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from symbolfit.symbolfit import *
from symbolfit.symbolfit import *
Detected IPython. Loading juliacall extension. See https://juliapy.github.io/PythonCall.jl/stable/compat/#IPython
Dataset¶
Five inputs are needed, which can be python lists or numpy arrays (more options will be added in future!):
x: independent variable (bin center location).y: dependent variable.y_up: upward uncertainty in y per bin.y_down: downward uncertainty in y per bin.bin_widths_1dbin widths in x.
- Elements in both y_up and y_down should be non-negative values.
- These values are the "delta" in y,
- y + y_up = y shifted up by one standard deviation.
- y - y_down = y shifted down by one standard deviation.
- If no uncertainty in the dataset, one can set both y_up and y_down to ones with the same shape as x.
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'''
CMS search for high-mass dijet resonances at sqrt(s) = 13 TeV
https://arxiv.org/abs/1911.03947
https://doi.org/10.1007/JHEP05(2020)033
Differential dijet spectrum (Figure 5), public data taken from HEPDATA
https://www.hepdata.net/record/ins1764471
'''
x=[1568.5, 1647.0, 1728.5, 1813.0, 1900.5, 1991.0, 2084.5, 2181.5, 2281.5, 2385.0, 2492.0, 2602.5, 2717.0, 2835.0, 2957.0, 3083.0, 3213.0, 3347.5, 3487.0, 3631.0, 3779.0, 3932.0, 4090.5, 4254.0, 4423.0, 4597.5, 4777.5, 4963.5, 5155.5, 5354.0, 5559.0, 5770.0, 5988.0, 6213.5, 6446.0, 6686.0, 6934.0, 7190.0, 7454.5, 7727.5, 8009.0, 8452.0]
y=[149.27999877929688, 109.44000244140625, 80.0770034790039, 58.715999603271484, 43.082000732421875, 31.559999465942383, 23.219999313354492, 16.982999801635742, 12.36400032043457, 9.121100425720215, 6.679200172424316, 4.889999866485596, 3.589400053024292, 2.5933001041412354, 1.902999997138977, 1.3653000593185425, 0.9902999997138977, 0.7092800140380859, 0.5142099857330322, 0.3630400002002716, 0.26298001408576965, 0.18937000632286072, 0.12946000695228577, 0.08928799629211426, 0.06131099909543991, 0.04499199986457825, 0.03179299831390381, 0.021355999633669853, 0.013650000095367432, 0.009144900366663933, 0.005454500205814838, 0.0038403000216931105, 0.0025553000159561634, 0.0015561999753117561, 0.0010168999433517456, 0.0005365100223571062, 0.00023088000307325274, 0.00022378000721801072, 0.00021629000548273325, 0.0, 7.628699677297845e-05, 1.2120999599574134e-05]
y_up=[0.11884000152349472, 0.09983699768781662, 0.08385500311851501, 0.07055199891328812, 0.0594169981777668, 0.05002899840474129, 0.042238999158144, 0.03539599850773811, 0.029911000281572342, 0.025085000321269035, 0.021276000887155533, 0.017805000767111778, 0.015064000152051449, 0.012597999535501003, 0.010623999871313572, 0.008864900097250938, 0.007441999856382608, 0.006189499981701374, 0.005183400120586157, 0.004302599932998419, 0.003619600087404251, 0.0030181999318301678, 0.002463799901306629, 0.002022000029683113, 0.0016528000123798847, 0.001401199959218502, 0.001164300017990172, 0.0009455800172872841, 0.0007514799945056438, 0.0006105700158514082, 0.0004726200131699443, 0.0003963200142607093, 0.0003233299939893186, 0.0002555900136940181, 0.00020963999850209802, 0.00015859999984968454, 0.00011385999823687598, 0.00011036000068997964, 0.00010666000162018463, 4.726000042865053e-05, 7.420800102408975e-05, 2.787400080705993e-05]
y_down=[0.11874999850988388, 0.09974599629640579, 0.08376699686050415, 0.07046700268983841, 0.059335000813007355, 0.049949999898672104, 0.042162999510765076, 0.035321999341249466, 0.02983899973332882, 0.02501700073480606, 0.02120799943804741, 0.017741000279784203, 0.015002000145614147, 0.012536999769508839, 0.010564999654889107, 0.008807900361716747, 0.0073866997845470905, 0.006136199925094843, 0.00513189984485507, 0.0042524999007582664, 0.0035707999486476183, 0.0029712000396102667, 0.002418200019747019, 0.0019777000416070223, 0.0016099000349640846, 0.001359499990940094, 0.0011238999431952834, 0.0009062800090759993, 0.0007132000173442066, 0.0005734399892389774, 0.0004362500039860606, 0.0003607299877330661, 0.00028870999813079834, 0.00022154999896883965, 0.00017612999363336712, 0.00012527000217232853, 7.989699952304363e-05, 7.743899914203212e-05, 7.484800153179094e-05, -0.0, 4.151900066062808e-05, 1.0026999916590285e-05]
bin_widths_1d=[77.0, 80.0, 83.0, 86.0, 89.0, 92.0, 95.0, 99.0, 101.0, 106.0, 108.0, 113.0, 116.0, 120.0, 124.0, 128.0, 132.0, 137.0, 142.0, 146.0, 150.0, 156.0, 161.0, 166.0, 172.0, 177.0, 183.0, 189.0, 195.0, 202.0, 208.0, 214.0, 222.0, 229.0, 236.0, 244.0, 252.0, 260.0, 269.0, 277.0, 286.0, 600.0]
'''
CMS search for high-mass dijet resonances at sqrt(s) = 13 TeV
https://arxiv.org/abs/1911.03947
https://doi.org/10.1007/JHEP05(2020)033
Differential dijet spectrum (Figure 5), public data taken from HEPDATA
https://www.hepdata.net/record/ins1764471
'''
x=[1568.5, 1647.0, 1728.5, 1813.0, 1900.5, 1991.0, 2084.5, 2181.5, 2281.5, 2385.0, 2492.0, 2602.5, 2717.0, 2835.0, 2957.0, 3083.0, 3213.0, 3347.5, 3487.0, 3631.0, 3779.0, 3932.0, 4090.5, 4254.0, 4423.0, 4597.5, 4777.5, 4963.5, 5155.5, 5354.0, 5559.0, 5770.0, 5988.0, 6213.5, 6446.0, 6686.0, 6934.0, 7190.0, 7454.5, 7727.5, 8009.0, 8452.0]
y=[149.27999877929688, 109.44000244140625, 80.0770034790039, 58.715999603271484, 43.082000732421875, 31.559999465942383, 23.219999313354492, 16.982999801635742, 12.36400032043457, 9.121100425720215, 6.679200172424316, 4.889999866485596, 3.589400053024292, 2.5933001041412354, 1.902999997138977, 1.3653000593185425, 0.9902999997138977, 0.7092800140380859, 0.5142099857330322, 0.3630400002002716, 0.26298001408576965, 0.18937000632286072, 0.12946000695228577, 0.08928799629211426, 0.06131099909543991, 0.04499199986457825, 0.03179299831390381, 0.021355999633669853, 0.013650000095367432, 0.009144900366663933, 0.005454500205814838, 0.0038403000216931105, 0.0025553000159561634, 0.0015561999753117561, 0.0010168999433517456, 0.0005365100223571062, 0.00023088000307325274, 0.00022378000721801072, 0.00021629000548273325, 0.0, 7.628699677297845e-05, 1.2120999599574134e-05]
y_up=[0.11884000152349472, 0.09983699768781662, 0.08385500311851501, 0.07055199891328812, 0.0594169981777668, 0.05002899840474129, 0.042238999158144, 0.03539599850773811, 0.029911000281572342, 0.025085000321269035, 0.021276000887155533, 0.017805000767111778, 0.015064000152051449, 0.012597999535501003, 0.010623999871313572, 0.008864900097250938, 0.007441999856382608, 0.006189499981701374, 0.005183400120586157, 0.004302599932998419, 0.003619600087404251, 0.0030181999318301678, 0.002463799901306629, 0.002022000029683113, 0.0016528000123798847, 0.001401199959218502, 0.001164300017990172, 0.0009455800172872841, 0.0007514799945056438, 0.0006105700158514082, 0.0004726200131699443, 0.0003963200142607093, 0.0003233299939893186, 0.0002555900136940181, 0.00020963999850209802, 0.00015859999984968454, 0.00011385999823687598, 0.00011036000068997964, 0.00010666000162018463, 4.726000042865053e-05, 7.420800102408975e-05, 2.787400080705993e-05]
y_down=[0.11874999850988388, 0.09974599629640579, 0.08376699686050415, 0.07046700268983841, 0.059335000813007355, 0.049949999898672104, 0.042162999510765076, 0.035321999341249466, 0.02983899973332882, 0.02501700073480606, 0.02120799943804741, 0.017741000279784203, 0.015002000145614147, 0.012536999769508839, 0.010564999654889107, 0.008807900361716747, 0.0073866997845470905, 0.006136199925094843, 0.00513189984485507, 0.0042524999007582664, 0.0035707999486476183, 0.0029712000396102667, 0.002418200019747019, 0.0019777000416070223, 0.0016099000349640846, 0.001359499990940094, 0.0011238999431952834, 0.0009062800090759993, 0.0007132000173442066, 0.0005734399892389774, 0.0004362500039860606, 0.0003607299877330661, 0.00028870999813079834, 0.00022154999896883965, 0.00017612999363336712, 0.00012527000217232853, 7.989699952304363e-05, 7.743899914203212e-05, 7.484800153179094e-05, -0.0, 4.151900066062808e-05, 1.0026999916590285e-05]
bin_widths_1d=[77.0, 80.0, 83.0, 86.0, 89.0, 92.0, 95.0, 99.0, 101.0, 106.0, 108.0, 113.0, 116.0, 120.0, 124.0, 128.0, 132.0, 137.0, 142.0, 146.0, 150.0, 156.0, 161.0, 166.0, 172.0, 177.0, 183.0, 189.0, 195.0, 202.0, 208.0, 214.0, 222.0, 229.0, 236.0, 244.0, 252.0, 260.0, 269.0, 277.0, 286.0, 600.0]
Plot the dataset to see what we will be fitting to:
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fig, axes = plt.subplots(figsize = (6, 4))
plt.errorbar(np.array(x).flatten(),
np.array(y).flatten(),
yerr = [np.array(y_down).flatten(), np.array(y_up).flatten()],
xerr = np.array(bin_widths_1d)/2,
fmt = '.', c = 'black', ecolor = 'grey', capsize = 0,
)
plt.savefig('img/dijet_template_spec/dataset.png')
fig, axes = plt.subplots(figsize = (6, 4))
plt.errorbar(np.array(x).flatten(),
np.array(y).flatten(),
yerr = [np.array(y_down).flatten(), np.array(y_up).flatten()],
xerr = np.array(bin_widths_1d)/2,
fmt = '.', c = 'black', ecolor = 'grey', capsize = 0,
)
plt.savefig('img/dijet_template_spec/dataset.png')
This is a steeply falling shape, let's plot in log scale:
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fig, axes = plt.subplots(figsize = (6, 4))
plt.errorbar(np.array(x).flatten(),
np.array(y).flatten(),
yerr = [np.array(y_down).flatten(), np.array(y_up).flatten()],
xerr = np.array(bin_widths_1d)/2,
fmt = '.', c = 'black', ecolor = 'grey', capsize = 0,
)
plt.xscale('log')
plt.yscale('log')
plt.savefig('img/dijet_template_spec/dataset_log.png')
fig, axes = plt.subplots(figsize = (6, 4))
plt.errorbar(np.array(x).flatten(),
np.array(y).flatten(),
yerr = [np.array(y_down).flatten(), np.array(y_up).flatten()],
xerr = np.array(bin_widths_1d)/2,
fmt = '.', c = 'black', ecolor = 'grey', capsize = 0,
)
plt.xscale('log')
plt.yscale('log')
plt.savefig('img/dijet_template_spec/dataset_log.png')
Configure the fit with TemplateExpressionSpec¶
Configure PySR to define the function space being searched for with symbolic regression:
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from pysr import PySRRegressor, TemplateExpressionSpec
expression_spec = TemplateExpressionSpec(
'p[1] * f(x/13000) ^ g(log(x/13000))',
expressions = ['f', 'g'],
variable_names = ['x'],
parameters = {'p': 1}
)
pysr_config = PySRRegressor(
expression_spec = expression_spec,
model_selection = 'accuracy',
niterations = 200,
maxsize = 40,
binary_operators = ['+', '*'],
elementwise_loss='loss(y, y_pred, weights) = (y - y_pred)^2 * weights',
)
from pysr import PySRRegressor, TemplateExpressionSpec
expression_spec = TemplateExpressionSpec(
'p[1] * f(x/13000) ^ g(log(x/13000))',
expressions = ['f', 'g'],
variable_names = ['x'],
parameters = {'p': 1}
)
pysr_config = PySRRegressor(
expression_spec = expression_spec,
model_selection = 'accuracy',
niterations = 200,
maxsize = 40,
binary_operators = ['+', '*'],
elementwise_loss='loss(y, y_pred, weights) = (y - y_pred)^2 * weights',
)
Here, we utilize PySR's TemplateExpressionSpec method (https://github.com/MilesCranmer/PySR/releases/tag/v1.4.0) to impose desired structure on the final expressions, which can potentially help narrowing down the function search space when domain knowledge is present.
For example, one can constrain to search for dijet functions (new physics searches at the CERN LHC) of the form f(x)^g(log(x)), where f and g are functions being searched for. One can further constrain to allow only + and * operators, restricting f(x) to be a polynomial of x and g(log(x)) to be a polynomial of log(x).
Loss function is a weighted MSE, where the weight is the sqaured uncertainty by default in SymbolFit.
For PySR options, please see:
Configure SymbolFit with the PySR config and for the re-optimization process:
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model = SymbolFit(
# Dataset: x, y, y_up, y_down.
x = x,
y = y,
y_up = y_up,
y_down = y_down,
# PySR configuration of the function space.
pysr_config = pysr_config,
# Constrain the maximum function size and over-write maxsize in pysr_config.
# Set a higher value for more complex shape, or when the lower one does not fit well.
max_complexity = 40,
# Whether to scale input x to be within 0 and 1 for the fits for numerical stability,
# as large x could lead to overflow when there is e.g. exp(x) -> exp(10000).
# So set this to False when your x's are or close to O(1), otherwise recommended to set True.
# After the fits, the functions will be unscaled to relect the original dataset.
input_rescale = False,
# ^ scaling needed here since the input x is O(1000).
# Whether to scale y for the fits for numerical stability,
# options are (when input_rescale is True): None / 'mean' / 'max' / 'l2'.
# This is useful to stabilize fits when your y's are very large or very small.
# After the fits, the functions will be unscaled to relect the original dataset.
scale_y_by = None,
# ^ scaling may or may not be needed here since the input y is widely spreading and not too extreme.
# Set a maximum standard error (%) for all parameters to avoid bad fits during re-optimization.
# In the refit loop, when any of the parameters returns a standard error larger than max_stderr,
# the fit is considered failed, and the fit will retry itself for fewer or other combination of varying parameters,
# by freezing some of the parameters to their initial values and kept fixed during re-optimization.
# This is to avoid bad fits when the objective is too complex to minimize, which could cause some parameters
# to have unrealistically large standard errors.
# In most cases 10 < max_stderr < 100 suffices.
max_stderr = 10,
# Consider y_up and y_down to weight the MSE loss during SR search and re-optimization.
fit_y_unc = True,
# Set a random seed for returning the same batch of functional forms every time (single-threaded),
# otherwise set None to explore more functions every time (multi-threaded and faster).
# In most cases the function space is huge, one can retry the fits with the exact same fit configuration
# and get completely different sets of candidate functions, merely by using different random seeds.
# So if the candidate functions are not satisfactory this time, rerun it few times more with
# random_seed = None or a different seed each time.
random_seed = None,
# Custome loss weight to set "(y - y_pred)^2 * loss_weights", overwriting that with y_up and y_down.
loss_weights = None
)
model = SymbolFit(
# Dataset: x, y, y_up, y_down.
x = x,
y = y,
y_up = y_up,
y_down = y_down,
# PySR configuration of the function space.
pysr_config = pysr_config,
# Constrain the maximum function size and over-write maxsize in pysr_config.
# Set a higher value for more complex shape, or when the lower one does not fit well.
max_complexity = 40,
# Whether to scale input x to be within 0 and 1 for the fits for numerical stability,
# as large x could lead to overflow when there is e.g. exp(x) -> exp(10000).
# So set this to False when your x's are or close to O(1), otherwise recommended to set True.
# After the fits, the functions will be unscaled to relect the original dataset.
input_rescale = False,
# ^ scaling needed here since the input x is O(1000).
# Whether to scale y for the fits for numerical stability,
# options are (when input_rescale is True): None / 'mean' / 'max' / 'l2'.
# This is useful to stabilize fits when your y's are very large or very small.
# After the fits, the functions will be unscaled to relect the original dataset.
scale_y_by = None,
# ^ scaling may or may not be needed here since the input y is widely spreading and not too extreme.
# Set a maximum standard error (%) for all parameters to avoid bad fits during re-optimization.
# In the refit loop, when any of the parameters returns a standard error larger than max_stderr,
# the fit is considered failed, and the fit will retry itself for fewer or other combination of varying parameters,
# by freezing some of the parameters to their initial values and kept fixed during re-optimization.
# This is to avoid bad fits when the objective is too complex to minimize, which could cause some parameters
# to have unrealistically large standard errors.
# In most cases 10 < max_stderr < 100 suffices.
max_stderr = 10,
# Consider y_up and y_down to weight the MSE loss during SR search and re-optimization.
fit_y_unc = True,
# Set a random seed for returning the same batch of functional forms every time (single-threaded),
# otherwise set None to explore more functions every time (multi-threaded and faster).
# In most cases the function space is huge, one can retry the fits with the exact same fit configuration
# and get completely different sets of candidate functions, merely by using different random seeds.
# So if the candidate functions are not satisfactory this time, rerun it few times more with
# random_seed = None or a different seed each time.
random_seed = None,
# Custome loss weight to set "(y - y_pred)^2 * loss_weights", overwriting that with y_up and y_down.
loss_weights = None
)
Symbol Fit it!¶
Run the fits: SR fit for functional form searching -> parameterization -> re-optimization fit for improved best-fits and uncertainty estimation -> evaluation.
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model.fit()
model.fit()
Compiling Julia backend... [ Info: Started!
Expressions evaluated per second: 9.100e+05
Progress: 4629 / 6200 total iterations (74.661%)
════════════════════════════════════════════════════════════════════════════════════════════════════
───────────────────────────────────────────────────────────────────────────────────────────────────
Complexity Loss Score Equation
2 1.702e-05 7.971e+00 ╭ f = 0.00084731
├ g = #1
╰ p = [5.0778e-05]
4 1.667e-05 1.061e-02 ╭ f = #1 * 4.0489
├ g = -7.022
╰ p = [1.0298]
6 6.209e-07 1.645e+00 ╭ f = (#1 + 0.19424) + #1
├ g = -11.021
╰ p = [0.015537]
10 3.484e-08 7.201e-01 ╭ f = (#1 * ((#1 * #1) * 3.8595)) + #1
├ g = -5.7409
╰ p = [0.0010902]
12 2.861e-08 9.862e-02 ╭ f = #1 + ((#1 + -0.077127) * (#1 * (#1 * 3.8893)))
├ g = -5.9162
╰ p = [0.00061992]
14 2.798e-08 1.098e-02 ╭ f = ((((#1 + -0.02974) * 3.8872) * (#1 + -0.042271)) * #1) +...
#1
├ g = -5.9088
╰ p = [0.00065676]
16 2.754e-08 8.084e-03 ╭ f = (#1 + ((((#1 + -0.027239) * (#1 + -0.07986)) * #1) * 3.8...
846)) * 1.3154
├ g = -6.0023
╰ p = [0.0025977]
18 2.282e-08 9.393e-02 ╭ f = (((((#1 * 7.3799) * ((#1 * #1) + #1)) + #1) * #1) * 0.33...
652) + #1
├ g = -5.701
╰ p = [0.0013533]
22 1.980e-08 3.543e-02 ╭ f = (#1 * (((#1 * ((((#1 * #1) * #1) + #1) * (#1 + 7.4331)))...
+ #1) * 0.39355)) + #1
├ g = -5.6558
╰ p = [0.0015657]
24 1.965e-08 3.979e-03 ╭ f = ((#1 + (#1 * ((((#1 * #1) * #1) + #1) * ((#1 * 1.168) + ...
7.4331)))) * (#1 * 0.39343)) + #1
├ g = -5.6522
╰ p = [0.0015775]
26 1.824e-08 3.715e-02 ╭ f = #1 + (((#1 + ((#1 * 7.4338) * (#1 + ((((#1 * #1) * #1) +...
#1) * (#1 * #1))))) * 0.41261) * #1)
├ g = -5.6359
╰ p = [0.0016614]
28 1.798e-08 7.074e-03 ╭ f = #1 + ((#1 * 0.41263) * (((((#1 * (#1 * (#1 + (((#1 * #1)...
* #1) * 1.2544)))) + #1) * 7.4338) * #1) + #1))
├ g = -5.6353
╰ p = [0.0016633]
30 1.743e-08 1.561e-02 ╭ f = (((((((#1 * #1) * (((#1 * 3.0224) * ((#1 * #1) * #1)) + ...
#1)) + #1) * (#1 * 7.4338)) + #1) * #1) * 0.41263) + #1
├ g = -5.6358
╰ p = [0.0016616]
32 1.720e-08 6.745e-03 ╭ f = ((#1 * ((((((((#1 * #1) * (#1 * #1)) * (#1 * 7.4338)) + ...
#1) * (#1 * #1)) + #1) * (#1 * 7.4338)) + #1)) * 0.41263) + #1
├ g = -5.6358
╰ p = [0.0016615]
34 1.702e-08 5.194e-03 ╭ f = ((#1 * 0.41263) * (#1 + ((#1 * (#1 + (#1 * (((((#1 * #1)...
* ((#1 * #1) * (#1 * 7.4338))) + #1) * #1) + 0.0011937)))) * ...
7.4338))) + #1
├ g = -5.6358
╰ p = [0.001662]
36 1.701e-08 1.563e-04 ╭ f = ((((((((((#1 * #1) + ((#1 * (#1 * #1)) * (((#1 * #1) * 7...
.4338) * #1))) + 0.0011937) * #1) + #1) * 7.4338) * #1) + #1) ...
* #1) * 0.41263) + #1
├ g = -5.6358
╰ p = [0.0016621]
38 1.696e-08 1.571e-03 ╭ f = ((#1 * 0.41263) * (#1 + ((#1 * ((#1 * ((((#1 * ((#1 * #1...
) * (((#1 * 7.4338) * (#1 + #1)) * #1))) + #1) * #1) + 0.00119...
37)) + #1)) * 7.4338))) + #1
├ g = -5.6358
╰ p = [0.001662]
40 1.694e-08 5.474e-04 ╭ f = ((#1 * 0.41263) * (#1 + ((#1 * ((#1 * ((((#1 * (((#1 * (...
(#1 * #1) * 7.4338)) * (#1 + (0.042545 + #1))) * #1)) + #1) * ...
#1) + 0.0011937)) + #1)) * 7.4338))) + #1
├ g = -5.6358
╰ p = [0.001662]
───────────────────────────────────────────────────────────────────────────────────────────────────
════════════════════════════════════════════════════════════════════════════════════════════════════
Press 'q' and then <enter> to stop execution early.
[ Info: Final population: [ Info: Results saved to:
───────────────────────────────────────────────────────────────────────────────────────────────────
Complexity Loss Score Equation
2 1.702e-05 7.971e+00 ╭ f = 0.00084731
├ g = #1
╰ p = [5.0778e-05]
4 1.667e-05 1.061e-02 ╭ f = #1 * 4.0489
├ g = -7.022
╰ p = [1.0298]
6 6.209e-07 1.645e+00 ╭ f = (#1 + 0.19424) + #1
├ g = -11.021
╰ p = [0.015537]
8 6.207e-07 1.259e-04 ╭ f = #1 + ((#1 + 0.19474) * 0.99367)
├ g = -11.021
╰ p = [0.014961]
10 3.484e-08 1.440e+00 ╭ f = (#1 * ((#1 * #1) * 3.8595)) + #1
├ g = -5.7409
╰ p = [0.0010902]
12 2.850e-08 1.005e-01 ╭ f = #1 + ((#1 * (#1 * 3.8906)) * (#1 + -0.073816))
├ g = -5.9091
╰ p = [0.00063503]
14 2.798e-08 9.119e-03 ╭ f = ((((#1 + -0.02974) * 3.8872) * (#1 + -0.042271)) * #1) +...
#1
├ g = -5.9088
╰ p = [0.00065676]
16 2.752e-08 8.318e-03 ╭ f = (((#1 * ((#1 + -0.027208) * (#1 + -0.079802))) * 3.8846)...
+ #1) * 1.1132
├ g = -6.0022
╰ p = [0.00095432]
18 2.282e-08 9.369e-02 ╭ f = (((((#1 * 7.3799) * ((#1 * #1) + #1)) + #1) * #1) * 0.33...
652) + #1
├ g = -5.701
╰ p = [0.0013533]
20 2.282e-08 6.437e-06 ╭ f = (((#1 * (#1 + ((#1 * 7.3799) * (#1 + (#1 * #1))))) * 0.3...
3652) + #1) * 1.0078
├ g = -5.701
╰ p = [0.0014142]
22 1.980e-08 7.086e-02 ╭ f = (#1 * (((#1 * ((((#1 * #1) * #1) + #1) * (#1 + 7.4331)))...
+ #1) * 0.39355)) + #1
├ g = -5.6558
╰ p = [0.0015657]
24 1.965e-08 3.989e-03 ╭ f = (((#1 + ((#1 * ((#1 * (#1 * #1)) + #1)) * ((#1 * 1.168) ...
+ 7.4331))) * #1) * 0.39343) + #1
├ g = -5.6522
╰ p = [0.0015776]
26 1.824e-08 3.714e-02 ╭ f = #1 + (((#1 + ((#1 * 7.4338) * (#1 + ((((#1 * #1) * #1) +...
#1) * (#1 * #1))))) * 0.41261) * #1)
├ g = -5.6359
╰ p = [0.0016614]
28 1.798e-08 7.140e-03 ╭ f = ((((((#1 * ((((#1 * #1) * (#1 * 1.2657)) + #1) * #1)) + ...
#1) * #1) * 7.4338) + #1) * (#1 * 0.41263)) + #1
├ g = -5.6353
╰ p = [0.0016633]
30 1.743e-08 1.555e-02 ╭ f = (((((((#1 * #1) * (((#1 * 3.0224) * ((#1 * #1) * #1)) + ...
#1)) + #1) * (#1 * 7.4338)) + #1) * #1) * 0.41263) + #1
├ g = -5.6358
╰ p = [0.0016616]
32 1.720e-08 6.745e-03 ╭ f = ((#1 * ((((((((#1 * #1) * (#1 * #1)) * (#1 * 7.4338)) + ...
#1) * (#1 * #1)) + #1) * (#1 * 7.4338)) + #1)) * 0.41263) + #1
├ g = -5.6358
╰ p = [0.0016615]
34 1.696e-08 6.950e-03 ╭ f = ((#1 + (#1 * (((#1 * ((#1 + (((#1 * #1) * #1) * ((#1 * 7...
.4338) * #1))) * #1)) + (#1 + 0.0012302)) * 7.4338))) * (#1 * ...
0.41265)) + #1
├ g = -5.6352
╰ p = [0.0016679]
36 1.695e-08 4.052e-04 ╭ f = #1 + ((((#1 * (((#1 + ((((#1 + -0.019916) * (((#1 * #1) ...
* 7.4338) * (#1 * #1))) + #1) * (#1 * #1))) + 0.0012465) * 7.4...
338)) + #1) * #1) * 0.41265)
├ g = -5.6351
╰ p = [0.0016682]
38 1.681e-08 4.096e-03 ╭ f = (#1 * ((#1 + (#1 * (((#1 + ((#1 + ((#1 * #1) * (#1 * (((...
(#1 + #1) * #1) * 7.4338) * #1)))) * (#1 * #1))) + 0.0011955) ...
* 7.4338))) * 0.41263)) + #1
├ g = -5.6358
╰ p = [0.0016658]
40 1.677e-08 1.036e-03 ╭ f = (((#1 * (((((#1 * (#1 + ((#1 * (((((#1 + #1) * #1) * #1)...
* (#1 * 7.4338)) + 0.042545)) * #1))) * #1) + #1) + 0.0012289...
) * 7.4338)) + #1) * (#1 * 0.41265)) + #1
├ g = -5.6352
╰ p = [0.0016679]
───────────────────────────────────────────────────────────────────────────────────────────────────
Attempting to load model from outputs_tmp/20250323_210508_RSfHIz/checkpoint.pkl...
Re-optimizing parameterized candidate function 1/20...
>>> loop of re-parameterization with less NDF for bad fits 2/8...
Re-optimizing parameterized candidate function 2/20...
>>> loop of re-parameterization with less NDF for bad fits 2/4...
Re-optimizing parameterized candidate function 3/20...
>>> loop of re-parameterization with less NDF for bad fits 2/8...
Re-optimizing parameterized candidate function 4/20...
>>> loop of re-parameterization with less NDF for bad fits 2/8...
Re-optimizing parameterized candidate function 5/20...
>>> loop of re-parameterization with less NDF for bad fits 2/8...
Re-optimizing parameterized candidate function 6/20...
>>> loop of re-parameterization with less NDF for bad fits 7/32...
Re-optimizing parameterized candidate function 7/20...
>>> loop of re-parameterization with less NDF for bad fits 33/64...
Re-optimizing parameterized candidate function 8/20...
>>> loop of re-parameterization with less NDF for bad fits 27/64...
Re-optimizing parameterized candidate function 9/20...
>>> loop of re-parameterization with less NDF for bad fits 23/64...
Re-optimizing parameterized candidate function 10/20...
>>> loop of re-parameterization with less NDF for bad fits 23/64...
Re-optimizing parameterized candidate function 11/20...
>>> loop of re-parameterization with less NDF for bad fits 24/64...
Re-optimizing parameterized candidate function 12/20...
>>> loop of re-parameterization with less NDF for bad fits 65/128...
Re-optimizing parameterized candidate function 13/20...
>>> loop of re-parameterization with less NDF for bad fits 66/128...
Re-optimizing parameterized candidate function 14/20...
>>> loop of re-parameterization with less NDF for bad fits 65/128...
Re-optimizing parameterized candidate function 15/20...
>>> loop of re-parameterization with less NDF for bad fits 65/128...
Re-optimizing parameterized candidate function 16/20...
>>> loop of re-parameterization with less NDF for bad fits 65/128...
Re-optimizing parameterized candidate function 17/20...
>>> loop of re-parameterization with less NDF for bad fits 168/256...
Re-optimizing parameterized candidate function 18/20...
>>> loop of re-parameterization with less NDF for bad fits 387/512...
Re-optimizing parameterized candidate function 19/20...
>>> loop of re-parameterization with less NDF for bad fits 166/256...
Re-optimizing parameterized candidate function 20/20...
>>> loop of re-parameterization with less NDF for bad fits 859/1024...
- outputs_tmp/20250323_210508_RSfHIz/hall_of_fame.csv
Save results to output files¶
Save results to csv tables:
candidates.csv: saves all candidate functions and evaluations in a csv table.candidates_compact.csv: saves a compact version for essential information without intermediate results.
In [8]:
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model.save_to_csv(output_dir = 'output_dijet_template_spec/')
model.save_to_csv(output_dir = 'output_dijet_template_spec/')
Saving full results >>> output_dijet_template_spec/candidates.csv Saving compact results >>> output_dijet_template_spec/candidates_compact.csv
Plot results to pdf files:
candidates.pdf: plots all candidate functions with associated uncertainties one by one for fit quality evaluation.candidates_sampling.pdf: plots all candidate functions with total uncertainty coverage generated by sampling parameters.candidates_gof.pdf: plots the goodness-of-fit scores.candidates_correlation.pdf: plots the correlation matrices for the parameters of the candidate functions.
In [9]:
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model.plot_to_pdf(
output_dir = 'output_dijet_template_spec/',
bin_widths_1d = bin_widths_1d,
plot_logy = True,
plot_logx = True,
sampling_95quantile = False
)
model.plot_to_pdf(
output_dir = 'output_dijet_template_spec/',
bin_widths_1d = bin_widths_1d,
plot_logy = True,
plot_logx = True,
sampling_95quantile = False
)
Plotting candidate functions 20/20 >>> output_dijet_template_spec/candidates.pdf Plotting candidate functions (sampling parameters) 20/20 >>> output_dijet_template_spec/candidates_sampling.pdf Plotting correlation matrices 20/20 >>> output_dijet_template_spec/candidates_correlation.pdf Plotting goodness-of-fit scores >>> output_dijet_template_spec/candidates_gof.pdf
