

In [1]:

    
%pylab inline









    



Populating the interactive namespace from numpy and matplotlib



In [2]:

    
matplotlib.rcParams.update({'font.size': 14})

Read prepared B data for track-based and vertex-based tagging



In [3]:

    
import pandas
Bdata_tracks = pandas.read_csv('models/Bdata_tracks_MC.csv')
Bdata_vertex = pandas.read_csv('models/Bdata_vertex_MC_v.csv')



In [4]:

    
Bdata_tracks.head()









    Out[4]:






  
    
      
      Bsign
      Bweight
      event_id
      track_relation_prob
    
  
  
    
      0
      -1
      1
      2498001_1
      0.652731
    
    
      1
      1
      1
      2498001_10
      1.892640
    
    
      2
      1
      1
      2498001_105
      1.077080
    
    
      3
      1
      1
      2498001_108
      0.985524
    
    
      4
      1
      1
      2498001_11
      1.086548



In [5]:

    
Bdata_vertex.head()









    Out[5]:






  
    
      
      Bsign
      Bweight
      event_id
      vertex_relation_prob
    
  
  
    
      0
      -1
      1
      2498001_160
      1.296642
    
    
      1
      -1
      1
      2498001_173
      1.671069
    
    
      2
      -1
      1
      2498001_39
      0.550335
    
    
      3
      1
      1
      2498001_43
      0.827923
    
    
      4
      1
      1
      2498001_89
      0.540587

Merge two datasets



In [6]:

    
Bdata = Bdata_vertex #pandas.merge(Bdata_tracks, Bdata_vertex, how='outer', on=['event_id', 'Bsign'])



In [7]:

    
Bdata.head()









    Out[7]:






  
    
      
      Bsign
      Bweight
      event_id
      vertex_relation_prob
    
  
  
    
      0
      -1
      1
      2498001_160
      1.296642
    
    
      1
      -1
      1
      2498001_173
      1.671069
    
    
      2
      -1
      1
      2498001_39
      0.550335
    
    
      3
      1
      1
      2498001_43
      0.827923
    
    
      4
      1
      1
      2498001_89
      0.540587

Obtain one weight column



In [8]:

    
# Bdata['Bweight'] = Bdata['Bweight_x'].copy()
# Bdata.ix[numpy.isnan(Bdata['Bweight'].values), 'Bweight'] = Bdata.ix[numpy.isnan(Bdata['Bweight'].values), 'Bweight_y']
# Bdata = Bdata.drop(['Bweight_x', 'Bweight_y'], axis=1)

# for Nan put 1 as non influence factor
# Bdata.ix[numpy.isnan(Bdata.track_relation_prob.values), 'track_relation_prob'] = 1.
Bdata.ix[numpy.isnan(Bdata.vertex_relation_prob.values), 'vertex_relation_prob'] = 1.



In [9]:

    
Bdata.head()









    Out[9]:






  
    
      
      Bsign
      Bweight
      event_id
      vertex_relation_prob
    
  
  
    
      0
      -1
      1
      2498001_160
      1.296642
    
    
      1
      -1
      1
      2498001_173
      1.671069
    
    
      2
      -1
      1
      2498001_39
      0.550335
    
    
      3
      1
      1
      2498001_43
      0.827923
    
    
      4
      1
      1
      2498001_89
      0.540587



In [10]:

    
relation_prob = Bdata['vertex_relation_prob'].values #* Bdata['vertex_relation_prob'].values
Bprob = relation_prob / (1 + relation_prob)
Bweight = Bdata.Bweight.values
Bsign = Bdata.Bsign.values



In [11]:

    
# sum(Bdata['vertex_relation_prob'].values == 0)



In [12]:

    
Bprob[~numpy.isfinite(Bprob)] = 0.5

2-folding calibration by isotonic



In [13]:

    
from utils import calibrate_probs
Bprob_calibrated, (iso_reg1, iso_reg2) = calibrate_probs(Bsign, Bweight, Bprob,
                                                         symmetrize=True, return_calibrator=True)

Add some small noise in prediction for stability



In [14]:

    
Bprob_calibrated = Bprob_calibrated + numpy.random.normal(size=len(Bprob_calibrated)) * 0.001



In [15]:

    
figure(figsize=(20, 7))

subplot(1,2,1)
hist(Bprob[Bsign == 1], weights=Bweight[Bsign == 1], bins=60, alpha=0.2,  label='$B^+$')
hist(Bprob[Bsign == -1], weights=Bweight[Bsign == -1], bins=60, alpha=0.2,  label='$B^-$')
legend(), xlabel('$P(B^+)$'), ylabel('events / 0.017')
xticks(fontsize=18), yticks(fontsize=18)
subplot(1,2,2)
hist(Bprob_calibrated[Bsign == 1], weights=Bweight[Bsign == 1], bins=80, alpha=0.2, 
      range=(0, 1), label='$B^+$')
hist(Bprob_calibrated[Bsign == -1], weights=Bweight[Bsign == -1], bins=80, alpha=0.2,
      range=(0, 1), label='$B^-$')
ylim(0, )
xticks(fontsize=18), yticks(fontsize=18)
# legend(), xlabel('calibrated $P(B^+)$'), ylabel('events / 0.017')
# plt.savefig('img/Bprob_iso_calibrated_PID_less.png' , format='png')
# plt.savefig('img/paper_B_prob.png', dpi=300, format='png', bbox_inches='tight')









    Out[15]:





((array([ 0. ,  0.2,  0.4,  0.6,  0.8,  1. ]),
  <a list of 6 Text xticklabel objects>),
 (array([    0.,  1000.,  2000.,  3000.,  4000.,  5000.,  6000.,  7000.,
          8000.,  9000.]), <a list of 10 Text yticklabel objects>))

AUC score and ROC curve for B+ vs B-



In [52]:

    
from utils import calculate_auc_with_and_without_untag_events, calculate_roc_with_untag_events
from sklearn.metrics import roc_curve

auc, auc_full = calculate_auc_with_and_without_untag_events(Bsign, Bprob_calibrated, Bweight, N_B)
print 'AUC for tagged:', auc, 'AUC with untag:', auc_full

figure(figsize=(12, 10))
fpr, tpr, _ = calculate_roc_with_untag_events(Bsign, Bprob_calibrated, Bweight, N_B)
plot(fpr, tpr, linewidth=2)
plot([0, 1], [0, 1], 'k--')
ylim(0, 1), xlim(0, 1)
xlabel('True positive rate (TPR)', fontsize=16)
ylabel('False positive rate (FPR)', fontsize=16)
grid()
# plt.savefig('img/poster_B_roc.png' , dpi=700, format='png', transparent=True)









    



AUC for tagged: 0.612968658183 AUC with untag: 0.55131762761

Symmetry $B^+$ vs $B^-$ checking

before calibration



In [20]:

    
figsize(12, 8)
for sign in [-1, 1]:
    hist(sign * (Bprob[Bsign == sign] - 0.5), bins=101, normed=True, alpha=0.2, 
         weights=Bweight[Bsign == sign], range=(-0.5, 0.5), label='$B^-$' if sign == -1 else '$B^+$')
legend(), title('Symmetry of $p(B^+)$ for $B^+$ and $B^-$, before calibration')









    Out[20]:





(<matplotlib.legend.Legend at 0x7fc49b48a490>,
 <matplotlib.text.Text at 0x7fc496102050>)

KS distance



In [21]:

    
fpr, tpr, _ = roc_curve(Bsign, (Bprob - 0.5) * Bsign, sample_weight=Bweight)



In [22]:

    
'KS distance', max(abs(fpr - tpr))









    Out[22]:





('KS distance', 0.0076533582573269365)



In [23]:

    
plot(fpr, tpr), grid()
plot([0, 1], [0, 1], 'k--')
xlim(0, 1), ylim(0, 1)









    Out[23]:





((0, 1), (0, 1))



In [24]:

    
from sklearn.metrics import roc_auc_score
roc_auc_score(Bsign, (Bprob - 0.5) * Bsign, sample_weight=Bweight)









    Out[24]:





0.49666032000144283

after calibration



In [25]:

    
figsize(12, 8)
for sign in [-1, 1]:
    hist(sign * (Bprob_calibrated[Bsign == sign] - 0.5) + 0.5, bins=101,  alpha=0.2,
         weights=Bweight[Bsign == sign], range=(0, 1), normed=True, label='$B^-$' if sign == -1 else '$B^+$')
legend(fontsize=32); ylim(0, ), xlim(0, 1)
xticks(fontsize=18), yticks(fontsize=18)
xlabel('$P($correct class$)$', fontsize=26)
# plt.savefig('img/paper_symmetry.png' , dpi=300, format='png',  bbox_inches='tight')









    Out[25]:





<matplotlib.text.Text at 0x7fc495c37f50>

KS distance



In [26]:

    
fpr, tpr, _ = roc_curve(Bsign, (Bprob_calibrated - 0.5) * Bsign, sample_weight=Bweight)



In [27]:

    
'KS distance', max(abs(fpr - tpr))









    Out[27]:





('KS distance', 0.0078280796936212038)



In [28]:

    
plot(fpr, tpr), grid()
plot([0, 1], [0, 1], 'k--')
xlim(0, 1), ylim(0, 1)









    Out[28]:





((0, 1), (0, 1))



In [29]:

    
roc_auc_score(Bsign, (Bprob_calibrated - 0.5) * Bsign, sample_weight=Bweight)









    Out[29]:





0.49666944297893789

D2 estimation with bootstrap calibration



In [30]:

    
from utils import compute_N_B_events_MC



In [31]:

    
from utils import result_table



In [32]:

    
N_B = compute_N_B_events_MC('datasets/MC/csv/Bu_JPsiK/Tracks.root', 'datasets/MC/csv/Bu_JPsiK/Vertices.root')



In [47]:

    
from utils import get_N_B_events, bootstrap_calibrate_prob, result_table

N_B_passed = Bweight.sum()
tagging_efficiency = N_B_passed / N_B
tagging_efficiency_delta = numpy.sqrt(N_B_passed) / N_B

D2, aucs = bootstrap_calibrate_prob(Bsign, Bweight, Bprob, symmetrize=True, n_calibrations=30)
print 'AUC', numpy.mean(aucs), numpy.var(aucs)

result = result_table(tagging_efficiency, tagging_efficiency_delta, D2, auc_full, 'Inclusive tagging, PID less')









    



AUC 0.612957395686 4.5020141528e-07



In [51]:

    
result









    Out[51]:






  
    
      
      name
      $\epsilon_{tag}, \%$
      $\Delta \epsilon_{tag}, \%$
      $D^2$
      $\Delta D^2$
      $\epsilon, \%$
      $\Delta \epsilon, \%$
      AUC, with untag
      $\Delta$ AUC, with untag
    
  
  
    
      0
      Inclusive tagging, PID less
      36.989612
      0.049843
      0.040663
      0.000454
      1.504121
      0.016917
      55.131763
      0



In [3]:

    
result









    Out[3]:






  
    
      
      name
      $\epsilon_{tag}, \%$
      $\Delta \epsilon_{tag}, \%$
      $D^2$
      $\Delta D^2$
      $\epsilon, \%$
      $\Delta \epsilon, \%$
      AUC, with untag
      $\Delta$ AUC, with untag
    
  
  
    
      0
      Inclusive tagging, PID less
      99.999556
      0.074515
      0.08447
      0
      8.446962
      0.006294
      66.368665
      0

Some plots

Isotonic transformation, and its reverse (too check symmetry)



In [33]:

    
x = numpy.linspace(0, 1, 100)
plot(x, -(iso_reg1.transform((1-x)) + iso_reg2.transform((1-x))) / 2 + 1, label='isotonic transformation reverse')
plot(x, (iso_reg1.transform(x) + iso_reg2.transform(x)) / 2, label='isotonic transformation')
legend(loc='best')
plot([0, 1], [0, 1], "k--")
xlabel('B prob'), ylabel('B prob calibrated')
# plt.savefig('img/iso_transformation_PID_less.png' , format='png')









    Out[33]:





(<matplotlib.text.Text at 0x7fc495693b90>,
 <matplotlib.text.Text at 0x7fc49562d050>)

Mistag checking



In [16]:

    
from utils import get_N_B_events, compute_mistag



In [17]:

    
bins = [0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45]
percentile_bins = [10, 20, 30, 40, 50, 60, 70, 80, 90]

before calibration



In [18]:

    
figsize(12, 10)
compute_mistag(Bprob, Bsign, Bweight, Bsign > -100, label="$B$", uniform=False,
               bins=percentile_bins)
compute_mistag(Bprob, Bsign, Bweight, Bsign == 1, label="$B^+$", uniform=False, 
               bins=percentile_bins)
compute_mistag(Bprob, Bsign, Bweight, Bsign == -1, label="$B^-$", uniform=False, 
               bins=percentile_bins)
legend(loc='best'),  xlabel('mistag probability'), ylabel('true mistag probability')
title('B prob, percentile bins')









    Out[18]:





<matplotlib.text.Text at 0x7f0bd738e090>






    



/moosefs/miniconda/envs/ipython_py2/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison
  if self._edgecolors == str('face'):

after calibration



In [19]:

    
figsize(12, 10)
compute_mistag(Bprob_calibrated, Bsign, Bweight, Bsign > -100, label="$B$", uniform=False,
               bins=percentile_bins)
compute_mistag(Bprob_calibrated, Bsign, Bweight, Bsign == 1, label="$B^+$", uniform=False, 
               bins=percentile_bins)
compute_mistag(Bprob_calibrated, Bsign, Bweight, Bsign == -1, label="$B^-$", uniform=False, 
               bins=percentile_bins)
legend(loc='best'),  xlabel('mistag probability'), ylabel('true mistag probability')
title('B prob isotonic calibrated, percentile bins')









    Out[19]:





<matplotlib.text.Text at 0x7f0bcc107fd0>



In [46]:

    
print numpy.average((2*(Bprob - 0.5))**2, weights=Bweight) * tagging_efficiency * 100
print numpy.average((2*(Bprob_calibrated - 0.5))**2, weights=Bweight) * tagging_efficiency * 100









    



6.03235897745
1.50282488033



In [ ]:

	Bsign	Bweight	event_id	track_relation_prob
0	-1	1	2498001_1	0.652731
1	1	1	2498001_10	1.892640
2	1	1	2498001_105	1.077080
3	1	1	2498001_108	0.985524
4	1	1	2498001_11	1.086548

	Bsign	Bweight	event_id	vertex_relation_prob
0	-1	1	2498001_160	1.296642
1	-1	1	2498001_173	1.671069
2	-1	1	2498001_39	0.550335
3	1	1	2498001_43	0.827923
4	1	1	2498001_89	0.540587