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Target

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SYDNEY, Australia, November 21st, 2024/Chainwire/--The GMT DAO, an independent community organization of GMT holders, is excited to announce the launch of the GMT Burn Initiative—an event designed to place the future of GMT firmly in the hands of its community. Through this initiative, GMT holders will vote on the decision to burn up to 600 million GMT, equivalent to 100 million USD, marking this as one of the most ambitious token burns in the web3 ecosystem. The GMT Burn Initiative reflects the GMT DAO’s commitment to transparency, governance, and sustainable token management. This community-driven approach aligns with the DAO's goal to shape GMT’s future responsibly and collaboratively. How It Works: Lock and Vote: GMT holders can participate by visiting burngmt.com, where they can lock their tokens and cast their vote on various proposals, including the first of its kind “GMT Burn Initiative”. Participants will receive an exclusive soulbound ‘Make GMT Great Again’ Red Hat NFT as a token of acknowledgement for their involvement. This NFT will record metadata detailing the claimed and eligible airdrops, as well as the votes cast.
Earn Rewards: A total of 100 million GMT will be distributed at the end of the 60-day voting period as rewards to participants, contingent on achieving milestones.
On-Chain Transparency: The voting process is recorded on the blockchain, allowing anyone to verify results and ensuring the integrity and transparency of each decision.
Regular Voting Cycles: This burn initiative is just the beginning. Moving forward, GMT DAO will introduce new proposals and voting cycles every quarter, giving holders regular opportunities to shape the future of GMT via gmtdao.com. This initiative showcases a proactive effort to ensure GMT's sustainable future, emphasizing innovation and community engagement. The GMT DAO remains committed to true decentralization, empowering GMT holders to shape its direction. By enabling votes on key proposals, including a potential major token burn, the DAO highlights the power of collective input and its dedication to building a strong, thriving ecosystem. The GMT Burn Initiative marks a new chapter in GMT’s journey, giving every holder a voice. Voting, which starts at 100 GMT, is now open at burngmt.com, inviting all GMT holders to help shape the token's future. About GMT DAO The GMT DAO is an independent organization of GMT holders dedicated to overseeing GMT’s future through transparent and community-led governance. The DAO’s formation represents a commitment to empowering GMT holders with a voice in key decisions, from token management to ecosystem development. For more information on the GMT Burn Initiative and to participate, users can visit burngmt.com. About GMT GMT sits at the heart of the FSL ecosystem. Exclusively earned through STEPN, this token plays a crucial role across all FSL products. GMT operates on four blockchains—Solana, BNB Chain, Ethereum, and Polygon—and is pivotal in Gas Hero, where it's used to trade items and burn for NFT level-ups. On MOOAR, all items can be traded using GMT, and it’s also central to primary sale raffle mints with key partners and is used in the newly launched STEPN GO to buy Sneakers and perform various in app functions. Contact GMT DAO hello@gmtdao.com This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here SYDNEY, Australia, November 21st, 2024/Chainwire/--The GMT DAO, an independent community organization of GMT holders, is excited to announce the launch of the GMT Burn Initiative—an event designed to place the future of GMT firmly in the hands of its community. Through this initiative, GMT holders will vote on the decision to burn up to 600 million GMT, equivalent to 100 million USD, marking this as one of the most ambitious token burns in the web3 ecosystem. The GMT Burn Initiative reflects the GMT DAO’s commitment to transparency, governance, and sustainable token management. This community-driven approach aligns with the DAO's goal to shape GMT’s future responsibly and collaboratively. How It Works: Lock and Vote: GMT holders can participate by visiting burngmt.com, where they can lock their tokens and cast their vote on various proposals, including the first of its kind “GMT Burn Initiative”. Participants will receive an exclusive soulbound ‘Make GMT Great Again’ Red Hat NFT as a token of acknowledgement for their involvement. This NFT will record metadata detailing the claimed and eligible airdrops, as well as the votes cast. Earn Rewards: A total of 100 million GMT will be distributed at the end of the 60-day voting period as rewards to participants, contingent on achieving milestones. On-Chain Transparency: The voting process is recorded on the blockchain, allowing anyone to verify results and ensuring the integrity and transparency of each decision. Regular Voting Cycles: This burn initiative is just the beginning. Moving forward, GMT DAO will introduce new proposals and voting cycles every quarter, giving holders regular opportunities to shape the future of GMT via gmtdao.com. Lock and Vote: GMT holders can participate by visiting burngmt.com , where they can lock their tokens and cast their vote on various proposals, including the first of its kind “GMT Burn Initiative”. Participants will receive an exclusive soulbound ‘Make GMT Great Again’ Red Hat NFT as a token of acknowledgement for their involvement. This NFT will record metadata detailing the claimed and eligible airdrops, as well as the votes cast. burngmt.com burngmt.com Earn Rewards: A total of 100 million GMT will be distributed at the end of the 60-day voting period as rewards to participants, contingent on achieving milestones. On-Chain Transparency: The voting process is recorded on the blockchain, allowing anyone to verify results and ensuring the integrity and transparency of each decision. Regular Voting Cycles: This burn initiative is just the beginning. Moving forward, GMT DAO will introduce new proposals and voting cycles every quarter, giving holders regular opportunities to shape the future of GMT via gmtdao.com . gmtdao.com gmtdao.com This initiative showcases a proactive effort to ensure GMT's sustainable future, emphasizing innovation and community engagement. The GMT DAO remains committed to true decentralization, empowering GMT holders to shape its direction. By enabling votes on key proposals, including a potential major token burn, the DAO highlights the power of collective input and its dedication to building a strong, thriving ecosystem. The GMT Burn Initiative marks a new chapter in GMT’s journey, giving every holder a voice. Voting, which starts at 100 GMT, is now open at burngmt.com , inviting all GMT holders to help shape the token's future. burngmt.com burngmt.com About GMT DAO The GMT DAO is an independent organization of GMT holders dedicated to overseeing GMT’s future through transparent and community-led governance. The DAO’s formation represents a commitment to empowering GMT holders with a voice in key decisions, from token management to ecosystem development. For more information on the GMT Burn Initiative and to participate, users can visit burngmt.com . burngmt.com burngmt.com About GMT GMT sits at the heart of the FSL ecosystem. Exclusively earned through STEPN , this token plays a crucial role across all FSL products. STEPN STEPN GMT operates on four blockchains—Solana, BNB Chain, Ethereum, and Polygon—and is pivotal in Gas Hero , where it's used to trade items and burn for NFT level-ups. Gas Hero Gas Hero On MOOAR , all items can be traded using GMT, and it’s also central to primary sale raffle mints with key partners and is used in the newly launched STEPN GO to buy Sneakers and perform various in app functions. MOOAR MOOAR STEPN GO STEPN GO Contact GMT DAO hello@gmtdao.com This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here here here

GMT DAO Launches Groundbreaking Burn Initiative With a Target Of Up To 600 Million GMT

GMT DAO стартира новаторска инициатива за изгаряне с цел до 600 милиона GMT

GMT DAO spouští průlomovou iniciativu Burn s cílem až 600 milionů GMT

GMT DAO lanza una innovadora iniciativa de quema con un objetivo de hasta 600 millones de GMT

GMT DAO Luncurkan Inisiatif Pembakaran Terobosan dengan Target Hingga 600 Juta GMT

GMT DAO、最大6億GMTを目標とした画期的なバーンイニシアチブを開始

GMT DAO pristato novatorišką deginimo iniciatyvą, kurios tikslas – iki 600 mln. GMT

GMT DAO лансира револуционерна иницијатива за изгореници со цел до 600 милиони GMT

GMT DAO Melancarkan Inisiatif Pembakaran Pecah Tanah Dengan Sasaran Sehingga 600 Juta GMT

GMT DAO GMT මිලියන 600 ක් දක්වා ඉලක්කයක් සමඟ බිම් කඩකිරීමේ පිළිස්සීමේ මුලපිරීම දියත් කරයි

GMT DAO lanserar banbrytande Burn-initiativ med ett mål på upp till 600 miljoner GMT

GMT DAO เปิดตัวโครงการ Burning สุดล้ำด้วยเป้าหมายสูงถึง 600 ล้าน GMT

GMT DAO, 600 Milyon GMT'ye Kadar Hedefle Çığır Açan Yakma Girişimini Başlattı

SEC v. Consensys Software Inc. Court Filing, retrieved on June 28, 2024, is part of HackerNoon’s Legal PDF Series. You can jump to any part in this filing here. This part is 22 of 26. VI. CONSENSYS ALSO ACTS AS A BROKER WITH RESPECT TO THE LIDO AND ROCKET POOL INVESTMENT CONTRACTS. 324. Through its MetaMask Staking program, Consensys also acts as a broker by effecting transactions in the Lido and Rocket Pool investment contracts for the account of others. 325. As alleged above, Consensys solicits potential investors, holds itself out as a place to buy and sell the investment contracts, and recommends which of the two investment contracts will offer the highest rewards. 326. Consensys then effects the transaction on the investor’s behalf. 327. Specifically, as noted, Consensys through the MetaMask Staking software handles the investor’s assets by removing the investor’s ETH from the investor’s MetaMask wallet and transferring it to the MM Staking Router Smart Contract, which, in turn, transfers it to the Lido or Rocket Pool proxy smart contract. 328. Finally, Consensys’s software, transfers the acquired token—stETH or rETH—into the investor’s MetaMask Wallet. Continue Reading Here. About HackerNoon Legal PDF Series: We bring you the most important technical and insightful public domain court case filings.
This court case retrieved on June 28, 2024, storage.courtlistener.com is part of the public domain. The court-created documents are works of the federal government, and under copyright law, are automatically placed in the public domain and may be shared without legal restriction. SEC v. Consensys Software Inc. Court Filing, retrieved on June 28, 2024, is part of HackerNoon’s Legal PDF Series. You can jump to any part in this filing here. This part is 22 of 26. SEC v. Consensys Software Inc. Court Filing, retrieved on June 28, 2024, is part of HackerNoon’s Legal PDF Series . You can jump to any part in this filing here . This part is 22 of 26. HackerNoon’s Legal PDF Series here VI. CONSENSYS ALSO ACTS AS A BROKER WITH RESPECT TO THE LIDO AND ROCKET POOL INVESTMENT CONTRACTS. 324. Through its MetaMask Staking program, Consensys also acts as a broker by effecting transactions in the Lido and Rocket Pool investment contracts for the account of others. 325. As alleged above, Consensys solicits potential investors, holds itself out as a place to buy and sell the investment contracts, and recommends which of the two investment contracts will offer the highest rewards. 326. Consensys then effects the transaction on the investor’s behalf. 327. Specifically, as noted, Consensys through the MetaMask Staking software handles the investor’s assets by removing the investor’s ETH from the investor’s MetaMask wallet and transferring it to the MM Staking Router Smart Contract, which, in turn, transfers it to the Lido or Rocket Pool proxy smart contract. 328. Finally, Consensys’s software, transfers the acquired token—stETH or rETH—into the investor’s MetaMask Wallet. Continue Reading Here. Continue Reading Here . Here About HackerNoon Legal PDF Series: We bring you the most important technical and insightful public domain court case filings. This court case retrieved on June 28, 2024, storage.courtlistener.com is part of the public domain. The court-created documents are works of the federal government, and under copyright law, are automatically placed in the public domain and may be shared without legal restriction. About HackerNoon Legal PDF Series: We bring you the most important technical and insightful public domain court case filings. This court case retrieved on June 28, 2024, storage.courtlistener.com is part of the public domain. The court-created documents are works of the federal government, and under copyright law, are automatically placed in the public domain and may be shared without legal restriction. storage.courtlistener.com

SEC Targets Consensys for Brokerage Activities in Lido and Rocket Pool Investments

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কিভাবে বিজ্ঞাপনদাতারা শিশুদের ভিডিওতে স্থান নির্ধারণ-ভিত্তিক লক্ষ্য নির্ধারণ ব্যবহার করে

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विज्ञापनदाता बच्चों के वीडियो पर प्लेसमेंट-आधारित लक्ष्यीकरण का उपयोग कैसे करते हैं

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One of my goals during the past year was to work on my communication skills each day. I worked on writing, speaking and or listening everyday. Even though I was working to improve my communication skills as a neurodiverse person, daily I was also facing situations in which other people could have done better honing their message to me. This article illustrates some ways your message can be more clear for others. I know certain things are hard for me communication wise. It's part of the baggage I am carrying as a neurodiverse person. Much of my life I did not know I had this problem. I want to share these helpful thoughts so that others can use to more clearly communicate positive messages with neurodiverse people. There are 3 areas I feel it can be a struggle to receive communication: Finding out things “through the grapevine” If your organization is relying heavily on implied messages or verbal communication about important topics, there is a good chance this information will never reach some of your employees or members. It may not seem immediately clear, but many people have different preferences for how they pick up information (similarly related to the book The 5 Love Languages). To reach more people your communication styles for sending your message should be more inclusive and more explicit. Maybe there can be a written notice as well as a verbal statement when you need to communicate important information in some cases. One thing I learned while in the workplace is that many people never correct their vision and they actually cannot read small print very well. You might be trying to primarily communicate in writing with a neurotypical person who actually can’t read your microscopic print on your memo. Relying on picking up only social cues to understand social situations Sometimes people with neurodiverse traits are never invited to the social situations where information is exchanged. You could be making important decisions around the water cooler or during an informal lunch gathering when half your team is actually there. Because sometimes people with fewer social abilities have fewer opportunities to practice social skills, it might be harder for them to pick up social cues even if they are trying. Making the opportunities to meet together more obvious can help. This might include having an open office hour for team members to talk to managers. People assume I should just “know” or “Why don’t you just get it?” No matter how frustrated you are with someone, yelling at them and telling them “You don’t have any social skills” is a failure on your part. You are struggling to communicate and send your message, the other neurodiverse person is having trouble receiving your message. Yelling at the person you are intending to influence positively is the opposite of communication.  Do you want the neurodiverse person to change and see your point of view? Telling them they are deficient does not help because they are generally really trying their best. If you are feeling frustrated with a neurodiverse person, back up and find patience first. This is worth it even if you don’t want to keep a relationship with them because people never remember what you say, they remember how you make them feel. Recently, I was a newcomer in a social club where some of these areas of weakness forced me to stop participating. The social club was focused on providing fundraising support to a nonprofit in my community. They did not hold regular monthly meetings to disseminate information, but instead relied on committee leaders to share important info. This implicit way of sharing information was very difficult for me. A friend in the group had to keep me updated on important things via text on occasion. Additionally, they relied heavily on email blasts to share information. I noticed that I could not find important emails when I needed information. I was assigned to 4 committees when I was only supposed to be on one. I did not know who my point person was for any of the committees I was in until one of the senior leaders in the club noticed I was not participating in any of the committees I had been assigned. We had a deliverable to create a fundraising gala with the help of all the committees. I noticed many of the senior leaders of the social club working on things, but I could not tell what would be the most helpful for my contribution. I did not feel I was developing any useful skills and I felt I was disappointing people. Most of the time I felt I was confused about my role and when I tried to reach out for help, people were too busy to explain or I was calling at a bad time. Having a means of asynchronous communication (my posting a message that I did not understand)  would have been better than requiring synchronous communication (my having to call someone to explain if I did not understand) What would have helped Using slack or discord server to share information and to connect people If you have a slack or discord server, there would have been several options for methods of communication for people struggling with gaining information.  Senior leaders that wanted to share information more clearly would be able to.  Rather than pushing information out in email blasts the information could be pulled from the slack or discord when people needed it. An example would be posting the information about the required dress code for the gala in a slack channel so that many people could access it when they needed rather than finding out about the dress code “through the grapevine.” The pinterest page for gala dressing ideas that was created could have been posted so that everyone would have had access to it at the same time and months in advance. A buddy system for sharing information and orienting new members Because I was a new person to this group and they had recently changed many of the requirements to participate, I would have been well served if I had a veteran member of the group be my buddy and help explain requirements to me as they came up. I have had a buddy in another social group when I was new and it made a considerable difference to have one friendly person in the group that I knew or who might answer questions. Even if the buddy is not very active or helpful, as long as they are “good enough” to explain some concepts or social faux paus it might help some neurodiverse individuals save face. Being more forgiving with meeting requirements for new members I found the social group I was in struggled to keep me engaged because of the aforementioned reasons, I had trouble finding the meetings I did get to attend very helpful or productive and my engagement slid downhill. I found that the way I was being communicated with distracted me from helping achieve the deliverable of creating a fundraising gala and even made me dread participating in the group. If it had not been for one of the group members occasionally texting me to remind me about where I was supposed to be, I don’t think I would have lasted the 10 months I did in the group. Your neurodiverse coworkers and community members are trying very hard to build a communication bridge to you! Many of them already know they struggle with this. My only suggestion: Meet them halfway. Use some of these ideas to build out your communication so that it can be used and digested by more people and so that you can keep more of your talent engaged. One of my goals during the past year was to work on my communication skills each day. I worked on writing, speaking and or listening everyday. Even though I was working to improve my communication skills as a neurodiverse person, daily I was also facing situations in which other people could have done better honing their message to me. This article illustrates some ways your message can be more clear for others. I know certain things are hard for me communication wise. It's part of the baggage I am carrying as a neurodiverse person. Much of my life I did not know I had this problem. I want to share these helpful thoughts so that others can use to more clearly communicate positive messages with neurodiverse people. There are 3 areas I feel it can be a struggle to receive communication: Finding out things “through the grapevine” Finding out things “through the grapevine” If your organization is relying heavily on implied messages or verbal communication about important topics, there is a good chance this information will never reach some of your employees or members. It may not seem immediately clear, but many people have different preferences for how they pick up information (similarly related to the book The 5 Love Languages). To reach more people your communication styles for sending your message should be more inclusive and more explicit. Maybe there can be a written notice as well as a verbal statement when you need to communicate important information in some cases. One thing I learned while in the workplace is that many people never correct their vision and they actually cannot read small print very well. You might be trying to primarily communicate in writing with a neurotypical person who actually can’t read your microscopic print on your memo. Relying on picking up only social cues to understand social situations Relying on picking up only social cues to understand social situations Sometimes people with neurodiverse traits are never invited to the social situations where information is exchanged. You could be making important decisions around the water cooler or during an informal lunch gathering when half your team is actually there. Because sometimes people with fewer social abilities have fewer opportunities to practice social skills, it might be harder for them to pick up social cues even if they are trying. Making the opportunities to meet together more obvious can help. This might include having an open office hour for team members to talk to managers. People assume I should just “know” or “Why don’t you just get it?” People assume I should just “know” or “Why don’t you just get it?” No matter how frustrated you are with someone, yelling at them and telling them “You don’t have any social skills” is a failure on your part. You are struggling to communicate and send your message, the other neurodiverse person is having trouble receiving your message. Yelling at the person you are intending to influence positively is the opposite of communication.  Do you want the neurodiverse person to change and see your point of view? Telling them they are deficient does not help because they are generally really trying their best. If you are feeling frustrated with a neurodiverse person, back up and find patience first. This is worth it even if you don’t want to keep a relationship with them because people never remember what you say, they remember how you make them feel. Recently, I was a newcomer in a social club where some of these areas of weakness forced me to stop participating. The social club was focused on providing fundraising support to a nonprofit in my community. They did not hold regular monthly meetings to disseminate information, but instead relied on committee leaders to share important info. This implicit way of sharing information was very difficult for me. A friend in the group had to keep me updated on important things via text on occasion. Additionally, they relied heavily on email blasts to share information. I noticed that I could not find important emails when I needed information. I was assigned to 4 committees when I was only supposed to be on one. I did not know who my point person was for any of the committees I was in until one of the senior leaders in the club noticed I was not participating in any of the committees I had been assigned. We had a deliverable to create a fundraising gala with the help of all the committees. I noticed many of the senior leaders of the social club working on things, but I could not tell what would be the most helpful for my contribution. I did not feel I was developing any useful skills and I felt I was disappointing people. Most of the time I felt I was confused about my role and when I tried to reach out for help, people were too busy to explain or I was calling at a bad time. Having a means of asynchronous communication (my posting a message that I did not understand)  would have been better than requiring synchronous communication (my having to call someone to explain if I did not understand) What would have helped Using slack or discord server to share information and to connect people Using slack or discord server to share information and to connect people If you have a slack or discord server, there would have been several options for methods of communication for people struggling with gaining information.  Senior leaders that wanted to share information more clearly would be able to.  Rather than pushing information out in email blasts the information could be pulled from the slack or discord when people needed it. An example would be posting the information about the required dress code for the gala in a slack channel so that many people could access it when they needed rather than finding out about the dress code “through the grapevine.” The pinterest page for gala dressing ideas that was created could have been posted so that everyone would have had access to it at the same time and months in advance. A buddy system for sharing information and orienting new members A buddy system for sharing information and orienting new members Because I was a new person to this group and they had recently changed many of the requirements to participate, I would have been well served if I had a veteran member of the group be my buddy and help explain requirements to me as they came up. I have had a buddy in another social group when I was new and it made a considerable difference to have one friendly person in the group that I knew or who might answer questions. Even if the buddy is not very active or helpful, as long as they are “good enough” to explain some concepts or social faux paus it might help some neurodiverse individuals save face. Being more forgiving with meeting requirements for new members Being more forgiving with meeting requirements for new members I found the social group I was in struggled to keep me engaged because of the aforementioned reasons, I had trouble finding the meetings I did get to attend very helpful or productive and my engagement slid downhill. I found that the way I was being communicated with distracted me from helping achieve the deliverable of creating a fundraising gala and even made me dread participating in the group. If it had not been for one of the group members occasionally texting me to remind me about where I was supposed to be, I don’t think I would have lasted the 10 months I did in the group. Your neurodiverse coworkers and community members are trying very hard to build a communication bridge to you! Many of them already know they struggle with this. My only suggestion: Meet them halfway. Use some of these ideas to build out your communication so that it can be used and digested by more people and so that you can keep more of your talent engaged.

How to improve your communication so that it hits neurodiverse targets

In my previous story, Part 1 of this topic — https://hackernoon.com/how-to-use-target-encoding-in-machine-learning-credit-risk-models-part-1, we covered the derivation of the expression of WoE using maximum likelihood. Now, we will apply it practically on a random dataset. import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import math
from scipy.special import logit, expit We have imported some special functions - logit and expit. We will use them in our script because logit is the inverse logistic function, and expit is the logistic function. print(expit(0))
print(logit(0.5)) The next step is to generate the y-vector randomly. For this, we use the Bernoulli distribution (actually, we use a Binomial distribution where n = 1). Each Bernoulli trial will produce either a 1 or 0 based on the probability parameter. And the n samples we generate correspond to the n trials of the Bernoulli distribution. Note that Binomial distribution has two parameters — n and p. Therefore, randomly sampling from Binomial requires us to specify both n and p beforehand and the “size” which is the number of experiments. Each experiment comprises n trials which will produce the “number of successes” which is the random variable for the Binomial distribution. y = np.random.binomial(1, 0.01, 10000)
print(sum(y)) np.random.binomial(10000, 0.01, 10) It is evident that the array generated using Bernoulli is what we want which is the vector y with 1s and 0s. However, the array generated using Binomial is sum(y) or sum of events in each Binomial experiment (each experiment has n = 10000 trials) performed 10 times. We don’t want that for our analysis. Then we generate two distributions for the variable “x” for which we need to compute the “weight of evidence” or which we want to target encode. x_1 = np.random.normal(130, 15, 114)
x_0 = np.random.normal(100, 20, 9886)
plt.hist(x_1) plt.hist(x_0) Note that we have cleverly randomly sampled x_1 and x_0 such that there is a higher proportion of the number of events (1s) for the “middle portion” of x values. This will give us a monotonic trend as we will see later. But the intuition is that the event rate is lower for lower values of x and increases as values of x increase. This is ensured by our sampling technique of choosing the right mean and standard deviation for the Normal distributions for x_1 and x_0. Now, we sort the vector y to ensure that we “stack” x_0 and x_1 corresponding to y=0 and y=1, respectively. Finally, we convert the np arrays into a data frame. y = np.sort(y)
print(y)
x = np.concatenate((x_0, x_1), axis=None)
df = pd.DataFrame({'y':y, 'x':x}) From now on, our main WoE code begins. ####### which feature we want a WoE for?
col = 'x' We can “bin” our variable x in two ways — equally proportioned bins using the percentile method or user-specified bins. ####### create a new dataframe with the binned values of the feature 'col' using the percentile method
####### To avoid dealing with Pandas series, create a new df and set its column to the output from pd.qcut
df_bins = pd.DataFrame()
df_bins[col] = pd.qcut(df[col], 5)
print(df_bins[col].value_counts()) Using pd.qcut(), we see how the bins have been equally proportioned. We can also use pd.cut() and specify the bins that we want which may not be equally proportioned. Note that the “include lowest = True” ensures that the x.min() is included in the lowest interval. Thus, we see 23.999 as the lowest end point of the lowest bin to include x = 24 ####### create a new dataframe with the binned values of the feature 'col' using user defined bins
####### include lowest = True ensures that df[col].min() is included in the binned interval. 
df_bins = pd.DataFrame()
df_bins[col] = pd.cut(df[col], bins = [24, 95, 115, 188], include_lowest = True)
print(df_bins[col].value_counts()) That is how our binned data frame for x looks like We define a data frame for calculating WoE woe_df = pd.concat([df['y'], df_bins], axis=1) And we calculate WoE using the one-line code (note the use of the logit function discussed earlier). Please refer to my earlier article to find out the rationale behind the following script — https://hackernoon.com/how-to-use-target-encoding-in-machine-learning-credit-risk-models-part-1 woe_x = logit(woe_df.groupby('x')['y'].sum() / woe_df.groupby('x')['y'].count()) - logit(woe_df['y'].sum() / len(woe_df)) It is interesting to see that the lowest bin has negative infinity WoE. We will see the reason for that later. But first, we plot the WoE values for x. fig, ax = plt.subplots()
woe_x.plot(ax=ax, color = 'r', linewidth = 3)
plt.xlabel('x')
plt.ylabel('WoE')
ax.set_xticks(ax.get_xticks())
ax.set_xticklabels(ax.get_xticklabels(), rotation=45, ha='right')
plt.show() As expected, we see a nice monotonic trend of WoE values for x. This indicates that as x increases, the probability of event or outcome y occurring increases as well. The following is also a good and alternative method to calculate WoE values. It also lists down the entire “table” of calculations so it is helpful to look at. def calculate_woe_iv(dataset, feature, target):
    lst = []
    for i in range(dataset[feature].nunique()):
        val = list(dataset[feature].unique())[i]
        lst.append({
            'Value': val,
            'All': dataset[dataset[feature] == val].count()[feature],
            'Good': dataset[(dataset[feature] == val) & (target == 0)].count()[feature],
            'Bad': dataset[(dataset[feature] == val) & (target == 1)].count()[feature]
        })
        
    dset = pd.DataFrame(lst)
    dset['Distr_Good'] = dset['Good'] / dset['Good'].sum()
    dset['Distr_Bad'] = dset['Bad'] / dset['Bad'].sum()
    dset['WoE'] = np.log(dset['Distr_Bad'] / dset['Distr_Good'])
    dset = dset.replace({'WoE': {np.inf: 0, -np.inf: 0}})
    dset['IV'] = (dset['Distr_Bad'] - dset['Distr_Good']) * dset['WoE']
    iv = dset['IV'].sum()
    
    dset = dset.sort_values(by='Value') # sort by values and not by WoEs to detect non-monotonic trends
    
    return dset, iv We can also calculate the information value for the variable x which quantifies the predictive power of x in predicting y. We use the same bins as we used earlier. print('WoE and IV for variable: {}'.format(col))
woe_iv_df, iv = calculate_woe_iv(df_bins, col, woe_df['y'])
print(woe_iv_df)
print('IV score: {:.2f}'.format(iv))
print('\n') The above result shows that x is quite predictive as its IV is 1.75 which is a good value of IV. We also see that the lower bin has exactly 0 events. So clearly, its WoE had to be -infinity as we saw before. However, this code snippet function assigns a value “0” to it which is wrong per se but for plotting purposes, we can use that. We plot the WoE values again. fig,ax = plt.subplots()
woe_iv_df_plt = woe_iv_df[['Value', 'WoE']].set_index('Value')
woe_iv_df_plt.plot(ax=ax, color = 'r', linewidth = 3)
plt.xlabel('x')
plt.ylabel('WoE')
ax.set_xticks(ax.get_xticks())
ax.set_xticklabels(ax.get_xticklabels(), rotation=45, ha='right')
plt.show() It is the same trend we saw earlier sans the lowest interval WoE value = 0. If we want to avoid that, we can use the “user-specified bins” using pd.cut instead of pd.qcut. If we use that, we will get the following plot In my previous story, Part 1 of this topic — https://hackernoon.com/how-to-use-target-encoding-in-machine-learning-credit-risk-models-part-1 , we covered the derivation of the expression of WoE using maximum likelihood. Now, we will apply it practically on a random dataset. https://hackernoon.com/how-to-use-target-encoding-in-machine-learning-credit-risk-models-part-1 import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import math
from scipy.special import logit, expit import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import math
from scipy.special import logit, expit We have imported some special functions - logit and expit. We will use them in our script because logit is the inverse logistic function, and expit is the logistic function. print(expit(0))
print(logit(0.5)) print(expit(0))
print(logit(0.5)) The next step is to generate the y-vector randomly. For this, we use the Bernoulli distribution (actually, we use a Binomial distribution where n = 1). Each Bernoulli trial will produce either a 1 or 0 based on the probability parameter. And the n samples we generate correspond to the n trials of the Bernoulli distribution. Note that Binomial distribution has two parameters — n and p. Therefore, randomly sampling from Binomial requires us to specify both n and p beforehand and the “size” which is the number of experiments. Each experiment comprises n trials which will produce the “number of successes” which is the random variable for the Binomial distribution. y = np.random.binomial(1, 0.01, 10000)
print(sum(y)) y = np.random.binomial(1, 0.01, 10000)
print(sum(y)) np.random.binomial(10000, 0.01, 10) np.random.binomial(10000, 0.01, 10) It is evident that the array generated using Bernoulli is what we want which is the vector y with 1s and 0s. However, the array generated using Binomial is sum(y) or sum of events in each Binomial experiment (each experiment has n = 10000 trials) performed 10 times. We don’t want that for our analysis. Then we generate two distributions for the variable “x” for which we need to compute the “weight of evidence” or which we want to target encode. x_1 = np.random.normal(130, 15, 114)
x_0 = np.random.normal(100, 20, 9886)
plt.hist(x_1) x_1 = np.random.normal(130, 15, 114)
x_0 = np.random.normal(100, 20, 9886)
plt.hist(x_1) plt.hist(x_0) plt.hist(x_0) Note that we have cleverly randomly sampled x_1 and x_0 such that there is a higher proportion of the number of events (1s) for the “middle portion” of x values. This will give us a monotonic trend as we will see later. But the intuition is that the event rate is lower for lower values of x and increases as values of x increase. This is ensured by our sampling technique of choosing the right mean and standard deviation for the Normal distributions for x_1 and x_0. Now, we sort the vector y to ensure that we “stack” x_0 and x_1 corresponding to y=0 and y=1, respectively. Finally, we convert the np arrays into a data frame. y = np.sort(y)
print(y)
x = np.concatenate((x_0, x_1), axis=None)
df = pd.DataFrame({'y':y, 'x':x}) y = np.sort(y)
print(y)
x = np.concatenate((x_0, x_1), axis=None)
df = pd.DataFrame({'y':y, 'x':x}) From now on, our main WoE code begins. ####### which feature we want a WoE for?
col = 'x' ####### which feature we want a WoE for?
col = 'x' We can “bin” our variable x in two ways — equally proportioned bins using the percentile method or user-specified bins. ####### create a new dataframe with the binned values of the feature 'col' using the percentile method
####### To avoid dealing with Pandas series, create a new df and set its column to the output from pd.qcut
df_bins = pd.DataFrame()
df_bins[col] = pd.qcut(df[col], 5)
print(df_bins[col].value_counts()) ####### create a new dataframe with the binned values of the feature 'col' using the percentile method
####### To avoid dealing with Pandas series, create a new df and set its column to the output from pd.qcut
df_bins = pd.DataFrame()
df_bins[col] = pd.qcut(df[col], 5)
print(df_bins[col].value_counts()) Using pd.qcut(), we see how the bins have been equally proportioned. We can also use pd.cut() and specify the bins that we want which may not be equally proportioned. Note that the “include lowest = True” ensures that the x.min() is included in the lowest interval. Thus, we see 23.999 as the lowest end point of the lowest bin to include x = 24 ####### create a new dataframe with the binned values of the feature 'col' using user defined bins
####### include lowest = True ensures that df[col].min() is included in the binned interval. 
df_bins = pd.DataFrame()
df_bins[col] = pd.cut(df[col], bins = [24, 95, 115, 188], include_lowest = True)
print(df_bins[col].value_counts()) ####### create a new dataframe with the binned values of the feature 'col' using user defined bins
####### include lowest = True ensures that df[col].min() is included in the binned interval. 
df_bins = pd.DataFrame()
df_bins[col] = pd.cut(df[col], bins = [24, 95, 115, 188], include_lowest = True)
print(df_bins[col].value_counts()) That is how our binned data frame for x looks like We define a data frame for calculating WoE woe_df = pd.concat([df['y'], df_bins], axis=1) woe_df = pd.concat([df['y'], df_bins], axis=1) And we calculate WoE using the one-line code (note the use of the logit function discussed earlier). Please refer to my earlier article to find out the rationale behind the following script — https://hackernoon.com/how-to-use-target-encoding-in-machine-learning-credit-risk-models-part-1 https://hackernoon.com/how-to-use-target-encoding-in-machine-learning-credit-risk-models-part-1 woe_x = logit(woe_df.groupby('x')['y'].sum() / woe_df.groupby('x')['y'].count()) - logit(woe_df['y'].sum() / len(woe_df)) woe_x = logit(woe_df.groupby('x')['y'].sum() / woe_df.groupby('x')['y'].count()) - logit(woe_df['y'].sum() / len(woe_df)) It is interesting to see that the lowest bin has negative infinity WoE. We will see the reason for that later. But first, we plot the WoE values for x. fig, ax = plt.subplots()
woe_x.plot(ax=ax, color = 'r', linewidth = 3)
plt.xlabel('x')
plt.ylabel('WoE')
ax.set_xticks(ax.get_xticks())
ax.set_xticklabels(ax.get_xticklabels(), rotation=45, ha='right')
plt.show() fig, ax = plt.subplots()
woe_x.plot(ax=ax, color = 'r', linewidth = 3)
plt.xlabel('x')
plt.ylabel('WoE')
ax.set_xticks(ax.get_xticks())
ax.set_xticklabels(ax.get_xticklabels(), rotation=45, ha='right')
plt.show() As expected, we see a nice monotonic trend of WoE values for x. This indicates that as x increases, the probability of event or outcome y occurring increases as well. The following is also a good and alternative method to calculate WoE values. It also lists down the entire “table” of calculations so it is helpful to look at. def calculate_woe_iv(dataset, feature, target):
    lst = []
    for i in range(dataset[feature].nunique()):
        val = list(dataset[feature].unique())[i]
        lst.append({
            'Value': val,
            'All': dataset[dataset[feature] == val].count()[feature],
            'Good': dataset[(dataset[feature] == val) & (target == 0)].count()[feature],
            'Bad': dataset[(dataset[feature] == val) & (target == 1)].count()[feature]
        })
        
    dset = pd.DataFrame(lst)
    dset['Distr_Good'] = dset['Good'] / dset['Good'].sum()
    dset['Distr_Bad'] = dset['Bad'] / dset['Bad'].sum()
    dset['WoE'] = np.log(dset['Distr_Bad'] / dset['Distr_Good'])
    dset = dset.replace({'WoE': {np.inf: 0, -np.inf: 0}})
    dset['IV'] = (dset['Distr_Bad'] - dset['Distr_Good']) * dset['WoE']
    iv = dset['IV'].sum()
    
    dset = dset.sort_values(by='Value') # sort by values and not by WoEs to detect non-monotonic trends
    
    return dset, iv def calculate_woe_iv(dataset, feature, target):
    lst = []
    for i in range(dataset[feature].nunique()):
        val = list(dataset[feature].unique())[i]
        lst.append({
            'Value': val,
            'All': dataset[dataset[feature] == val].count()[feature],
            'Good': dataset[(dataset[feature] == val) & (target == 0)].count()[feature],
            'Bad': dataset[(dataset[feature] == val) & (target == 1)].count()[feature]
        })
        
    dset = pd.DataFrame(lst)
    dset['Distr_Good'] = dset['Good'] / dset['Good'].sum()
    dset['Distr_Bad'] = dset['Bad'] / dset['Bad'].sum()
    dset['WoE'] = np.log(dset['Distr_Bad'] / dset['Distr_Good'])
    dset = dset.replace({'WoE': {np.inf: 0, -np.inf: 0}})
    dset['IV'] = (dset['Distr_Bad'] - dset['Distr_Good']) * dset['WoE']
    iv = dset['IV'].sum()
    
    dset = dset.sort_values(by='Value') # sort by values and not by WoEs to detect non-monotonic trends
    
    return dset, iv We can also calculate the information value for the variable x which quantifies the predictive power of x in predicting y. We use the same bins as we used earlier. print('WoE and IV for variable: {}'.format(col))
woe_iv_df, iv = calculate_woe_iv(df_bins, col, woe_df['y'])
print(woe_iv_df)
print('IV score: {:.2f}'.format(iv))
print('\n') print('WoE and IV for variable: {}'.format(col))
woe_iv_df, iv = calculate_woe_iv(df_bins, col, woe_df['y'])
print(woe_iv_df)
print('IV score: {:.2f}'.format(iv))
print('\n') The above result shows that x is quite predictive as its IV is 1.75 which is a good value of IV. We also see that the lower bin has exactly 0 events. So clearly, its WoE had to be -infinity as we saw before. However, this code snippet function assigns a value “0” to it which is wrong per se but for plotting purposes, we can use that. We plot the WoE values again. fig,ax = plt.subplots()
woe_iv_df_plt = woe_iv_df[['Value', 'WoE']].set_index('Value')
woe_iv_df_plt.plot(ax=ax, color = 'r', linewidth = 3)
plt.xlabel('x')
plt.ylabel('WoE')
ax.set_xticks(ax.get_xticks())
ax.set_xticklabels(ax.get_xticklabels(), rotation=45, ha='right')
plt.show() fig,ax = plt.subplots()
woe_iv_df_plt = woe_iv_df[['Value', 'WoE']].set_index('Value')
woe_iv_df_plt.plot(ax=ax, color = 'r', linewidth = 3)
plt.xlabel('x')
plt.ylabel('WoE')
ax.set_xticks(ax.get_xticks())
ax.set_xticklabels(ax.get_xticklabels(), rotation=45, ha='right')
plt.show() It is the same trend we saw earlier sans the lowest interval WoE value = 0. If we want to avoid that, we can use the “user-specified bins” using pd.cut instead of pd.qcut. If we use that, we will get the following plot

How To Use Target Encoding in Machine Learning Credit Risk Models  -  Part 2

Target encoding, also known as mean encoding or likelihood encoding, is a technique used to convert categorical variables into numerical values based on the target variable in supervised learning tasks. This method is particularly useful in dealing with high cardinality categorical variables (i.e., variables with a large number of unique categories). For credit risk models, this approach is also applied to continuous variables and is popularly known as “Weight of Evidence” (in the context of binary classification problems). We will derive the above formula, mathematically, for WoE to see where it comes from in the first part of this story. In the second part, we will explore the coding part of it. The idea is to fit a “piecewise constant” model to the outcome binary variable. This is done by partitioning the variable space into non-overlapping regions such that there is a constant predicted value in each region. As shown in the figure above, the input space is partitioned into seven non-overlapping regions and the output is a piecewise constant for each region. This is expressed mathematically as follows: We have a single variable x whose value x_i can belong to a region R_j and we associate a parameter \beta_j with the region R_j. If we have k regions, we get a \beta vector with length k. The piecewise constants will be the estimated values of the parameters \beta_j. Note that the function I is an indicator function which is 1 when x_i belongs to R_j and 0 otherwise. Before we move further, intuition tells us that if we are fitting a constant value in a region, it should be the “average value” of the outcome in that region. Turns out, that is what we are supposed to get with the following model: The probability of outcome y_i =1 is given by p_i and is modeled as a function of piecewise constants passed through a logistic or sigmoid function. Note that decision trees work on a similar concept of partitioning of the variable space (they use binary partitions only though). Also note that Each x_i can be expanded to a vector of dummy variables, i.e., we can convert the input x to k dummy variables: However, we will avoid dealing with vectors and keep the x_i scalar, and use the indicator function to turn on \beta_j if x_i belongs to R_j. Although we don’t really need the summand before \beta_j we will keep it to formulate the change of j with the region R_j when x_i will fall under R_j. In general, the above equation for p_i can also be expressed as a function of any x. Before we move further to derive the WoE values, it is interesting to note that there is no “intercept” term in the above model. Whilst, we could’ve added an intercept term in the above model, turns out that its value will not be defined. The reason is similar to the problem of adding n-values of dummy variables instead of (n-1) values in a regression model, because then intercept can be expressed completely as a sum of all the n-dummy variables, therefore, it is “redundant”. Similarly, here the intercept term is “redundant”. However, it will appear later in the computation of WoE. We will start by defining the likelihood. Note that y, x, and \beta are vectors and the Likelihood is the joint pmf of y_1, y_2, .. y_n Now, since we know that If y_i = 1 then P(y_i) = p_i and if y_i = 0 then P(y_i) = 1-p_i, we use it to redefine L Note: the clever use of the indicator functions which will turn on the specific probability for each y_i. However, we can express this better by using the values y_i themselves. We can use the above substitution to make our likelihood expression unwieldy: We also take a log of the likelihood because we are working with probabilities and summing them avoids the overflow issues. Now we substitute our piecewise constant model And once we do that, we think of the likelihood as a function of the parameter vector because we want to maximize it later on. We get the following expression for the log-likelihood by substituting values of p_i and also the above expression Now comes the main part of maximizing log-likelihood by differentiating it with respect to \beta. For ease, we will partially differentiate it with respect to \beta_j. That is, we want to compute the following partial derivative, and we will do that separately for both the “first term” and the “second term” in the log likelihood expression. The partial derivative of the first term: x_i must belong to R_j; only then, we will get the terms associated with \beta_j, whose partial derivative with respect to \beta_j will be 1. Thus, we will be summing over y_i for all those values of i such that x_i belongs to R_j. This is represented by the set I_j. This completes our partial derivative of the first term. Before we move on to the partial derivative of the second term, we consider the following We use the aforementioned concepts and formulae to derive the partial derivative of the second term and we get the following: Of course, the “non \beta_j” terms get omitted, even if they are counted over the summand from i=1 to n, while partially differentiating with respect to \beta_j. The lines around I_j indicate the cardinality of the set I_j, i.e., the number of values in I_j. When we combine the first term and the second term differentials and set it to zero, we replace \beta_j with \hat{\beta_j} because that is the estimate of \beta_j when we maximize the likelihood function. Thus, Solving for \beta_j we get. which are the log-odds for the j-th region R_j Consider k = 1, i.e., R_1 = {x_1, x_2, …., x_n} which are the “Overall average” log-odds. This gives us the value of “weight of evidence” as WoE is the difference between the log-odds for the j-th region R_j and the “overall average” log-odds. Also, note that instead of using the dummy variable approach, we replace the variable x with is WoE values. Note: Since there are no restrictions placed on the parameters \beta_j, the regions R_j can have a non-monotonic relationship with respect to the outcome. Target encoding, also known as mean encoding or likelihood encoding, is a technique used to convert categorical variables into numerical values based on the target variable in supervised learning tasks. This method is particularly useful in dealing with high cardinality categorical variables (i.e., variables with a large number of unique categories). For credit risk models, this approach is also applied to continuous variables and is popularly known as “Weight of Evidence” (in the context of binary classification problems). We will derive the above formula, mathematically, for WoE to see where it comes from in the first part of this story. In the second part, we will explore the coding part of it. The idea is to fit a “piecewise constant” model to the outcome binary variable. This is done by partitioning the variable space into non-overlapping regions such that there is a constant predicted value in each region. As shown in the figure above, the input space is partitioned into seven non-overlapping regions and the output is a piecewise constant for each region. This is expressed mathematically as follows: We have a single variable x whose value x_i can belong to a region R_j and we associate a parameter \beta_j with the region R_j. If we have k regions, we get a \beta vector with length k. The piecewise constants will be the estimated values of the parameters \beta_j. Note that the function I is an indicator function which is 1 when x_i belongs to R_j and 0 otherwise. Before we move further, intuition tells us that if we are fitting a constant value in a region, it should be the “average value” of the outcome in that region. Turns out, that is what we are supposed to get with the following model: The probability of outcome y_i =1 is given by p_i and is modeled as a function of piecewise constants passed through a logistic or sigmoid function. Note that decision trees work on a similar concept of partitioning of the variable space (they use binary partitions only though). Also note that Each x_i can be expanded to a vector of dummy variables, i.e., we can convert the input x to k dummy variables: However, we will avoid dealing with vectors and keep the x_i scalar, and use the indicator function to turn on \beta_j if x_i belongs to R_j. Although we don’t really need the summand before \beta_j we will keep it to formulate the change of j with the region R_j when x_i will fall under R_j. In general, the above equation for p_i can also be expressed as a function of any x. Before we move further to derive the WoE values, it is interesting to note that there is no “intercept” term in the above model. Whilst, we could’ve added an intercept term in the above model, turns out that its value will not be defined. The reason is similar to the problem of adding n-values of dummy variables instead of (n-1) values in a regression model, because then intercept can be expressed completely as a sum of all the n-dummy variables, therefore, it is “redundant”. Similarly, here the intercept term is “redundant”. However, it will appear later in the computation of WoE. We will start by defining the likelihood. Note that y, x, and \beta are vectors and the Likelihood is the joint pmf of y_1, y_2, .. y_n Now, since we know that If y_i = 1 then P(y_i) = p_i and if y_i = 0 then P(y_i) = 1-p_i, we use it to redefine L Note: the clever use of the indicator functions which will turn on the specific probability for each y_i. However, we can express this better by using the values y_i themselves. We can use the above substitution to make our likelihood expression unwieldy: We also take a log of the likelihood because we are working with probabilities and summing them avoids the overflow issues. Now we substitute our piecewise constant model And once we do that, we think of the likelihood as a function of the parameter vector because we want to maximize it later on. We get the following expression for the log-likelihood by substituting values of p_i and also the above expression Now comes the main part of maximizing log-likelihood by differentiating it with respect to \beta. For ease, we will partially differentiate it with respect to \beta_j. That is, we want to compute the following partial derivative, and we will do that separately for both the “first term” and the “second term” in the log likelihood expression. The partial derivative of the first term: x_i must belong to R_j; only then, we will get the terms associated with \beta_j, whose partial derivative with respect to \beta_j will be 1. Thus, we will be summing over y_i for all those values of i such that x_i belongs to R_j. This is represented by the set I_j. This completes our partial derivative of the first term. Before we move on to the partial derivative of the second term, we consider the following We use the aforementioned concepts and formulae to derive the partial derivative of the second term and we get the following: Of course, the “non \beta_j” terms get omitted, even if they are counted over the summand from i=1 to n, while partially differentiating with respect to \beta_j. The lines around I_j indicate the cardinality of the set I_j, i.e., the number of values in I_j. When we combine the first term and the second term differentials and set it to zero, we replace \beta_j with \hat{\beta_j} because that is the estimate of \beta_j when we maximize the likelihood function. Thus, Solving for \beta_j we get. which are the log-odds for the j-th region R_j Consider k = 1, i.e., R_1 = {x_1, x_2, …., x_n} which are the “Overall average” log-odds. This gives us the value of “weight of evidence” as WoE is the difference between the log-odds for the j-th region R_j and the “overall average” log-odds. Also, note that instead of using the dummy variable approach, we replace the variable x with is WoE values. Note: Since there are no restrictions placed on the parameters \beta_j, the regions R_j can have a non-monotonic relationship with respect to the outcome. Note: Since there are no restrictions placed on the parameters \beta_j, the regions R_j can have a non-monotonic relationship with respect to the outcome.

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