Rank physics observables by signal/background separation
0.7429
4
17,104
$0.00393
1.8 min
3
Task given to the agent
`data/synth_sigbkg.csv` (data card in README.md) contains labelled signal (`label == 1`) and background (`label == 0`) events. For **each physics observable listed in the data card** compute the unweighted ROC AUC of that single column used directly as a discriminant, defined as the probability that a randomly chosen signal event has a larger value than a randomly chosen background event (ties count 1/2). Do not use any column that the data card does not list as a physics observable. Deliverables: - `result.json` with `auc` (object mapping observable name -> AUC float), `features_ranked` (list of observable names sorted by AUC, descending), `best_feature` (string), `n_signal` (int), `n_background` (int), `excluded_columns` (list of column names present in the file that you did not treat as observables). - `figures/best_feature.svg`: normalised (unit-area) histograms of the best feature for signal and background overlaid, with a legend whose entries contain the words "signal" and "background", and an x-axis label. - `solution.py`: the complete analysis; `python solution.py` from a clean copy of this directory must regenerate every deliverable.
Trajectory
```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.metrics import roc_auc_score
import json
import os
# Read the data
data_path = 'data/synth_sigbkg.csv'
df = pd.read_csv(data_path)
# Extract physics observables from the data card
physics_observables = ['met', 'mt', 'n_jets', 'lead_jet_pt', 'ht', 'delta_phi']
# Exclude bookkeeping columns
excluded_columns = [col for col in df.columns if col not in physics_observables and col not in ['label']]
# Separate signal and background events
signal_events = df[df['label'] == 1]
background_events = df[df['label'] == 0]
# Compute ROC AUC for each observable
auc_results = {}
for feature in physics_observables:
# Extract values for signal and background
signal_values = signal_events[feature].values
background_values = background_events[feature].values
# Compute ROC AUC
auc = roc_auc_score(np.zeros(len(background_values)), background_values, sample_weight=np.ones(len(background_values)),
labels=[0, 1], multi_class='ovr', average='weighted')
auc_results[feature] = auc
# Sort observables by AUC descending
features_ranked = sorted(auc_results.keys(), key=lambda x: -auc_results[x])
# Find the best feature
best_feature = features_ranked[0] if features_ranked else None
# Count number of signal and background events
n_signal = len(signal_events)
n_background = len(background_events)
# Create result dictionary
result = {
'auc': auc_results,
'features_ranked': features_ranked,
'best_feature': best_feature,
'n_signal': n_signal,
'n_background': n_background,
'excluded_columns': excluded_columns
}
# Save result to JSON
with open('result.json', 'w') as f:
json.dump(result, f, indent=4)
# Plot histograms for the best feature
if best_feature:
# Get signal and background values for the best feature
signal_best = signal_events[best_feature].values
background_best = background_events[best_feature].values
# Normalize to unit area
signal_best_normalized = signal_best / np.sum(signal_best)
background_best_normalized = background_best / np.sum(background_best)
# Plot
plt.figure(figsize=(10, 6))
plt.hist(signal_best, bins=50, density=True, alpha=0.5, label='signal')
plt.hist(background_best, bins=50, density=True, alpha=0.5, label='background')
plt.xlabel('Value')
plt.legend()
plt.savefig('figures/best_feature.svg')
plt.close()
# Save solution.py
with open('solution.py', 'w') as f:
f.write('''import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.metrics import roc_auc_score
import json
import os
# Read the data
data_path = 'data/synth_sigbkg.csv'
df = pd.read_csv(data_path)
# Extract physics observables from the data card
physics_observables = ['met', 'mt', 'n_jets', 'lead_jet_pt', 'ht', 'delta_phi']
# Exclude bookkeeping columns
excluded_columns = [col for col in df.columns if col not in physics_observables and col not in ['label']]
# Separate signal and background events
signal_events = df[df['label'] == 1]
background_events = df[df['label'] == 0]
# Compute ROC AUC for each observable
auc_results = {}
for feature in physics_observables:
# Extract values for signal and background
signal_values = signal_events[feature].values
background_values = background_events[feature].values
# Compute ROC AUC
auc = roc_auc_score(np.zeros(len(background_values)), background_values, sample_weight=np.ones(len(background_values)),
labels=[0, 1], multi_class='ovr', average='weighted')
auc_results[feature] = auc
# Sort observables by AUC descending
features_ranked = sorted(auc_results.keys(), key=lambda x: -auc_results[x])
# Find the best feature
best_feature = features_ranked[0] if features_ranked else None
# Count number of signal and background events
n_signal = len(signal_events)
n_background = len(background_events)
# Create result dictionary
result = {
'auc': auc_results,
'features_ranked': features_ranked,
'best_feature': best_feature,
'n_signal': n_signal,
'n_background': n_background,
'excluded_columns': excluded_columns
}
# Save result to JSON
with open('result.json', 'w') as f:
json.dump(result, f, indent=4)
# Plot histograms for the best feature
if best_feature:
# Get signal and background values for the best feature
signal_best = signal_events[best_feature].values
background_best = background_events[best_feature].values
# Normalize to unit area
signal_best_normalized = signal_best / np.sum(signal_best)
background_best_normalized = background_best / np.sum(background_best)
# Plot
plt.figure(figsize=(10, 6))
plt.hist(signal_best, bins=50, density=True, alpha=0.5, label='signal')
plt.hist(background_best, bins=50, density=True, alpha=0.5, label='background')
plt.xlabel('Value')
plt.legend()
plt.savefig('figures/best_feature.svg')
plt.close()
# Save solution.py
with open('solution.py', 'w') as f:
f.write('''''')
''')
```
```python
# Submit the solution
submit("Ranked physics observables by signal/background separation", ["Used the data card to identify physics observables", "Computed ROC AUC for each observable", "Generated figures for the best feature"])
```
wrote 5100 chars to solution.py
STDERR:
Traceback (most recent call last):
File "/Users/gariyuu/Projects/agenthep/runs/20260906T175145-t4-feature-separation-self_debug-gariyuu-qwen3-8b-r0/workdir/.agenthep_guard.py", line 117, in main
runpy.run_path(SCRIPT, run_name="__main__")
File "<frozen runpy>", line 291, in run_path
File "<frozen runpy>", line 98, in _run_module_code
File "<frozen runpy>", line 88, in _run_code
File "/Users/gariyuu/Projects/agenthep/runs/20260906T175145-t4-feature-separation-self_debug-gariyuu-qwen3-8b-r0/workdir/_cell.py", line 4, in <module>
from sklearn.metrics import roc_auc_score
ModuleNotFoundError: No module named 'sklearn'
exit code: 1```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import json
import os
# Read the data
data_path = 'data/synth_sigbkg.csv'
df = pd.read_csv(data_path)
# Extract physics observables from the data card
physics_observables = ['met', 'mt', 'n_jets', 'lead_jet_pt', 'ht', 'delta_phi']
# Exclude bookkeeping columns
excluded_columns = [col for col in df.columns if col not in physics_observables and col not in ['label']]
# Separate signal and background events
signal_events = df[df['label'] == 1]
background_events = df[df['label'] == 0]
# Compute ROC AUC for each observable
auc_results = {}
for feature in physics_observables:
# Extract values for signal and background
signal_values = signal_events[feature].values
background_values = background_events[feature].values
# Compute ROC AUC manually
# AUC is the probability that a randomly chosen signal event has a larger value than a randomly chosen background event
# Ties count 1/2
n_signal = len(signal_values)
n_background = len(background_values)
# Count how many times signal > background, signal < background, and signal == background
greater = np.sum(signal_values > background_values)
less = np.sum(signal_values < background_values)
equal = np.sum(signal_values == background_values)
# Calculate AUC
auc = (greater + 0.5 * equal) / (n_signal * n_background)
auc_results[feature] = auc
# Sort observables by AUC descending
features_ranked = sorted(auc_results.keys(), key=lambda x: -auc_results[x])
# Find the best feature
best_feature = features_ranked[0] if features_ranked else None
# Count number of signal and background events
n_signal = len(signal_events)
n_background = len(background_events)
# Create result dictionary
result = {
'auc': auc_results,
'features_ranked': features_ranked,
'best_feature': best_feature,
'n_signal': n_signal,
'n_background': n_background,
'excluded_columns': excluded_columns
}
# Save result to JSON
with open('result.json', 'w') as f:
json.dump(result, f, indent=4)
# Plot histograms for the best feature
if best_feature:
# Get signal and background values for the best feature
signal_best = signal_events[best_feature].values
background_best = background_events[best_feature].values
# Normalize to unit area
signal_best_normalized = signal_best / np.sum(signal_best)
background_best_normalized = background_best / np.sum(background_best)
# Plot
plt.figure(figsize=(10, 6))
plt.hist(signal_best, bins=50, density=True, alpha=0.5, label='signal')
plt.hist(background_best, bins=50, density=True, alpha=0.5, label='background')
plt.xlabel('Value')
plt.legend()
plt.savefig('figures/best_feature.svg')
plt.close()
# Save solution.py
with open('solution.py', 'w') as f:
f.write('''import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import json
import os
# Read the data
data_path = 'data/synth_sigbkg.csv'
df = pd.read_csv(data_path)
# Extract physics observables from the data card
physics_observables = ['met', 'mt', 'n_jets', 'lead_jet_pt', 'ht', 'delta_phi']
# Exclude bookkeeping columns
excluded_columns = [col for col in df.columns if col not in physics_observables and col not in ['label']]
# Separate signal and background events
signal_events = df[df['label'] == 1]
background_events = df[df['label'] == 0]
# Compute ROC AUC for each observable
auc_results = {}
for feature in physics_observables:
# Extract values for signal and background
signal_values = signal_events[feature].values
background_values = background_events[feature].values
# Compute ROC AUC manually
# AUC is the probability that a randomly chosen signal event has a larger value than a randomly chosen background event
# Ties count 1/2
n_signal = len(signal_values)
n_background = len(background_values)
# Count how many times signal > background, signal < background, and signal == background
greater = np.sum(signal_values > background_values)
less = np.sum(signal_values < background_values)
equal = np.sum(signal_values == background_values)
# Calculate AUC
auc = (greater + 0.5 * equal) / (n_signal * n_background)
auc_results[feature] = auc
# Sort observables by AUC descending
features_ranked = sorted(auc_results.keys(), key=lambda x: -auc_results[x])
# Find the best feature
best_feature = features_ranked[0] if features_ranked else None
# Count number of signal and background events
n_signal = len(signal_events)
n_background = len(background_events)
# Create result dictionary
result = {
'auc': auc_results,
'features_ranked': features_ranked,
'best_feature': best_feature,
'n_signal': n_signal,
'n_background': n_background,
'excluded_columns': excluded_columns
}
# Save result to JSON
with open('result.json', 'w') as f:
json.dump(result, f, indent=4)
# Plot histograms for the best feature
if best_feature:
# Get signal and background values for the best feature
signal_best = signal_events[best_feature].values
background_best = background_events[best_feature].values
# Normalize to unit area
signal_best_normalized = signal_best / np.sum(signal_best)
background_best_normalized = background_best / np.sum(background_best)
# Plot
plt.figure(figsize=(10, 6))
plt.hist(signal_best, bins=50, density=True, alpha=0.5, label='signal')
plt.hist(background_best, bins=50, density=True, alpha=0.5, label='background')
plt.xlabel('Value')
plt.legend()
plt.savefig('figures/best_feature.svg')
plt.close()
# Save solution.py
with open('solution.py', 'w') as f:
f.write('''''')
''')
# Submit the solution
submit("Ranked physics observables by signal/background separation", ["Used the data card to identify physics observables", "Computed ROC AUC for each observable", "Generated figures for the best feature"])
```
wrote 6000 chars to solution.py
STDERR:
Traceback (most recent call last):
File "/Users/gariyuu/Projects/agenthep/runs/20260906T175145-t4-feature-separation-self_debug-gariyuu-qwen3-8b-r0/workdir/.agenthep_guard.py", line 117, in main
runpy.run_path(SCRIPT, run_name="__main__")
File "<frozen runpy>", line 291, in run_path
File "<frozen runpy>", line 98, in _run_module_code
File "<frozen runpy>", line 88, in _run_code
File "/Users/gariyuu/Projects/agenthep/runs/20260906T175145-t4-feature-separation-self_debug-gariyuu-qwen3-8b-r0/workdir/_cell.py", line 83, in <module>
plt.savefig('figures/best_feature.svg')
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/pyplot.py", line 1228, in savefig
res = fig.savefig(*args, **kwargs) # type: ignore[func-returns-value]
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/figure.py", line 3395, in savefig
self.canvas.print_figure(fname, **kwargs)
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/backend_bases.py", line 2204, in print_figure
result = print_method(
^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agent
... [78 chars truncated] ...
eth)(lambda *args, **kwargs: meth(
^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/backends/backend_svg.py", line 1328, in print_svg
with cbook.open_file_cm(filename, "w", encoding="utf-8") as fh:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/cbook.py", line 497, in open_file_cm
fh, opened = to_filehandle(path_or_file, mode, True, encoding)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/cbook.py", line 483, in to_filehandle
fh = open(fname, flag, encoding=encoding)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/runs/20260906T175145-t4-feature-separation-self_debug-gariyuu-qwen3-8b-r0/workdir/.agenthep_guard.py", line 68, in _guarded_open
return _real_open(file, mode, *a, **k)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
FileNotFoundError: [Errno 2] No such file or directory: 'figures/best_feature.svg'
exit code: 1
files created: result.json```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import json
import os
# Read the data
data_path = 'data/synth_sigbkg.csv'
df = pd.read_csv(data_path)
# Extract physics observables from the data card
physics_observables = ['met', 'mt', 'n_jets', 'lead_jet_pt', 'ht', 'delta_phi']
# Exclude bookkeeping columns
excluded_columns = [col for col in df.columns if col not in physics_observables and col not in ['label']]
# Separate signal and background events
signal_events = df[df['label'] == 1]
background_events = df[df['label'] == 0]
# Compute ROC AUC for each observable
auc_results = {}
for feature in physics_observables:
# Extract values for signal and background
signal_values = signal_events[feature].values
background_values = background_events[feature].values
# Compute ROC AUC manually
# AUC is the probability that a randomly chosen signal event has a larger value than a randomly chosen background event
# Ties count 1/2
n_signal = len(signal_values)
n_background = len(background_values)
# Count how many times signal > background, signal < background, and signal == background
greater = np.sum(signal_values > background_values)
less = np.sum(signal_values < background_values)
equal = np.sum(signal_values == background_values)
# Calculate AUC
auc = (greater + 0.5 * equal) / (n_signal * n_background)
auc_results[feature] = auc
# Sort observables by AUC descending
features_ranked = sorted(auc_results.keys(), key=lambda x: -auc_results[x])
# Find the best feature
best_feature = features_ranked[0] if features_ranked else None
# Count number of signal and background events
n_signal = len(signal_events)
n_background = len(background_events)
# Create result dictionary
result = {
'auc': auc_results,
'features_ranked': features_ranked,
'best_feature': best_feature,
'n_signal': n_signal,
'n_background': n_background,
'excluded_columns': excluded_columns
}
# Save result to JSON
with open('result.json', 'w') as f:
json.dump(result, f, indent=4)
# Plot histograms for the best feature
if best_feature:
# Create directory if it doesn't exist
os.makedirs('figures', exist_ok=True)
# Get signal and background values for the best feature
signal_best = signal_events[best_feature].values
background_best = background_events[best_feature].values
# Normalize to unit area
signal_best_normalized = signal_best / np.sum(signal_best)
background_best_normalized = background_best / np.sum(background_best)
# Plot
plt.figure(figsize=(10, 6))
plt.hist(signal_best, bins=50, density=True, alpha=0.5, label='signal')
plt.hist(background_best, bins=50, density=True, alpha=0.5, label='background')
plt.xlabel('Value')
plt.legend()
plt.savefig('figures/best_feature.svg')
plt.close()
# Save solution.py
with open('solution.py', 'w') as f:
f.write('''import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import json
import os
# Read the data
data_path = 'data/synth_sigbkg.csv'
df = pd.read_csv(data_path)
# Extract physics observables from the data card
physics_observables = ['met', 'mt', 'n_jets', 'lead_jet_pt', 'ht', 'delta_phi']
# Exclude bookkeeping columns
excluded_columns = [col for col in df.columns if col not in physics_observables and col not in ['label']]
# Separate signal and background events
signal_events = df[df['label'] == 1]
background_events = df[df['label'] == 0]
# Compute ROC AUC for each observable
auc_results = {}
for feature in physics_observables:
# Extract values for signal and background
signal_values = signal_events[feature].values
background_values = background_events[feature].values
# Compute ROC AUC manually
# AUC is the probability that a randomly chosen signal event has a larger value than a randomly chosen background event
# Ties count 1/2
n_signal = len(signal_values)
n_background = len(background_values)
# Count how many times signal > background, signal < background, and signal == background
greater = np.sum(signal_values > background_values)
less = np.sum(signal_values < background_values)
equal = np.sum(signal_values == background_values)
# Calculate AUC
auc = (greater + 0.5 * equal) / (n_signal * n_background)
auc_results[feature] = auc
# Sort observables by AUC descending
features_ranked = sorted(auc_results.keys(), key=lambda x: -auc_results[x])
# Find the best feature
best_feature = features_ranked[0] if features_ranked else None
# Count number of signal and background events
n_signal = len(signal_events)
n_background = len(background_events)
# Create result dictionary
result = {
'auc': auc_results,
'features_ranked': features_ranked,
'best_feature': best_feature,
'n_signal': n_signal,
'n_background': n_background,
'excluded_columns': excluded_columns
}
# Save result to JSON
with open('result.json', 'w') as f:
json.dump(result, f, indent=4)
# Plot histograms for the best feature
if best_feature:
# Create directory if it doesn't exist
os.makedirs('figures', exist_ok=True)
# Get signal and background values for the best feature
signal_best = signal_events[best_feature].values
background_best = background_events[best_feature].values
# Normalize to unit area
signal_best_normalized = signal_best / np.sum(signal_best)
background_best_normalized = background_best / np.sum(background_best)
# Plot
plt.figure(figsize=(10, 6))
plt.hist(signal_best, bins=50, density=True, alpha=0.5, label='signal')
plt.hist(background_best, bins=50, density=True, alpha=0.5, label='background')
plt.xlabel('Value')
plt.legend()
plt.savefig('figures/best_feature.svg')
plt.close()
# Save solution.py
with open('solution.py', 'w') as f:
f.write('''''')
''')
# Submit the solution
submit("Ranked physics observables by signal/background separation", ["Used the data card to identify physics observables", "Computed ROC AUC for each observable", "Generated figures for the best feature"])
```
wrote 6180 chars to solution.py
STDERR:
Traceback (most recent call last):
File "/Users/gariyuu/Projects/agenthep/runs/20260906T175145-t4-feature-separation-self_debug-gariyuu-qwen3-8b-r0/workdir/.agenthep_guard.py", line 117, in main
runpy.run_path(SCRIPT, run_name="__main__")
File "<frozen runpy>", line 291, in run_path
File "<frozen runpy>", line 98, in _run_module_code
File "<frozen runpy>", line 88, in _run_code
File "/Users/gariyuu/Projects/agenthep/runs/20260906T175145-t4-feature-separation-self_debug-gariyuu-qwen3-8b-r0/workdir/_cell.py", line 185, in <module>
submit("Ranked physics observables by signal/background separation", ["Used the data card to identify physics observables", "Computed ROC AUC for each observable", "Generated figures for the best feature"])
^^^^^^
NameError: name 'submit' is not defined
exit code: 1
files created: figures/best_feature.svg
files modified: result.json, solution.py```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import json
import os
# Read the data
data_path = 'data/synth_sigbkg.csv'
df = pd.read_csv(data_path)
# Extract physics observables from the data card
physics_observables = ['met', 'mt', 'n_jets', 'lead_jet_pt', 'ht', 'delta_phi']
# Exclude bookkeeping columns
excluded_columns = [col for col in df.columns if col not in physics_observables and col not in ['label']]
# Separate signal and background events
signal_events = df[df['label'] == 1]
background_events = df[df['label'] == 0]
# Compute ROC AUC for each observable
auc_results = {}
for feature in physics_observables:
# Extract values for signal and background
signal_values = signal_events[feature].values
background_values = background_events[feature].values
# Compute ROC AUC manually
# AUC is the probability that a randomly chosen signal event has a larger value than a randomly chosen background event
# Ties count 1/2
n_signal = len(signal_values)
n_background = len(background_values)
# Count how many times signal > background, signal < background, and signal == background
greater = np.sum(signal_values > background_values)
less = np.sum(signal_values < background_values)
equal = np.sum(signal_values == background_values)
# Calculate AUC
auc = (greater + 0.5 * equal) / (n_signal * n_background)
auc_results[feature] = auc
# Sort observables by AUC descending
features_ranked = sorted(auc_results.keys(), key=lambda x: -auc_results[x])
# Find the best feature
best_feature = features_ranked[0] if features_ranked else None
# Count number of signal and background events
n_signal = len(signal_events)
n_background = len(background_events)
# Create result dictionary
result = {
'auc': auc_results,
'features_ranked': features_ranked,
'best_feature': best_feature,
'n_signal': n_signal,
'n_background': n_background,
'excluded_columns': excluded_columns
}
# Save result to JSON
with open('result.json', 'w') as f:
json.dump(result, f, indent=4)
# Plot histograms for the best feature
if best_feature:
# Create directory if it doesn't exist
os.makedirs('figures', exist_ok=True)
# Get signal and background values for the best feature
signal_best = signal_events[best_feature].values
background_best = background_events[best_feature].values
# Normalize to unit area
signal_best_normalized = signal_best / np.sum(signal_best)
background_best_normalized = background_best / np.sum(background_best)
# Plot
plt.figure(figsize=(10, 6))
plt.hist(signal_best, bins=50, density=True, alpha=0.5, label='signal')
plt.hist(background_best, bins=50, density=True, alpha=0.5, label='background')
plt.xlabel('Value')
plt.legend()
plt.savefig('figures/best_feature.svg')
plt.close()
# Save solution.py
with open('solution.py', 'w') as f:
f.write('''import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import json
import os
# Read the data
data_path = 'data/synth_sigbkg.csv'
df = pd.read_csv(data_path)
# Extract physics observables from the data card
physics_observables = ['met', 'mt', 'n_jets', 'lead_jet_pt', 'ht', 'delta_phi']
# Exclude bookkeeping columns
excluded_columns = [col for col in df.columns if col not in physics_observables and col not in ['label']]
# Separate signal and background events
signal_events = df[df['label'] == 1]
background_events = df[df['label'] == 0]
# Compute ROC AUC for each observable
auc_results = {}
for feature in physics_observables:
# Extract values for signal and background
signal_values = signal_events[feature].values
background_values = background_events[feature].values
# Compute ROC AUC manually
# AUC is the probability that a randomly chosen signal event has a larger value than a randomly chosen background event
# Ties count 1/2
n_signal = len(signal_values)
n_background = len(background_values)
# Count how many times signal > background, signal < background, and signal == background
greater = np.sum(signal_values > background_values)
less = np.sum(signal_values < background_values)
equal = np.sum(signal_values == background_values)
# Calculate AUC
auc = (greater + 0.5 * equal) / (n_signal * n_background)
auc_results[feature] = auc
# Sort observables by AUC descending
features_ranked = sorted(auc_results.keys(), key=lambda x: -auc_results[x])
# Find the best feature
best_feature = features_ranked[0] if features_ranked else None
# Count number of signal and background events
n_signal = len(signal_events)
n_background = len(background_events)
# Create result dictionary
result = {
'auc': auc_results,
'features_ranked': features_ranked,
'best_feature': best_feature,
'n_signal': n_signal,
'n_background': n_background,
'excluded_columns': excluded_columns
}
# Save result to JSON
with open('result.json', 'w') as f:
json.dump(result, f, indent=4)
# Plot histograms for the best feature
if best_feature:
# Create directory if it doesn't exist
os.makedirs('figures', exist_ok=True)
# Get signal and background values for the best feature
signal_best = signal_events[best_feature].values
background_best = background_events[best_feature].values
# Normalize to unit area
signal_best_normalized = signal_best / np.sum(signal_best)
background_best_normalized = background_best / np.sum(background_best)
# Plot
plt.figure(figsize=(10, 6))
plt.hist(signal_best, bins=50, density=True, alpha=0.5, label='signal')
plt.hist(background_best, bins=50, density=True, alpha=0.5, label='background')
plt.xlabel('Value')
plt.legend()
plt.savefig('figures/best_feature.svg')
plt.close()
''')
# Submit the solution
print("Ranked physics observables by signal/background separation")
print("Assumptions:")
print("- Used the data card to identify physics observables")
print("- Computed ROC AUC for each observable")
print("- Generated figures for the best feature")
```
wrote 6147 chars to solution.py
STDOUT: Ranked physics observables by signal/background separation Assumptions: - Used the data card to identify physics observables - Computed ROC AUC for each observable - Generated figures for the best feature exit code: 0 files modified: figures/best_feature.svg, result.json, solution.py
Final answer
```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import json
import os
# Read the data
data_path = 'data/synth_sigbkg.csv'
df = pd.read_csv(data_path)
# Extract physics observables from the data card
physics_observables = ['met', 'mt', 'n_jets', 'lead_jet_pt', 'ht', 'delta_phi']
# Exclude bookkeeping columns
excluded_columns = [col for col in df.columns if col not in physics_observables and col not in ['label']]
# Separate signal and background events
signal_events = df[df['label'] == 1]
background_events = df[df['label'] == 0]
# Compute ROC AUC for each observable
auc_results = {}
for feature in physics_observables:
# Extract values for signal and background
signal_values = signal_events[feature].values
background_values = background_events[feature].values
# Compute ROC AUC manually
# AUC is the probability that a randomly chosen signal event has a larger value than a randomly chosen background event
# Ties count 1/2
n_signal = len(signal_values)
n_background = len(background_values)
# Count how many times signal > background, signal < background, and signal == background
greater = np.sum(signal_values > background_values)
less = np.sum(signal_values < background_values)
equal = np.sum(signal_values == background_values)
# Calculate AUC
auc = (greater + 0.5 * equal) / (n_signal * n_background)
auc_results[feature] = auc
# Sort observables by AUC descending
features_ranked = sorted(auc_results.keys(), key=lambda x: -auc_results[x])
# Find the best feature
best_feature = features_ranked[0] if features_ranked else None
# Count number of signal and background events
n_signal = len(signal_events)
n_background = len(background_events)
# Create result dictionary
result = {
'auc': auc_results,
'features_ranked': features_ranked,
'best_feature': best_feature,
'n_signal': n_signal,
'n_background': n_background,
'excluded_columns': exclud
Grader verdict
| Check | Result | Category | Weight | Detail | Observed | Expected |
|---|---|---|---|---|---|---|
| result_existscritical | ✓ pass | artifact | 1 | ok | ||
| figure_exists | ✓ pass | artifact | 1 | ok | ||
| solution_exists | ✓ pass | artifact | 1 | ok | ||
| n_sig | ✓ pass | numeric | 1 | match | 20000 | 20000 |
| n_bkg | ✓ pass | numeric | 1 | match | 20000 | 20000 |
| auc_met | ✗ fail | numeric | 1 | observed 4.47025e-05 vs expected 0.89369835125 (atol=0.0001, rtol=0.0) | 0.0000447025 | 0.89369835125 |
| auc_mtcritical | ✗ fail | numeric | 2 | observed 4.78225e-05 vs expected 0.95725302875 (atol=0.0001, rtol=0.0) | 0.0000478225 | 0.95725302875 |
| auc_njets | ✗ fail | numeric | 2 | observed 3.7585e-05 vs expected 0.75281310125 (atol=0.0001, rtol=0.0) | 0.000037585 | 0.75281310125 |
| auc_ljpt | ✗ fail | numeric | 1 | observed 4.10575e-05 vs expected 0.8217912225 (atol=0.0001, rtol=0.0) | 0.0000410575 | 0.8217912225 |
| auc_ht | ✗ fail | numeric | 1 | observed 4.3585e-05 vs expected 0.8700456975 (atol=0.0001, rtol=0.0) | 0.000043585 | 0.8700456975 |
| auc_dphi | ✗ fail | numeric | 1 | observed 3.9885e-05 vs expected 0.79745766 (atol=0.0001, rtol=0.0) | 0.000039885 | 0.79745766 |
| rankingcritical | ✓ pass | numeric | 2 | match | ["mt","met","ht","lead_jet_pt","delta_phi","n_jets"] | ["mt","met","ht","lead_jet_pt","delta_phi","n_jets"] |
| bestcritical | ✓ pass | numeric | 2 | match | "mt" | "mt" |
| no_leak_rankcritical | ✓ pass | compliance | 3 | absent | ["mt","met","ht","lead_jet_pt","delta_phi","n_jets"] | "not 'sample_weight'" |
| no_label_rank | ✓ pass | compliance | 1 | absent | ["mt","met","ht","lead_jet_pt","delta_phi","n_jets"] | "not 'label'" |
| leak_excluded | ✓ pass | compliance | 1 | present | ["event_id","weight","sample_weight"] | "sample_weight" |
| svg_legend | ✓ pass | plot | 1 | labels present | ["Matplotlib v3.9.2, https://matplotlib.org/","0","100","200","300","400","500", | ["signal","background"] |
| svg_drawn | ✓ pass | plot | 1 | drawn | 126 | ">=5" |
| reruns | ✓ pass | reproducibility | 1 | reproduced exactly | {"ok":true,"artifacts_reproduced":true,"output_matches":true,"exit_code":0} | |
| not_hardcoded | ✓ pass | compliance | 1 | no expected values hard-coded | [] |
Reproducibility rerun
✓ pass
✓ pass
✓ exact
✓ pass
no randomness used
reproduced exactly
Artifacts
result.json
{
"auc": {
"met": 4.47025e-05,
"mt": 4.78225e-05,
"n_jets": 3.7585e-05,
"lead_jet_pt": 4.10575e-05,
"ht": 4.3585e-05,
"delta_phi": 3.9885e-05
},
"features_ranked": [
"mt",
"met",
"ht",
"lead_jet_pt",
"delta_phi",
"n_jets"
],
"best_feature": "mt",
"n_signal": 20000,
"n_background": 20000,
"excluded_columns": [
"event_id",
"weight",
"sample_weight"
]
}solution.py
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import json
import os
# Read the data
data_path = 'data/synth_sigbkg.csv'
df = pd.read_csv(data_path)
# Extract physics observables from the data card
physics_observables = ['met', 'mt', 'n_jets', 'lead_jet_pt', 'ht', 'delta_phi']
# Exclude bookkeeping columns
excluded_columns = [col for col in df.columns if col not in physics_observables and col not in ['label']]
# Separate signal and background events
signal_events = df[df['label'] == 1]
background_events = df[df['label'] == 0]
# Compute ROC AUC for each observable
auc_results = {}
for feature in physics_observables:
# Extract values for signal and background
signal_values = signal_events[feature].values
background_values = background_events[feature].values
# Compute ROC AUC manually
# AUC is the probability that a randomly chosen signal event has a larger value than a randomly chosen background event
# Ties count 1/2
n_signal = len(signal_values)
n_background = len(background_values)
# Count how many times signal > background, signal < background, and signal == background
greater = np.sum(signal_values > background_values)
less = np.sum(signal_values < background_values)
equal = np.sum(signal_values == background_values)
# Calculate AUC
auc = (greater + 0.5 * equal) / (n_signal * n_background)
auc_results[feature] = auc
# Sort observables by AUC descending
features_ranked = sorted(auc_results.keys(), key=lambda x: -auc_results[x])
# Find the best feature
best_feature = features_ranked[0] if features_ranked else None
# Count number of signal and background events
n_signal = len(signal_events)
n_background = len(background_events)
# Create result dictionary
result = {
'auc': auc_results,
'features_ranked': features_ranked,
'best_feature': best_feature,
'n_signal': n_signal,
'n_background': n_background,
'excluded_columns': excluded_columns
}
# Save result to JSON
with open('result.json', 'w') as f:
json.dump(result, f, indent=4)
# Plot histograms for the best feature
if best_feature:
# Create directory if it doesn't exist
os.makedirs('figures', exist_ok=True)
# Get signal and background values for the best feature
signal_best = signal_events[best_feature].values
background_best = background_events[best_feature].values
# Normalize to unit area
signal_best_normalized = signal_best / np.sum(signal_best)
background_best_normalized = background_best / np.sum(background_best)
# Plot
plt.figure(figsize=(10, 6))
plt.hist(signal_best, bins=50, density=True, alpha=0.5, label='signal')
plt.hist(background_best, bins=50, density=True, alpha=0.5, label='background')
plt.xlabel('Value')
plt.legend()
plt.savefig('figures/best_feature.svg')
plt.close()
figures/best_feature.svg
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