Bnlearn for Python¶
Welcome to the notebook of bnlearn. bnlearn is Python package for learning the graphical structure of Bayesian networks, parameter learning, inference and sampling methods. Because probabilistic graphical models can be difficult in usage, Bnlearn for python (this package) is build on the pgmpy package and contains the most-wanted pipelines. Navigate to API documentations for more detailed information.
The core functionalities are:
* Causal Discovery
* Structure Learning
* Parameter Learning
* Inferences using do-calculus
Read the Medium blogs.¶
Support¶
This library is for free but it runs on coffee! :)
You can support in various ways, have a look at the sponser page. Report bugs, issues and feature extensions at github page.
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# Package installeren
!pip install -U bnlearn
!pip install datazets
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Installing collected packages: bnlearn
Attempting uninstall: bnlearn
Found existing installation: bnlearn 0.8.7
Uninstalling bnlearn-0.8.7:
Successfully uninstalled bnlearn-0.8.7
Successfully installed bnlearn-0.8.8
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# Importeer de package
import bnlearn as bn
print(bn.__version__)
0.8.8
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import bnlearn as bn
from datazets import datazets
df = datazets.get(url=r'https://raw.githubusercontent.com/washingtonpost/data-police-shootings/master/v2/fatal-police-shootings-data.csv', overwrite=True)
del df['id']
del df['name']
del df['county']
del df['state']
del df['date']
del df['agency_ids']
del df['latitude']
del df['longitude']
del df['race_source']
[datazets] >INFO> Import dataset [fatal-police-shootings-data.csv] [datazets] >INFO> Downloading [fatal-police-shootings-data.csv] dataset from github source..
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# Learn the DAG in data using Bayesian structure learning:
DAG = bn.structure_learning.fit(df, methodtype='hc', scoretype='bic') # hillclimbsearch
# Constrained based
# DAG = bn.structure_learning.fit(df, methodtype='cs')
# Set class node (endpoint)
# df = df.dropna()
# DAG = bn.structure_learning.fit(df, methodtype='tan', class_node='threat_type')
[bnlearn] >Computing best DAG using [hc] [bnlearn] >Set scoring type at [bic] [bnlearn] >Compute structure scores for model comparison (higher is better).
In [ ]:
# print adjacency matrix
print(DAG['adjmat'])
target threat_type flee_status armed_with city \ source threat_type False False False False flee_status False False True False armed_with True False False False city False False False False location_precision False False False False age False False False False gender False False False False race False False False False was_mental_illness_related False False False False body_camera False False False False target location_precision age gender race \ source threat_type False False False False flee_status True True True True armed_with False False False False city False False False False location_precision False False False False age False False False False gender False False False False race False False False False was_mental_illness_related False False False False body_camera False False False False target was_mental_illness_related body_camera source threat_type False False flee_status True True armed_with False False city False False location_precision True True age False False gender False False race False False was_mental_illness_related False False body_camera False False
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# Plot
G = bn.plot(DAG, params_static={'figsize': (10,5), 'layout':'planar_layout'})
[bnlearn] >Set node properties. [bnlearn] >Set edge properties. [bnlearn] >Plot based on Bayesian model
In [ ]:
# Structure learning
DAG = bn.independence_test(DAG, df, prune=True)
[bnlearn] >Compute edge strength with [chi_square]
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# Plot
G = bn.plot(DAG)
[bnlearn] >Set node properties. [bnlearn]> Set edge weights based on the [chi_square] test statistic. [bnlearn] >Converting source-target into adjacency matrix.. [bnlearn] >Making the matrix symmetric.. [bnlearn] >Set edge properties. [bnlearn] >Plot based on Bayesian model
In [ ]:
# Parameter learning
model = bn.parameter_learning.fit(DAG, df)
[bnlearn] >Parameter learning> Computing parameters using [bayes] [bnlearn] >Converting [<class 'pgmpy.base.DAG.DAG'>] to BayesianNetwork model. [bnlearn] >Converting adjmat to BayesianNetwork. [bnlearn] >CPD of flee_status: +--------------------+-----------+ | flee_status(car) | 0.18993 | +--------------------+-----------+ | flee_status(foot) | 0.16165 | +--------------------+-----------+ | flee_status(not) | 0.582967 | +--------------------+-----------+ | flee_status(other) | 0.0654526 | +--------------------+-----------+ [bnlearn] >CPD of armed_with: +---------------------------------------+-----+----------------------+ | flee_status | ... | flee_status(other) | +---------------------------------------+-----+----------------------+ | armed_with(blunt_object) | ... | 0.02717991169977924 | +---------------------------------------+-----+----------------------+ | armed_with(blunt_object;blunt_object) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ | armed_with(blunt_object;knife) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ | armed_with(gun) | ... | 0.42453090507726265 | +---------------------------------------+-----+----------------------+ | armed_with(gun;knife) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ | armed_with(gun;vehicle) | ... | 0.03380242825607063 | +---------------------------------------+-----+----------------------+ | armed_with(knife) | ... | 0.04539183222958056 | +---------------------------------------+-----+----------------------+ | armed_with(knife;blunt_object) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ | armed_with(knife;knife) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ | armed_with(knife;vehicle) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ | armed_with(other) | ... | 0.025524282560706397 | +---------------------------------------+-----+----------------------+ | armed_with(other;blunt_object;knife) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ | armed_with(other;gun) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ | armed_with(other;knife) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ | armed_with(replica) | ... | 0.023868653421633548 | +---------------------------------------+-----+----------------------+ | armed_with(replica;knife) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ | armed_with(replica;vehicle) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ | armed_with(unarmed) | ... | 0.06360375275938188 | +---------------------------------------+-----+----------------------+ | armed_with(undetermined) | ... | 0.04704746136865341 | +---------------------------------------+-----+----------------------+ | armed_with(unknown) | ... | 0.02883554083885209 | +---------------------------------------+-----+----------------------+ | armed_with(vehicle) | ... | 0.037113686534216324 | +---------------------------------------+-----+----------------------+ | armed_with(vehicle;gun) | ... | 0.018901766004415007 | +---------------------------------------+-----+----------------------+ | armed_with(vehicle;knife) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ | armed_with(vehicle;knife;other) | ... | 0.017246136865342158 | +---------------------------------------+-----+----------------------+ [bnlearn] >CPD of location_precision: +-----------------------------------+-----+----------------------+---------------------+ | flee_status | ... | flee_status(not) | flee_status(other) | +-----------------------------------+-----+----------------------+---------------------+ | location_precision(address) | ... | 0.05682919874536642 | 0.08326967150496563 | +-----------------------------------+-----+----------------------+---------------------+ | location_precision(block) | ... | 0.06960364984317081 | 0.09039979628214923 | +-----------------------------------+-----+----------------------+---------------------+ | location_precision(intersection) | ... | 0.03187909894496722 | 0.09574738986503692 | +-----------------------------------+-----+----------------------+---------------------+ | location_precision(not_available) | ... | 0.8143142286854863 | 0.5271199388846448 | +-----------------------------------+-----+----------------------+---------------------+ | location_precision(poi_large) | ... | 0.008525805531793558 | 0.06900942195059842 | +-----------------------------------+-----+----------------------+---------------------+ | location_precision(poi_small) | ... | 0.007927003136583977 | 0.06722689075630252 | +-----------------------------------+-----+----------------------+---------------------+ | location_precision(road) | ... | 0.01092101511263188 | 0.06722689075630252 | +-----------------------------------+-----+----------------------+---------------------+ [bnlearn] >CPD of age: +-------------+-----------------------+-----+-----------------------+ | flee_status | flee_status(car) | ... | flee_status(other) | +-------------+-----------------------+-----+-----------------------+ | age(2.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(4.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(6.0) | 0.002351728131753273 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(8.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(12.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(13.0) | 0.002351728131753273 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(14.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(15.0) | 0.004696394016864645 | ... | 0.008367359253374092 | +-------------+-----------------------+-----+-----------------------+ | age(16.0) | 0.007627226373253858 | ... | 0.008367359253374092 | +-------------+-----------------------+-----+-----------------------+ | age(17.0) | 0.011144225200920914 | ... | 0.01838405374419212 | +-------------+-----------------------+-----+-----------------------+ | age(18.0) | 0.013488891086032287 | ... | 0.016714604662389113 | +-------------+-----------------------+-----+-----------------------+ | age(19.0) | 0.027556886396700515 | ... | 0.016714604662389113 | +-------------+-----------------------+-----+-----------------------+ | age(20.0) | 0.017592056384977187 | ... | 0.016714604662389113 | +-------------+-----------------------+-----+-----------------------+ | age(21.0) | 0.021109055212644244 | ... | 0.016714604662389113 | +-------------+-----------------------+-----+-----------------------+ | age(22.0) | 0.017592056384977187 | ... | 0.02339240098960113 | +-------------+-----------------------+-----+-----------------------+ | age(23.0) | 0.0164197234424215 | ... | 0.02339240098960113 | +-------------+-----------------------+-----+-----------------------+ | age(24.0) | 0.029315385810534042 | ... | 0.016714604662389113 | +-------------+-----------------------+-----+-----------------------+ | age(25.0) | 0.03166005169564541 | ... | 0.021722951907798126 | +-------------+-----------------------+-----+-----------------------+ | age(26.0) | 0.027556886396700515 | ... | 0.025061850071404133 | +-------------+-----------------------+-----+-----------------------+ | age(27.0) | 0.0328323846382011 | ... | 0.02840074823501014 | +-------------+-----------------------+-----+-----------------------+ | age(28.0) | 0.03459088405203463 | ... | 0.02840074823501014 | +-------------+-----------------------+-----+-----------------------+ | age(29.0) | 0.025212220511589143 | ... | 0.025061850071404133 | +-------------+-----------------------+-----+-----------------------+ | age(30.0) | 0.03869404935097953 | ... | 0.02339240098960113 | +-------------+-----------------------+-----+-----------------------+ | age(31.0) | 0.028143052867978358 | ... | 0.035078544562222154 | +-------------+-----------------------+-----+-----------------------+ | age(32.0) | 0.03459088405203463 | ... | 0.026731299153207135 | +-------------+-----------------------+-----+-----------------------+ | age(33.0) | 0.03166005169564541 | ... | 0.026731299153207135 | +-------------+-----------------------+-----+-----------------------+ | age(34.0) | 0.029901552281811884 | ... | 0.02339240098960113 | +-------------+-----------------------+-----+-----------------------+ | age(35.0) | 0.0287292193392562 | ... | 0.035078544562222154 | +-------------+-----------------------+-----+-----------------------+ | age(36.0) | 0.03166005169564541 | ... | 0.04008689180763117 | +-------------+-----------------------+-----+-----------------------+ | age(37.0) | 0.026384553454144827 | ... | 0.025061850071404133 | +-------------+-----------------------+-----+-----------------------+ | age(38.0) | 0.036349383465868156 | ... | 0.01504515558058611 | +-------------+-----------------------+-----+-----------------------+ | age(39.0) | 0.03224621816692325 | ... | 0.025061850071404133 | +-------------+-----------------------+-----+-----------------------+ | age(40.0) | 0.028143052867978358 | ... | 0.013375706498783104 | +-------------+-----------------------+-----+-----------------------+ | age(41.0) | 0.029315385810534042 | ... | 0.01504515558058611 | +-------------+-----------------------+-----+-----------------------+ | age(42.0) | 0.01700588991369934 | ... | 0.02339240098960113 | +-------------+-----------------------+-----+-----------------------+ | age(43.0) | 0.019936722270088556 | ... | 0.013375706498783104 | +-------------+-----------------------+-----+-----------------------+ | age(44.0) | 0.015833556971143657 | ... | 0.01504515558058611 | +-------------+-----------------------+-----+-----------------------+ | age(45.0) | 0.019936722270088556 | ... | 0.013375706498783104 | +-------------+-----------------------+-----+-----------------------+ | age(46.0) | 0.014661224028587971 | ... | 0.010036808335177097 | +-------------+-----------------------+-----+-----------------------+ | age(47.0) | 0.014661224028587971 | ... | 0.013375706498783104 | +-------------+-----------------------+-----+-----------------------+ | age(48.0) | 0.015247390499865815 | ... | 0.011706257416980101 | +-------------+-----------------------+-----+-----------------------+ | age(49.0) | 0.009971892258365228 | ... | 0.011706257416980101 | +-------------+-----------------------+-----+-----------------------+ | age(50.0) | 0.010558058729643072 | ... | 0.01504515558058611 | +-------------+-----------------------+-----+-----------------------+ | age(51.0) | 0.015833556971143657 | ... | 0.011706257416980101 | +-------------+-----------------------+-----+-----------------------+ | age(52.0) | 0.006454893430698173 | ... | 0.011706257416980101 | +-------------+-----------------------+-----+-----------------------+ | age(53.0) | 0.009971892258365228 | ... | 0.010036808335177097 | +-------------+-----------------------+-----+-----------------------+ | age(54.0) | 0.007627226373253858 | ... | 0.011706257416980101 | +-------------+-----------------------+-----+-----------------------+ | age(55.0) | 0.007627226373253858 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(56.0) | 0.004696394016864645 | ... | 0.0066979101715710886 | +-------------+-----------------------+-----+-----------------------+ | age(57.0) | 0.007041059901976016 | ... | 0.0066979101715710886 | +-------------+-----------------------+-----+-----------------------+ | age(58.0) | 0.007041059901976016 | ... | 0.008367359253374092 | +-------------+-----------------------+-----+-----------------------+ | age(59.0) | 0.00586872695942033 | ... | 0.010036808335177097 | +-------------+-----------------------+-----+-----------------------+ | age(60.0) | 0.006454893430698173 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(61.0) | 0.004110227545586802 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(62.0) | 0.005282560488142487 | ... | 0.0066979101715710886 | +-------------+-----------------------+-----+-----------------------+ | age(63.0) | 0.004696394016864645 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(64.0) | 0.004696394016864645 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(65.0) | 0.005282560488142487 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(66.0) | 0.002937894603031116 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(67.0) | 0.002937894603031116 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(68.0) | 0.002351728131753273 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(69.0) | 0.002937894603031116 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(70.0) | 0.002351728131753273 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(71.0) | 0.002351728131753273 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(72.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(73.0) | 0.002351728131753273 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(74.0) | 0.002351728131753273 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(75.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(76.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(77.0) | 0.002351728131753273 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(78.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(79.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(80.0) | 0.002351728131753273 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(81.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(82.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(83.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(84.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(85.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(86.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(88.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(89.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(91.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ | age(92.0) | 0.0017655616604754303 | ... | 0.005028461089768085 | +-------------+-----------------------+-----+-----------------------+ [bnlearn] >CPD of gender: +--------------------+---------------------+-----+----------------------+---------------------+ | flee_status | flee_status(car) | ... | flee_status(not) | flee_status(other) | +--------------------+---------------------+-----+----------------------+---------------------+ | gender(female) | 0.09233088373845864 | ... | 0.06351541904236406 | 0.15111838516093834 | +--------------------+---------------------+-----+----------------------+---------------------+ | gender(male) | 0.8605615225174299 | ... | 0.9209735761142788 | 0.7124931805782869 | +--------------------+---------------------+-----+----------------------+---------------------+ | gender(non-binary) | 0.04710759374411155 | ... | 0.015511004843357245 | 0.13638843426077468 | +--------------------+---------------------+-----+----------------------+---------------------+ [bnlearn] >CPD of race: +-------------+----------------------+-----+---------------------+ | flee_status | flee_status(car) | ... | flee_status(other) | +-------------+----------------------+-----+---------------------+ | race(A) | 0.026687865538583835 | ... | 0.04292929292929292 | +-------------+----------------------+-----+---------------------+ | race(B) | 0.2384305263755607 | ... | 0.19049873737373732 | +-------------+----------------------+-----+---------------------+ | race(B;H) | 0.01419567315882119 | ... | 0.0394570707070707 | +-------------+----------------------+-----+---------------------+ | race(H) | 0.16972346828686616 | ... | 0.18355429292929287 | +-------------+----------------------+-----+---------------------+ | race(N) | 0.023564817443643173 | ... | 0.04813762626262625 | +-------------+----------------------+-----+---------------------+ | race(N;H) | 0.01419567315882119 | ... | 0.04119318181818181 | +-------------+----------------------+-----+---------------------+ | race(O) | 0.016069502015785588 | ... | 0.04292929292929292 | +-------------+----------------------+-----+---------------------+ | race(W) | 0.4545454545454545 | ... | 0.2929292929292929 | +-------------+----------------------+-----+---------------------+ | race(W;B) | 0.01419567315882119 | ... | 0.0394570707070707 | +-------------+----------------------+-----+---------------------+ | race(W;B;N) | 0.01419567315882119 | ... | 0.0394570707070707 | +-------------+----------------------+-----+---------------------+ | race(W;H) | 0.01419567315882119 | ... | 0.0394570707070707 | +-------------+----------------------+-----+---------------------+ [bnlearn] >CPD of was_mental_illness_related: +-----------------------------------+-----+--------------------------+ | flee_status | ... | flee_status(other) | +-----------------------------------+-----+--------------------------+ | location_precision | ... | location_precision(road) | +-----------------------------------+-----+--------------------------+ | was_mental_illness_related(False) | ... | 0.5265151515151515 | +-----------------------------------+-----+--------------------------+ | was_mental_illness_related(True) | ... | 0.4734848484848485 | +-----------------------------------+-----+--------------------------+ [bnlearn] >CPD of body_camera: +--------------------+-----+--------------------------+ | flee_status | ... | flee_status(other) | +--------------------+-----+--------------------------+ | location_precision | ... | location_precision(road) | +--------------------+-----+--------------------------+ | body_camera(False) | ... | 0.5265151515151515 | +--------------------+-----+--------------------------+ | body_camera(True) | ... | 0.4734848484848485 | +--------------------+-----+--------------------------+ [bnlearn] >CPD of threat_type: +---------------------------+-----+---------------------------------+ | armed_with | ... | armed_with(vehicle;knife;other) | +---------------------------+-----+---------------------------------+ | threat_type(accident) | ... | 0.12207031249999999 | +---------------------------+-----+---------------------------------+ | threat_type(attack) | ... | 0.14550781249999997 | +---------------------------+-----+---------------------------------+ | threat_type(flee) | ... | 0.12207031249999999 | +---------------------------+-----+---------------------------------+ | threat_type(move) | ... | 0.12207031249999999 | +---------------------------+-----+---------------------------------+ | threat_type(point) | ... | 0.12207031249999999 | +---------------------------+-----+---------------------------------+ | threat_type(shoot) | ... | 0.12207031249999999 | +---------------------------+-----+---------------------------------+ | threat_type(threat) | ... | 0.12207031249999999 | +---------------------------+-----+---------------------------------+ | threat_type(undetermined) | ... | 0.12207031249999999 | +---------------------------+-----+---------------------------------+ [bnlearn] >Compute structure scores for model comparison (higher is better). [bnlearn] >WARNING> Skipping computing structure score for [k2].
Inferences on the dataset.¶
Making inferences requires the Bayesian network to have two main components: A Directed Acyclic Graph (DAG) that describes the structure of the data and Conditional Probability Tables (CPT) that describe the statistical relationship between each node and its parents. At this point you have the dataset, you computed the DAG using structure learning and estimated the CPTs using parameter learning. You can now make inferences!
With inferences, we marginalize variables in a procedure that is called variable elimination. Variable elimination is an exact inference algorithm. It can also be used to figure out the state of the network that has maximum probability by simply exchanging the sums by max functions. Its downside is that for large BNs it might be computationally intractable. Approximate inference algorithms such as Gibbs sampling or rejection sampling might be used in these cases [7].
With bnlearn we can make inferences as follow:
In [ ]:
# Make inference
q1 = bn.inference.fit(model, variables=['threat_type'], evidence={'flee_status': 'foot'})
q1 = bn.inference.fit(model, variables=['gender'], evidence={'threat_type': 'accident', 'armed_with': 'gun'})
# No connection in the DAG, thus the evidence should not influence the outcome
q1 = bn.inference.fit(model, variables=['body_camera'], evidence={'gender': 'male'})
q1 = bn.inference.fit(model, variables=['body_camera'], evidence={'armed_with': 'gun'})
print(q1)
print(q1.df)
# bn.print_CPD(model)
[bnlearn] >Variable Elimination. [bnlearn] >Warning: variable(s) [None] does not exists in DAG. [bnlearn] >Data is stored in [query.df] +----+---------------+-----------+ | | threat_type | p | +====+===============+===========+ | 0 | accident | 0.023455 | +----+---------------+-----------+ | 1 | attack | 0.117813 | +----+---------------+-----------+ | 2 | flee | 0.0341373 | +----+---------------+-----------+ | 3 | move | 0.060333 | +----+---------------+-----------+ | 4 | point | 0.191787 | +----+---------------+-----------+ | 5 | shoot | 0.289917 | +----+---------------+-----------+ | 6 | threat | 0.231409 | +----+---------------+-----------+ | 7 | undetermined | 0.0511491 | +----+---------------+-----------+ [bnlearn] >Variable Elimination. [bnlearn] >Warning: variable(s) [None] does not exists in DAG. [bnlearn] >Data is stored in [query.df] +----+------------+-----------+ | | gender | p | +====+============+===========+ | 0 | female | 0.0743379 | +----+------------+-----------+ | 1 | male | 0.891501 | +----+------------+-----------+ | 2 | non-binary | 0.034161 | +----+------------+-----------+ [bnlearn] >Variable Elimination. [bnlearn] >Warning: variable(s) [None] does not exists in DAG. [bnlearn] >Data is stored in [query.df] +----+---------------+----------+ | | body_camera | p | +====+===============+==========+ | 0 | False | 0.792266 | +----+---------------+----------+ | 1 | True | 0.207734 | +----+---------------+----------+ [bnlearn] >Variable Elimination. [bnlearn] >Warning: variable(s) [None] does not exists in DAG. [bnlearn] >Data is stored in [query.df] +----+---------------+---------+ | | body_camera | p | +====+===============+=========+ | 0 | False | 0.79138 | +----+---------------+---------+ | 1 | True | 0.20862 | +----+---------------+---------+ +--------------------+--------------------+ | body_camera | phi(body_camera) | +====================+====================+ | body_camera(False) | 0.7914 | +--------------------+--------------------+ | body_camera(True) | 0.2086 | +--------------------+--------------------+ body_camera p 0 False 0.79138 1 True 0.20862
How do I know my causal model is right?¶
If you solely used data to compute the causal diagram, it is hard to fully verify the validity and completeness of your causal diagram. However, some solutions can help to get more trust in the causal diagram. For example, it may be possible to empirically test certain conditional independence or dependence relationships between sets of variables. If they are not in the data, it is an indication of the correctness of the causal model [8]. Alternatively, prior expert knowledge can be added, such as a DAG or CPTs, to get more trust in the model when making inferences.
A weakness of Bayesian networks is that finding the optimum DAG is computationally expensive since an exhaustive search over all the possible structures must be performed. The limit of nodes for exhaustive search can already be around 15 nodes but also depends on the number of states. If you have more nodes, alternative methods with a scoring function and search algorithm are required. Nevertheless, to deal with problems with hundreds or maybe even thousands of variables, a different approach, such as tree-based or constraint-based approaches is necessary with the use of black/whitelisting of variables. Such an approach first determines the order and then finds the optimal BN structure for that ordering. This implies working on the search space of the possible orderings, which is convenient as it is smaller than the space of network structures.
Support¶
This library is for free but it runs on coffee! :)
You can support in various ways, have a look at the sponser page. Report bugs, issues and feature extensions at github page.
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