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Rendering Points and Lines
Mayavi has several ways to render 3D line and point data. The default is to use surfaces, which uses more resources. There are kwargs that can be changed to make it render with 2-D lines and points that make plotting large amounts of data more efficient.
LinePlot | # plot the data as a line
# change the tube radius to see the difference
mlab.figure('Line')
mlab.clf()
mlab.plot3d(y[:,0], y[:,1], y[:,2], tube_radius=.1)
mlab.colorbar()
# plot the data as a line, with color representing the time evolution
mlab.figure('Line')
mlab.clf()
mlab.plot3d(y[:,0], y[:,1], y[:,2], t, tube_ra... | code_examples/python_mayavi/mayavi_intermediate.ipynb | thehackerwithin/berkeley | bsd-3-clause |
Point Plot | # plot the data as a line, with color representing the time evolution
mlab.figure()
# By default, mayavi will plot points as spheres, so each point will
# be represented by a surface.
# Using mode='2dvertex' is needed for plotting large numbers of points.
mlab.figure('Points')
mlab.clf()
mlab.points3d(y[:,0], y[:,1]... | code_examples/python_mayavi/mayavi_intermediate.ipynb | thehackerwithin/berkeley | bsd-3-clause |
Line + Point Plot | # plot the data as a line, with color representing the time evolution
mlab.figure('Line and Points')
mlab.clf()
# plot the data as a line, with color representing the time evolution
mlab.plot3d(y[:,0], y[:,1], y[:,2], t, tube_radius=None, line_width=1 )
mlab.colorbar()
# By default, mayavi will plot points as spheres... | code_examples/python_mayavi/mayavi_intermediate.ipynb | thehackerwithin/berkeley | bsd-3-clause |
Contour Plot
Let's see how long the particle spends in each location | h3d = np.histogramdd(y, bins=50)
# generate the midpoint coordinates
xg,yg,zg = h3d[1]
xm = xg[1:] - .5*(xg[1]-xg[0])
ym = yg[1:] - .5*(yg[1]-yg[0])
zm = zg[1:] - .5*(zg[1]-zg[0])
xg, yg, zg = np.meshgrid(xm, ym, zm)
mlab.figure('contour')
mlab.clf()
mlab.contour3d( h3d[0], opacity=.5, contours=25 ) | code_examples/python_mayavi/mayavi_intermediate.ipynb | thehackerwithin/berkeley | bsd-3-clause |
Animation
Animation can be accomplished with a mlab.animate decorator. You must define a function that yields to the animate decorator. The yield defines when mayavi will rerender the image. | # plot the data as a line
mlab.figure('Animate')
mlab.clf()
# mlab.plot3d(y[:,0], y[:,1], y[:,2], tube_radius=None)
# mlab.colorbar()
a = mlab.points3d(y0[0], y0[1], y0[2], mode='2dvertex')
# number of points to plot
# n_plot = n_time
n_plot = 1000
@mlab.animate(delay=10, ui=True )
def anim():
for i in range(n_t... | code_examples/python_mayavi/mayavi_intermediate.ipynb | thehackerwithin/berkeley | bsd-3-clause |
First we need to define materials that will be used in the problem. We'll create three materials for the fuel, water, and cladding of the fuel pins. | # 1.6 enriched fuel
fuel = openmc.Material(name='1.6% Fuel')
fuel.set_density('g/cm3', 10.31341)
fuel.add_nuclide('U235', 3.7503e-4)
fuel.add_nuclide('U238', 2.2625e-2)
fuel.add_nuclide('O16', 4.6007e-2)
# borated water
water = openmc.Material(name='Borated Water')
water.set_density('g/cm3', 0.740582)
water.add_nuclid... | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
With our three materials, we can now create a Materials object that can be exported to an actual XML file. | # Instantiate a Materials object
materials_file = openmc.Materials([fuel, water, zircaloy])
# Export to "materials.xml"
materials_file.export_to_xml() | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Now let's move on to the geometry. This problem will be a square array of fuel pins and control rod guide tubes for which we can use OpenMC's lattice/universe feature. The basic universe will have three regions for the fuel, the clad, and the surrounding coolant. The first step is to create the bounding surfaces for fu... | # Create cylinders for the fuel and clad
fuel_outer_radius = openmc.ZCylinder(x0=0.0, y0=0.0, R=0.39218)
clad_outer_radius = openmc.ZCylinder(x0=0.0, y0=0.0, R=0.45720)
# Create boundary planes to surround the geometry
min_x = openmc.XPlane(x0=-10.71, boundary_type='reflective')
max_x = openmc.XPlane(x0=+10.71, bounda... | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
With the surfaces defined, we can now construct a fuel pin cell from cells that are defined by intersections of half-spaces created by the surfaces. | # Create a Universe to encapsulate a fuel pin
fuel_pin_universe = openmc.Universe(name='1.6% Fuel Pin')
# Create fuel Cell
fuel_cell = openmc.Cell(name='1.6% Fuel')
fuel_cell.fill = fuel
fuel_cell.region = -fuel_outer_radius
fuel_pin_universe.add_cell(fuel_cell)
# Create a clad Cell
clad_cell = openmc.Cell(name='1.6%... | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Likewise, we can construct a control rod guide tube with the same surfaces. | # Create a Universe to encapsulate a control rod guide tube
guide_tube_universe = openmc.Universe(name='Guide Tube')
# Create guide tube Cell
guide_tube_cell = openmc.Cell(name='Guide Tube Water')
guide_tube_cell.fill = water
guide_tube_cell.region = -fuel_outer_radius
guide_tube_universe.add_cell(guide_tube_cell)
# ... | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Using the pin cell universe, we can construct a 17x17 rectangular lattice with a 1.26 cm pitch. | # Create fuel assembly Lattice
assembly = openmc.RectLattice(name='1.6% Fuel Assembly')
assembly.pitch = (1.26, 1.26)
assembly.lower_left = [-1.26 * 17. / 2.0] * 2 | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Next, we create a NumPy array of fuel pin and guide tube universes for the lattice. | # Create array indices for guide tube locations in lattice
template_x = np.array([5, 8, 11, 3, 13, 2, 5, 8, 11, 14, 2, 5, 8,
11, 14, 2, 5, 8, 11, 14, 3, 13, 5, 8, 11])
template_y = np.array([2, 2, 2, 3, 3, 5, 5, 5, 5, 5, 8, 8, 8, 8,
8, 11, 11, 11, 11, 11, 13, 13, 14, 14, 14... | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
OpenMC requires that there is a "root" universe. Let us create a root cell that is filled by the assembly and then assign it to the root universe. | # Create root Cell
root_cell = openmc.Cell(name='root cell')
root_cell.fill = assembly
# Add boundary planes
root_cell.region = +min_x & -max_x & +min_y & -max_y & +min_z & -max_z
# Create root Universe
root_universe = openmc.Universe(universe_id=0, name='root universe')
root_universe.add_cell(root_cell) | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
We now must create a geometry that is assigned a root universe and export it to XML. | # Create Geometry and set root Universe
geometry = openmc.Geometry(root_universe)
# Export to "geometry.xml"
geometry.export_to_xml() | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
With the geometry and materials finished, we now just need to define simulation parameters. In this case, we will use 10 inactive batches and 40 active batches each with 2500 particles. | # OpenMC simulation parameters
batches = 50
inactive = 10
particles = 10000
# Instantiate a Settings object
settings_file = openmc.Settings()
settings_file.batches = batches
settings_file.inactive = inactive
settings_file.particles = particles
settings_file.output = {'tallies': False}
# Create an initial uniform spat... | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Let us also create a Plots file that we can use to verify that our fuel assembly geometry was created successfully. | # Instantiate a Plot
plot = openmc.Plot(plot_id=1)
plot.filename = 'materials-xy'
plot.origin = [0, 0, 0]
plot.pixels = [250, 250]
plot.width = [-10.71*2, -10.71*2]
plot.color_by = 'material'
# Instantiate a Plots object, add Plot, and export to "plots.xml"
plot_file = openmc.Plots([plot])
plot_file.export_to_xml() | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
With the plots.xml file, we can now generate and view the plot. OpenMC outputs plots in .ppm format, which can be converted into a compressed format like .png with the convert utility. | # Run openmc in plotting mode
openmc.plot_geometry(output=False)
# Convert OpenMC's funky ppm to png
!convert materials-xy.ppm materials-xy.png
# Display the materials plot inline
Image(filename='materials-xy.png') | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
As we can see from the plot, we have a nice array of fuel and guide tube pin cells with fuel, cladding, and water!
Create an MGXS Library
Now we are ready to generate multi-group cross sections! First, let's define a 2-group structure using the built-in EnergyGroups class. | # Instantiate a 2-group EnergyGroups object
groups = openmc.mgxs.EnergyGroups()
groups.group_edges = np.array([0., 0.625, 20.0e6]) | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Next, we will instantiate an openmc.mgxs.Library for the energy groups with the fuel assembly geometry. | # Initialize a 2-group MGXS Library for OpenMOC
mgxs_lib = openmc.mgxs.Library(geometry)
mgxs_lib.energy_groups = groups | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Now, we must specify to the Library which types of cross sections to compute. In particular, the following are the multi-group cross section MGXS subclasses that are mapped to string codes accepted by the Library class:
TotalXS ("total")
TransportXS ("transport" or "nu-transport with nu set to True)
AbsorptionXS ("abs... | # Specify multi-group cross section types to compute
mgxs_lib.mgxs_types = ['nu-transport', 'nu-fission', 'fission', 'nu-scatter matrix', 'chi'] | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Now we must specify the type of domain over which we would like the Library to compute multi-group cross sections. The domain type corresponds to the type of tally filter to be used in the tallies created to compute multi-group cross sections. At the present time, the Library supports "material", "cell", "universe", an... | # Specify a "cell" domain type for the cross section tally filters
mgxs_lib.domain_type = 'cell'
# Specify the cell domains over which to compute multi-group cross sections
mgxs_lib.domains = geometry.get_all_material_cells().values() | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
We can easily instruct the Library to compute multi-group cross sections on a nuclide-by-nuclide basis with the boolean Library.by_nuclide property. By default, by_nuclide is set to False, but we will set it to True here. | # Compute cross sections on a nuclide-by-nuclide basis
mgxs_lib.by_nuclide = True | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Lastly, we use the Library to construct the tallies needed to compute all of the requested multi-group cross sections in each domain and nuclide. | # Construct all tallies needed for the multi-group cross section library
mgxs_lib.build_library() | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
The tallies can now be export to a "tallies.xml" input file for OpenMC.
NOTE: At this point the Library has constructed nearly 100 distinct Tally objects. The overhead to tally in OpenMC scales as $O(N)$ for $N$ tallies, which can become a bottleneck for large tally datasets. To compensate for this, the Python API's T... | # Create a "tallies.xml" file for the MGXS Library
tallies_file = openmc.Tallies()
mgxs_lib.add_to_tallies_file(tallies_file, merge=True) | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
In addition, we instantiate a fission rate mesh tally to compare with OpenMOC. | # Instantiate a tally Mesh
mesh = openmc.Mesh(mesh_id=1)
mesh.type = 'regular'
mesh.dimension = [17, 17]
mesh.lower_left = [-10.71, -10.71]
mesh.upper_right = [+10.71, +10.71]
# Instantiate tally Filter
mesh_filter = openmc.MeshFilter(mesh)
# Instantiate the Tally
tally = openmc.Tally(name='mesh tally')
tally.filters... | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Tally Data Processing
Our simulation ran successfully and created statepoint and summary output files. We begin our analysis by instantiating a StatePoint object. | # Load the last statepoint file
sp = openmc.StatePoint('statepoint.50.h5') | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
The statepoint is now ready to be analyzed by the Library. We simply have to load the tallies from the statepoint into the Library and our MGXS objects will compute the cross sections for us under-the-hood. | # Initialize MGXS Library with OpenMC statepoint data
mgxs_lib.load_from_statepoint(sp) | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Voila! Our multi-group cross sections are now ready to rock 'n roll!
Extracting and Storing MGXS Data
The Library supports a rich API to automate a variety of tasks, including multi-group cross section data retrieval and storage. We will highlight a few of these features here. First, the Library.get_mgxs(...) method al... | # Retrieve the NuFissionXS object for the fuel cell from the library
fuel_mgxs = mgxs_lib.get_mgxs(fuel_cell, 'nu-fission') | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
The NuFissionXS object supports all of the methods described previously in the openmc.mgxs tutorials, such as Pandas DataFrames:
Note that since so few histories were simulated, we should expect a few division-by-error errors as some tallies have not yet scored any results. | df = fuel_mgxs.get_pandas_dataframe()
df | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Similarly, we can use the MGXS.print_xs(...) method to view a string representation of the multi-group cross section data. | fuel_mgxs.print_xs() | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
One can export the entire Library to HDF5 with the Library.build_hdf5_store(...) method as follows: | # Store the cross section data in an "mgxs/mgxs.h5" HDF5 binary file
mgxs_lib.build_hdf5_store(filename='mgxs.h5', directory='mgxs') | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
The HDF5 store will contain the numerical multi-group cross section data indexed by domain, nuclide and cross section type. Some data workflows may be optimized by storing and retrieving binary representations of the MGXS objects in the Library. This feature is supported through the Library.dump_to_file(...) and Librar... | # Store a Library and its MGXS objects in a pickled binary file "mgxs/mgxs.pkl"
mgxs_lib.dump_to_file(filename='mgxs', directory='mgxs')
# Instantiate a new MGXS Library from the pickled binary file "mgxs/mgxs.pkl"
mgxs_lib = openmc.mgxs.Library.load_from_file(filename='mgxs', directory='mgxs') | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
The Library class may be used to leverage the energy condensation features supported by the MGXS class. In particular, one can use the Library.get_condensed_library(...) with a coarse group structure which is a subset of the original "fine" group structure as shown below. | # Create a 1-group structure
coarse_groups = openmc.mgxs.EnergyGroups(group_edges=[0., 20.0e6])
# Create a new MGXS Library on the coarse 1-group structure
coarse_mgxs_lib = mgxs_lib.get_condensed_library(coarse_groups)
# Retrieve the NuFissionXS object for the fuel cell from the 1-group library
coarse_fuel_mgxs = co... | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Verification with OpenMOC
Of course it is always a good idea to verify that one's cross sections are accurate. We can easily do so here with the deterministic transport code OpenMOC. We first construct an equivalent OpenMOC geometry. | # Create an OpenMOC Geometry from the OpenMC Geometry
openmoc_geometry = get_openmoc_geometry(mgxs_lib.geometry) | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Now, we can inject the multi-group cross sections into the equivalent fuel assembly OpenMOC geometry. The openmoc.materialize module supports the loading of Library objects from OpenMC as illustrated below. | # Load the library into the OpenMOC geometry
materials = load_openmc_mgxs_lib(mgxs_lib, openmoc_geometry) | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
We are now ready to run OpenMOC to verify our cross-sections from OpenMC. | # Generate tracks for OpenMOC
track_generator = openmoc.TrackGenerator(openmoc_geometry, num_azim=32, azim_spacing=0.1)
track_generator.generateTracks()
# Run OpenMOC
solver = openmoc.CPUSolver(track_generator)
solver.computeEigenvalue() | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
We report the eigenvalues computed by OpenMC and OpenMOC here together to summarize our results. | # Print report of keff and bias with OpenMC
openmoc_keff = solver.getKeff()
openmc_keff = sp.k_combined.nominal_value
bias = (openmoc_keff - openmc_keff) * 1e5
print('openmc keff = {0:1.6f}'.format(openmc_keff))
print('openmoc keff = {0:1.6f}'.format(openmoc_keff))
print('bias [pcm]: {0:1.1f}'.format(bias)) | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
There is a non-trivial bias between the eigenvalues computed by OpenMC and OpenMOC. One can show that these biases do not converge to <100 pcm with more particle histories. For heterogeneous geometries, additional measures must be taken to address the following three sources of bias:
Appropriate transport-corrected cr... | # Get the OpenMC fission rate mesh tally data
mesh_tally = sp.get_tally(name='mesh tally')
openmc_fission_rates = mesh_tally.get_values(scores=['nu-fission'])
# Reshape array to 2D for plotting
openmc_fission_rates.shape = (17,17)
# Normalize to the average pin power
openmc_fission_rates /= np.mean(openmc_fission_rat... | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Next, we extract OpenMOC's volume-averaged fission rates into a 2D 17x17 NumPy array. | # Create OpenMOC Mesh on which to tally fission rates
openmoc_mesh = openmoc.process.Mesh()
openmoc_mesh.dimension = np.array(mesh.dimension)
openmoc_mesh.lower_left = np.array(mesh.lower_left)
openmoc_mesh.upper_right = np.array(mesh.upper_right)
openmoc_mesh.width = openmoc_mesh.upper_right - openmoc_mesh.lower_left
... | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Now we can easily use Matplotlib to visualize the fission rates from OpenMC and OpenMOC side-by-side. | # Ignore zero fission rates in guide tubes with Matplotlib color scheme
openmc_fission_rates[openmc_fission_rates == 0] = np.nan
openmoc_fission_rates[openmoc_fission_rates == 0] = np.nan
# Plot OpenMC's fission rates in the left subplot
fig = plt.subplot(121)
plt.imshow(openmc_fission_rates, interpolation='none', cma... | examples/jupyter/mgxs-part-iii.ipynb | johnnyliu27/openmc | mit |
Efter at have hentet vores rensede data, hvor vi minder os selv om at vi har: <br>
* dansker_set
* topklub_set
* ikke_topklub_set
* overall_set
Det første, vi gerne vil kigge lidt på, er, om vi var grundige nok i vores foranalyse. Derfor laver vi et heatmap, der skal fortælle os hvor stor sammenhængen er (korrelation)... | corr = overall_set.corr()
fig = plt.figure(figsize=(20, 16))
ax = sb.heatmap(corr, xticklabels=corr.columns.values,
yticklabels=corr.columns.values,
linewidths=0.25, vmax=1.0, square=True,
linecolor='black', annot=False
)
plt.show() | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Hvad vi ser her, er en korrelationsmatrix. Jo mørkere farver, des højere korrelation, rød for positiv- og blå for negativ-korrelation. <br>
Vi ser altså at der er høj korrelation, i vores nedre højre hjørne; Dette er spilpositionerne. Vi ser også et stort blåt kryds, som er målmandsdata. Disse har meget negativ korrela... | overall_set['label'] = overall_set['Club'].isin(topklub_set.Club).astype(int)
y = overall_set['label']
X = overall_set.iloc[:,0:-1].select_dtypes(include=['float64', 'int64']) | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Vi kan kigge lidt overordnet på tallene mellem de 2 klasser. | overall_set.groupby('label').mean() | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Observationer
Alderen siger ikke rigtig noget om, hvorvidt du spiller for en topklub eller ej
Topklubsspillere er i gennemsnittet en faktor 10 mere værd end ikke-topklub spillere
Topklubsspillere er i gennemsnittet generelt ca. 10+ på alt i forhold til ikke-topklub spillere
Vi er nu klar til at gå i gang med vores fø... | # hent nødvendige pakker fra Scikit Learn biblioteket (generelt super hvis man vil lave data science)
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Vi fitter nu en logistic regression classifier til vores data, og fitter en model, så den kan genkende om man spiller for en topklub eller ej, og evaluere resultatet: | model = LogisticRegression()
model = model.fit(X,y)
model.score(X,y) | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Altså har vores model ret i
{{'{:.0f}'.format(100*model.score(X, y))}}% af tiden i træningssættet. <br>
Pretty good!! Den har altså fundet nogle mønstre der kan mappe data til labels, og gætter ikke bare.
Men vi kan ikke vide, om den har overfittet, og derved har tilpasset sig for godt til sit kendte data, så nyt data... | X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2)
print('Træningsæt størrelse: {} - Testsæt størrelse: {}'.format(len(X_train), len(X_test))) | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Og vi er nu klar til at prøve igen!
Logistisk regression 2.0
Igen fitter vi en logistisk regression til vores træningsdata, og danner en model, men denne gang uden at bruge testdatasættet. | model2 = LogisticRegression()
model2 = model2.fit(X_train, y_train)
model2.score(X_train, y_train) | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Modellen matcher nu
{{'{:.0f}'.format(100*model2.score(X, y))}}% af tiden i træningssættet. <br>
Men har den overfittet?
Evaluering af modellen
Vi genererer derfor vores y forudsigelse og også sandsynlighederne for vores testsæt, da disse bruges til at evaluere modellen. | y_pred = model2.predict(X_test)
y_probs = model2.predict_proba(X_test)
# Evalueringsmålinger
from sklearn import metrics
print('Nøjagtigheden af vores logistiske regressions models prediction på testsættet er {:.0f}'.format(100*metrics.accuracy_score(y_test, y_pred))+'%', '\n')
print('Arealet under vores ROC AUC kurve... | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Det ser jo ret fornuftigt ud.<br>
For at sige noget om vores nye model, kan vi også lave en "confusion_matrix"
<img src='http://revolution-computing.typepad.com/.a/6a010534b1db25970b01bb08c97955970d-pi',
align="center"
width="40%"
alt="confusion matrix">
T og F står for henholdsvist True og False<br>
P og N... | confusion_matrix = metrics.confusion_matrix(y_test, y_pred)
print(confusion_matrix) | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Resultatet fortæller os, at vi har {{confusion_matrix[0,0]}}+{{confusion_matrix[1,1]}} = {{confusion_matrix[0,0]+confusion_matrix[1,1]}} korrekte forudsigelser og {{confusion_matrix[0,1]}}+{{confusion_matrix[1,0]}} = {{confusion_matrix[0,1]+confusion_matrix[1,0]}} ukorrekte
Man kan også bede classifieren om en rapport: | print(metrics.classification_report(y_test, y_pred)) | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Logistisk regression med krydsvalidering
Vi er egentlig meget tilfredse med vores model, men ofte kan det være en god idé at teste på flere små testsæt, og holde dem op mod hinanden. <br>
Her laver vi en 10-folds krydsvalidering og får altså 10 scorer ud: | # 10-folds cross-validation
from sklearn.model_selection import cross_val_score
scores = cross_val_score(LogisticRegression(), X, y, scoring='accuracy', cv=10)
print(scores,'\n')
print(scores.mean()) | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Her preformer modellen altså i gennemsnit
{{'{:.0f}'.format(100*scores.mean())}}%.
Det lyder meget lovende, men vi holder os til vores model2 og kan nu prøve modellen af på det rigtige datasæt
Danskersættet
Vi skal nu prøve vores model på vores danske spillere<br>
Opgave:
Vi skal lave prediction og probability på vor... | dansker_pred = None ### Fjern NONE og UDFYLD MIG ###
dansker_probs = None ### Fjern NONE og UDFYLD MIG ### | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Modellen har fundet {{np.bincount(dansker_pred)[0]}} nuller og {{np.bincount(dansker_pred)[1]}} ét-taller
Hvis du satte top_klub_ratio til 75 i Opgave 1 i Data Cleaning, skulle der være omkring 27-28 ét-taller. <br>
top_klub_ratio blev sat til: {{top_klub_ratio}}
Vi tilføjer disse kolonner til vores dataframe. | dansker_set_df = dansker_set.copy()
dansker_set_df[['prob1','prob2']] = pd.DataFrame(dansker_probs, index=dansker_set.index)
dansker_set_df['Probabilities [0,1]'] = dansker_set_df[['prob1','prob2']].values.tolist()
dansker_set_df['Prediction'] = pd.Series(dansker_pred, index=dansker_set.index)
del dansker_set_df['prob1... | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Og sortere listen, så de bedste danske spillere står øvers, og tilføjer et index, så vi kan få et bedre overblik | dansker_set_df.loc[:,'pred=1'] = dansker_set_df['Probabilities [0,1]'].map(lambda x: x[1]).sort_values(ascending=False)
dansker_sorted = dansker_set_df.sort_values('pred=1', ascending=False)
dansker_sorted = dansker_sorted[['Name', 'Club', 'Overall', 'Potential', 'Probabilities [0,1]', 'Prediction']]
dansker_sorted.loc... | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Efter flot hattrick mod Irland, kan man vidst ikke være i tvivl om Kong Christian tager pladsen på tronen
<img src='kongen.png',
align="center"
width="40%"
alt="kongen">
Men hvilke danske spillere spiller egentlig for topklubber, og hvordan er de rangeret i forhold til vores model? | dansker_sorted[dansker_sorted['Club'].isin(top_clubs)].set_index('in') | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Man kan undre sig over hvad Jacob Larsen laver hos stopklubben Borussia Dortmund, men en hurtig googling viser, at han simpelthen blev headhuntet til klubben som 16-årig.
Og så er der jo nok nogen, der vil spørger - Hvad med Bendtner?
Så han skal da også lige have en plads i vores analyse: | dansker_sorted.loc[dansker_sorted.Name == 'N. Bendtner'].set_index('in') | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Opgave:
Vi kan også kigge på ham i det store billede. Prøv evt. at lege lidt rundt med forskellige spillere eller andre features.<br>
Er der noget specielt, der kunne være sjovt at kigge på? | df.loc[df.Name == 'N. Bendtner'] | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Ekstra lege/analyse opgaver
Danske Rezan Corlu som ellers ligger ret lavt selv på potentiale har alligevel sikret sig en plads hos A.S. Roma i en alder af 20 år.
Men hvordan var det egentlig med de topklub spillere? Hvor langt ned kan man gå i potentiale, og stadig spille for en topklub? | top_df = df[df.Club.isin(top_clubs)]
top_df[top_df.Overall < 70].sort_values('Overall', ascending=True) | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Vi kan altså se, at der bliver satset på ungdommen, hvor deres kommende potentiale nok taler for deres plads i en storklub.<br>
Men hvad så med ikke-topklubsspillere og deres performance? | bund_df = df[~df.Club.isin(top_clubs)]
bund_df[bund_df.Overall > 70] | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Måske er de 22 klubber, vi har udvalgt ikke helt nok til at beskrive topklubber | top_clubs | Teknisk Tirsdag Tutorial (Supervised Learning).ipynb | mssalvador/Fifa2018 | apache-2.0 |
Значение теорем сходимости (Б.Т. Поляк Введение в оптимизацию, гл. 1, $\S$ 6)
Что дают теоремы сходимости
класс задач, для которых можно рассчитывать на применимость метода (важно не завышать условия!)
выпуклость
гладкость
качественное поведение метода
существенно ли начальное приближение
по какому функционалу ест... | def binary_search(f, a, b, epsilon, callback=None):
c = (a + b) / 2.0
while abs(b - a) > epsilon:
# Check left subsegment
y = (a + c) / 2.0
if f(y) <= f(c):
b = c
c = y
else:
# Check right subsegment
z = (b + c) / 2.0
if f(c... | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Метод золотого сечения
Идея:
делить отрезок $[a,b]$ не на две равные насти,
а в пропорции "золотого сечения".
Оценим скорость сходимости аналогично методу дихотомии:
$$
|x_{K+1} - x^*| \leq b_{K+1} - a_{K+1} = \left( \frac{1}{\tau} \right)^{N-1} (b - a) \approx 0.618^K(b-a),
$$
где $\tau = \frac{\sqrt{5} + 1}{2}$.
К... | def golden_search(f, a, b, tol=1e-5, callback=None):
tau = (np.sqrt(5) + 1) / 2.0
y = a + (b - a) / tau**2
z = a + (b - a) / tau
while b - a > tol:
if f(y) <= f(z):
b = z
z = y
y = a + (b - a) / tau**2
else:
a = y
y = z
... | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Сравнение методов одномерной минимизации | plt.figure(figsize=(10,6))
plt.semilogy(np.arange(1, len(approximation_bs) + 1), np.abs(x_true - np.array(approximation_bs, dtype=np.float64)), label="Binary search")
plt.semilogy(np.arange(1, len(approximation_gs) + 1), np.abs(x_true - np.array(approximation_gs, dtype=np.float64)), label="Golden search")
plt.xlabel(r"... | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Пример иного поведения методов
$$
f(x) = \sin(\sin(\sin(\sqrt{x}))), \; x \in [2, 60]
$$ | f = lambda x: np.sin(np.sin(np.sin(np.sqrt(x))))
x_true = (3 * np.pi / 2)**2
a = 2
b = 60
epsilon = 1e-8
plt.plot(np.linspace(a,b), f(np.linspace(a,b)))
plt.xticks(fontsize = 28)
_ = plt.yticks(fontsize = 28) | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Сравнение скорости сходимости и времени работы методов
Метод дихотомии | left_boud_bs = []
right_bound_bs = []
approximation_bs = []
callback_bs = lambda a, b: my_callback(a, b,
left_boud_bs, right_bound_bs, approximation_bs)
x_opt = binary_search(f, a, b, epsilon, callback_bs)
print(np.abs(x_opt - x_true)) | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Метод золотого сечения | left_boud_gs = []
right_bound_gs = []
approximation_gs = []
cb_gs = lambda a, b: my_callback(a, b, left_boud_gs, right_bound_gs, approximation_gs)
x_gs = golden_search(f, a, b, epsilon, cb_gs)
print(np.abs(x_opt - x_true)) | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Сходимость | plt.figure(figsize=(8,6))
plt.semilogy(np.abs(x_true - np.array(approximation_bs, dtype=np.float64)), label="Binary")
plt.semilogy(np.abs(x_true - np.array(approximation_gs, dtype=np.float64)), label="Golden")
plt.legend(fontsize=28)
plt.xticks(fontsize=28)
_ = plt.yticks(fontsize=28)
plt.xlabel(r"Number of iterations,... | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Время работы | %timeit binary_search(f, a, b, epsilon)
%timeit golden_search(f, a, b, epsilon) | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Резюме
Введение в численные методы оптимизации
Общая схема работы метода
Способы сравнения методов оптимизации
Зоопарк задач и методов
Одномерная минимизация
Методы спуска. Градиентный спуск и его ускоренные модификации
Что такое методы спуска?
Последовательность $x_k$ генерируется по правилу
$$
x_{k+1} = x_k + \alph... | %matplotlib notebook
import matplotlib.pyplot as plt
plt.rc("text", usetex=True)
import ipywidgets as ipywidg
import numpy as np
import liboptpy.unconstr_solvers as methods
import liboptpy.step_size as ss
from tqdm import tqdm
f = lambda x: np.power(x, 2)
gradf = lambda x: 2 * x
fig = plt.figure()
ax = fig.add_subplo... | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
$f(x) = x\log x$ | x_range = np.linspace(1e-10, 4)
plt.plot(x_range, x_range * np.log(x_range))
x0 = 1
f = lambda x: x * np.log(x)
grad = lambda x: np.log(x) + 1
beta1 = 0.3
beta2 = 0.7
plot_alpha(f, grad, x0, -grad(x0), np.linspace(1e-3, 0.9, 10), beta1, beta2) | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Backtracking
```python
def SelectStepSize(x, f, h, rho, alpha0, beta1, beta2):
# 0 < rho < 1
# alpha0 - initial guess of step size
# beta1 and beta2 - constants from conditions
alpha = alpha0
# Check violating sufficient decrease and curvature conditions
while (f(x - alpha * h) >= f(x) + beta1 * alpha gra... | def GradientDescent(f, gradf, x0, epsilon, num_iter, line_search,
disp=False, callback=None, **kwargs):
x = x0.copy()
iteration = 0
opt_arg = {"f": f, "grad_f": gradf}
for key in kwargs:
opt_arg[key] = kwargs[key]
while True:
gradient = gradf(x)
alpha = l... | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Выбор шага
Реализации различных способов выбора шага приведены тут
Зависимость от обусловленности матрицы $f''(x)$
Рассмотрим задачу
$$
\min f(x),
$$
где
$$ f(x) = x^{\top}Ax, \; A = \begin{bmatrix} 1 & 0\ 0 & \gamma \end{bmatrix} $$
$$
f'(x) = 2Ax
$$ | def my_f(x, A):
return 0.5 * x.dot(A.dot(x))
def my_gradf(x, A):
return A.dot(x)
plt.rc("text", usetex=True)
gammas = [0.1, 0.5, 1, 2, 3, 4, 5, 10, 20, 50, 100, 1000, 5000, 10000]
# gammas = [1]
num_iter_converg = []
for g in gammas:
A = np.array([[1, 0],
[0, g]], dtype=np.float64)
... | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
При неудачном начальном приближении сходимость для плохо обусловенной задачи очень медленная
При случайном начальном приближении сходимость может быть гораздо быстрее теоретических оценок
Эксперимент на многомерной задаче
Пусть $A \in \mathbb{R}^{m \times n}$. Рассмотрим систему линейных неравенств: $Ax \leq 1$ при ус... | import numpy as np
n = 1000
m = 2000
A = np.random.rand(n, m)
x = cvx.Variable(n)
obj = cvx.Minimize(cvx.sum(-cvx.log(1 - A.T * x)) -
cvx.sum(cvx.log(1 - cvx.square(x))))
prob = cvx.Problem(obj)
prob.solve(solver="SCS", verbose=True)
x = x.value
print("Optimal value =", prob.value) | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Решение с помощью градиентного спуска | import cvxpy as cvx
print(cvx.installed_solvers())
# !pip install jax
# !pip install jaxlib
import jax.numpy as jnp
import jax
# from jax.config import config
# config.update("jax_enable_x64", True)
A = jnp.array(A)
print(A.dtype)
x0 = jnp.zeros(n)
f = lambda x: -jnp.sum(jnp.log(1 - A.T@x)) - jnp.sum(jnp.log(1 - x... | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Подробнее про jax, его возможности и особенности можно посмотреть например тут | gd = methods.fo.GradientDescent(f, grad_f_jax, ss.Backtracking("Armijo", rho=0.5, beta=0.1, init_alpha=1.))
x = gd.solve(x0, tol=1e-5, max_iter=100, disp=True)
x_conv = gd.get_convergence()
grad_conv = [jnp.linalg.norm(grad_f_jax(x)) for x in x_conv]
plt.figure(figsize=(8,6))
plt.semilogy(grad_conv, label=r"$\| f'(x_k... | Spring2021/intro_gd.ipynb | amkatrutsa/MIPT-Opt | mit |
Request Data
In order to request data we are using Graphql (a query language for APIs, more info at: http://graphql.org/).
We provide the function to make a data request, all you need is a query and variables | def makeGraphqlRequest(query, variables):
return GraphQLClient.request(query, variables) | spot-oa/oa/proxy/ipynb_templates/Advanced_Mode_master.ipynb | LedaLima/incubator-spot | apache-2.0 |
Now that we have a function, we can run a query like this:
*Note: There's no need to manually set the date for the query, by default the code will read the date from the current path | suspicious_query = """query($date:SpotDateType) {
proxy {
suspicious(date:$date)
{ clientIp
clientToServerBytes
datetime
... | spot-oa/oa/proxy/ipynb_templates/Advanced_Mode_master.ipynb | LedaLima/incubator-spot | apache-2.0 |
Pandas Dataframes
The following cell loads the results into a pandas dataframe
For more information on how to use pandas, you can learn more here: https://pandas.pydata.org/pandas-docs/stable/10min.html | df = pd.read_json(json.dumps(results))
##Printing only the selected column list from the dataframe
##Unless specified otherwise,
print df[['clientIp','uriQuery','datetime','clientToServerBytes','serverToClientBytes', 'host']]
| spot-oa/oa/proxy/ipynb_templates/Advanced_Mode_master.ipynb | LedaLima/incubator-spot | apache-2.0 |
Additional operations
Additional operations can be performed on the dataframe like sorting the data, filtering it and grouping it
Filtering the data | ##Filter results where the destination port = 3389
##The resulting data will be stored in df2
df2 = df[df['clientIp'].isin(['10.173.202.136'])]
print df2[['clientIp','uriQuery','datetime','host']] | spot-oa/oa/proxy/ipynb_templates/Advanced_Mode_master.ipynb | LedaLima/incubator-spot | apache-2.0 |
Ordering the data | srtd = df.sort_values(by="host")
print srtd[['host','clientIp','uriQuery','datetime']] | spot-oa/oa/proxy/ipynb_templates/Advanced_Mode_master.ipynb | LedaLima/incubator-spot | apache-2.0 |
Grouping the data | ## This command will group the results by pairs of source-destination IP
## summarizing all other columns
grpd = df.groupby(['clientIp','host']).sum()
## This will print the resulting dataframe displaying the input and output bytes columnns
print grpd[["clientToServerBytes","serverToClientBytes"]] | spot-oa/oa/proxy/ipynb_templates/Advanced_Mode_master.ipynb | LedaLima/incubator-spot | apache-2.0 |
Reset Scored Connections
Uncomment and execute the following cell to reset all scored connections for this day | # reset_scores = """mutation($date:SpotDateType!) {
# proxy{
# resetScoredConnections(date:$date){
# success
# }
# }
# }"""
# variables={
# 'date': datetime.datetime.strptime(date, '%Y%m%d').strftim... | spot-oa/oa/proxy/ipynb_templates/Advanced_Mode_master.ipynb | LedaLima/incubator-spot | apache-2.0 |
Sandbox
At this point you can perform your own analysis using the previously provided functions as a guide.
Happy threat hunting! | #Your code here | spot-oa/oa/proxy/ipynb_templates/Advanced_Mode_master.ipynb | LedaLima/incubator-spot | apache-2.0 |
Load the database | reload(ximudata)
dbfilename = "/home/kjartan/Dropbox/Public/nvg201209.hdf5"
db = ximudata.NVGData(dbfilename); | notebooks/.ipynb_checkpoints/Get started-checkpoint.ipynb | alfkjartan/nvgimu | gpl-3.0 |
Explore contents of the database file | dbfile = db.hdfFile;
print "Subjects: ", dbfile.keys()
print "Trials: ", dbfile['S5'].keys()
print "IMUs: ", dbfile['S5/B'].keys()
print "Attributes of example trial", dbfile['S5/B'].attrs.keys()
print "Shape of example IMU data entry", dbfile['S5/B/N'].shape
| notebooks/.ipynb_checkpoints/Get started-checkpoint.ipynb | alfkjartan/nvgimu | gpl-3.0 |
The content of the raw IMU file
The columns of the IMU data contain:
0: Packet number,
1: Gyroscope X (deg/s),
2: Gyroscope Y (deg/s),
3: Gyroscope Z (deg/s),
4: Accelerometer X (g),
5: Accelerometer Y (g),
6: Accelerometer Z (g),
7: Magnetometer X (G),
8: Magnetometer Y (G),
9: Magnetometer Z (G)
Plot example data | db.plot_imu_data() | notebooks/.ipynb_checkpoints/Get started-checkpoint.ipynb | alfkjartan/nvgimu | gpl-3.0 |
Implemented analysis methods | print [s for s in dir(db) if s.startswith("get")] | notebooks/.ipynb_checkpoints/Get started-checkpoint.ipynb | alfkjartan/nvgimu | gpl-3.0 |
Is it possible to make the sketch so coarse that its estimates are wrong even for this data set? | s = Sketch(0.9, 0.9, 10)
f = open('CM_small.txt')
results_coarse_CM = CM_top_users(f,s)
print(results_coarse_CM) | count-min-101/CountMinSketch.ipynb | fionapigott/Data-Science-45min-Intros | unlicense |
Yes! (if you try enough) Why?
The 'w' parameter goes like ceiling(exp(1)/epsilon), which is always >=~ 3.
The 'd' parameter goes like ceiling(log(1/delta), which is always >= 1.
So, you're dealing with a space with minimum size 3 x 1. With 10 records, it's possible that all 4 users map their counts to the point. So ... | f = open('CM_large.txt')
%time results_exact = exact_top_users(f)
print(results_exact)
# this could take a few minutes
f = open('CM_large.txt')
s = Sketch(10**-4, 0.001, 10)
%time results_CM = CM_top_users(f,s)
print(results_CM) | count-min-101/CountMinSketch.ipynb | fionapigott/Data-Science-45min-Intros | unlicense |
For this precision and dataset size, the CM algo takes much longer than the exact solution. In fact, the crossover point at which the CM sketch can achieve reasonable accuracy in the same time as the exact solution is a very large number of entries. | for item in zip(results_exact,results_CM):
print(item)
# the CM sketch gets the top entry (an outlier) correct but doesn't do well estimating the order of the more degenerate counts
# let's decrease the precision via both the epsilon and delta parameters, and see whether it still gets the "heavy-hitter" correct
f... | count-min-101/CountMinSketch.ipynb | fionapigott/Data-Science-45min-Intros | unlicense |
使用 Tensorflow Lattice 实现道德形状约束
<table class="tfo-notebook-buttons" align="left">
<td><a target="_blank" href="https://tensorflow.google.cn/lattice/tutorials/shape_constraints_for_ethics"><img src="https://tensorflow.google.cn/images/tf_logo_32px.png">在 TensorFlow.org 上查看 </a></td>
<td><a target="_blank" href="https... | #@test {"skip": true}
!pip install tensorflow-lattice seaborn | site/zh-cn/lattice/tutorials/shape_constraints_for_ethics.ipynb | tensorflow/docs-l10n | apache-2.0 |
导入所需的软件包： | import tensorflow as tf
import logging
import matplotlib.pyplot as plt
import numpy as np
import os
import pandas as pd
import seaborn as sns
from sklearn.model_selection import train_test_split
import sys
import tensorflow_lattice as tfl
logging.disable(sys.maxsize) | site/zh-cn/lattice/tutorials/shape_constraints_for_ethics.ipynb | tensorflow/docs-l10n | apache-2.0 |
本教程中使用的默认值： | # List of learning rate hyperparameters to try.
# For a longer list of reasonable hyperparameters, try [0.001, 0.01, 0.1].
LEARNING_RATES = [0.01]
# Default number of training epochs and batch sizes.
NUM_EPOCHS = 1000
BATCH_SIZE = 1000
# Directory containing dataset files.
DATA_DIR = 'https://raw.githubusercontent.com/... | site/zh-cn/lattice/tutorials/shape_constraints_for_ethics.ipynb | tensorflow/docs-l10n | apache-2.0 |
案例研究 1：法学院入学
在本教程的第一部分中，我们将考虑一个使用法学院招生委员会 (LSAC) 的 Law School Admissions 数据集的案例研究。我们将训练分类器利用以下两个特征来预测学生是否会通过考试：学生的 LSAT 分数和本科生的 GPA。
假设分类器的分数用于指导法学院的招生或奖学金评定。根据基于成绩的社会规范，我们预期具有更高 GPA 和更高 LSAT 分数的学生应当从分类器中获得更高的分数。但是，我们会观察到，模型很容易违反这些直观的规范，有时会惩罚 GPA 或 LSAT 分数较高的人员。
为了解决这种不公平的惩罚问题，我们可以施加单调性约束，这样在其他条件相同的情况下，模型永远不会惩罚更高的 GPA ... | # Load data file.
law_file_name = 'lsac.csv'
law_file_path = os.path.join(DATA_DIR, law_file_name)
raw_law_df = pd.read_csv(law_file_path, delimiter=',') | site/zh-cn/lattice/tutorials/shape_constraints_for_ethics.ipynb | tensorflow/docs-l10n | apache-2.0 |
预处理数据集： | # Define label column name.
LAW_LABEL = 'pass_bar'
def preprocess_law_data(input_df):
# Drop rows with where the label or features of interest are missing.
output_df = input_df[~input_df[LAW_LABEL].isna() & ~input_df['ugpa'].isna() &
(input_df['ugpa'] > 0) & ~input_df['lsat'].isna()]
retur... | site/zh-cn/lattice/tutorials/shape_constraints_for_ethics.ipynb | tensorflow/docs-l10n | apache-2.0 |
将数据划分为训练/验证/测试集 | def split_dataset(input_df, random_state=888):
"""Splits an input dataset into train, val, and test sets."""
train_df, test_val_df = train_test_split(
input_df, test_size=0.3, random_state=random_state)
val_df, test_df = train_test_split(
test_val_df, test_size=0.66, random_state=random_state)
retur... | site/zh-cn/lattice/tutorials/shape_constraints_for_ethics.ipynb | tensorflow/docs-l10n | apache-2.0 |
可视化数据分布
首先，我们可视化数据的分布。我们将为所有通过考试的学生以及所有未通过考试的学生绘制 GPA 和 LSAT 分数。 | def plot_dataset_contour(input_df, title):
plt.rcParams['font.family'] = ['serif']
g = sns.jointplot(
x='ugpa',
y='lsat',
data=input_df,
kind='kde',
xlim=[1.4, 4],
ylim=[0, 50])
g.plot_joint(plt.scatter, c='b', s=10, linewidth=1, marker='+')
g.ax_joint.collections[0].set_alph... | site/zh-cn/lattice/tutorials/shape_constraints_for_ethics.ipynb | tensorflow/docs-l10n | apache-2.0 |
训练校准线性模型以预测考试的通过情况
接下来，我们将通过 TFL 训练校准线性模型，以预测学生是否会通过考试。两个输入特征分别是 LSAT 分数和本科 GPA，而训练标签将是学生是否通过了考试。
我们首先在没有任何约束的情况下训练校准线性模型。然后，我们在具有单调性约束的情况下训练校准线性模型，并观察模型输出和准确率的差异。
用于训练 TFL 校准线性 Estimator 的辅助函数
下面这些函数将用于此法学院案例研究以及下面的信用违约案例研究。 | def train_tfl_estimator(train_df, monotonicity, learning_rate, num_epochs,
batch_size, get_input_fn,
get_feature_columns_and_configs):
"""Trains a TFL calibrated linear estimator.
Args:
train_df: pandas dataframe containing training data.
monotonicity: if 0, ... | site/zh-cn/lattice/tutorials/shape_constraints_for_ethics.ipynb | tensorflow/docs-l10n | apache-2.0 |
用于配置法学院数据集特征的辅助函数
下面这些辅助函数专用于法学院案例研究。 | def get_input_fn_law(input_df, num_epochs, batch_size=None):
"""Gets TF input_fn for law school models."""
return tf.compat.v1.estimator.inputs.pandas_input_fn(
x=input_df[['ugpa', 'lsat']],
y=input_df['pass_bar'],
num_epochs=num_epochs,
batch_size=batch_size or len(input_df),
shuffle=... | site/zh-cn/lattice/tutorials/shape_constraints_for_ethics.ipynb | tensorflow/docs-l10n | apache-2.0 |
用于可视化训练的模型输出的辅助函数 | def get_predicted_probabilities(estimator, input_df, get_input_fn):
predictions = estimator.predict(
input_fn=get_input_fn(input_df=input_df, num_epochs=1))
return [prediction['probabilities'][1] for prediction in predictions]
def plot_model_contour(estimator, input_df, num_keypoints=20):
x = np.linspace(... | site/zh-cn/lattice/tutorials/shape_constraints_for_ethics.ipynb | tensorflow/docs-l10n | apache-2.0 |
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