머신러닝 프로그래밍 7주차-

import numpy as np

a = np.ones(100)

array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])

b= np.random.normal(1,0.1,100)# 평균이 1이고 표준편차가 0.1인 정규분포로 부터 난수 100개 생성

array([0.97777185, 0.98398675, 0.94203985, 0.96656572, 1.00709019,
       1.0497622 , 0.96236362, 0.94215869, 1.14313934, 1.06626483,
       1.07222044, 0.96907718, 1.09328525, 1.01428879, 0.99743022,
       1.05123665, 0.97750048, 1.19943427, 1.04019463, 0.93845923,
       1.10171774, 0.87025746, 0.96583052, 1.12502477, 0.91861731,
       1.03612639, 0.95089956, 1.1687044 , 1.0131394 , 1.0454912 ,
       1.0853099 , 0.83046361, 1.1266614 , 0.87358764, 1.06788066,
       0.8998934 , 1.12559594, 1.04656097, 0.8632176 , 0.70048947,
       0.81431239, 1.05997469, 0.9706232 , 0.98432544, 1.11460571,
       0.91796196, 1.13906552, 0.96105183, 1.09157658, 0.89177187,
       1.1446978 , 0.77456377, 0.92751414, 1.1670938 , 1.10685298,
       0.98986861, 1.00165298, 0.98290513, 0.92796829, 0.95037699,
       1.13012849, 0.96037249, 1.01713011, 0.80452703, 0.97696354,
       0.88146593, 1.1782316 , 0.9284739 , 1.04709084, 1.11922683,
       1.09832903, 0.98434657, 0.99634479, 0.85623119, 1.00355355,
       0.9961457 , 0.87942069, 1.00271762, 1.06216093, 1.10690729,
       0.97759756, 1.02155774, 0.98558842, 1.05658287, 1.06089831,
       1.02774696, 0.94782946, 0.97020057, 0.89131065, 0.75332352,
       1.02233651, 1.03393441, 1.05898539, 0.91805673, 1.1004976 ,
       1.08372229, 0.94313999, 0.95202034, 1.05565755, 0.98232214])

b>1

array([False, False, False, False,  True,  True, False, False,  True,
        True,  True, False,  True,  True, False,  True, False,  True,
        True, False,  True, False, False,  True, False,  True, False,
        True,  True,  True,  True, False,  True, False,  True, False,
        True,  True, False, False, False,  True, False, False,  True,
       False,  True, False,  True, False,  True, False, False,  True,
        True, False,  True, False, False, False,  True, False,  True,
       False, False, False,  True, False,  True,  True,  True, False,
       False, False,  True, False, False,  True,  True,  True, False,
        True, False,  True,  True,  True, False, False, False, False,
        True,  True,  True, False,  True,  True, False, False,  True,
       False])

(b>1).shape

(100,)

b[b>1].shape

(49,)

import matplotlib.pyplot as plt

x1 = np.random.normal(0.5,0.05,10000)
x2 = np.random.normal(0.7,0.05,10000)
y1 = np.zeros(x1.shape)
y2 = np.ones(x2.shape)

plt.hist(x1,bins=100,range=(0,1))

(array([  0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,
          0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,
          0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   1.,   1.,   0.,
          6.,   4.,   9.,  17.,  41.,  56.,  81., 132., 176., 277., 335.,
        419., 519., 701., 702., 757., 799., 800., 738., 667., 659., 495.,
        454., 328., 269., 199., 138.,  81.,  55.,  38.,  22.,   9.,   6.,
          7.,   0.,   1.,   1.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,
          0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,
          0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,
          0.]),
 array([0.  , 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 ,
        0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21,
        0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32,
        0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43,
        0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54,
        0.55, 0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64, 0.65,
        0.66, 0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75, 0.76,
        0.77, 0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87,
        0.88, 0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98,
        0.99, 1.  ]),
 <BarContainer object of 100 artists>)

output_10_1

plt.hist(x2,bins=100,range=(0,1))

(array([  0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,
          0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,
          0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,
          0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,
          0.,   0.,   0.,   0.,   0.,   1.,   0.,   2.,   3.,   7.,   8.,
         13.,  20.,  41.,  68.,  97., 144., 188., 266., 361., 436., 552.,
        587., 688., 756., 795., 748., 782., 686., 639., 515., 397., 363.,
        268., 203., 140.,  80.,  72.,  32.,  17.,  10.,  10.,   3.,   0.,
          0.,   1.,   0.,   1.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,
          0.]),
 array([0.  , 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 ,
        0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21,
        0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32,
        0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43,
        0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54,
        0.55, 0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64, 0.65,
        0.66, 0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75, 0.76,
        0.77, 0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87,
        0.88, 0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98,
        0.99, 1.  ]),
 <BarContainer object of 100 artists>)

output_11_1

plt.hist(x1,bins=100,range=(0,1), histtype='step');
plt.hist(x2,bins=100,range=(0,1), histtype='step');

output_12_0

x = np.concatenate([x1,x2])
y = np.concatenate([y1,y2])
data = np.stack([x,y], axis=1)

data

array([[0.4183939 , 0.        ],
       [0.4895116 , 0.        ],
       [0.51567366, 0.        ],
       ...,
       [0.70447126, 1.        ],
       [0.68865738, 1.        ],
       [0.69542455, 1.        ]])

np.random.shuffle(data)

data

array([[0.57605798, 1.        ],
       [0.77539521, 1.        ],
       [0.54907111, 0.        ],
       ...,
       [0.49509234, 0.        ],
       [0.7628574 , 1.        ],
       [0.68707178, 1.        ]])

plt.hist(data[:,0],bins=100,range=(0,1));

output_17_0

sel_data = data[data[:,0]>0.8]

sel_data

array([[0.81165318, 1.        ],
       [0.80263781, 1.        ],
       [0.82385545, 1.        ],
       [0.8214418 , 1.        ],
       [0.80033043, 1.        ],
       [0.81568348, 1.        ],
       [0.80432364, 1.        ],
       [0.8083785 , 1.        ],
       [0.84060815, 1.        ],
       [0.85065641, 1.        ],
       [0.81233148, 1.        ],
       [0.8263521 , 1.        ],
       [0.8133503 , 1.        ],
       [0.86349671, 1.        ],
       [0.81340036, 1.        ],
       [0.80735976, 1.        ],
       [0.86959636, 1.        ],
       [0.81226178, 1.        ],
       [0.84693677, 1.        ],
       [0.80850068, 1.        ],
       [0.81627508, 1.        ],
       [0.81482788, 1.        ],
       [0.81695395, 1.        ],
       [0.80526562, 1.        ],
       [0.83575697, 1.        ],
       [0.85176691, 1.        ],
       [0.80455917, 1.        ],
       [0.81335375, 1.        ],
       [0.81428494, 1.        ],
       [0.83362813, 1.        ],
       [0.83734837, 1.        ],
       [0.80415421, 1.        ],
       [0.82875158, 1.        ],
       [0.8062281 , 1.        ],
       [0.80382984, 1.        ],
       [0.81836662, 1.        ],
       [0.81072679, 1.        ],
       [0.83973388, 1.        ],
       [0.81549191, 1.        ],
       [0.82326061, 1.        ],
       [0.80066759, 1.        ],
       [0.81373003, 1.        ],
       [0.82508685, 1.        ],
       [0.81494587, 1.        ],
       [0.81078856, 1.        ],
       [0.80504681, 1.        ],
       [0.82098318, 1.        ],
       [0.83820205, 1.        ],
       [0.82425738, 1.        ],
       [0.80487546, 1.        ],
       [0.80701297, 1.        ],
       [0.89453327, 1.        ],
       [0.81991323, 1.        ],
       [0.8098942 , 1.        ],
       [0.80413292, 1.        ],
       [0.85100033, 1.        ],
       [0.81421128, 1.        ],
       [0.80676607, 1.        ],
       [0.80141653, 1.        ],
       [0.80139114, 1.        ],
       [0.81511669, 1.        ],
       [0.83885153, 1.        ],
       [0.81307102, 1.        ],
       [0.82241146, 1.        ],
       [0.83373345, 1.        ],
       [0.91246089, 1.        ],
       [0.84664972, 1.        ],
       [0.80937481, 1.        ],
       [0.81696979, 1.        ],
       [0.82983364, 1.        ],
       [0.82889887, 1.        ],
       [0.8152268 , 1.        ],
       [0.80291748, 1.        ],
       [0.80291059, 1.        ],
       [0.80115424, 1.        ],
       [0.80216712, 1.        ],
       [0.81044013, 1.        ],
       [0.84058709, 1.        ],
       [0.82236298, 1.        ],
       [0.85458728, 1.        ],
       [0.85618517, 1.        ],
       [0.80035678, 1.        ],
       [0.81574262, 1.        ],
       [0.8449593 , 1.        ],
       [0.8245717 , 1.        ],
       [0.83242091, 1.        ],
       [0.81127278, 1.        ],
       [0.82155598, 1.        ],
       [0.81337871, 1.        ],
       [0.80764822, 1.        ],
       [0.81464373, 1.        ],
       [0.8361569 , 1.        ],
       [0.80607568, 1.        ],
       [0.80057084, 1.        ],
       [0.80911594, 1.        ],
       [0.82344224, 1.        ],
       [0.82856835, 1.        ],
       [0.85742125, 1.        ],
       [0.8196721 , 1.        ],
       [0.82290079, 1.        ],
       [0.81969492, 1.        ],
       [0.81345997, 1.        ],
       [0.81305835, 1.        ],
       [0.80737807, 1.        ],
       [0.8005669 , 1.        ],
       [0.80315232, 1.        ],
       [0.80179872, 1.        ],
       [0.80169282, 1.        ],
       [0.80001723, 1.        ],
       [0.80097394, 1.        ],
       [0.8136235 , 1.        ],
       [0.80085574, 1.        ],
       [0.81349148, 1.        ],
       [0.8065315 , 1.        ],
       [0.82627532, 1.        ],
       [0.8140628 , 1.        ],
       [0.80142591, 1.        ],
       [0.82758688, 1.        ],
       [0.84777368, 1.        ],
       [0.82055656, 1.        ],
       [0.81928733, 1.        ],
       [0.81904779, 1.        ],
       [0.82210618, 1.        ],
       [0.84364951, 1.        ],
       [0.80133502, 1.        ],
       [0.824142  , 1.        ],
       [0.81116521, 1.        ],
       [0.81199943, 1.        ],
       [0.80357964, 1.        ],
       [0.82875595, 1.        ],
       [0.8328148 , 1.        ],
       [0.80145292, 1.        ],
       [0.81689152, 1.        ],
       [0.81070281, 1.        ],
       [0.80339362, 1.        ],
       [0.8508766 , 1.        ],
       [0.80369647, 1.        ],
       [0.8141915 , 1.        ],
       [0.8055556 , 1.        ],
       [0.80905277, 1.        ],
       [0.80396785, 1.        ],
       [0.80506775, 1.        ],
       [0.80956595, 1.        ],
       [0.82891594, 1.        ],
       [0.81214957, 1.        ],
       [0.80258541, 1.        ],
       [0.81400993, 1.        ],
       [0.81372049, 1.        ],
       [0.80084081, 1.        ],
       [0.80859481, 1.        ],
       [0.81039975, 1.        ],
       [0.80941424, 1.        ],
       [0.80834086, 1.        ],
       [0.82339794, 1.        ],
       [0.82765484, 1.        ],
       [0.81115585, 1.        ],
       [0.8171495 , 1.        ],
       [0.8198595 , 1.        ],
       [0.81736972, 1.        ],
       [0.81664392, 1.        ],
       [0.80764148, 1.        ],
       [0.84318007, 1.        ],
       [0.85302204, 1.        ],
       [0.81287536, 1.        ],
       [0.8241014 , 1.        ],
       [0.80196997, 1.        ],
       [0.81143291, 1.        ],
       [0.86045636, 1.        ],
       [0.80398193, 1.        ],
       [0.80151311, 1.        ],
       [0.81838909, 1.        ],
       [0.80255265, 1.        ],
       [0.80955001, 1.        ],
       [0.80454231, 1.        ],
       [0.85773189, 1.        ],
       [0.8384785 , 1.        ],
       [0.81902944, 1.        ],
       [0.81348711, 1.        ],
       [0.84635442, 1.        ],
       [0.81760282, 1.        ],
       [0.82596631, 1.        ],
       [0.82995913, 1.        ],
       [0.83682619, 1.        ],
       [0.83409501, 1.        ],
       [0.80047697, 1.        ],
       [0.80734296, 1.        ],
       [0.8059881 , 1.        ],
       [0.82476778, 1.        ],
       [0.81327218, 1.        ],
       [0.80860131, 1.        ],
       [0.81310922, 1.        ],
       [0.80131171, 1.        ],
       [0.81567426, 1.        ],
       [0.80905161, 1.        ],
       [0.80144976, 1.        ],
       [0.83103294, 1.        ],
       [0.81802314, 1.        ],
       [0.83410648, 1.        ],
       [0.85541751, 1.        ],
       [0.81448533, 1.        ],
       [0.81698358, 1.        ],
       [0.80039402, 1.        ],
       [0.81655001, 1.        ],
       [0.80556376, 1.        ],
       [0.81141204, 1.        ],
       [0.82692522, 1.        ],
       [0.81300262, 1.        ],
       [0.8256454 , 1.        ],
       [0.81946536, 1.        ],
       [0.80059009, 1.        ],
       [0.83324685, 1.        ],
       [0.81018158, 1.        ],
       [0.84461793, 1.        ],
       [0.81513809, 1.        ],
       [0.80160006, 1.        ],
       [0.80589886, 1.        ],
       [0.80905643, 1.        ],
       [0.81051081, 1.        ],
       [0.80133695, 1.        ],
       [0.83223093, 1.        ],
       [0.80975691, 1.        ],
       [0.80923785, 1.        ],
       [0.81708379, 1.        ],
       [0.81252704, 1.        ],
       [0.80881386, 1.        ],
       [0.80165153, 1.        ]])

sel_data.shape

(226, 2)

plt.hist(sel_data[:,0],bins=100,range=(0,1));

output_21_0

plt.hist(sel_data[:,1],bins=100,range=(0,1));

output_22_0

data[data[:,1]==1].shape

(10000, 2)

nSigTotal= data[data[:,1]==1].shape

nSigTotal= len(data[data[:,1]==1])

nSigSelected = len(sel_data[sel_data[:,1]==1])
print("True Positive Rate(TPR) =", nSigSelected/nSigTotal*100,"%")

True Positive Rate(TPR) = 2.26 %

nNoiseTotal = len(data[data[:,1]==0])
#nNegSelected = len(data[(~(data[:,0]>0.6))& (data[:,1]==0)])
nNoiseSelected = nNoiseTotal - len(sel_data[sel_data[:,1]==0])
print("False Negative Rate(FNR) = ", nNoiseSelected/nNoiseTotal*100,"%")

False Negative Rate(FNR) =  100.0 %

# nSigTotal = len(data[data[:,1]==1])
# nNoiseTotal = len(data[data[:,1]==0])

# for i in range(100):
#     t = i/100
#     nSigSelected = len(data[(data[:,1]==1) & (data[:,0]>t)])
#     nNoiseNegSelected = len(data[(data[:,1]==0) & (data[:,0]<=t)])
    
#     tpr = nSigSelected/nSigTotal
#     fnr = nNoiseNegSelected/nNoiseTotal
    
#     print(t,tpr,fnr)
    

# #2번째 방법
# nSigTotal = len(data[data[:,1]==1])
# nNoiseTotal = len(data[data[:,1]==0])

# for t in np.linspace(0,1,101):
    
#     nSigSelected = len(data[(data[:,1]==1) & (data[:,0]>t)])
#     nNoiseNegSelected = len(data[(data[:,1]==0) & (data[:,0]<=t)])
    
#     tpr = nSigSelected/nSigTotal
#     fnr = nNoiseNegSelected/nNoiseTotal
    
#     print(t,tpr,fnr)
    

#3번째 방법
nSigTotal = len(data[data[:,1]==1])
nNoiseTotal = len(data[data[:,1]==0])
ts = []
tprs, fnrs = [], []
accs = []
for t in np.linspace(0,1,101):
    
    nSigSelected = len(data[(data[:,1]==1) & (data[:,0]>t)])
    nNoiseNegSelected = len(data[(data[:,1]==0) & (data[:,0]<=t)])
    
    tpr = nSigSelected/nSigTotal
    fnr = nNoiseNegSelected/nNoiseTotal
    acc = (nSigSelected+nNoiseNegSelected)/(nSigTotal+nNoiseTotal)
    
#     print(t,tpr,fnr)
    ts.append(t)
    tprs.append(tpr)
    fnrs.append(fnr)
    accs.append(acc)
    
plt.plot(ts, tprs)
plt.plot(ts, fnrs)
plt.plot(ts, accs)

[<matplotlib.lines.Line2D at 0x18687564a90>]

output_30_1

#3번째 방법
nSigTotal = len(data[data[:,1]==1])
nNoiseTotal = len(data[data[:,1]==0])
ts = []
tprs, fprs = [], []
accs = []
for t in np.linspace(0,1,101):
    
    nSigSelected = len(data[(data[:,1]==1) & (data[:,0]>t)])
    nNoiseSelected = len(data[(data[:,1]==0) & (data[:,0]>t)])
    
    tpr = nSigSelected/nSigTotal
    fpr = nNoiseSelected/nNoiseTotal
    acc = (nSigSelected+nNoiseTotal-nNoiseSelected)/(nSigTotal+nNoiseTotal)
    
#     print(t,tpr,fnr)
    ts.append(t)
    tprs.append(tpr)
    fprs.append(fpr)
    accs.append(acc)
    
plt.plot(ts, tprs, label="TPR")
plt.plot(ts, fprs, label="FPR")
plt.plot(ts, accs, label="Accuracy")
plt.legend()

<matplotlib.legend.Legend at 0x186872a0278>

output_31_1

plt.plot(fprs, tprs, '.-') #ROC CURVE

[<matplotlib.lines.Line2D at 0x18688709470>]

output_32_1

from sklearn.metrics import roc_curve, auc 

help(roc_curve)

Help on function roc_curve in module sklearn.metrics._ranking:

roc_curve(y_true, y_score, *, pos_label=None, sample_weight=None, drop_intermediate=True)
    Compute Receiver operating characteristic (ROC).
    
    Note: this implementation is restricted to the binary classification task.
    
    Read more in the :ref:`User Guide <roc_metrics>`.
    
    Parameters
    ----------
    y_true : ndarray of shape (n_samples,)
        True binary labels. If labels are not either {-1, 1} or {0, 1}, then
        pos_label should be explicitly given.
    
    y_score : ndarray of shape (n_samples,)
        Target scores, can either be probability estimates of the positive
        class, confidence values, or non-thresholded measure of decisions
        (as returned by "decision_function" on some classifiers).
    
    pos_label : int or str, default=None
        The label of the positive class.
        When ``pos_label=None``, if `y_true` is in {-1, 1} or {0, 1},
        ``pos_label`` is set to 1, otherwise an error will be raised.
    
    sample_weight : array-like of shape (n_samples,), default=None
        Sample weights.
    
    drop_intermediate : bool, default=True
        Whether to drop some suboptimal thresholds which would not appear
        on a plotted ROC curve. This is useful in order to create lighter
        ROC curves.
    
        .. versionadded:: 0.17
           parameter *drop_intermediate*.
    
    Returns
    -------
    fpr : ndarray of shape (>2,)
        Increasing false positive rates such that element i is the false
        positive rate of predictions with score >= `thresholds[i]`.
    
    tpr : ndarray of shape (>2,)
        Increasing true positive rates such that element `i` is the true
        positive rate of predictions with score >= `thresholds[i]`.
    
    thresholds : ndarray of shape = (n_thresholds,)
        Decreasing thresholds on the decision function used to compute
        fpr and tpr. `thresholds[0]` represents no instances being predicted
        and is arbitrarily set to `max(y_score) + 1`.
    
    See Also
    --------
    plot_roc_curve : Plot Receiver operating characteristic (ROC) curve.
    RocCurveDisplay : ROC Curve visualization.
    det_curve: Compute error rates for different probability thresholds.
    roc_auc_score : Compute the area under the ROC curve.
    
    Notes
    -----
    Since the thresholds are sorted from low to high values, they
    are reversed upon returning them to ensure they correspond to both ``fpr``
    and ``tpr``, which are sorted in reversed order during their calculation.
    
    References
    ----------
    .. [1] `Wikipedia entry for the Receiver operating characteristic
            <https://en.wikipedia.org/wiki/Receiver_operating_characteristic>`_
    
    .. [2] Fawcett T. An introduction to ROC analysis[J]. Pattern Recognition
           Letters, 2006, 27(8):861-874.
    
    Examples
    --------
    >>> import numpy as np
    >>> from sklearn import metrics
    >>> y = np.array([1, 1, 2, 2])
    >>> scores = np.array([0.1, 0.4, 0.35, 0.8])
    >>> fpr, tpr, thresholds = metrics.roc_curve(y, scores, pos_label=2)
    >>> fpr
    array([0. , 0. , 0.5, 0.5, 1. ])
    >>> tpr
    array([0. , 0.5, 0.5, 1. , 1. ])
    >>> thresholds
    array([1.8 , 0.8 , 0.4 , 0.35, 0.1 ])

roc_curve(data[:,1],data[:,0])

(array([0.000e+00, 0.000e+00, 0.000e+00, 1.000e-04, 1.000e-04, 2.000e-04,
        2.000e-04, 3.000e-04, 3.000e-04, 4.000e-04, 4.000e-04, 5.000e-04,
        5.000e-04, 6.000e-04, 6.000e-04, 7.000e-04, 7.000e-04, 8.000e-04,
        8.000e-04, 9.000e-04, 9.000e-04, 1.000e-03, 1.000e-03, 1.100e-03,
        1.100e-03, 1.200e-03, 1.200e-03, 1.300e-03, 1.300e-03, 1.400e-03,
        1.400e-03, 1.500e-03, 1.500e-03, 1.600e-03, 1.600e-03, 1.700e-03,
        1.700e-03, 1.800e-03, 1.800e-03, 1.900e-03, 1.900e-03, 2.000e-03,
        2.000e-03, 2.100e-03, 2.100e-03, 2.200e-03, 2.200e-03, 2.300e-03,
        2.300e-03, 2.400e-03, 2.400e-03, 2.500e-03, 2.500e-03, 2.600e-03,
        2.600e-03, 2.700e-03, 2.700e-03, 2.800e-03, 2.800e-03, 2.900e-03,
        2.900e-03, 3.000e-03, 3.000e-03, 3.100e-03, 3.100e-03, 3.200e-03,
        3.200e-03, 3.300e-03, 3.300e-03, 3.400e-03, 3.400e-03, 3.600e-03,
        3.600e-03, 3.700e-03, 3.700e-03, 3.800e-03, 3.800e-03, 3.900e-03,
        3.900e-03, 4.000e-03, 4.000e-03, 4.100e-03, 4.100e-03, 4.200e-03,
        4.200e-03, 4.300e-03, 4.300e-03, 4.400e-03, 4.400e-03, 4.500e-03,
        4.500e-03, 4.600e-03, 4.600e-03, 4.700e-03, 4.700e-03, 4.900e-03,
        4.900e-03, 5.000e-03, 5.000e-03, 5.100e-03, 5.100e-03, 5.200e-03,
        5.200e-03, 5.300e-03, 5.300e-03, 5.400e-03, 5.400e-03, 5.500e-03,
        5.500e-03, 5.700e-03, 5.700e-03, 5.800e-03, 5.800e-03, 6.000e-03,
        6.000e-03, 6.100e-03, 6.100e-03, 6.200e-03, 6.200e-03, 6.300e-03,
        6.300e-03, 6.400e-03, 6.400e-03, 6.600e-03, 6.600e-03, 6.700e-03,
        6.700e-03, 6.800e-03, 6.800e-03, 7.000e-03, 7.000e-03, 7.100e-03,
        7.100e-03, 7.300e-03, 7.300e-03, 7.400e-03, 7.400e-03, 7.500e-03,
        7.500e-03, 7.600e-03, 7.600e-03, 7.700e-03, 7.700e-03, 7.800e-03,
        7.800e-03, 7.900e-03, 7.900e-03, 8.100e-03, 8.100e-03, 8.200e-03,
        8.200e-03, 8.300e-03, 8.300e-03, 8.400e-03, 8.400e-03, 8.500e-03,
        8.500e-03, 8.600e-03, 8.600e-03, 8.700e-03, 8.700e-03, 8.800e-03,
        8.800e-03, 8.900e-03, 8.900e-03, 9.000e-03, 9.000e-03, 9.100e-03,
        9.100e-03, 9.200e-03, 9.200e-03, 9.300e-03, 9.300e-03, 9.400e-03,
        9.400e-03, 9.500e-03, 9.500e-03, 9.600e-03, 9.600e-03, 9.700e-03,
        9.700e-03, 9.800e-03, 9.800e-03, 9.900e-03, 9.900e-03, 1.000e-02,
        1.000e-02, 1.040e-02, 1.040e-02, 1.050e-02, 1.050e-02, 1.060e-02,
        1.060e-02, 1.070e-02, 1.070e-02, 1.080e-02, 1.080e-02, 1.090e-02,
        1.090e-02, 1.100e-02, 1.100e-02, 1.110e-02, 1.110e-02, 1.120e-02,
        1.120e-02, 1.130e-02, 1.130e-02, 1.140e-02, 1.140e-02, 1.200e-02,
        1.200e-02, 1.220e-02, 1.220e-02, 1.240e-02, 1.240e-02, 1.250e-02,
        1.250e-02, 1.260e-02, 1.260e-02, 1.270e-02, 1.270e-02, 1.280e-02,
        1.280e-02, 1.290e-02, 1.290e-02, 1.300e-02, 1.300e-02, 1.310e-02,
        1.310e-02, 1.320e-02, 1.320e-02, 1.340e-02, 1.340e-02, 1.360e-02,
        1.360e-02, 1.370e-02, 1.370e-02, 1.380e-02, 1.380e-02, 1.390e-02,
        1.390e-02, 1.400e-02, 1.400e-02, 1.410e-02, 1.410e-02, 1.420e-02,
        1.420e-02, 1.430e-02, 1.430e-02, 1.450e-02, 1.450e-02, 1.460e-02,
        1.460e-02, 1.470e-02, 1.470e-02, 1.480e-02, 1.480e-02, 1.490e-02,
        1.490e-02, 1.500e-02, 1.500e-02, 1.510e-02, 1.510e-02, 1.520e-02,
        1.520e-02, 1.530e-02, 1.530e-02, 1.550e-02, 1.550e-02, 1.560e-02,
        1.560e-02, 1.570e-02, 1.570e-02, 1.590e-02, 1.590e-02, 1.600e-02,
        1.600e-02, 1.640e-02, 1.640e-02, 1.650e-02, 1.650e-02, 1.660e-02,
        1.660e-02, 1.680e-02, 1.680e-02, 1.700e-02, 1.700e-02, 1.710e-02,
        1.710e-02, 1.750e-02, 1.750e-02, 1.760e-02, 1.760e-02, 1.800e-02,
        1.800e-02, 1.810e-02, 1.810e-02, 1.820e-02, 1.820e-02, 1.840e-02,
        1.840e-02, 1.850e-02, 1.850e-02, 1.860e-02, 1.860e-02, 1.870e-02,
        1.870e-02, 1.880e-02, 1.880e-02, 1.890e-02, 1.890e-02, 1.910e-02,
        1.910e-02, 1.920e-02, 1.920e-02, 1.960e-02, 1.960e-02, 1.970e-02,
        1.970e-02, 1.980e-02, 1.980e-02, 1.990e-02, 1.990e-02, 2.000e-02,
        2.000e-02, 2.020e-02, 2.020e-02, 2.030e-02, 2.030e-02, 2.040e-02,
        2.040e-02, 2.060e-02, 2.060e-02, 2.070e-02, 2.070e-02, 2.080e-02,
        2.080e-02, 2.090e-02, 2.090e-02, 2.100e-02, 2.100e-02, 2.140e-02,
        2.140e-02, 2.150e-02, 2.150e-02, 2.170e-02, 2.170e-02, 2.190e-02,
        2.190e-02, 2.200e-02, 2.200e-02, 2.230e-02, 2.230e-02, 2.240e-02,
        2.240e-02, 2.250e-02, 2.250e-02, 2.280e-02, 2.280e-02, 2.330e-02,
        2.330e-02, 2.340e-02, 2.340e-02, 2.350e-02, 2.350e-02, 2.360e-02,
        2.360e-02, 2.370e-02, 2.370e-02, 2.380e-02, 2.380e-02, 2.410e-02,
        2.410e-02, 2.440e-02, 2.440e-02, 2.460e-02, 2.460e-02, 2.480e-02,
        2.480e-02, 2.490e-02, 2.490e-02, 2.500e-02, 2.500e-02, 2.540e-02,
        2.540e-02, 2.570e-02, 2.570e-02, 2.590e-02, 2.590e-02, 2.610e-02,
        2.610e-02, 2.630e-02, 2.630e-02, 2.640e-02, 2.640e-02, 2.660e-02,
        2.660e-02, 2.670e-02, 2.670e-02, 2.710e-02, 2.710e-02, 2.730e-02,
        2.730e-02, 2.760e-02, 2.760e-02, 2.820e-02, 2.820e-02, 2.860e-02,
        2.860e-02, 2.890e-02, 2.890e-02, 2.930e-02, 2.930e-02, 2.940e-02,
        2.940e-02, 2.950e-02, 2.950e-02, 2.990e-02, 2.990e-02, 3.010e-02,
        3.010e-02, 3.030e-02, 3.030e-02, 3.050e-02, 3.050e-02, 3.070e-02,
        3.070e-02, 3.090e-02, 3.090e-02, 3.110e-02, 3.110e-02, 3.130e-02,
        3.130e-02, 3.250e-02, 3.250e-02, 3.270e-02, 3.270e-02, 3.290e-02,
        3.290e-02, 3.300e-02, 3.300e-02, 3.330e-02, 3.330e-02, 3.360e-02,
        3.360e-02, 3.440e-02, 3.440e-02, 3.450e-02, 3.450e-02, 3.470e-02,
        3.470e-02, 3.480e-02, 3.480e-02, 3.500e-02, 3.500e-02, 3.520e-02,
        3.520e-02, 3.580e-02, 3.580e-02, 3.610e-02, 3.610e-02, 3.640e-02,
        3.640e-02, 3.650e-02, 3.650e-02, 3.660e-02, 3.660e-02, 3.680e-02,
        3.680e-02, 3.690e-02, 3.690e-02, 3.700e-02, 3.700e-02, 3.750e-02,
        3.750e-02, 3.760e-02, 3.760e-02, 3.790e-02, 3.790e-02, 3.800e-02,
        3.800e-02, 3.810e-02, 3.810e-02, 3.870e-02, 3.870e-02, 3.880e-02,
        3.880e-02, 3.900e-02, 3.900e-02, 3.950e-02, 3.950e-02, 4.080e-02,
        4.080e-02, 4.110e-02, 4.110e-02, 4.130e-02, 4.130e-02, 4.140e-02,
        4.140e-02, 4.160e-02, 4.160e-02, 4.210e-02, 4.210e-02, 4.260e-02,
        4.260e-02, 4.270e-02, 4.270e-02, 4.280e-02, 4.280e-02, 4.330e-02,
        4.330e-02, 4.370e-02, 4.370e-02, 4.410e-02, 4.410e-02, 4.570e-02,
        4.570e-02, 4.580e-02, 4.580e-02, 4.700e-02, 4.700e-02, 4.730e-02,
        4.730e-02, 4.750e-02, 4.750e-02, 4.820e-02, 4.820e-02, 4.860e-02,
        4.860e-02, 4.890e-02, 4.890e-02, 4.960e-02, 4.960e-02, 4.970e-02,
        4.970e-02, 4.990e-02, 4.990e-02, 5.010e-02, 5.010e-02, 5.060e-02,
        5.060e-02, 5.140e-02, 5.140e-02, 5.170e-02, 5.170e-02, 5.210e-02,
        5.210e-02, 5.260e-02, 5.260e-02, 5.270e-02, 5.270e-02, 5.290e-02,
        5.290e-02, 5.310e-02, 5.310e-02, 5.420e-02, 5.420e-02, 5.430e-02,
        5.430e-02, 5.440e-02, 5.440e-02, 5.460e-02, 5.460e-02, 5.470e-02,
        5.470e-02, 5.570e-02, 5.570e-02, 5.600e-02, 5.600e-02, 5.610e-02,
        5.610e-02, 5.630e-02, 5.630e-02, 5.670e-02, 5.670e-02, 5.700e-02,
        5.700e-02, 5.720e-02, 5.720e-02, 5.740e-02, 5.740e-02, 5.810e-02,
        5.810e-02, 5.950e-02, 5.950e-02, 5.960e-02, 5.960e-02, 6.010e-02,
        6.010e-02, 6.140e-02, 6.140e-02, 6.230e-02, 6.230e-02, 6.290e-02,
        6.290e-02, 6.310e-02, 6.310e-02, 6.500e-02, 6.500e-02, 6.570e-02,
        6.570e-02, 6.590e-02, 6.590e-02, 6.600e-02, 6.600e-02, 6.670e-02,
        6.670e-02, 6.680e-02, 6.680e-02, 6.720e-02, 6.720e-02, 6.800e-02,
        6.800e-02, 6.980e-02, 6.980e-02, 7.100e-02, 7.100e-02, 7.200e-02,
        7.200e-02, 7.290e-02, 7.290e-02, 7.350e-02, 7.350e-02, 7.390e-02,
        7.390e-02, 7.440e-02, 7.440e-02, 7.490e-02, 7.490e-02, 7.500e-02,
        7.500e-02, 7.610e-02, 7.610e-02, 7.770e-02, 7.770e-02, 7.820e-02,
        7.820e-02, 7.980e-02, 7.980e-02, 8.040e-02, 8.040e-02, 8.240e-02,
        8.240e-02, 8.260e-02, 8.260e-02, 8.290e-02, 8.290e-02, 8.580e-02,
        8.580e-02, 8.940e-02, 8.940e-02, 8.970e-02, 8.970e-02, 9.110e-02,
        9.110e-02, 9.140e-02, 9.140e-02, 9.150e-02, 9.150e-02, 9.200e-02,
        9.200e-02, 9.260e-02, 9.260e-02, 9.480e-02, 9.480e-02, 1.020e-01,
        1.020e-01, 1.031e-01, 1.031e-01, 1.054e-01, 1.054e-01, 1.069e-01,
        1.069e-01, 1.115e-01, 1.115e-01, 1.121e-01, 1.121e-01, 1.122e-01,
        1.122e-01, 1.137e-01, 1.137e-01, 1.177e-01, 1.177e-01, 1.182e-01,
        1.182e-01, 1.183e-01, 1.183e-01, 1.206e-01, 1.206e-01, 1.214e-01,
        1.214e-01, 1.262e-01, 1.262e-01, 1.321e-01, 1.321e-01, 1.346e-01,
        1.346e-01, 1.412e-01, 1.412e-01, 1.422e-01, 1.422e-01, 1.439e-01,
        1.439e-01, 1.580e-01, 1.580e-01, 1.586e-01, 1.586e-01, 1.735e-01,
        1.735e-01, 1.748e-01, 1.748e-01, 1.819e-01, 1.819e-01, 1.845e-01,
        1.845e-01, 1.897e-01, 1.897e-01, 1.972e-01, 1.972e-01, 1.978e-01,
        1.978e-01, 2.062e-01, 2.062e-01, 2.246e-01, 2.246e-01, 2.268e-01,
        2.268e-01, 2.362e-01, 2.362e-01, 2.372e-01, 2.372e-01, 2.500e-01,
        2.500e-01, 2.694e-01, 2.694e-01, 2.733e-01, 2.733e-01, 3.197e-01,
        3.197e-01, 3.308e-01, 3.308e-01, 3.407e-01, 3.407e-01, 3.829e-01,
        3.829e-01, 3.967e-01, 3.967e-01, 5.562e-01, 5.562e-01, 1.000e+00]),
 array([0.000e+00, 1.000e-04, 5.207e-01, 5.207e-01, 6.289e-01, 6.289e-01,
        7.325e-01, 7.325e-01, 7.571e-01, 7.571e-01, 7.586e-01, 7.586e-01,
        7.699e-01, 7.699e-01, 7.702e-01, 7.702e-01, 7.726e-01, 7.726e-01,
        7.728e-01, 7.728e-01, 7.807e-01, 7.807e-01, 8.033e-01, 8.033e-01,
        8.070e-01, 8.070e-01, 8.232e-01, 8.232e-01, 8.322e-01, 8.322e-01,
        8.344e-01, 8.344e-01, 8.366e-01, 8.366e-01, 8.510e-01, 8.510e-01,
        8.532e-01, 8.532e-01, 8.555e-01, 8.555e-01, 8.581e-01, 8.581e-01,
        8.602e-01, 8.602e-01, 8.607e-01, 8.607e-01, 8.667e-01, 8.667e-01,
        8.672e-01, 8.672e-01, 8.800e-01, 8.800e-01, 8.820e-01, 8.820e-01,
        8.869e-01, 8.869e-01, 8.883e-01, 8.883e-01, 8.907e-01, 8.907e-01,
        8.979e-01, 8.979e-01, 8.985e-01, 8.985e-01, 8.986e-01, 8.986e-01,
        8.994e-01, 8.994e-01, 9.012e-01, 9.012e-01, 9.017e-01, 9.017e-01,
        9.037e-01, 9.037e-01, 9.040e-01, 9.040e-01, 9.047e-01, 9.047e-01,
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        9.160e-01, 9.160e-01, 9.162e-01, 9.162e-01, 9.163e-01, 9.163e-01,
        9.165e-01, 9.165e-01, 9.184e-01, 9.184e-01, 9.201e-01, 9.201e-01,
        9.205e-01, 9.205e-01, 9.243e-01, 9.243e-01, 9.251e-01, 9.251e-01,
        9.261e-01, 9.261e-01, 9.271e-01, 9.271e-01, 9.274e-01, 9.274e-01,
        9.287e-01, 9.287e-01, 9.306e-01, 9.306e-01, 9.307e-01, 9.307e-01,
        9.308e-01, 9.308e-01, 9.318e-01, 9.318e-01, 9.320e-01, 9.320e-01,
        9.322e-01, 9.322e-01, 9.342e-01, 9.342e-01, 9.345e-01, 9.345e-01,
        9.352e-01, 9.352e-01, 9.354e-01, 9.354e-01, 9.359e-01, 9.359e-01,
        9.360e-01, 9.360e-01, 9.365e-01, 9.365e-01, 9.372e-01, 9.372e-01,
        9.393e-01, 9.393e-01, 9.396e-01, 9.396e-01, 9.408e-01, 9.408e-01,
        9.409e-01, 9.409e-01, 9.410e-01, 9.410e-01, 9.414e-01, 9.414e-01,
        9.421e-01, 9.421e-01, 9.425e-01, 9.425e-01, 9.426e-01, 9.426e-01,
        9.441e-01, 9.441e-01, 9.465e-01, 9.465e-01, 9.467e-01, 9.467e-01,
        9.480e-01, 9.480e-01, 9.484e-01, 9.484e-01, 9.495e-01, 9.495e-01,
        9.504e-01, 9.504e-01, 9.505e-01, 9.505e-01, 9.507e-01, 9.507e-01,
        9.511e-01, 9.511e-01, 9.512e-01, 9.512e-01, 9.522e-01, 9.522e-01,
        9.532e-01, 9.532e-01, 9.533e-01, 9.533e-01, 9.535e-01, 9.535e-01,
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        0.58112345, 0.58104419, 0.58103776, 0.58102229, 0.58100014,
        0.58068749, 0.58065847, 0.58064658, 0.5806141 , 0.58061106,
        0.58060435, 0.58054014, 0.58047772, 0.58045687, 0.58045146,
        0.5801075 , 0.57999139, 0.57995777, 0.57991538, 0.57987058,
        0.57986521, 0.5798144 , 0.57974525, 0.57962072, 0.57955743,
        0.57942032, 0.57939593, 0.57927672, 0.57920288, 0.57917599,
        0.5791476 , 0.57892303, 0.57890569, 0.57844254, 0.57842076,
        0.57836271, 0.57835835, 0.57811765, 0.57811375, 0.57764495,
        0.57763915, 0.5771997 , 0.5771836 , 0.57693794, 0.57691386,
        0.57682551, 0.57677027, 0.5761342 , 0.57605798, 0.57562614,
        0.57561976, 0.57554906, 0.57553841, 0.57551417, 0.5754849 ,
        0.57527427, 0.57526061, 0.57520142, 0.57517677, 0.5749784 ,
        0.57496244, 0.57469582, 0.57458128, 0.57408399, 0.57406256,
        0.57376997, 0.57373791, 0.57348267, 0.57347634, 0.57327754,
        0.57326721, 0.57299522, 0.57299209, 0.57294105, 0.57293693,
        0.57277666, 0.57275032, 0.57265101, 0.57261529, 0.5726018 ,
        0.57258254, 0.57235756, 0.57228811, 0.57192825, 0.57191189,
        0.57166862, 0.57160726, 0.57108055, 0.57094484, 0.57086078,
        0.57084998, 0.5702555 , 0.57015498, 0.5700167 , 0.56989316,
        0.56987969, 0.56981919, 0.5688992 , 0.56883559, 0.56777186,
        0.56770361, 0.56757309, 0.56751088, 0.56711888, 0.56709472,
        0.56704119, 0.56691041, 0.56685268, 0.56681272, 0.56673081,
        0.56665221, 0.56649637, 0.56644638, 0.56594464, 0.56593939,
        0.5638471 , 0.56384365, 0.56354672, 0.5635332 , 0.56309789,
        0.5630914 , 0.56264388, 0.56264035, 0.56137921, 0.56137803,
        0.56115447, 0.56114285, 0.56112973, 0.56112282, 0.56063812,
        0.5605762 , 0.55939359, 0.55939241, 0.55925177, 0.55925093,
        0.55922614, 0.55920927, 0.5587424 , 0.55870059, 0.55858969,
        0.55856023, 0.55733003, 0.55732718, 0.55593983, 0.55589878,
        0.5553892 , 0.55537878, 0.55407901, 0.55406627, 0.55375938,
        0.5537486 , 0.55342299, 0.55341626, 0.55060152, 0.55059931,
        0.55046078, 0.55042169, 0.54726394, 0.54726187, 0.54700242,
        0.54699656, 0.54567792, 0.54566368, 0.5451405 , 0.54511565,
        0.54415695, 0.54412654, 0.54252761, 0.54251445, 0.54244522,
        0.54240043, 0.54079565, 0.54079228, 0.53766036, 0.53765297,
        0.53735306, 0.53734885, 0.53590671, 0.53589149, 0.53567736,
        0.53567212, 0.53394471, 0.53394417, 0.53093643, 0.53091403,
        0.53028912, 0.5302855 , 0.52323124, 0.52321114, 0.521713  ,
        0.52169873, 0.52033302, 0.52032647, 0.51461583, 0.51459536,
        0.51275255, 0.51274682, 0.49281305, 0.49279693, 0.30362619]))

fpr ,tpr, thr = roc_curve(data[:,1],data[:,0])

plt.plot(fpr, tpr, '.-')

[<matplotlib.lines.Line2D at 0x1868b0e92e8>]

output_37_1

plt.plot(thr, fpr)

[<matplotlib.lines.Line2D at 0x1868b24f0b8>]

output_38_1

auc(fpr, tpr)

0.9972922600000002

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