# How CI metrics is calculated?

In week 2 lab, we generated bias report using clarify. In that report i see CI of blouse is more than dresses. As per the formula CI = n(a)-n(b)/n(a)+n(b)

If i look at the data, i see that no of dresses is more than no of blouses. In that case why CI is dress is less than CI of blouse. I am confused please help in understanding this.

Value(s)/Threshold: Blouses

name description value
CI Class Imbalance (CI) 0.736321
DPL Difference in Positive Proportions in Labels (DPL) 0.016356
JS Jensen-Shannon Divergence (JS) 0.000186
KL Kullback-Liebler Divergence (KL) 0.000737
KS Kolmogorov-Smirnov Distance (KS) 0.016356
LP L-p Norm (LP) 0.023131
TVD Total Variation Distance (TVD) 0.016356

Value(s)/Threshold: Dresses

name description value
CI Class Imbalance (CI) 0.45682
DPL Difference in Positive Proportions in Labels (DPL) 0.022482
JS Jensen-Shannon Divergence (JS) 0.000352
KL Kullback-Liebler Divergence (KL) 0.001392
KS Kolmogorov-Smirnov Distance (KS) 0.022482
LP L-p Norm (LP) 0.031795
TVD Total Variation Distance (TVD) 0.022482

Value(s)/Threshold: Pants

name description value
CI Class Imbalance (CI) 0.880668
DPL Difference in Positive Proportions in Labels (DPL) -0.026661
JS Jensen-Shannon Divergence (JS) 0.000522
KL Kullback-Liebler Divergence (KL) 0.002119
KS Kolmogorov-Smirnov Distance (KS) 0.026661
LP L-p Norm (LP) 0.037704
TVD Total Variation Distance (TVD) 0.026661

Value(s)/Threshold: Knits

name description value
CI Class Imbalance (CI) 0.59109
DPL Difference in Positive Proportions in Labels (DPL) 0.011213
JS Jensen-Shannon Divergence (JS) 0.000088
KL Kullback-Liebler Divergence (KL) 0.00035
KS Kolmogorov-Smirnov Distance (KS) 0.011213
LP L-p Norm (LP) 0.015857
TVD Total Variation Distance (TVD) 0.011213

Value(s)/Threshold: Intimates

name description value
CI Class Imbalance (CI) 0.987006
DPL Difference in Positive Proportions in Labels (DPL) -0.025599
JS Jensen-Shannon Divergence (JS) 0.000483
KL Kullback-Liebler Divergence (KL) 0.001959
KS Kolmogorov-Smirnov Distance (KS) 0.025599
LP L-p Norm (LP) 0.036203
TVD Total Variation Distance (TVD) 0.025599

Value(s)/Threshold: Outerwear

name description value
CI Class Imbalance (CI) 0.971802
DPL Difference in Positive Proportions in Labels (DPL) -0.026121
JS Jensen-Shannon Divergence (JS) 0.000503
KL Kullback-Liebler Divergence (KL) 0.00204
KS Kolmogorov-Smirnov Distance (KS) 0.026121
LP L-p Norm (LP) 0.036941
TVD Total Variation Distance (TVD) 0.026121

Value(s)/Threshold: Lounge

name description value
CI Class Imbalance (CI) 0.940864
DPL Difference in Positive Proportions in Labels (DPL) -0.045509
JS Jensen-Shannon Divergence (JS) 0.001573
KL Kullback-Liebler Divergence (KL) 0.006474
KS Kolmogorov-Smirnov Distance (KS) 0.045509
LP L-p Norm (LP) 0.06436
TVD Total Variation Distance (TVD) 0.045509

Value(s)/Threshold: Sweaters

name description value
CI Class Imbalance (CI) 0.878016
DPL Difference in Positive Proportions in Labels (DPL) 0.021044
JS Jensen-Shannon Divergence (JS) 0.000305
KL Kullback-Liebler Divergence (KL) 0.001207
KS Kolmogorov-Smirnov Distance (KS) 0.021044
LP L-p Norm (LP) 0.029761
TVD Total Variation Distance (TVD) 0.021044

Value(s)/Threshold: Skirts

name description value
CI Class Imbalance (CI) 0.92018
DPL Difference in Positive Proportions in Labels (DPL) -0.021053
JS Jensen-Shannon Divergence (JS) 0.000323
KL Kullback-Liebler Divergence (KL) 0.001308
KS Kolmogorov-Smirnov Distance (KS) 0.021053
LP L-p Norm (LP) 0.029773
TVD Total Variation Distance (TVD) 0.021053

Value(s)/Threshold: Fine gauge

name description value
CI Class Imbalance (CI) 0.906391
DPL Difference in Positive Proportions in Labels (DPL) -0.020859
JS Jensen-Shannon Divergence (JS) 0.000317
KL Kullback-Liebler Divergence (KL) 0.001283
KS Kolmogorov-Smirnov Distance (KS) 0.020859
LP L-p Norm (LP) 0.0295
TVD Total Variation Distance (TVD) 0.020859

Value(s)/Threshold: Sleep

name description value
CI Class Imbalance (CI) 0.981084
DPL Difference in Positive Proportions in Labels (DPL) -0.047723
JS Jensen-Shannon Divergence (JS) 0.001743
KL Kullback-Liebler Divergence (KL) 0.007185
KS Kolmogorov-Smirnov Distance (KS) 0.047723
LP L-p Norm (LP) 0.067491
TVD Total Variation Distance (TVD) 0.047723

Value(s)/Threshold: Jackets

name description value
CI Class Imbalance (CI) 0.939627
DPL Difference in Positive Proportions in Labels (DPL) -0.035868
JS Jensen-Shannon Divergence (JS) 0.000961
KL Kullback-Liebler Divergence (KL) 0.003928
KS Kolmogorov-Smirnov Distance (KS) 0.035868
LP L-p Norm (LP) 0.050725
TVD Total Variation Distance (TVD) 0.035868

Value(s)/Threshold: Swim

name description value
CI Class Imbalance (CI) 0.970653
DPL Difference in Positive Proportions in Labels (DPL) 0.01162
JS Jensen-Shannon Divergence (JS) 0.000094
KL Kullback-Liebler Divergence (KL) 0.000373
KS Kolmogorov-Smirnov Distance (KS) 0.01162
LP L-p Norm (LP) 0.016433
TVD Total Variation Distance (TVD) 0.01162

Value(s)/Threshold: Trend

name description value
CI Class Imbalance (CI) 0.98957
DPL Difference in Positive Proportions in Labels (DPL) 0.110042
JS Jensen-Shannon Divergence (JS) 0.00748
KL Kullback-Liebler Divergence (KL) 0.028876
KS Kolmogorov-Smirnov Distance (KS) 0.110042
LP L-p Norm (LP) 0.155623
TVD Total Variation Distance (TVD) 0.110042

Value(s)/Threshold: Jeans

name description value
CI Class Imbalance (CI) 0.902413
DPL Difference in Positive Proportions in Labels (DPL) -0.055597
JS Jensen-Shannon Divergence (JS) 0.002382
KL Kullback-Liebler Divergence (KL) 0.009875
KS Kolmogorov-Smirnov Distance (KS) 0.055597
LP L-p Norm (LP) 0.078626
TVD Total Variation Distance (TVD) 0.055597

Value(s)/Threshold: Legwear

name description value
CI Class Imbalance (CI) 0.986034
DPL Difference in Positive Proportions in Labels (DPL) -0.027173
JS Jensen-Shannon Divergence (JS) 0.000545
KL Kullback-Liebler Divergence (KL) 0.002215
KS Kolmogorov-Smirnov Distance (KS) 0.027173
LP L-p Norm (LP) 0.038428
TVD Total Variation Distance (TVD) 0.027173

Value(s)/Threshold: Shorts

name description value
CI Class Imbalance (CI) 0.973128
DPL Difference in Positive Proportions in Labels (DPL) -0.019247
JS Jensen-Shannon Divergence (JS) 0.00027
KL Kullback-Liebler Divergence (KL) 0.001091
KS Kolmogorov-Smirnov Distance (KS) 0.019247
LP L-p Norm (LP) 0.027219
TVD Total Variation Distance (TVD) 0.019247

Value(s)/Threshold: Layering

name description value
CI Class Imbalance (CI) 0.988332
DPL Difference in Positive Proportions in Labels (DPL) -0.086077
JS Jensen-Shannon Divergence (JS) 0.006138
KL Kullback-Liebler Divergence (KL) 0.026226
KS Kolmogorov-Smirnov Distance (KS) 0.086077
LP L-p Norm (LP) 0.121732
TVD Total Variation Distance (TVD) 0.086077

Hello @vjain1136,

The reason why CI of Dresses is less than CI of Blouses is that Dresses class is much balanced than Blouses class. The range of CI is between -1 and 1.

Letâ€™s suppose there are two classes that have 50 data points in each class. This binary class is nicely balanced so the CI will be 0.

Because there are not only two classes in the product_category,
CI for Blouses :
n(a) = total number except Blouses = 19643
n(b) = number of Blouses = 2983
n(a)-n(b)/n(a)+n(b) = (19643-2983)/(19643+2983) = 0.736321047

CI for Dresses :
n(a) = total number except Dresses = 16481
n(b) = number of Dresses = 6145
n(a)-n(b)/n(a)+n(b) = (16481-6145)/(16481+6145) = 0.456819588

Best regards,

1 Like

Thank you Bj Kim for such a clear explanation. I understand the concept now.

You are very welcome @vjain1136.

Happy learning

Hello @bj.kim,

Can you please elaborate on the â€śbalanceâ€ť here â€śDresses class is much balanced than Blouses classâ€ť?

Also, C.I of product category measures if a product category has more reviews than any other product category. Here Dresses have more reviews than any other category(27.2%). So, the C.I of Dresses should be higher than Blouses, no?

Thank you!

According to the developer guide, â€śClass imbalance (CI) bias occurs when a facet value d has fewer training samples when compared with another facet a in the dataset.â€ť.

The Dresses category has more reviews so less imbalanced(close to zero) than others.

Please check here for more detail.

Best regards,

Thank you @bj.kim for the explanation. I understand the values now.