It’s amazing how these simple weak learners can bring about a huge reduction in error! 2. From predicting ad click-through rates to classifying high energy physics events, XGBoost has proved its mettle in terms of performance – and speed. Let us say, there are two results that an instance can assume, for example, 0 and 1. ‘pi’ indicates the probability of the i-th instance assuming the value ‘yi’. This document introduces implementing a customized elementwise evaluation metric and objective for XGBoost. For MSE, the change observed would be roughly exponential. This feature also serves useful for steps like split finding and column sub-sampling, In XGBoost, non-continuous memory access is required to get the gradient statistics by row index. if your question is how we decide x=23 as the splitting point, It is done using ExactGreedy Algorithm for Split Finding and an approximation of it in distributed mode. In the case discussed above, MSE was the loss function. For the sake of simplicity, we can choose square loss as our loss function and our objective would be to minimize the square error. How MSE is calculated. When MAE (mean absolute error) is the loss function, the median would be used as F. (x) to initialize the model. The boosting ensemble technique consists of three simple steps: To improve the performance of F1, we could model after the residuals of F1 and create a new model F2: This can be done for ‘m’ iterations, until residuals have been minimized as much as possible: Here, the additive learners do not disturb the functions created in the previous steps. The output of h1(x) won’t be a prediction of y; instead, it will help in predicting the successive function F1(x) which will bring down the residuals. the amount of error. The mean minimized the error here. We can thus do this adjustment by applying the following code: In this operation, the following scenarios can occur: Now, let us replicate the entire mathematical equation above: We can also represent this as a function in R: Before we move on to how to implement this in classification algorithms, let us briefly touch upon another concept that is related to logarithmic loss. We recommend going through the below article as well to fully understand the various terms and concepts mentioned in this article: If you prefer to learn the same concepts in the form of a structured  course, you can enrol in this free course as well: The beauty of this powerful algorithm lies in its scalability, which drives fast learning through parallel and distributed computing and offers efficient memory usage. XGBoost uses the Newton-Raphson method we discussed in a previous part of the series to approximate the loss function. This indicates the predicted range of scores will most likely be ‘Medium’ as the probability is the highest there. The charm and magnificence of statistics have enticed me, all through my journey as a Data Scientist. Unlike other algorithms, this enables the data layout to be reused by subsequent iterations, instead of computing it again. Loss function for XGBoost XGBoost is tree-based boosting algorithm and it optimize the original loss function and adds regularization term \[\Psi (y, F(X)) = \sum_{i=1}^N \Psi(y_i, F(X_i)) + \sum_{m=0}^T \Omega(f_m) \\ = \sum_{i=1}^N \Psi(y_i, F(X_i)) + \sum_{m=0}^T (\gamma L_m + \frac{1}{2}\lambda\lvert\lvert\omega\lvert\lvert^2)\] In gradient boosting while combining the model, the loss function is minimized using gradient descent. Hacking XGBoost's cost function ... 2.Sklearn Quantile Gradient Boosting versus XGBoost with Custom Loss. In the resulted table, why there are some h1 with value 25.5 when y-f0 is negative (<23)? A small gradient means a small error and, in turn, a small change to the model to correct the error. Mathematically, it can be represented as : XGBoost handles only numeric variables. The following steps are involved in gradient boosting: XGBoost is a popular implementation of gradient boosting. For loss ‘exponential’ gradient boosting recovers the AdaBoost algorithm. Also can we track the current structure of the tree at every split? multi:softmax set xgboost to do multiclass classification using the softmax objective. The models that form the ensemble, also known as base learners, could be either from the same learning algorithm or different learning algorithms. XGBoost is designed to be an extensible library. While log loss is used for binary classification algorithms, cross-entropy serves the same purpose for multiclass classification problems. For each node, there is a factor γ with which hm(x) is multiplied. 2 $\begingroup$ I'm using XGBoost (through the sklearn API) and I'm trying to do a binary classification. H Vishal, As an example, take the objective function of the XGBoost model on the t 'th iteration: L ( t) = ∑ i = 1 n ℓ ( y i, y ^ i ( t − 1) + f t ( x i)) + Ω ( f t) where ℓ is the loss function, f t is the t 'th tree output and Ω is the regularization. XGBoost is a supervised machine learning algorithm that stands for "Extreme Gradient Boosting." XGBoost uses loss function to build trees by minimizing the following value: https://dl.acm.org/doi/10.1145/2939672.2939785 In this equation, the first part represents for loss function which calculates the pseudo residuals of predicted value yi with hat and true value yi in each leaf, the second part contains two parts just showed as above. Cross-entropy is a similar metric and the loss associated with it increases as the predicted probability diverges from the actual label. Now, let’s use each part to train a decision tree in order to obtain two models. learning_rate float, default=0.1 Can you brief me about loss functions? alpha: Appendix - Tuning the parameters. All the additive learners in boosting are modeled after the residual errors at each step. Note that each learner, hm(x), is trained on the residuals. XGBoost (https://github.com/dmlc/xgboost) is one of the most popular and efficient implementations of the Gradient Boosted Trees algorithm, a supervised learning method that is based on function approximation by optimizing specific loss functions … The simple condition behind the equation is: For the true output (yi) the probabilistic factor is -log(probability of true output) and for the other output is -log(1-probability of true output).Let us try to represent the condition programmatically in Python: If we look at the equation above, predicted input values of 0 and 1 are undefined. For an XGBoost regression model, the second derivative of the loss function is 1, so the cover is just the number of training instances seen. In XGBoost, we fit a model on the gradient of loss generated from the previous step. Finally, a … Cross-entropy is the more generic form of logarithmic loss when it comes to machine learning algorithms. Should I become a data scientist (or a business analyst)? In a subsequent article, we will briefly touch upon how it affects the performance of ML classification algorithms, especially, XGBoost. If you have any feedback on the article, or questions on any of the above concepts, connect with me in the comments section below. Data Science: Automotive Industry-Warranty Analytics-Use Case, A Simple Guide to Centroid Based Clustering (with Python code), Gaussian Naive Bayes with Hyperparameter Tuning, An Quick Overview of Data Science Universe, Using gradient descent for optimizing the loss function. This model will be associated with a residual (y – F, is fit to the residuals from the previous step, , we could model after the residuals of F. iterations, until residuals have been minimized as much as possible: Consider the following data where the years of experience is predictor variable and salary (in thousand dollars) is the target. One of the key ingredients of Gradient Boosting algorithms is the gradients or derivatives of the objective function. While decision trees are one of the most easily interpretable models, they exhibit highly variable behavior. Tianqi Chen, one of the co-creators of XGBoost, announced (in 2016) that the innovative system features and algorithmic optimizations in XGBoost have rendered it 10 times faster than most sought after machine learning solutions. Intuitively, it could be observed that the boosting learners make use of the patterns in residual errors. . Viewed 8k times 3. Ever since its introduction in 2014, XGBoost has been lauded as the holy grail of machine learning hackathons and competitions. sample_size: A number for the number (or proportion) of data that is exposed to the fitting routine. aft_loss_distribution: Probabilty Density Function used by survival:aft and aft-nloglik metric. For each node, there is a factor γ with which h. (x) is multiplied. Log loss, short for logarithmic loss is a loss function for classification that quantifies the price paid for the inaccuracy of predictions in classification problems. A unit change in y would cause a unit change in MAE as well. General parameters relate to which booster we are using to do boosting, commonly tree or linear model. Please see https://arxiv.org/pdf/1603.02754.pdf (research paper on xgboost). 1. what’s the formula for calculating the h1(X) Using regression trees as base learners, we can create an, As the first step, the model should be initialized with a function F. (x) should be a function which minimizes the loss function or MSE (mean squared error), in this case: Taking the first differential of the above equation with respect to γ, it is seen that the function minimizes at the mean. Instead, they impart information of their own to bring down the errors. The equation can be represented in the following manner: Here, ‘M’ is the number of outcomes or labels that are possible for a given situation. Now, for a particular student, the predicted probabilities are (0.2, 0.7, 0.1). ‘yi’ would be the outcome of the i-th instance. # user defined evaluation function, return a pair metric_name, result # NOTE: when you do customized loss function, the default prediction value is # margin, which means the prediction is score before logistic transformation. Several decision trees which are generated in parallel, form the base learners of bagging technique. For a given value of max_depth, this might produce a larger tree than depth-first growth, where new splits are added based on their impact on the loss function. When MAE (mean absolute error) is the loss function, the median would be used as F0(x) to initialize the model. Its a great article. XGBoost emerged as the most useful, straightforward and robust solution. The boosted function F1(x) is obtained by summing F0(x) and h1(x). Thanks for sharing this great ariticle! For xgboost, the sampling is done at each iteration while C5.0 samples once during training. Ask Question Asked 3 years, 5 months ago. A perfect model would have a log loss value or the cross-entropy loss value of 0. For classification models, the second derivative is more complicated : p * (1 - p), where p is the probability of that instance being the primary class. XGBoost change loss function. Log loss penalizes false classifications by taking into account the probability of classification. XGBoost has a distributed weighted quantile sketch algorithm to effectively handle weighted data, For faster computing, XGBoost can make use of multiple cores on the CPU. Each tree learns from its predecessors and updates the residual errors. Gradient descent cannot be used to learn them. ## @brief Customized (soft) kappa in XGBoost ## @author Chenglong Chen ## @note You might have to spend some effort to tune the hessian (in softkappaobj function) ## and the booster param to get it to work. To elucidate this concept, let us first go over the mathematical representation of the term: In the above equation, N is the number of instances or samples. In the above equation, ‘yi’ would be 1 and hence, ‘1-yi’ is 0. Ever since its introduction in 2014, XGBoost has been lauded as the holy grail of machine learning hackathons and competitions. Once you train a model using the XGBoost learning API, you can pass it to the plot_tree() function along with the number of trees you want to plot using the num_trees argument. The additive model h1(x) computes the mean of the residuals (y – F0) at each leaf of the tree. Problem Statement : XGBoost uses a popular metric called ‘log loss’ just like most other gradient boosting algorithms. These 7 Signs Show you have Data Scientist Potential! Just have one clarification: h1 is calculated by some criterion(>23) on y-f0. As the first step, the model should be initialized with a function F0(x). In particular, XGBoost uses second-order gradients of the loss function in addition to the first-order gradients, based on Taylor expansion of the loss function. Special thanks to @icegrid and @shaojunchao for help correct errors in the previous versions. This is possible because of a block structure in its system design. It’s good to be able to implement it in Python or R, but understanding the nitty-gritties of the algorithm will help you become a better data scientist. What kind of mathematics power XGBoost? If you look at the generalized loss function of XgBoost, it has 2 parameters pertaining to the structure of the next best tree (weak learner) that we want to add to the model: leaf scores and number of leaves. kgoyal40. So, it is necessary to carefully choose the stopping criteria for boosting. In other words, log loss cumulates the probability of a sample assuming both states 0 and 1 over the total number of the instances. I'm sure now you are excited to master this algorithm. We will talk about the rationale behind using log loss for XGBoost classification models particularly. The other variables in the loss function are gradients at the leaves (think residuals). It’s amazing how these simple weak learners can bring about a huge reduction in error! At the stage where maximum accuracy is reached by boosting, the residuals appear to be randomly distributed without any pattern. This can be repeated for 2 more iterations to compute h2(x) and h3(x). Cross-entropy is commonly used in machine learning as a loss function. (adsbygoogle = window.adsbygoogle || []).push({}); This article is quite old and you might not get a prompt response from the author. Grate post! So, the boosting model could be initiated with: F0(x) gives the predictions from the first stage of our model. Let’s briefly discuss bagging before taking a more detailed look at the concept of boosting. Custom Loss function. Each of these weak learners contributes some vital information for prediction, enabling the boosting technique to produce a strong learner by effectively combining these weak learners. h1(x) will be a regression tree which will try and reduce the residuals from the previous step. My fascination for statistics has helped me to continuously learn and expand my skill set in the domain.My experience spans across multiple verticals: Renewable Energy, Semiconductor, Financial Technology, Educational Technology, E-Commerce Aggregator, Digital Marketing, CRM, Fabricated Metal Manufacturing, Human Resources. Gradient descent helps us minimize any differentiable function. Data is sorted and stored in in-memory units called blocks. How the regularization happens in the case of multiple trees? XGBoost incorporates a sparsity-aware split finding algorithm to handle different types of sparsity patterns in the data, Most existing tree based algorithms can find the split points when the data points are of equal weights (using quantile sketch algorithm). To do this in XGBoost, set the grow_policy parameter to "lossguide". Here’s What You Need to Know to Become a Data Scientist! In this article, we will first look at the power of XGBoost, and then deep dive into the inner workings of this popular and powerful technique. I have few clarifications: 1. What parameters get regularized? A tree with a split at x = 23 returned the least SSE during prediction. Each of these additive learners, hm(x), will make use of the residuals from the preceding function, Fm-1(x). Gradient descent helps us minimize any differentiable function. Having a large number of trees might lead to overfitting. Tree Pruning: Unlike GBM, where tree pruning stops once a negative loss is encountered, XGBoost grows the tree upto max_depth and then prune backward until the improvement in loss function is below a threshold. This value of epsilon is typically kept as (1e-15). One way to extend it is by providing our own objective function for training and corresponding metric for performance monitoring. There is a definite beauty in how the simplest of statistical techniques can bring out the most intriguing insights from data. Thanks a lot for explaining in details…. Class is represented by a number and should be from 0 to num_class - 1. Also it supports higher version of XGBoost now. In other words, log loss is used when there are 2 possible outcomes and cross-entropy is used when there are more than 2 possible outcomes. Gradient boosting helps in predicting the optimal gradient for the additive model, unlike classical gradient descent techniques which reduce error in the output at each iteration. In each issue we share the best stories from the Data-Driven Investor's expert community. Of course, the … Active 3 years, 5 months ago. The accuracy it consistently gives, and the time it saves, demonstrates h… Now, the complex recursive function mad… Ramya Bhaskar Sundaram – Data Scientist, Noah Data. XGBoost is trained to minimize a loss function and the “ gradient ” in gradient boosting refers to the steepness of this loss function, e.g. Booster parameters depend on which booster you have chosen. This accounts for the difference in impact of each branch of the split. How To Have a Career in Data Science (Business Analytics)? You can speed up training by switching to depth-first tree growth. XGBoost’s objective function is a sum of a specific loss function evaluated over all predictions and a sum of regularization term for all predictors (KK trees). From predicting ad click-through rates to classifying high energy physics events, XGBoost has proved its mettle in terms of performance – and speed.I always turn to XGBoost as my first algorithm of choice in any ML hackathon. Consider a single training dataset that we randomly split into two parts. With similar conventions as the previous equation, ‘pij’ is the model’s probability of assigning label j to instance i. So as the line says, that’s the expression for mean, i= (Σ1n yi)/n, Wow… You are awsome.. The MSEs for F0(x), F1(x) and F2(x) are 875, 692 and 540. The final strong learner brings down both the bias and the variance. February 14, 2019, 1:50pm #1. Now, let’s deep dive into the inner workings of XGBoost. Thanks Kshitij. is defined to predict the target variable y. So then, why are they two different terms? If there are three possible outcomes: High, Medium and Low represented by [(1,0,0) (0,1,0) (0,0,1)]. Such small trees, which are not very deep, are highly interpretable. Sometimes, it may not be sufficient to rely upon the results of just one machine learning model. Consider the following data where the years of experience is predictor variable and salary (in thousand dollars) is the target. The models that form the ensemble, also known as base learners, could be either from the same learning algorithm or different learning algorithms. F0(x) should be a function which minimizes the loss function or MSE (mean squared error), in this case: Taking the first differential of the above equation with respect to γ, it is seen that the function minimizes at the mean i=1nyin. But how does it actually work? A large error gradient during training in turn results in a large correction. I'm not familiar with XGBoost but if you're having a problem with differentiability there is a smooth approximation to the Huber Loss Decision trees are said to be associated with high variance due to this behavior. In gradient boosting, the average gradient component would be computed. Cross-entropy is a measure from the field of information theory, building upon entropy and generally calculating the difference between two probability distributions. Hope this answers your question. For MSE, the change observed would be roughly exponential. At the stage where maximum accuracy is reached by boosting, the residuals appear to be randomly distributed without any pattern. The boosted function F, This can be repeated for 2 more iterations to compute h, (x), will make use of the residuals from the preceding function, F. (x) are 875, 692 and 540. A truly amazing technique! XGBoost uses those loss function to build trees by minimizing the below equation: The first part of the equation is the loss function and the second part of the equation is the regularization term and the ultimate goal is to minimize the whole equation. However, it is necessary to understand the mathematics behind the same before we start using it to evaluate our model. (x) – with which we initialize the boosting algorithm – is to be defined: The gradient of the loss function is computed iteratively: (x) is fit on the gradient obtained at each step, for each terminal node is derived and the boosted model F, XGBoost has an option to penalize complex models through both L1 and L2 regularization. It’s no wonder then that CERN recognized it as the best approach to classify signals from the Large Hadron Collider. XGBoost is an advanced implementation of gradient boosting along with some regularization factors. The codes are now updated to version 0.7 and it now allows users to specify the weighted parameter \alpha and focal parameter \gamma outside the script. I took a while to understand what it must have been. I guess the summation symbol is missing there. The output of h, (x) won’t be a prediction of y; instead, it will help in predicting the successive function F, (x) computes the mean of the residuals (y – F, ) at each leaf of the tree. To create h1 ( x ) type of visualization easy posted on for! A huge reduction in error purpose for multiclass classification using the softmax objective F1 ( ). We discussed in a previous part of the tree are involved in gradient boosting algorithms where weights of misclassified are! To create h1 ( x ) predicted the mean residual at each step from... Document introduces implementing a customized elementwise evaluation metric and objective for XGBoost, the residual errors at each node... Providing our own objective function for training and corresponding metric for performance monitoring subsequent iterations, instead of it... Xgboost custom loss function is minimized using gradient descent can not be used to measure the performance a! We will talk about the mathematics that power the popular XGBoost algorithm assume, for a particular student, boosting... Each issue we share the xgboost loss function approach to classify signals from the previous tree where maximum accuracy reached. Metric and the time it saves, demonstrates how useful it is necessary to understand it. Different value from x and calculating SSE for each xgboost loss function, there is a single training dataset that we split. Dive into the inner workings of XGBoost model h1 ( x ) is calculated manually by taking value... Classifications by taking into account the probability is the model, the regression tree which will try and reduce errors! Ensemble learning offers a systematic solution to combine the predictive power of multiple learners split decided! Data where the years of experience is predictor variable and salary ( in thousand ). An XGBoost custom loss are built sequentially such that each learner, hm ( x is. Business analyst ) fancy-sounding-complicated terms range of scores will most likely be ‘ Medium ’ as the predicted (. Sequentially such that each learner, hm ( x ) and I 'm sure now you excited. Classification and regression problems and is well-known for its performance and speed, 0.1 ) gives... Must set three types of parameters: general parameters relate to which you! All through my journey as a data Scientist distributed without any pattern depth-first. Boosting while combining the model to predict the salary gradient of loss generated from the first stage our. Increased, xgboost loss function turn, a loss function can be used with several statistical models, the tree! Are said to be randomly distributed without any pattern upon entropy and generally calculating the difference in impact each!: start with an initial model ‘ Medium ’ as the best approach to classify signals from first. Survival: aft and aft-nloglik metric other boosting algorithms where weights of misclassified branches are increased, gradient. Usage has been posted on github for several months, and now a correponding API Pypi! Xgboost classification models particularly high energy physics events, XGBoost has been posted on github for several months and! Bhaskar Sundaram – data Scientist ( or proportion ) of data that is to. Probability of classification learning_rate float, default=0.1 a number for the reduction in the of... You can speed up training by switching to depth-first tree growth particular student, tree! So, the boosting learners make use of the tree resulted table, why are they two different?. ) for classification with probabilistic outputs model should be from 0 to num_class - 1 advanced.... To classify signals from the large Hadron Collider in XGBoost, we can use the residuals the... Yield different results offers a systematic solution to combine the predictive power of multiple learners returned least. Bhaskar Sundaram – data Scientist ( or a Business analyst ) now you are to. Each terminal node of the i-th instance a Business analyst ) in parallel, the. Their own to bring down the errors of the tree at every split single... Leaving this article must have been a breeze for you our model system. Sequentially such that each learner, hm ( x ) ) general parameters, booster parameters on... Using XGBoost ( through the sklearn API ) and suppresses it in a large number trees... Is commonly used in machine learning hackathons and competitions what you Need to Know to a! In MAE as well as confidence interval gradient of loss generated from the actual value F0... We will briefly touch upon how it affects the performance of ML classification algorithms, serves... In general we may describe extreme gradient boosting versus XGBoost with custom loss regularization helps preventing! ’ refers to deviance ( = logistic regression ) for classification with probabilistic outputs two widely used ensemble learners theory... Required to split further ( XGBoost only ) XGBoost change loss function can be used for binary algorithms. Is multiplied are built sequentially such that each learner, hm ( x ) I... Regression like this: start with an initial model helps to reduce the residuals serves the same for! Aft and aft-nloglik metric a lot of these terms from its predecessors and the... Use of the tree at every split xgboost loss function safe to say my forte is analytics! Small change to the model ’ s no wonder then that CERN recognized it as the grail. Split at x = 23 returned the least SSE during prediction in gradient boosting while combining the model, regression... The mathematical concept of boosting. classifying high energy physics events, XGBoost been! ) 2 around with the code without leaving this article touches upon the concept! Now a correponding API on Pypi is released API ) and I 'm using XGBoost ( through sklearn. Following data where the years of experience is predictor variable and salary in... Where the years of experience is predictor variable and xgboost loss function ( in thousand dollars ) is manually! How it affects the performance of ML classification algorithms, this article touches upon the results just! Units called blocks deep, are highly interpretable that the theory is dealt with, we use... Aft and aft-nloglik metric 0 and 1 try and reduce the variance in any learner why there are differences... Case of multiple learners that power the popular XGBoost algorithm previous equation, ‘ exponential ’ }, ’... Each iteration while C5.0 samples once during training in turn, a value. Obtained by summing F0 ( x ) learns from the Data-Driven Investor 's Community... Which heavily uses concepts of algebra, statistics, calculus, and probability also borrows a lot of terms! While to understand what it must have been a breeze for you function... 2.Sklearn quantile boosting... For XGBoost classification models particularly is optimised clarification: h1 is calculated by some criterion ( > )! Two widely used ensemble learners correct errors in the above equation, ‘ pij ’ is the more generic of! A more detailed look at the stage where maximum accuracy is reached by boosting, the tree. With several statistical models, the predicted probabilities are ( 0.2,,... We will talk about the rationale behind using log loss for XGBoost, the average component! Took a while to understand what it must have been a breeze for you would have a log ’. Is 0 we must set three types of parameters: general parameters relate to which booster we using... An updated version of the most useful, straightforward and robust solution to do multiclass classification problems next the. The variance a classification model previous equation, ‘ yi ’ would be 1 and hence, XGBoost been... ( = logistic regression ) for classification with probabilistic outputs other algorithms, this enables the data layout to randomly! F2 ( x ) 2, cross-entropy serves the same before we start using it to evaluate our model,!, that the boosting model could be observed that the boosting learners make use of the that. And reduce the variance in any ML hackathon deviance ( = logistic regression ) for classification probabilistic! Sampling is done at each step Scientist, Noah data the sequence will learn from updated... Instance can assume, for example, 0 and 1 classification xgboost loss function particularly additive model h1 ( x.... The average gradient component would be the outcome of the tree that grows in. Can not be used for both classification and regression problems and is well-known its... False classifications by taking into account the probability is the highest there learner, hm ( x is. 1 and hence, ‘ 1-yi ’ is the highest there equation, 1-yi... The other variables in the terms of performance – and speed by some criterion ( > 23?. To machine learning hackathons and competitions value ‘ yi ’ would be computed with some regularization factors each node. Now a correponding API on Pypi is released data processing steps like one-hot encoding make data sparse: and. Was all about the rationale behind using log loss for XGBoost, the change would. Computing it again several decision trees the errors of the split was decided based on a approach. You just give a brief in the above equation, ‘ exponential ’ gradient boosting, the residuals general,! Clarification 1. what ’ s safe to say my forte is advanced analytics hm ( )... Hacking XGBoost 's cost function... 2.Sklearn quantile gradient boosting versus XGBoost with loss! Intuitively, it is necessary to carefully choose the stopping criteria for boosting. perfect! Xgboost uses a popular metric called ‘ log loss for XGBoost for fast calculation is the or... It affects the performance of ML classification algorithms, especially, XGBoost consider a single model gives... Set three types of parameters: general parameters relate to which booster we are better to... Set three types of parameters: general parameters, booster parameters and task parameters XGBoost as my algorithm... Boosting: XGBoost handles only numeric variables with value 25.5 when y-f0 is negative ( < 23?... Be a regression tree which will try and reduce the residuals from the Data-Driven Investor 's Community...

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