.261639376011903E-5 at 1412588030284
error: 8.009390808734914E-5 at 1412588040433
error: 3.5667389872503174E-5 at 1412588049176
error: 6.686345694268794E-5 at 1412588057937
error: 6.492900014604511E-5 at 1412588067124
error: 2.8709682698803304E-5 at 1412588076591
Calibrated
error: 0.12283588778298232 at 1412588095804
error: 0.06734689401269783 at 1412588096008
error: 0.08202427250069447 at 1412588096210
error: 0.009125868090623329 at 1412588096437
error: 0.02370906736888987 at 1412588096708
error: 0.061729871366266405 at 1412588097013
error: 0.005303302363843675 at 1412588097318
error: 0.0132107241097436 at 1412588097586
error: 0.04947564926318184 at 1412588097884
error: 0.0027130234216898195 at 1412588098134
error: 0.00777109400968799 at 1412588098444
error: 0.03557238065169925 at 1412588098725
error: 0.0012684945620320513 at 1412588099028
error: 0.004707108373747947 at 1412588099362
error: 0.02296395393643073 at 1412588099722
error: 5.628445113616308E-4 at 1412588100087
error: 0.0027959802023483143 at 1412588100402
error: 0.013543437291183753 at 1412588100735
error: 2.4419009522826145E-4 at 1412588101171
error: 0.0015876828700689084 at 1412588101513
error: 0.007451464602969695 at 1412588101932
error: 1.0561038573350697E-4 at 1412588102317
error: 8.595522937915052E-4 at 1412588102785
error: 0.00389643723865832 at 1412588103344
error: 4.59926284801572E-5 at 1412588103875
error: 4.468585100072085E-4 at 1412588104572
error: 0.001965049017029566 at 1412588105137
error: 2.024341879241442E-5 at 1412588105706
error: 2.251356055541293E-4 at 1412588106258
error: 9.662161650241316E-4 at 1412588106926
error: 9.007157354916817E-6 at 1412588107478
Map calibrated
If you plot the differences in a graph it actually scares...
https://drive.google.com/file/d/0BzzgOwBUb-lyaE5SaEk1ZkhSYVE/view?usp=sharing
https://drive.google.com/file/d/0BzzgOwBUb-lyLTNPeTVad1FpVGs/view?usp=sharing
It looks that there are not an actual modern schema or syntax to serialise factor graphs. There are many ways to encode them but since a factor represents a function we have to deal with polymorphism, that is that a factor may be a discrete function (with sparse values or not), a gaussian, ... So a flexible schema would be required to grant scalability. I've made a workaround with json but I would like to check some factor representations and compare them.
{
"variables" : {
"cloudy" : 2,
"sprinkler" : 2,
"rain" : 2,
"wet_grass" : 2
},
"factors" : [
{
"variables" : ["cloudy"],
"values" : [
{"assignment" : {"cloudy" : 0}, "value" : 0.5},
{"assignment" : {"cloudy" : 1}, "value" : 0.5}
]
},
{
"variables" : ["sprinkler", "cloudy"],
"values" : [
{"assignment" : {"sprinkler" : 0, "cloudy" : 0}, "value" : 0.5},
{"assignment" : {"sprinkler" : 1, "cloudy" : 0}, "value" : 0.5},
{"assignment" : {"sprinkler" : 0, "cloudy" : 1}, "value" : 0.9},
{"assignment" : {"sprinkler" : 1, "cloudy" : 1}, "value" : 0.1}
]
},
{
"variables" : ["rain", "cloudy"],
"values" : [
{"assignment" : {"rain" : 0, "cloudy" : 0}, "value" : 0.8},
{"assignment" : {"rain" : 1, "cloudy" : 0}, "value" : 0.2},
{"assignment" : {"rain" : 0, "cloudy" : 1}, "value" : 0.2},
{"assignment" : {"rain" : 1, "cloudy" : 1}, "value" : 0.8}
]
},
{
"variables" : ["wet_grass", "sprinkler", "rain"],
"values" : [
{"assignment" : {"wet_grass" : 0, "sprinkler" : 0, "rain" : 0}, "value" : 1.0},
{"assignment" : {"wet_grass" : 1, "sprinkler" : 0, "rain" : 0}, "value" : 0.0},
{"assignment" : {"wet_grass" : 0, "sprinkler" : 1, "rain" : 0}, "value" : 0.1},
{"assignment" : {"wet_grass" : 1, "sprinkler" : 1, "rain" : 0}, "value" : 0.9},
{"assignment" : {"wet_grass" : 0, "sprinkler" : 0, "rain" : 1}, "value" : 0.1},
{"assignment" : {"wet_grass" : 1, "sprinkler" : 0, "rain" : 1}, "value" : 0.9},
{"assignment" : {"wet_grass" : 0, "sprinkler" : 1, "rain" : 1}, "value" : 0.01},
{"assignment" : {"wet_grass" : 1, "sprinkler" : 1, "rain" : 1}, "value" : 0.99}
]
}
]
}
Tree Reparametrization (TRP) selects a set of trees, each of which spans a large number of clusters, and whose union covers all of the edges in the network. The TRP algorithm then iteratively selects a tree and does an upward-downward calibration of the tree, keeping all other messages fixed. Of course, calibrating this tree has the effect of "uncalibrating" other trees, and so this process repeats.
- Probabilistic Graphical Models Box 11.B
As described in the paper that can be downloaded http://ttic.uchicago.edu/~tamir/papers/norm-prod-ieee-final-corr.pdf
Schedule message when graph structure allows:
Use scala style from apache/spark:
https://github.com/apache/spark/blob/master/scalastyle-config.xml
Vertex: initial potentials and updating potentials
Edge: deltas in both directions
Message aggregation: d1 * d2
Message generation: updating potential marginalized to stepset / incoming delta and normalize
Message processing: updating potential := initial potential * deltas
Sparse matrix (http://en.wikipedia.org/wiki/Sparse_matrix) are those that takes values at small amount of cells, and therefore store all the values is a waste of memory. There are two cases:
This concept can be applied to discrete factors that are actually multidimensional matrices.
Same build:
$SPARK_HOME/bin/spark-submit --class "com.blackbox.gmx.example.Student" --master local[4] target/scala-2.10/gmx_2.10-1.0.jar
Cluster Graph built
Cluster with 8 clusters
error: 0.0654881172839506 at 1412700248917
error: 0.08341474233689133 at 1412700249673
error: 0.07509828700926946 at 1412700250405
error: 0.04373545719848248 at 1412700251057
error: 0.06800458034992825 at 1412700251701
error: 0.05593939274381361 at 1412700252295
error: 0.02856050623243219 at 1412700252730
error: 0.10687774530501093 at 1412700253164
error: 0.01726229748329744 at 1412700253578
error: 0.009527547159413133 at 1412700253898
error: 0.01543337151929534 at 1412700254288
error: 0.01295290471366622 at 1412700254613
error: 0.004791139421929123 at 1412700254942
error: 0.013548817400343896 at 1412700255300
error: 0.0033719088173315157 at 1412700255672
error: 0.00160183920248516 at 1412700256043
error: 0.0030624380147187703 at 1412700256503
error: 0.0024814727596545387 at 1412700256912
error: 7.25498646743708E-4 at 1412700257311
error: 0.0017878726548758066 at 1412700257779
error: 6.002763397696782E-4 at 1412700258166
error: 2.668207097736408E-4 at 1412700258569
error: 5.450913105309635E-4 at 1412700258972
error: 4.360996485491701E-4 at 1412700259372
error: 1.1588967799769118E-4 at 1412700259837
error: 2.680201310171418E-4 at 1412700260290
error: 1.0197383024739067E-4 at 1412700260744
error: 4.4090801951427004E-5 at 1412700261210
error: 9.248972086044061E-5 at 1412700261749
error: 7.367926909925668E-5 at 1412700262295
error: 1.88277013243677E-5 at 1412700262825
error: 4.246672212695515E-5 at 1412700263396
error: 1.6966558968674908E-5 at 1412700263957
error: 7.244358197173231E-6 at 1412700264565
Calibrated
error: 0.08788149145538879 at 1412700265878
error: 0.15997087527286608 at 1412700266068
error: 0.03452498478996678 at 1412700266276
error: 0.031508382715638814 at 1412700266481
error: 0.13015097389951538 at 1412700266684
error: 0.08289713261795872 at 1412700266914
error: 0.03943056472399397 at 1412700267123
error: 0.08586561341656541 at 1412700267377
error: 0.01791185360445833 at 1412700267593
error: 0.018261565839008037 at 1412700267819
error: 0.05140561893189333 at 1412700268087
error: 0.015751244254026783 at 1412700268325
error: 0.0024108536283455953 at 1412700268581
error: 0.00869843094817362 at 1412700268884
error: 0.0023468709244813153 at 1412700269164
error: 8.455094195599025E-5 at 1412700269443
error: 8.455094195599009E-5 at 1412700269750
error: 2.407412430484045E-34 at 1412700270032
Map calibrated
marginals
ArrayFactor [AbstractArrayFactor with scope {INTELLIGENCE (card=2)} and values {0.734806629834254,0.2651933701657459}]
ArrayFactor [AbstractArrayFactor with scope {LETTER (card=2),GRADE (card=3)} and values {0.09263094874226793,0.035973441454726696,0.013597429051248602,0.8336785386804113,0.023982294303151134,1.373477681944303E-4}]
ArrayFactor [AbstractArrayFactor with scope {SAT (card=2)} and values {0.5,0.5}]
ArrayFactor [AbstractArrayFactor with scope {DIFFICULTY (card=2)} and values {0.845179020095127,0.15482097990487298}]
ArrayFactor [AbstractArrayFactor with scope {GRADE (card=3)} and values {0.9263094874226792,0.05995573575787783,0.013734776819443031}]
ArrayFactor [AbstractArrayFactor with scope {GRADE (card=3),DIFFICULTY (card=2),INTELLIGENCE (card=2)} and values {0.39865800117270195,0.002255059827917999,0.006395331268974536,0.057694865905484616,0.034626521958369336,3.70219866551525E-4,0.39865800117270195,0.002255059827917999,0.006395331268974536,0.057694865905484616,0.034626521958369336,3.70219866551525E-4}]
ArrayFactor [AbstractArrayFactor with scope {SAT (card=2),INTELLIGENCE (card=2)} and values {0.3674033149171271,0.13259668508287292,0.3674033149171271,0.13259668508287292}]
ArrayFactor [AbstractArrayFactor with scope {LETTER (card=2)} and values {0.142865151373684,0.8571348486263161}]
maps
ArrayFactor [AbstractArrayFactor with scope {LETTER (card=2)} and values {0.1,0.9}]
ArrayFactor [AbstractArrayFactor with scope {LETTER (card=2),GRADE (card=3)} and values {0.09774214090968877,0.01228305692524889,0.0020857610674204835,0.879679268187199,0.008188704616832593,2.1068293610307917E-5}]
ArrayFactor [AbstractArrayFactor with scope {GRADE (card=3)} and values {0.9830811897654246,0.014587878330324043,0.0023309319042514754}]
ArrayFactor [AbstractArrayFactor with scope {DIFFICULTY (card=2)} and values {0.8735740036545014,0.1264259963454986}]
ArrayFactor [AbstractArrayFactor with scope {GRADE (card=3),DIFFICULTY (card=2),INTELLIGENCE (card=2)} and values {0.4307738616467811,3.4819948613079154E-4,0.0011235236752486866,0.06234276023606536,0.005346615199798237,6.503975597572816E-5,0.4307738616467811,3.4819948613079154E-4,0.0011235236752486866,0.06234276023606536,0.005346615199798237,6.503975597572816E-5}]
ArrayFactor [AbstractArrayFactor with scope {INTELLIGENCE (card=2)} and values {0.734806629834254,0.2651933701657459}]
ArrayFactor [AbstractArrayFactor with scope {SAT (card=2)} and values {0.5,0.5}]
ArrayFactor [AbstractArrayFactor with scope {SAT (card=2),INTELLIGENCE (card=2)} and values {0.3674033149171271,0.13259668508287292,0.3674033149171271,0.13259668508287292}]
$SPARK_HOME/bin/spark-submit --class "com.blackbox.gmx.example.Student" --master local[4] target/scala-2.10/gmx_2.10-1.0.jar
Cluster Graph built
Cluster with 8 clusters
error: 0.0613490866717057 at 1412700442030
error: 0.03034749482764568 at 1412700442854
error: 0.01679456833820894 at 1412700443599
error: 0.04103024342460169 at 1412700444242
error: 0.02697099805839067 at 1412700444874
error: 0.014550803216732154 at 1412700445467
error: 0.0350738165469253 at 1412700445931
error: 0.02338162548708511 at 1412700446391
error: 0.012297222121285718 at 1412700446791
error: 0.02914123208605337 at 1412700447123
error: 0.019729279843793468 at 1412700447482
error: 0.010128862471221314 at 1412700447807
error: 0.023502899948822917 at 1412700448148
error: 0.01617730597520799 at 1412700448507
error: 0.00812940446284152 at 1412700448883
error: 0.01839076122016555 at 1412700449248
error: 0.012879421157519572 at 1412700449726
error: 0.006360901288843781 at 1412700450124
error: 0.01396655222350034 at 1412700450528
error: 0.009956514315467974 at 1412700451010
error: 0.004857991090787082 at 1412700451410
error: 0.010306263988590842 at 1412700451788
error: 0.007480908166309211 at 1412700452181
error: 0.00362782329142685 at 1412700452618
error: 0.007403998994120884 at 1412700453034
error: 0.00547262558221468 at 1412700453460
error: 0.002654915907621452 at 1412700453908
error: 0.005191112934769255 at 1412700454394
error: 0.00390709870927531 at 1412700454933
error: 0.0019087456135176125 at 1412700455471
error: 0.003562205705455709 at 1412700456037
error: 0.0027297617853948857 at 1412700456627
error: 0.001351618067410742 at 1412700457237
error: 0.0023996751967033285 at 1412700457894
error: 0.0018718999396941825 at 1412700458567
error: 9.450612333670903E-4 at 1412700459218
error: 0.001591749550692266 at 1412700459887
error: 0.001263596309067183 at 1412700460575
error: 6.540120516298157E-4 at 1412700461342
error: 0.0010426735254852127 at 1412700462111
error: 8.42032392455015E-4 at 1412700462969
error: 4.4890014175408407E-4 at 1412700463820
error: 6.763131263132559E-4 at 1412700464815
error: 5.553653937040373E-4 at 1412700465783
error: 3.061637696053671E-4 at 1412700466761
error: 4.3545039606555187E-4 at 1412700467800
error: 3.6339537355794654E-4 at 1412700468915
error: 2.078164451033659E-4 at 1412700470054
error: 2.789129759484473E-4 at 1412700471275
error: 2.3638994804346805E-4 at 1412700472529
error: 1.405707250516063E-4 at 1412700473951
error: 1.7806044538865907E-4 at 1412700475296
error: 1.5314542944478354E-4 at 1412700476670
error: 9.485494206989771E-5 at 1412700478155
error: 1.1348826418573315E-4 at 1412700479748
error: 9.896121689948542E-5 at 1412700481285
error: 6.39062077746496E-5 at 1412700482919
error: 7.23151181865718E-5 at 1412700484597
error: 6.386545019112331E-5 at 1412700486713
error: 4.3016168418758604E-5 at 1412700488571
error: 4.6122607517393423E-5 at 1412700490476
error: 4.120643424280222E-5 at 1412700492652
error: 2.8943163706122562E-5 at 1412700494700
error: 2.947320718562405E-5 at 1412700497232
error: 2.6603284406378926E-5 at 1412700499377
error: 1.9473771977773015E-5 at 1412700501682
error: 1.8884687336247628E-5 at 1412700504167
error: 1.7197879064427714E-5 at 1412700506893
error: 1.3105778985360542E-5 at 1412700509882
error: 1.2140205738990239E-5 at 1412700512555
error: 1.113824629741423E-5 at 1412700515861
error: 8.82402865317684E-6 at 1412700518945
Calibrated
error: 0.09993894444203227 at 1412700526040
error: 0.05781491295981514 at 1412700526405
error: 0.016629558115686276 at 1412700526609
error: 0.04371193761895504 at 1412700526780
error: 0.041499210240868334 at 1412700526975
error: 0.008174255807986914 at 1412700527167
error: 0.02967628296739122 at 1412700527381
error: 0.034465123203038524 at 1412700527574
error: 0.004428036568707985 at 1412700527770
error: 0.020573569702940053 at 1412700527988
error: 0.0250075136361148 at 1412700528220
error: 0.002670770841552942 at 1412700528464
error: 0.013599545654512563 at 1412700528706
error: 0.016117789742760374 at 1412700528949
error: 0.0016294745899280028 at 1412700529221
error: 0.008314636704889692 at 1412700529592
error: 0.009460614347695491 at 1412700529960
error: 9.484376522221207E-4 at 1412700530327
error: 0.004721260997133544 at 1412700530647
error: 0.0051802720061431915 at 1412700530965
error: 5.214651210163904E-4 at 1412700531289
error: 0.0025284629496722783 at 1412700531846
error: 0.0026984067494074393 at 1412700532273
error: 2.73234097262464E-4 at 1412700532667
error: 0.0012970977603062035 at 1412700533119
error: 0.0013570181601332025 at 1412700533546
error: 1.3807999259979217E-4 at 1412700534051
error: 6.453900523249521E-4 at 1412700534626
error: 6.65914682319315E-4 at 1412700535387
error: 6.799529394909593E-5 at 1412700535962
error: 3.143514976762522E-4 at 1412700536491
error: 3.212804424970773E-4 at 1412700537037
error: 3.288219845624559E-5 at 1412700537629
error: 1.5087340549206887E-4 at 1412700538222
error: 1.532052878931821E-4 at 1412700538848
error: 1.570391833495863E-5 at 1412700539497
error: 7.16828094367051E-5 at 1412700540139
error: 7.247290989386099E-5 at 1412700541152
error: 7.435764918620324E-6 at 1412700542227
Map calibrated
marginals
ArrayFactor [AbstractArrayFactor with scope {LETTER (card=2)} and values {0.989946905093049,0.010053094906951091}]
ArrayFactor [AbstractArrayFactor with scope {INTELLIGENCE (card=2)} and values {0.734806629834254,0.2651933701657459}]
ArrayFactor [AbstractArrayFactor with scope {SAT (card=2)} and values {0.5,0.5}]
ArrayFactor [AbstractArrayFactor with scope {DIFFICULTY (card=2)} and values {0.9452766346827345,0.05472336531726544}]
ArrayFactor [AbstractArrayFactor with scope {LETTER (card=2),GRADE (card=3)} and values {7.749501127436174E-7,6.171488165746366E-5,0.9898904984391491,6.974551014692557E-6,4.114325443830911E-5,0.009998893923627768}]
ArrayFactor [AbstractArrayFactor with scope {GRADE (card=3)} and values {7.749501127436173E-6,1.0285813609577276E-4,0.9998893923627767}]
ArrayFactor [AbstractArrayFactor with scope {SAT (card=2),INTELLIGENCE (card=2)} and values {0.3674033149171271,0.13259668508287292,0.3674033149171271,0.13259668508287292}]
ArrayFactor [AbstractArrayFactor with scope {GRADE (card=3),DIFFICULTY (card=2),INTELLIGENCE (card=2)} and values {1.498991587743437E-4,2.5272176106920663E-5,0.059380930077625314,4.2120293511534443E-5,0.07917457343683375,0.3612272048571481,1.498991587743437E-4,2.5272176106920663E-5,0.059380930077625314,4.2120293511534443E-5,0.07917457343683375,0.3612272048571481}]
maps
ArrayFactor [AbstractArrayFactor with scope {GRADE (card=3),DIFFICULTY (card=2),INTELLIGENCE (card=2)} and values {0.0011978685983252944,2.375353377851629E-7,2.318812171319791E-4,3.958922296419382E-7,3.0917495617597217E-4,0.4982604418007993,0.0011978685983252944,2.375353377851629E-7,2.318812171319791E-4,3.958922296419382E-7,3.0917495617597217E-4,0.4982604418007993}]
ArrayFactor [AbstractArrayFactor with scope {SAT (card=2)} and values {0.5,0.5}]
ArrayFactor [AbstractArrayFactor with scope {GRADE (card=3)} and values {4.735463212997269E-5,1.2502294700068801E-9,0.9999526441176406}]
ArrayFactor [AbstractArrayFactor with scope {LETTER (card=2),GRADE (card=3)} and values {4.7354632129972735E-6,7.501376820041283E-10,0.9899531176764642,4.261916891697546E-5,5.000917880027522E-10,0.009999526441176406}]
ArrayFactor [AbstractArrayFactor with scope {INTELLIGENCE (card=2)} and values {0.734806629834254,0.2651933701657459}]
ArrayFactor [AbstractArrayFactor with scope {SAT (card=2),INTELLIGENCE (card=2)} and values {0.3674033149171271,0.13259668508287292,0.3674033149171271,0.13259668508287292}]
ArrayFactor [AbstractArrayFactor with scope {DIFFICULTY (card=2)} and values {0.9452786832683161,0.054721316731683865}]
ArrayFactor [AbstractArrayFactor with scope {LETTER (card=2)} and values {0.99,0.01}]
Use LogFactor instead of Factor.
Take care of marginalization of LogFactor. Read http://www.mathworks.es/matlabcentral/fileexchange/25273-methods-for-calculating-precise-logarithm-of-a-sum-and-subtraction
A second observation is that nonconvergence is often due to oscillations in the beliefs. This observation suggests that we dampen the oscillations by reducing the difference between two subsequent updates. [...] We can replace this line by a damped (or smoothed) version that averages the update delta i --> j with the previous message between two cliques.
- Probabilistic Graphical Models, Box 11.B - Skill: Making loopy belief propagation work in practice
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A server is a program made to process requests and deliver data to clients.
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