# Gini Index For Decision Trees – Part III

Contributor:
QuantInsti
Visit: QuantInsti

Calculation of Gini Index of Open Interest for Positive Past Trend

P(Open Interest=High): 2/6

P(Open Interest=Low): 4/6

If (Open Interest = High & Return = Up), probability = 2/2

If (Open Interest = High & Return = Down), probability = 0

Gini index = 1 – (sq(2/2) + sq(0)) = 0

If (Open Interest = Low & Return = Up), probability = 2/4

If (Open Interest = Low & Return = Down), probability = 2/4

Gini index = 1 – (sq(0) + sq(2/4)) = 0.50

Weighted sum of the Gini Indices can be calculated as follows:

Gini Index for Open Interest = (2/6)*0 + (4/6)*0.50 = 0.33

Calculation of Gini Index for Trading Volume

If (Trading Volume = High & Return = Up), probability = 4/4

If (Trading Volume = High & Return = Down), probability = 0

Gini index = 1 – (sq(4/4) + sq(0)) = 0

If (Trading Volume = Low & Return = Up), probability = 0

If (Trading Volume = Low & Return = Down), probability = 2/2

Gini index = 1 – (sq(0) + sq(2/2)) = 0

Weighted sum of the Gini Indices can be calculated as follows:

Gini Index for Trading Volume = (4/6)*0 + (2/6)*0 = 0

We will split the node further using the ‘Trading Volume’ feature, as it has the minimum Gini index.

Conclusion

Gini Index, unlike information gain, isn’t computationally intensive as it doesn’t involve the logarithm function used to calculate entropy in information gain, which is why Gini Index is preferred over Information gain.

##### Disclosure: Interactive Brokers

Information posted on IBKR Traders’ Insight that is provided by third-parties and not by Interactive Brokers does NOT constitute a recommendation by Interactive Brokers that you should contract for the services of that third party. Third-party participants who contribute to IBKR Traders’ Insight are independent of Interactive Brokers and Interactive Brokers does not make any representations or warranties concerning the services offered, their past or future performance, or the accuracy of the information provided by the third party. Past performance is no guarantee of future results.

This material is from QuantInsti and is being posted with permission from QuantInsti. The views expressed in this material are solely those of the author and/or QuantInsti and IBKR is not endorsing or recommending any investment or trading discussed in the material. This material is not and should not be construed as an offer to sell or the solicitation of an offer to buy any security. To the extent that this material discusses general market activity, industry or sector trends or other broad based economic or political conditions, it should not be construed as research or investment advice. To the extent that it includes references to specific securities, commodities, currencies, or other instruments, those references do not constitute a recommendation to buy, sell or hold such security. This material does not and is not intended to take into account the particular financial conditions, investment objectives or requirements of individual customers. Before acting on this material, you should consider whether it is suitable for your particular circumstances and, as necessary, seek professional advice.

In accordance with EU regulation: The statements in this document shall not be considered as an objective or independent explanation of the matters. Please note that this document (a) has not been prepared in accordance with legal requirements designed to promote the independence of investment research, and (b) is not subject to any prohibition on dealing ahead of the dissemination or publication of investment research.

Any trading symbols displayed are for illustrative purposes only and are not intended to portray recommendations.