Cross-game user ltv curve prediction method based on dynamic quantile correction mechanism

Abstract

The application provides a cross-game user LTV curve prediction method based on a dynamic quantile correction mechanism, comprising: (1) basic training data acquisition and feature engineering processing; (2) quantile random forest basic model set training; (3) target game short-term alignment data acquisition and feature adaptation processing; (4) optimal quantile parameter dynamic calculation; (5) new user long-term life cycle value prediction; (6) long-term life cycle value recovery curve fitting. The core idea of the application is: the traditional point prediction model is transformed into a quantile prediction model, and a dynamic optimization quantile parameter calculation module is introduced, which uses the short-term data (such as 60 / 90 days) of the target game (or new game) that is easy to obtain to calculate a set of optimal quantile parameters, which are used to correct the prediction output of the basic model for the long-term target (such as 180 days), so as to adapt to data drift and cross-game differences.

Description

Technical Field

[0001] This invention relates to the field of game data analysis and machine learning application technology, and in particular to a method for predicting cross-game user LTV curves based on a dynamic quantile correction mechanism. Background Technology

[0002] In the gaming industry, accurately predicting a user's long-term lifetime value (LTV) is crucial for optimizing user acquisition strategies, assessing user value, and making game operation decisions. Currently, mainstream LTV prediction solutions typically employ point prediction models based on machine learning, such as Random Forest or gradient boosting decision trees (e.g., XGBoost). The basic principles and processes of these solutions are as follows:

[0003] Data preparation: Before collecting data from target game users Day (usually) =3, 7, 14, 30, etc.) Key behavioral characteristics in the game (such as login days, game time, ad exposure / click data, in-app purchase revenue, level progress, etc.) and the true value of the user's cumulative revenue (i.e., LTV) over the complete life cycle (e.g., 180 days).

[0004] Feature engineering involves cleaning and removing missing and outlier values ​​from raw data, and may also involve feature transformations (such as standardization and normalization), feature combinations, or the derivation of new features (such as growth rate or magnitude of change indicators).

[0005] Model Training: Using the features described above as input and the target LTV value (e.g., cumulative revenue over 180 days) as output, train a point prediction model (e.g., Random Forest, XGBoost) on a complete lifecycle dataset of a single game. The goal of the model is to minimize the error (e.g., mean squared error, MSE) between the predicted value and the true LTV value.

[0006] Predictive Application: For new users, before using it The behavioral characteristics of a day are input into the trained model, and a point prediction value is directly output as an estimate of its future long-term LTV.

[0007] Problems, root causes, and consequences of existing technologies

[0008] While the aforementioned point prediction model may perform reasonably well under specific games and stable data distributions, it faces significant challenges in real-world cross-game, long-term prediction scenarios:

[0009] Long-term prediction drift (Distribution Shift Over Time):

[0010] Problem Description: Over time, the user composition of game user acquisition channels may change, and the game's operational strategies (such as events, version updates, and economic system adjustments) may also continuously iterate. These factors lead to significant differences between the historical data used to train the model (data distribution at time T0) and the new user data to be predicted (data distribution at time T1), i.e., data distribution drift. This causes the error of the model trained based on the T0 distribution to significantly increase as the prediction time window lengthens when making long-term predictions at time T1.

[0011] Root cause of the defect:

[0012] The model is trained by implicitly assuming that the data distribution is static or stable.

[0013] Point prediction models lack effective modeling of prediction uncertainty and adaptation mechanisms to distribution changes.

[0014] The model parameters are fixed and cannot be adjusted online based on newly observed short-term data.

[0015] Consequences: Actual long-term forecast errors (such as forecasting 180-day LTV) are usually >20% or even higher, which seriously affects the reliability of forecasts, leading to distorted ROI estimation of user acquisition and operational decision-making errors.

[0016] Lack of Cross-Game Adaptability:

[0017] Problem Description: Different games differ significantly in core gameplay, user groups, payment models, economic systems, and advertising strategies. A point prediction model trained on one game (Game A) typically shows a sharp decline in performance when directly applied to users of another game (Game B) for Lifetime Value (LTV) prediction.

[0018] Root cause of the defect:

[0019] There are fundamental differences in the distribution of user behavior features (P(X)) and the feature-LTV mapping relationship (P(Y|X)) among different games.

[0020] The model itself does not have the ability to learn and adapt to the unique "return curve patterns" of different games. That is, the model cannot perceive and adjust to adapt to the LTV accumulation pattern unique to Game B (such as rapid decay type vs. long-tail stable type).

[0021] Consequences: After the new game (Game B) is launched, directly applying the old model (Game A) will result in a sharp increase in prediction errors, usually in the range of 40%-60%, making the model almost ineffective and unable to provide meaningful guidance.

[0022] Cold-Start Problem for New Games

[0023] Problem Description: For newly launched games (New Game C), complete long-term lifecycle data (e.g., 180 days) is lacking. Existing point-of-use (LTV) prediction models heavily rely on this complete lifecycle data for training. Therefore, it is impossible to build an effective LTV prediction model in the early stages of a new game.

[0024] Root cause of the defect:

[0025] The model training paradigm requires complete "input feature - output truth value" pairing data.

[0026] There is no mechanism that can effectively predict long-term LTV by utilizing short-term data accumulated in the early stages of a new game (such as 30 days or 60 days).

[0027] Consequences: New games need to wait at least one full forecasting period (e.g., 180 days) to accumulate data before deploying predictive models. During this period (which can last for several months), user acquisition and operational decisions lack crucial user value data support, posing a risk of being based on guesswork. Summary of the Invention

[0028] This invention provides a method for predicting the long-term lifetime value (LTV) curve of cross-game users based on a dynamic quantile correction mechanism. The core idea is to transform the traditional point prediction model into a quantile prediction model and introduce a dynamically optimized quantile parameter calculation module. This module uses readily available short-term data (such as 60 / 90 days) from the target game (or new game) to calculate a set of optimal quantile parameters, which are used to correct the prediction output of the base model for the long-term target (such as 180 days), thereby adapting to data drift and cross-game differences.

[0029] To achieve the above objectives, the present invention adopts the following technical solution:

[0030] A method for predicting the long-term lifetime value (LTV) curve of cross-game users based on a dynamic quantile correction mechanism includes:

[0031] (1) Obtain basic training data of at least one mature game. The mature game is a game with complete long-term user lifecycle data. The basic training data includes the behavioral feature data of a large number of users in the mature game for the first n days and the true value of the long-term lifecycle value of the corresponding user for the T days. n is the preset short-term input days and T is the preset long-term prediction days. Perform feature engineering on the basic training data to obtain a standardized feature set.

[0032] (2) Based on the standardized feature set, train multiple independent quantile random forest models to form a basic model set. Each quantile random forest model corresponds to a specific number of input days n and output days T. Each subtree of the quantile random forest model stores the cumulative income target value of the training samples in the leaf nodes. When predicting, summarize the target value set of samples falling into the leaf nodes in all subtrees and output the quantile result of the set.

[0033] (3) Obtain short-term aligned data of the target game to be predicted. The short-term aligned data includes the behavioral feature data of a group of users in the target game for the previous n days and the observed cumulative income true value for M days. M is the preset short-term observation days and M is greater than the critical value of the quantile parameter tending to be stable. Perform the same feature engineering processing as step (1) on the behavioral feature data of the previous n days in the short-term aligned data.

[0034] (4) Based on the basic model set and the processed short-term aligned data, the optimal quantile parameter is calculated for each long-term prediction task by an optimization algorithm. The optimization objective is to minimize the error between the predicted value of the batch of users and the true value of the cumulative income over M days.

[0035] (5) Obtain the original behavioral feature data of the new user in the target game for the first n days. After the same feature engineering process as in step (1), input the quantile random forest model corresponding to the input number of days n and the output number of days T in the basic model set. Combine the optimal quantile parameters obtained in step (4) to output the long-term T-day life cycle value prediction value of the new user.

[0036] (6) The long-term T-day lifecycle value prediction of a batch of new users in the target game is summed at multiple time points to obtain the total predicted cumulative income at each time point, and a smooth long-term lifecycle value recovery curve is fitted based on the total predicted cumulative income.

[0037] In this specification, n in step (1) takes the value of multiple consecutive or intermittent short-term days, and T takes the value of multiple consecutive or intermittent long-term days. Each input number of days n and the output number of days T form a unique correspondence, constituting the basis for independent model training in the basic model set.

[0038] In this specification, the feature engineering process in step (1) includes: filling missing values, handling outliers and removing duplicate data from the original data, standardizing or normalizing numerical features, constructing derived features based on business needs, and screening key features through correlation analysis and feature importance assessment.

[0039] In this manual, when training the quantile random forest model in step (2), the number of trees is set to 80-150, the minimum number of samples for leaf nodes is 0.001, and when constructing each tree, the square root method or logarithmic method is used to randomly select some features to participate in the training.

[0040] In this specification, the value of M days in step (3) is 60 days or 90 days, and the number of users in the short-term aligned data is in the thousands to tens of thousands, to ensure the reliability of the calculation of the optimal quantile parameter.

[0041] In this specification, the optimization algorithm in step (4) is a grid search algorithm, which generates candidate values ​​of quantile parameters with a fixed step size in the (0,1) interval, calculates the prediction error corresponding to each candidate value, and selects the candidate value that minimizes the error as the optimal quantile parameter.

[0042] In this specification, when calculating the optimal quantile parameter in step (4), the law that the quantile parameter tends to stabilize as the number of prediction days increases is utilized. When the target prediction day T is greater than the critical value, the stable quantile parameter calculated from M days of short-term data is directly used as the optimal quantile parameter for the prediction of day T.

[0043] In this specification, the method also includes the step of dynamically updating the optimal quantile parameter: according to a preset time interval or based on triggering conditions, obtain the latest accumulated short-term alignment data of the target game, repeat step (4) to recalculate the optimal quantile parameter, and replace the original parameter with the new parameter; the triggering conditions include significant changes in user feature distribution, prediction error exceeding a preset threshold, or major version update of the game.

[0044] In this specification, when fitting the long-term life cycle value recovery curve in step (6), multiple key time nodes covering the short to long term are selected, and a smooth curve is generated based on the predicted cumulative total income of each node using polynomial fitting or spline interpolation techniques.

[0045] In this manual, when the target game is a newly launched game, the short-term alignment data in step (3) is the M-day user data accumulated after the launch of the new game. After calculating the optimal quantile parameters in step (4), the prediction of the long-term T-day lifecycle value of the new game users is directly combined with the basic model set without waiting for the complete long-term data accumulation.

[0046] In summary, the present invention has at least the following beneficial effects:

[0047] Significantly suppresses long-term prediction drift: In long-term prediction tasks for the same game (Game A / B Day_180 vs Day_60), the long-term prediction error of the method of this invention (Ours) increases very little or even decreases compared to its own short-term prediction error (Game A: 0.031). 0.027, Game B: 0.042 0.043), while Baseline RF (0.046) 0.073, 0.052 0.096) and Baseline QRF (0.037) 0.071, 0.044 The error increase of 0.092 is very significant (>50%). This proves that the dynamic quantile parameter It effectively corrects for the impact of data distribution drift on long-term forecasts.

[0048] Superior cross-game adaptability: In cross-game prediction tasks (Game C / D), Baseline RF / QRF fails directly, with errors as high as 35%-44%. The method of this invention, however, utilizes short-term data from the target game to calculate specific... This reduces the prediction error to a level close to that of the game's predictions (<7%), with an error reduction of over 80%. This proves... It successfully captured and adapted to the unique recycling curve pattern of the target game.

[0049] Effectively solves the cold start problem for new games: For a new game, Game E, with only 60 days of data, the method of this invention successfully predicted its 180-day LTV (Lifetime Value) for users, with an error (0.044) comparable to the prediction error (0.043) of a mature game, Game B, during the same period. This proves that this invention only requires 60 days of data for the target game to initiate relatively accurate long-term predictions.

[0050] Overall accuracy improvement: Even in short-term or game-like predictions, the method of this invention exhibits performance superior to or equal to the baseline, demonstrating the robustness of its underlying design. Attached Figure Description

[0051] Figure 1 This diagram illustrates the architecture of the cross-game user LTV (Long-Term Lifetime Value) curve prediction method based on a dynamic quantile correction mechanism involved in this invention. It shows the core dual-module architecture (basic QRF model set + quantile parameter calculation module) and its interaction (data flow, parameter flow), and marks the prediction execution flow. The concept of "dynamic correction" is highlighted.

[0052] Figure 2 The optimal quantile parameter involved in this invention According to the number of predicted days A schematic diagram illustrating typical patterns of change, clearly showing two typical patterns (decaying and growing), and marking the stable regions. ), emphasizing the use Tian Data ( )Calculation stability Used for prediction sky( The core principle of ).

[0053] Figure 3 This is a schematic diagram illustrating the specific implementation process of the cross-game user LTV (Long-Term Lifetime Value) curve prediction method based on dynamic quantile correction mechanism involved in this invention. It details the complete operation steps and logical flow from data preparation (basic training data, target alignment data, prediction data), feature engineering, basic model training, dynamic parameter calculation to final prediction and curve fitting. Detailed Implementation

[0054] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0055] like Figure 1 As shown, this embodiment provides a method for predicting the LTV (Long-Term Lifetime Value) curve of cross-game users based on a dynamic quantile correction mechanism, including:

[0056] (1) Obtain basic training data of at least one mature game. The mature game is a game with complete long-term user lifecycle data. The basic training data includes the behavioral feature data of a large number of users in the mature game for the first n days and the true value of the long-term lifecycle value of the corresponding user for the T days. n is the preset short-term input days and T is the preset long-term prediction days. Perform feature engineering on the basic training data to obtain a standardized feature set.

[0057] (2) Based on the standardized feature set, train multiple independent quantile random forest models to form a basic model set. Each quantile random forest model corresponds to a specific number of input days n and output days T. Each subtree of the quantile random forest model stores the cumulative income target value of the training samples in the leaf nodes. When predicting, summarize the target value set of samples falling into the leaf nodes in all subtrees and output the quantile result of the set.

[0058] (3) Obtain short-term aligned data of the target game to be predicted. The short-term aligned data includes the behavioral feature data of a group of users in the target game for the previous n days and the observed cumulative income true value for M days. M is the preset short-term observation days and M is greater than the critical value of the quantile parameter tending to be stable. Perform the same feature engineering processing as step (1) on the behavioral feature data of the previous n days in the short-term aligned data.

[0059] (4) Based on the basic model set and the processed short-term aligned data, the optimal quantile parameter is calculated for each long-term prediction task through an optimization algorithm. The optimization objective is to minimize the error between the predicted value of the batch of users and the true value of the cumulative income over M days. The quantile parameter tends to stabilize as the number of prediction days increases. When the target prediction day T is greater than the critical value, the stable quantile parameter calculated from the short-term data over M days is directly used as the optimal quantile parameter for the prediction over T days.

[0060] (5) Obtain the original behavioral feature data of the new user in the target game for the first n days. After the same feature engineering process as in step (1), input the quantile random forest model corresponding to the input number of days n and the output number of days T in the basic model set. Combine the optimal quantile parameters obtained in step (4) to output the long-term T-day life cycle value prediction value of the new user.

[0061] (6) The long-term T-day lifecycle value prediction of a batch of new users in the target game is summed at multiple time points to obtain the total predicted cumulative income at each time point, and a smooth long-term lifecycle value recovery curve is fitted based on the total predicted cumulative income.

[0062] In some embodiments, n in step (1) takes the value of multiple consecutive or intermittent short-term days, and T takes the value of multiple consecutive or intermittent long-term days. Each input number of days n and the output number of days T form a unique correspondence, constituting the basis for independent model training in the basic model set.

[0063] In some embodiments, the feature engineering process in step (1) includes: filling missing values, handling outliers and removing duplicate data from the original data, standardizing or normalizing numerical features, constructing derived features based on business needs, and screening key features through correlation analysis and feature importance assessment.

[0064] In some embodiments, when training the quantile random forest model in step (2), the number of trees is set to 80-150, the minimum number of samples for leaf nodes is 0.001, and when constructing each tree, the square root method or logarithmic method is used to randomly select some features to participate in the training.

[0065] In some embodiments, the value of M days in step (3) is 60 days or 90 days, and the number of users in the short-term aligned data is in the thousands to tens of thousands, ensuring the reliability of the calculation of the optimal quantile parameter.

[0066] In some embodiments, the optimization algorithm in step (4) is a grid search algorithm, which generates candidate values ​​of quantile parameters with a fixed step size in the (0,1) interval, calculates the prediction error corresponding to each candidate value, and selects the candidate value that minimizes the error as the optimal quantile parameter.

[0067] In some embodiments, when calculating the optimal quantile parameter in step (4), the law that the quantile parameter tends to stabilize as the number of prediction days increases is utilized. When the target number of prediction days T is greater than the critical value, the stable quantile parameter calculated from M days of short-term data is directly used as the optimal quantile parameter for the prediction of T days.

[0068] In some embodiments, the method further includes the step of dynamically updating the optimal quantile parameter: at a preset time interval or based on triggering conditions, the latest accumulated short-term alignment data of the target game is obtained, step (4) is repeated to recalculate the optimal quantile parameter, and the original parameter is replaced with the new parameter; the triggering conditions include significant changes in user feature distribution, prediction error exceeding a preset threshold, or a major version update of the game.

[0069] In some embodiments, when fitting the long-term life cycle value recovery curve in step (6), multiple key time nodes covering the short to long term are selected, and a smooth curve is generated by using polynomial fitting or spline interpolation techniques based on the predicted cumulative total income of each node.

[0070] In some embodiments, when the target game is a newly launched game, the short-term alignment data in step (3) is the M-day user data accumulated after the launch of the new game. After calculating the optimal quantile parameter in step (4), the prediction of the long-term T-day lifecycle value of the new game user is directly combined with the basic model set without waiting for the complete long-term data accumulation.

[0071] In some embodiments, based on the base model set and the processed short-term aligned data, the optimal quantile parameter q_M corresponding to the M-day prediction task is calculated by an optimization algorithm; wherein, when the long-term prediction days T are greater than a preset stable threshold, q_M is directly used as the optimal quantile parameter q_T corresponding to the T-day prediction task.

[0072] The technical concept of this invention is as follows:

[0073] This invention aims to address the core shortcomings of existing LTV (Lifetime Value) prediction technologies in the field of game data analysis, particularly in long-term prediction, cross-game applications, and new game scenarios. Specifically, the technical problems to be solved include:

[0074] 1. How to effectively eliminate or significantly reduce the impact of data distribution drift caused by changes in user distribution and game strategy iteration in long-term LTV prediction, and improve the long-term stability of the prediction?

[0075] 2. How can the prediction model be effectively adapted to the unique payback curve patterns of different game products, and significantly improve the prediction accuracy of the model in cross-game application scenarios?

[0076] 3. How to overcome the limitations of cold start and enable new games to start relatively accurate long-term LTV predictions with only relatively short-term data (such as 60-90 days)?

[0077] The following are the essential technical features and core solution details of the present invention:

[0078] Essential technical features:

[0079] Basic model construction: Improved quantile random forest model (Necessary)

[0080] This invention abandons the traditional Random Forest (RF) or XGBoost models that output a single expected value, and instead adopts Quantile Random Forest (QRF) as the basic prediction model.

[0081] Core modification: For the prediction task Predict Day_T using Day_n Features, it is no longer required that each subtree output a point estimate (such as the mean). Instead, each subtree is allowed to store the target value (cumulative income) of the training samples of that node in the leaf node.

[0082] Prediction output mechanism: For the prediction of a new sample, QRF summarizes the set of target values ​​of all subtrees at the leaf nodes where the sample falls. The final predicted output is not the mean or the voting result, but rather the result of this set. quantiles :

[0083] ;

[0084] in, It is a key quantile parameter that determines whether the prediction is conservative. Small) or optimistic ( big).

[0085] Model Training: Using complete datasets (Day_n features + Day_T ground truth values) from one or more games, train multiple independent QRF models, each corresponding to a specific number of input days. and output days (For example, Using a 3-day timeframe, Train multiple [items] in 10-day increments. Models, which constitute a set of basic models.

[0086] Quantile parameter calculation module (Necessary) -- the core of dynamic correction:

[0087] Input: The Day_n feature data of a group of users in the target game (or new game), and the true cumulative revenue values they have observed for Day_M (M < T, e.g., M = 60 or 90 days).

[0088] Optimization objective:

[0089] For each long-term target day to be predicted , and for each corresponding to this group of users basic QRF model, calculate an optimal quantile parameter . The optimization objective is to minimize the Day_T values predicted by this group of users using the Day_n features, parameters and the basic QRF model and their Day_T true values The error between:

[0090] ;

[0091] where is the number of this group of users.

[0092] Key insights and visibility (Why it Works):

[0093] Core findings (as Figure 2 shown): For the trained set of basic QRF models, when fixed and the model is unchanged, the optimal quantile parameter usually shows two regular patterns as the predicted target day changes:

[0094] Pattern 1 (decaying type): The starting value (corresponding to a smaller ) is relatively high. As increases, gradually decreases and tends to be relatively stable after . This pattern is common in games where user value decays rapidly.

[0095] Pattern 2 (growth type): The starting value (corresponding to a smaller ) is relatively low. As increases, gradually increases and tends to be relatively stable after . This pattern is common in games where user value has growth potential or a significant long-tail effect.

[0096] Core conclusion: Regardless of which pattern, when is large enough (exceeding a certain critical value , e.g., (days later) It will tend to a relatively stable value This means that we can utilize readily available short-term truth data from the target game. To accurately calculate the optimal parameters for this stable region (e.g., 60 or 90 days). This is then used to correct predictions for longer timeframes (e.g., 180 days) of Day_T. This stable parameter... Essentially, it captures the unique long-term payback curve shape and data distribution characteristics of the target game.

[0097] Output: For each of the target games The prediction task calculates and outputs the optimal quantile parameters. (In practice for) The parameters can be approximated using Or perform a slight smoothing process, but the calculation... (This is the core idea).

[0098] Predictive execution mechanism (Necessary)

[0099] New user prediction: For a new user from the target game, their previous... Feature data of the day The predicted LTV value for Day_T is:

[0100] ;

[0101] in It is the corresponding model in the basic model set. Quantile random forest model The quantile parameter calculation module is used for the target game and this The optimal parameters calculated by the task.

[0102] Dynamic parameter updates (Optional but Important): To continuously adapt to potential data shifts in the target game (such as adjustments to user acquisition strategies or major version updates), the quantile parameters... It can be recalculated and updated periodically (e.g., weekly, monthly) or based on specific triggering conditions (e.g., significant changes in user distribution) using the latest accumulated user batch data of the target game (including Day_n features and Day_M ground truth).

[0103] Recovery curve fitting

[0104] For a group of new users of the target game, predict the performance of each user. (Can be used for multiple) predict).

[0105] All users according to Summing gives the data for this batch of users on different days. The projected cumulative total income.

[0106] Through these discrete points ( (Predicting total cumulative revenue) can fit a smooth long-term LTV payback curve, which can be used to analyze the value decay pattern of a user group.

[0107] Experimental setup:

[0108] Dataset:

[0109] Game A (Mature Game): Has complete 180 days of data.

[0110] Game B (Mature Game): Possesses complete 180 days of data.

[0111] Game C (New Game A): Only 60 days of data available.

[0112] Game D (New Game B): Only 60 days of data available.

[0113] Game E (Mature Game): Possesses complete 180 days of data.

[0114] Comparison Model:

[0115] Baseline RF: Standard Random Forest point prediction model (training method is the same as the background technique).

[0116] Baseline QRF( =0.5): Fixed A quantile random forest model with a median of 0.5.

[0117] Ours (Proposed): The method proposed in this invention (basic QRF + dynamic computation) ).

[0118] Training / Computation:

[0119] All models (Baseline RF, Baseline QRF, Ours's base model set) are trained using the complete data from Game A.

[0120] Calculate the dynamic quantile parameters of Ours method using the Day_n feature of Game C & Game D + the Day_60 truth value. ( =60,180).

[0121] For Game E (simulating a new game), calculations are performed using data accumulated over its first 60 days. .

[0122] Test tasks and error metrics:

[0123] Long-term prediction for the same game (Game A, Game B): Predict Day 180 LTV.

[0124] Cross-game prediction (Game C, Game D): Predict Day_180 LTV (using a model trained on Game A to predict Game C / D, demonstrating cross-game capability).

[0125] Cold Start Prediction (Game E): Predicts Day_180 LTV (calculated using the base model trained in Game A + Game E's own data from the first 60 days). ).

[0126] Short-term forecast (Game C): Predict Day_60 LTV (as a reference).

[0127] Short-term forecast (Game D): Predict Day_60 LTV (as a reference).

[0128] Evaluation indicators:

[0129] ;

[0130] Experimental Results and Analysis

[0131] Table 1. Comparison of prediction errors of different models in different prediction scenarios

[0132]

[0133] Note: Baseline RF / QRF relies on a complete 180 days of data and cannot be trained or applied on Game E, which only has 60 days of data.

[0134] Summary of technical effects:

[0135] Significantly suppresses long-term prediction drift: In long-term prediction tasks for the same game (Game A / B Day_180 vs Day_60), the long-term prediction error of the method of this invention (Ours) increases very little or even decreases compared to its own short-term prediction error (Game A: 0.031). 0.027, Game B: 0.042 0.043), while Baseline RF (0.046) 0.073, 0.052 0.096) and Baseline QRF (0.037) 0.071, 0.044 The error increase of 0.092 is very significant (>50%). This proves that the dynamic quantile parameter It effectively corrects for the impact of data distribution drift on long-term forecasts.

[0136] Superior cross-game adaptability: In cross-game prediction tasks (Game C / D), Baseline RF / QRF fails directly, with errors as high as 35%-44%. The method of this invention, however, utilizes short-term data from the target game to calculate specific... This reduces the prediction error to a level close to that of the game's predictions (<7%), with an error reduction of over 80%. This proves... It successfully captured and adapted to the unique recycling curve pattern of the target game.

[0137] Effectively solves the cold start problem for new games: For a new game, Game E, with only 60 days of data, the method of this invention successfully predicted its 180-day LTV (Lifetime Value) for users, with an error (0.044) comparable to the prediction error (0.043) of a mature game, Game B, during the same period. This proves that this invention only requires 60 days of data for the target game to initiate relatively accurate long-term predictions.

[0138] Overall accuracy improvement: Even in short-term or game-like predictions, the method of this invention exhibits performance that is better than or equal to the baseline, demonstrating the robustness of its underlying design.

[0139] The following is a prediction for 180 days. Taking the recovery curve as an example, the implementation process of the prediction scheme is described in detail (reference). Figure 3 ):

[0140] The basic model training phase (A - typically performed on a server cluster or high-performance computing platform):

[0141] A1. Acquiring Basic Training Data: Select at least one mature game with a complete user lifecycle (e.g., Game A). Obtain the following data from a large number of users:

[0142] Before the user sky( Behavioral feature vectors with multiple values ​​(e.g., 3, 6, 9, ..., 30, with a step size of 3 days). (Including but not limited to: login days, game time, number / type / ECPM of ad impressions, number of key actions, growth rate indicators, etc.)

[0143] Users sky( The true value of cumulative income (taking multiple values, such as 10, 20, 30, ..., 180, with a step size of 10 days). .

[0144] Key point: for each Combination preparation The training sample pairs.

[0145] A2. Feature Engineering (Critical and Necessary):

[0146] Data cleaning: Handling missing values ​​(e.g., filling, deleting), outliers (e.g., quantile-based truncation or capping), and duplicate data.

[0147] Missing value handling details: For numerical features, missing values ​​can be filled using the mean / median of the feature; for categorical features, missing values ​​can be filled using the mode or by adding a new missing category. Avoid directly deleting samples containing missing values ​​unless the proportion of missing values ​​is extremely high and cannot represent the business requirements.

[0148] Outlier handling details: Detection and handling are performed using a quantile-based (IQR) method.

[0149] Calculate the 25th percentile (Q1) and 75th percentile (Q3) of the feature.

[0150] Calculate the interquartile range (IQR) as IQR = Q3 - Q1;

[0151] Define the lower bound for outliers as Q1 - 1.5 * IQR;

[0152] Define the upper bound for outliers as Q³ + 1.5 * IQR;

[0153] Values ​​below the Lower Bound or above the Upper Bound are considered outliers.

[0154] Handling methods: The capping method replaces outliers with Lower Bound or Upper Bound; the truncation method is similar; or they are set as missing values ​​and then handled according to the missing value strategy.

[0155] Feature processing: Standardize (StandardScaler) or normalize (MinMaxScaler) the features. For subsequent use of distance-based models (such as decision trees in QRF, which are generally insensitive to scale, but preprocessing helps to make feature importance comparable and accelerates convergence), standardization is suitable when the features roughly follow a normal distribution; normalization is suitable when the feature boundaries are known or there are clear range requirements. In practice, standardization is more commonly used.

[0156] Feature Construction (Optional but Recommended): Based on business understanding and data analysis, construct new features, for example:

[0157] Statistics for different time windows (the first 3 days, the first 7 days, etc.) (mean, sum, maximum, minimum, standard deviation).

[0158] Growth rate characteristics (e.g., (Day 7 revenue - Day 3 revenue) / Day 3 revenue).

[0159] Variation range characteristics (e.g., max(Day1-7 revenue)-min(Day1-7 revenue)).

[0160] Behavioral metrics (such as average login duration and ad display density).

[0161] Feature selection (optional): Important features can be selected using methods such as correlation analysis and feature importance assessment (model-based) to reduce dimensionality, thereby reducing redundancy and noise and improving model efficiency and robustness. Details are as follows:

[0162] Model-based feature importance: Calculate feature importance based on the initially trained QRF model (or RF / XGBoost model), and retain the top-k features (e.g., the top 20 features) based on their importance ranking.

[0163] Correlation filtering: Calculate the Pearson correlation coefficient or Spearman rank correlation coefficient between features. For highly correlated feature pairs (e.g., |r|>0.8), remove one of them.

[0164] Variance filtering: Removes features with extremely low variance (close to constant).

[0165] Output: The cleaned, processed, and constructed feature set, used for each Model training.

[0166] A3. Quantile Random Forest Model Training (Required):

[0167] For each one that needs to be covered Combinations (e.g.) =3,6,...30; =10,20,...,180):

[0168] Extract the corresponding data from the base dataset. Sample pairs.

[0169] Train a standalone model using the quantile random forest algorithm (obtained by overriding the predict method of Python's sklearn.ensemble.RandomForestRegressor). The key hyperparameter settings for the model are as follows:

[0170] Number of trees (n_estimators): 80-150 (preferably 100). Too few trees may lead to underfitting and poor generalization, while too many trees will increase computational cost and make it easy to overfit. 100 is a good balance between accuracy and efficiency.

[0171] Minimum number of samples per leaf node (min_samples_leaf): 0.001. Setting this parameter prevents the generation of overly complex trees (too few samples per leaf node), helps control model variance, and improves generalization ability.

[0172] Maximum feature tree (max_features): sqrt or log2. Default values ​​or commonly used values ​​are fine. This randomly selects some features when building each tree, increasing the randomness and diversity of the model.

[0173] Other optional parameters include: maximum depth (max_depth), minimum number of samples required to split internal nodes (min_samples_split), etc. These can be left unrestricted or adjusted according to the data size.

[0174] (Key point: The model configuration must allow storing the target values ​​of leaf node samples to calculate quantiles)

[0175] Output: Set of basic QRF models { for all required }

[0176] Quantile parameter calculation phase (B - executed in the target game environment or analytics platform):

[0177] B1. Target Alignment Data Acquisition (Required): Acquire the following data from a sufficient number (e.g., several thousand to tens of thousands) of users in the target game to be predicted (e.g., a new game, Game C):

[0178] Before the user The feature vector of n (where the value of n must match the base model set, such as 3, 6, ..., 30) (Requires the same feature processing procedure as step A2).

[0179] The number of days the user has observed so far. True value of cumulative income (e.g., M=60 or 90 days) .

[0180] (Key points:) It needs to be greater than the critical value (Usually 60 or 90 days)

[0181] B2. Calculation of dynamic quantile parameters (core and essential):

[0182] For each of the basic model sets that needs to be used for long-term prediction (For example Model =180) :

[0183] After processing with this batch of target users Features, input to In the model, the quantile parameter for each user is obtained. Predicted values (Note: At this time) (The variable to be optimized)

[0184] Define the optimization objective function :

[0185] ;

[0186] in It's the number of users. User The true LTV value for the day.

[0187] Optimization process:

[0188] Optimization variables ( ): Quantile parameters The range of values ​​for is (0, 1).

[0189] Optimization algorithm: due to These are typically univariate, non-convex, and possibly non-smooth functions. Grid search is recommended to find the global optimum or near-optimal. Specifically, candidate nodes are generated in the interval (0,1) with a fixed step size (e.g., 0.01 or 0.02). Value. Calculate each candidate. Below Choose to make smallest As This method is simple, intuitive, easy to implement, and guarantees finding the optimal value within the discrete grid.

[0190] Number of iterations: For grid search, the number of iterations is determined by the step size (e.g., a step size of 0.01 will result in a maximum of 99 evaluations).

[0191] Initial value (optional): For new tasks, The initial search can start from 0.5 (median) and explore both sides, because Monotonically increasing, therefore, during the exploration process... Adding to the exploration can terminate the exploration or reverse the exploration direction. For The initial value of the task can be obtained from start.

[0192] Implementation method:

[0193] when When, use directly Optimize the calculation of the truth value:

[0194] ;

[0195] when At this time, the target game does not have The true value of heaven ,use Figure 2 The revealed pattern has been optimized and corrected as follows:

[0196] ;

[0197] That is, calculation in optimal in terms of task and this As ( Approximate optimal quantile parameters for the task .

[0198] Output: For the target game and each The task calculates a set of optimal quantile parameters { }

[0199] B3. Parameter Update Module (Optional):

[0200] Parameter update trigger conditions (any one of these conditions must be met to trigger a recalculation).

[0201] Periodic updates: Preset fixed time intervals, such as once a week or once a month.

[0202] Updates based on changes in data distribution:

[0203] Conceptual drift detection: Periodically calculate the Day_n feature distribution (such as the mean, variance, and quantiles of key features) of newly arriving users and compare it with the previous calculation. The differences between the user characteristic distributions of the batches used. Commonly used quantification methods include: Population Stability Index (PSI) (if PSI>0.25, a warning of data distribution change is issued), KS test (KS test is performed on key continuous features, and if the p-value is below the significance level, the data distribution is considered to have changed significantly).

[0204] Predictive performance monitoring: For batch users with a Day_M truth value, real-time monitoring is performed using the current... Predict the LTV of its Day_M. If the error continues to exceed a preset threshold (e.g., 20% higher than the historical average error) or the error shows an upward trend for N consecutive days, an update is triggered.

[0205] Business event trigger: When the game undergoes a major version update, core economic system adjustment, or major user acquisition channel / strategy change, an update will be forcibly triggered when there is sufficient data.

[0206] Use the latest accumulated data of the target game to satisfy A batch of new user data with a retention requirement of 60 days.

[0207] Repeat steps B1 and B2 to recalculate the optimal quantile parameters. }

[0208] Update the parameters used in the prediction service to the latest calculated values ​​so that the model can continuously adapt to changes.

[0209] Prediction and curve fitting stage (C - executed on an online prediction service or analysis platform):

[0210] C1. New User Prediction Data Acquisition (Required): Obtain the first few days of data for predicting new users (or new batches of users) in the target game. sky( The original behavioral feature data (within the range supported by the basic model) is required. For each new user's original feature data, the same feature engineering process as steps A2 and B1 (including cleaning, transformation, construction, etc.) is applied to generate processed feature vectors. .

[0211] C2. Long-Term LTV Forecasting (Core Essential): For the target number of days to be forecasted. :

[0212] Select a model from the base model set. .

[0213] Obtain the corresponding optimal quantile parameters from the parameter set calculated for the target game. .

[0214] User characteristics and parameters Input Model The user's prediction was obtained. Daily LTV Value .

[0215] ;

[0216] C3. Recovery curve fitting (necessary):

[0217] For a new batch of users (such as users acquired through a user acquisition campaign), repeat step C3 to calculate the time points at which each user in this batch reaches a new user group. (like Predicted LTV values ​​(e.g., 10, 20, 30, 60, 90, 120, 150, 180 days) .

[0218] For this group of users at each time point Predicted values Summing is performed to obtain the data of this user group. The predicted cumulative total revenue for the day .

[0219] A set of points ;

[0220] Using curve fitting techniques (such as polynomial fitting, spline interpolation, etc.), based on points... A smooth long-term LTV payback curve is fitted to visually demonstrate the expected accumulation process of the user group's value.

[0221] The key technical points of this invention are as follows:

[0222] A Quantile Random Forest-Based LTV Prediction Framework: This framework models the user's long-term LTV prediction task as a quantile prediction problem, using a quantile random forest model to replace the traditional point estimation model, outputting the predicted value at a given quantile. (Core Feature)

[0223] Mechanism for calculating dynamic optimal quantile parameters:

[0224] Utilize a group of users of the target game (or new game) The characteristic data of the day and its shorter period ( sky, Significantly smaller than the predicted target ,and ,like True value data of cumulative income (60 / 90 days).

[0225] By optimizing the algorithm, for each long-term target number of days that needs to be predicted... and the corresponding basic model Calculate an optimal quantile parameter specific to the target game and the prediction task. (Core innovation: solving drift and cross-product issues).

[0226] The principle of using short-term optimal parameters to correct long-term forecasts: based on discovered quantile parameters. Follow The steady law of change (i.e., when) back (Tends to stabilize), will be in a shorter period of time ( The optimal quantile parameters calculated on ) (or based on) Naïve value optimization ) Applied to longer-term ( The prediction (core principle, especially for cold start protection).

[0227] Cross-game long-term LTV prediction method: Integrating points 1-3 above, a complete method for predicting user long-term LTV curves applicable to different game products is formed. This includes the entire process of basic model training (optionally using data from other games), calculation of dynamic parameters for the target game, prediction of target game users, and curve fitting.

[0228] Dynamic update mechanism: The optimal quantile parameters are periodically recalculated and updated using newly generated data from the target game. To adapt to the continuous changes in data distribution.

[0229] The system for implementing the above method includes a system architecture comprising a module for storing and computing the basic QRF model set, a module for computing dynamic quantile parameters, a prediction execution module for receiving user features and outputting prediction results, and a parameter update module.

[0230] In some embodiments, to further enhance the generalization ability, parameter optimization efficiency, and predictive foresight of the base model, this invention employs a three-way interactive technology combination of "meta-learning to enhance the base model + Bayesian optimization-transfer learning collaborative optimization + temporal prediction parameter correction," achieving deep fusion through bidirectional feedback and parameter transfer between algorithms, as detailed below:

[0231] I. Meta-learning Reinforced Quantile Random Forest Base Model (MAML-QRF)

[0232] The core is to obtain a basic model with the ability to quickly adapt across games through training on multiple game tasks, providing a high-quality initial state for subsequent parameter optimization. The training and adaptation process is as follows:

[0233] 1. Model Building and Meta-Learning Training

[0234] The base model uses quantile random forest (QRF) for the prediction task. (Based on the previous) Celestial Feature Prediction (LTV), each subtree stores the training samples of the leaf nodes. The daily cumulative income target value is predicted, and the output is the quantile result of the target value set. The expression is:

[0235] ;in, For a single user Tianxing feature vector ( , (for feature dimensions) This is the set of parameters for the QRF model (including tree structure, target values ​​of leaf node samples, etc.). Quantile parameters ( (This determines whether the forecast leans towards a conservative or optimistic approach.) For the sample In parameters The set of all leaf nodes of the subtrees that fall into the fall. leaf node The target value of the sample.

[0236] The training phase introduces a Model-Independent Meta-Learning (MAML) framework, which will... The dataset of a mature game is regarded as Individual learning tasks ( For the first This game users Celestial characteristic matrix, For the corresponding The goal is to learn meta-initialization parameters (LTV truth vectors). (Initial parameters of the basic model with rapid cross-game adaptation capability), the training process is implemented through inner and outer double loops:

[0237] Inner loop: Random sampling in each iteration Tasks (such as) ,all (Combination), for each task use Data calculation error Update parameters using gradient descent:

[0238] ;in, (Inner loop learning rate) For error pair The gradient.

[0239] Outer loop: Use each task Remaining Data calculation error Update meta parameters:

[0240] ;in, (Outer loop learning rate) For the elementary error pair The gradient.

[0241] Termination condition: Elementary error continuous The decrease in the next iteration is less than Output .

[0242] 2. Fine-tuning the target game model

[0243] For the target game to be predicted (This can be for new games or mature games that require cross-game prediction), obtain its users Heavenly Feature Matrix ( , (ranging from thousands to tens of thousands), using Sample pairs conduct Subgradient descent fine-tuning yields the basic model parameters adapted to the target game:

[0244] ;in, For the first Error function of the second fine-tuning ( , For the target game users True value of LTV observations over the days. and ).

[0245] II. Bayesian Optimization-Transfer Learning Collaborative Optimization (BO-TL)

[0246] The core idea is to use historical parameters from similar source games as priors, and then use Bayesian optimization to efficiently search for the optimal quantile parameters of the target game. It also forms a bidirectional optimization with the meta-learning model, and the specific process is as follows:

[0247] 1. Prior construction for transfer learning

[0248] First calculate the target game Domain similarity with all source games ( As the source game, These are the weighting coefficients; For game type similarity, a value of 1 is assigned to games of the same type, and a value of 0.2 is assigned to games of different types. To calculate the distribution difference for user profile similarity, the MAE method is used. ; For payment model similarity, a value of 1 is assigned to the same model and 0.5 to the mixed model.

[0249] Select the two source games with the highest similarity , Its historical best quantile parameter , (The optimal source game verified through historical iterations) The value constitutes the prior distribution:

[0250] ;in, , The similarity value. (Prior distribution standard deviation, ensuring that the distribution is concentrated near the historical optimal parameters). It follows a normal distribution.

[0251] 2. Bayesian optimization process

[0252] To minimize the prediction error, the objective function is constructed as follows:

[0253] ;in, Quantile parameters The corresponding mean square error (measures the difference between the predicted value and the mean square error) (The deviation of the true value of the observation).

[0254] Gaussian processes (GP) are used as surrogate models for modeling. and The mapping relationship, the mean function of GP Covariance function:

[0255] ;in, (GP signal variance) (Length scale) (Noise variance) Dirac function ( Select 1 otherwise select 0. These are candidate values ​​for different quantile parameters.

[0256] The next sampling point is selected based on the surrogate model and the expectation improvement (EI) acquisition function:

[0257] ;in, The current minimum error (the minimum error corresponding to the sampled candidate value) ), , These are the cumulative distribution function and probability density function of the standard normal distribution, respectively. For the proxy model in The standard deviation of the forecast (a measure of forecast uncertainty).

[0258] The initial sampling points are set in conjunction with the transfer learning prior. After each sampling, a new sample is used. Update the GP model and output the optimal parameters after 20 iterations. (Optimal quantile parameters obtained by Bayesian optimization search).

[0259] 3. Two-way interaction with the meta-learning model

[0260] Positive support: The error calculation of Bayesian optimization depends on the fine-tuning after meta-learning. , Cross-game compatibility has been reduced. The noise reduces the accuracy of optimization.

[0261] Reverse optimization: If Then Re-execute the 1D model fine-tuning by replacing 0.5, and obtain the optimized parameters:

[0262] ;in, for right The gradient is used to achieve coordinated optimization of model parameters and quantile parameters.

[0263] III. Time Series Prediction Parameter Correction (LSTM-Q)

[0264] The core idea is to predict future trends using the historical parameter sequence of the target game, dynamically correct the Bayesian optimization results, and simultaneously receive real-time parameter feedback from the Bayesian optimization to form a closed loop, as detailed below:

[0265] 1. Time series model construction and training

[0266] Collect target game past A sequence of historical best parameters for each time window (each time window is 1 week). ( For the first The optimal quantile parameters for the time window (including historical Bayesian optimization results), categorized by... Divided into training set and verification set .

[0267] A single-hidden-layer LSTM model is used (input dimension 1, hidden layer neurons 32, output dimension 1, activation function). (with a dropout rate of 0.2%), training sample pairs are constructed. ( The input sequence has a time step of 3. For tags, (5 groups of samples in total), loss function:

[0268] ;in, For the LSTM model, the first Predicted values ​​for the group of samples (predicted values ​​of quantile parameters output by the model).

[0269] Use the Adam optimizer (learning rate) Training for 100 rounds to validate set loss. Stop at time, the final model output is the first Forecast parameters for the time window: ;in, The optimal quantile parameter for time series forecasting (reflecting the future trend of parameter changes).

[0270] 2. Two-way interactive fusion with Bayesian optimization

[0271] Data feedback: obtained through Bayesian optimization (No. (Optimal BO parameters for the time window) (Added to...) Updated to This provides the latest data for the next time series forecast;

[0272] Search constraints: Time series prediction Narrowing the search scope of Bayesian optimization to Reduce invalid searches;

[0273] Weighted fusion: Optimizing weight coefficients using the validation set. ( (balancing historical optimization with future prediction) Optimal example Final quantile parameters: ;in, These are the final fusion parameters used for long-term LTV prediction (combining real-time adaptability with future foresight).

[0274] IV. Final Forecast Execution and Core Contributions

[0275] (a) Long-term LTV forecasting formula

[0276] Will and Substituting into the QRF model, we can obtain the target game's new users. Forecasted LTV value for the day:

[0277] ;in, For new users The celestial behavior is a feature vector (processed with feature engineering consistent with the basic training phase). For new users Daily LTV forecast.

[0278] (II) Core Contributions of the Technology Portfolio

[0279] 1. Meta-learning and Bayesian optimization mutually empower each other: Meta-learning Reduced The noise reduces the accuracy of BO optimization. The above; BO Reverse fine-tuning of the meta-model reduces the short-term data requirements of the target game. (from User drop user).

[0280] 2. Synergistic Effect of Bayesian Optimization and Temporal Series Forecasting: Temporal Series Forecasting Improve BO search efficiency (The number of iterations starts from) Second drop (times); BO's Updating the time series enables the LSTM model to capture parameter fluctuations during the game's operational cycle, improving predictive foresight. .

[0281] 3. Three-way integration breaks through scene limitations: In cross-game scenarios, the error is reduced compared to a single model. In the case of a new game's cold start, only... Tian Data can achieve this. LTV prediction, with error controlled within [missing information]. Within this scope, the core pain points of traditional methods have been resolved.

[0282] V. The new process is as follows:

[0283] (1) Obtain basic training data for multiple mature games. The mature games are games with complete long-term user lifecycle data. The basic training data includes the behavioral feature data of a large number of users in each mature game for the first n days and the true value of the long-term lifecycle value of the corresponding user for the T days (n is the preset short-term input days and T is the preset long-term prediction days). Perform feature engineering processing (including missing value filling, outlier processing, duplicate data removal, numerical feature standardization / normalization, derivative feature construction and key feature screening) on ​​the basic training data of each game to obtain the standardized feature set corresponding to each game, and construct a multi-game task training dataset as a whole.

[0284] (2) Based on the multi-game task training dataset, a model-independent meta-learning (MAML) framework is introduced to train a set of quantile random forest basic models: the “n-day features - T-day LTV ground truth” of a single game is regarded as an independent learning task, and the meta-initialization parameters are obtained through inner and outer double loop training (the parameters are fine-tuned using single-task data in the inner loop and the meta-parameters are optimized using multi-task validation data in the outer loop); based on the meta-initialization parameters, for each specific combination of input days n and output days T, an independent quantile random forest model is trained (80-150 trees, minimum number of samples per leaf node is 0.001, and features are selected using the square root method / logarithmic method). Each subtree stores the cumulative income target value of the training samples of the leaf nodes. During prediction, the target value set of samples falling into the leaf nodes in all subtrees is summarized, and the quantile result of the set is output, which finally constitutes a set of basic models that support subsequent fine-tuning.

[0285] (3) Obtain short-term alignment data of the target game to be predicted. The short-term alignment data includes the behavioral feature data of thousands to tens of thousands of users in the target game in the previous n days and the observed cumulative revenue truth value of M days (M is 60 days or 90 days and is greater than the critical value of the quantile parameter tending to be stable); perform the same feature engineering processing as step (1) on the behavioral feature data of the previous n days in the short-term alignment data; at the same time, calculate the domain similarity between the target game and each mature game (weighted matching degree based on game type, user profile and payment mode), filter the top 2 source games with the highest similarity and extract their historical best quantile parameters; if the target game has an operating history, collect its historical best quantile parameter sequence for the past 8 time windows for time series prediction model training.

[0286] (4) Based on the aforementioned basic model set, the processed short-term aligned data, and the preprocessing results of step (3), the final optimal quantile parameters are calculated through the collaborative mechanism of "Bayesian optimization-transfer learning-temporal prediction": ① Construct the objective function of Bayesian optimization (minimize the mean square error between the predicted value and the true value of the cumulative income over M days), construct the prior distribution using the historical optimal quantile parameters of similar source games, and set the initial sampling points to be distributed around the prior parameters; ② Use a Gaussian process as a proxy model for Bayesian optimization, obtain the function iterative selection of sampling points through expectation improvement (EI), and search for the optimal quantile parameters. ③ If the target game has a historical parameter sequence, train a single-hidden-layer LSTM time series prediction model, input the historical parameters of the latest 3 time windows, and output the predicted parameters of future time windows. ④ Optimize the weight coefficients α (α∈(0,1)) using the validation set, and apply the formula ⑤ Obtain the final quantile parameters; Calculate the prediction error. If the error is lower than the initial threshold, use it as a feedback signal for subsequent meta-model fine-tuning.

[0287] (5) Obtain the original behavioral feature data of new users in the target game for the first n days. After the same feature engineering process as in step (1), perform target game adaptation fine-tuning based on the basic model set in step (2): combine the meta-initialization parameters The corresponding error gradient is updated through three gradient descent iterations to obtain the model parameters adapted to the target game; the processed new user features are input into the adapted quantile random forest model (corresponding to the input number of days n and the output number of days T), combined with the results obtained in step (4). Output the long-term T-day lifetime value prediction for this new user.

[0288] (6) For the long-term T-day lifecycle value prediction of a batch of new users in the target game, sum them up according to multiple key time nodes covering the short to long term to obtain the total predicted cumulative income value of each time node; based on the total predicted cumulative income value, combined with the parameter trend of time series prediction, use polynomial fitting or spline interpolation technology to generate a smooth long-term lifecycle value recovery curve; at the same time, according to the preset time interval or triggering conditions (significant change in user characteristic distribution, prediction error exceeding the threshold, major game version update), use the latest accumulated short-term aligned data and parameter sequence of the target game to repeat steps (3)-(4) to update the quantile parameters and model adaptation parameters, and continuously optimize the prediction accuracy of the recovery curve.

Claims

1. A method for predicting the LTV curve of cross-game users based on a dynamic quantile correction mechanism, characterized in that, include: (1) Obtain basic training data of at least one mature game. The mature game is a game with complete long-term user lifecycle data. The basic training data includes the user’s behavioral feature data for the first n days in the mature game and the true value of the user’s long-term lifecycle value for T days. n is the preset short-term input days and T is the preset long-term prediction days. Perform feature engineering on the basic training data to obtain a standardized feature set. (2) Based on the standardized feature set, train multiple independent quantile random forest models to form a basic model set. Each quantile random forest model corresponds to a specific number of input days n and output days T. Each subtree of the quantile random forest model stores the cumulative income target value of the training samples in the leaf nodes. When predicting, summarize the target value set of samples falling into the leaf nodes in all subtrees and output the quantile result of the set. (3) Obtain short-term aligned data of the target game to be predicted. The short-term aligned data includes the behavioral feature data of a group of users in the target game for the previous n days and the observed cumulative income true value for M days. M is the preset short-term observation days and M is greater than the critical value of the quantile parameter tending to be stable. Perform the same feature engineering processing as step (1) on the behavioral feature data of the previous n days in the short-term aligned data. (4) Based on the basic model set and the processed short-term aligned data, the optimal quantile parameter is calculated for each long-term prediction task through an optimization algorithm. The optimization objective is to minimize the error between the predicted value of the cumulative income of the batch of users over M days and the true value of the cumulative income over M days. (5) Obtain the behavioral feature data of the new user in the target game for the first n days. After the same feature engineering process as in step (1), input the quantile random forest model corresponding to the input number n and output number T in the basic model set. Combine the optimal quantile parameters obtained in step (4) to output the long-term T-day life cycle value prediction value of the new user. (6) The long-term T-day lifecycle value prediction of a batch of new users in the target game is summed at multiple time points to obtain the total predicted cumulative income at each time point, and a smooth long-term lifecycle value recovery curve is fitted based on the total predicted cumulative income. The optimization algorithm in step (4) is a grid search algorithm. It generates candidate values ​​of quantile parameters with a fixed step size in the interval (0,1), calculates the prediction error corresponding to each candidate value, and selects the candidate value that minimizes the error as the optimal quantile parameter. In step (4), when calculating the optimal quantile parameter, the law that the quantile parameter tends to stabilize as the number of prediction days increases is utilized. When the target prediction day T is greater than the critical value, the stable quantile parameter calculated from M days of short-term data is directly used as the optimal quantile parameter for the prediction of day T.

2. The cross-game user LTV curve prediction method based on dynamic quantile correction mechanism according to claim 1, characterized in that, In step (1), n ​​takes the value of multiple consecutive or intermittent short-term days, and T takes the value of multiple consecutive or intermittent long-term days. Each input number of days n and the output number of days T form a unique correspondence, constituting the basis for independent model training in the basic model set.

3. The cross-game user LTV curve prediction method based on dynamic quantile correction mechanism according to claim 1, characterized in that, The feature engineering process in step (1) includes: filling missing values, handling outliers and removing duplicate data from the original data, standardizing or normalizing numerical features, constructing derived features based on business needs, and screening key features through correlation analysis and feature importance assessment.

4. The cross-game user LTV curve prediction method based on dynamic quantile correction mechanism according to claim 1, characterized in that, In step (2), when training the quantile random forest model, the number of trees is set to 80-150, the minimum number of samples for leaf nodes is 0.001, and the square root method or logarithmic method is used to randomly select some features to participate in the training when constructing each tree.

5. The cross-game user LTV curve prediction method based on dynamic quantile correction mechanism according to claim 1, characterized in that, In step (3), M days can be 60 days or 90 days. The number of users in the short-term aligned data is in the thousands to tens of thousands, ensuring the reliability of the optimal quantile parameter calculation.

6. The cross-game user LTV curve prediction method based on dynamic quantile correction mechanism according to claim 1, characterized in that, It also includes the step of dynamically updating the optimal quantile parameter: according to a preset time interval or based on the triggering condition, obtain the latest accumulated short-term alignment data of the target game, repeat step (4) to recalculate the optimal quantile parameter, and replace the original parameter with the new parameter; the triggering condition includes significant changes in user feature distribution and prediction error exceeding a preset threshold.

7. The cross-game user LTV curve prediction method based on dynamic quantile correction mechanism according to claim 1, characterized in that, In step (6), when fitting the long-term life cycle value recovery curve, multiple key time nodes covering the short to long term are selected. Based on the predicted cumulative total income of each node, a smooth curve is generated using polynomial fitting or spline interpolation techniques.

8. The cross-game user LTV curve prediction method based on dynamic quantile correction mechanism according to claim 1, characterized in that, When the target game is a newly launched game, the short-term alignment data in step (3) is the M-day user data accumulated after the launch of the newly launched game. After calculating the optimal quantile parameters in step (4), the prediction of the long-term T-day lifecycle value of the users of the newly launched game is directly combined with the basic model set.

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