Decision tree hyperparameter tuning grid search. You will find a way to automate this process.

Looking at the documentation, I am Sep 30, 2023 · Introduction to LightGBM and Hyperparameter Tuning. Apr 11, 2023 · Grid Search is an exhaustive search method where we define a grid of hyperparameter values and train the model on all possible combinations. The best performance for the model was proven to be Model A1, selected by the TPOT optimization with the . We achieved an unspectacular improvement in accuracy of 0. Metrics to assess the performance of our models; mlr to train our model’s hyperparameters. The first is the model that you are optimizing. Sci-kit learn’s Decision Tree classifier algorithm has a lot of hyperparameters. If the proper hyperparameter tuning of a machine learning classifier is performed, significantly higher accuracy can be obtained. model_selection import RandomizedSearchCV # Number of trees in random forest. The basic way to perform hyperparameter tuning is to try all the possible combinations of parameters. Image by Yoshua Bengio et al. The train function can be used to. Rather a fixed number of parameter settings is sampled from Feb 9, 2022 · The GridSearchCVclass in Sklearn serves a dual purpose in tuning your model. Using an entropy criterion, permitting an unrestricted maximum depth, selecting six features, and designating four as the optimal minimum samples leaf are the optimal settings found in this random search. To close out this tutorial, let’s take a look at how we can improve our model’s accuracy by tuning some of its hyper-parameters. This function dictates the sample distributions of each hyper-parameter. The most common options available are categorical, integer, float, or log uniform. This is also called tuning . We then choose the combination that gives the best performance, typically measured using cross-validation. Note that in the docs you also have suggested values for several Grid search, true to its name, picks out a grid of hyperparameter values, evaluates every one of them, and returns the winner. param_grid – A dictionary with parameter names as keys and lists of parameter values. com Feb 25, 2024 · Adopting a standardized hyperparameter tuning process makes machine learning models and research more replicable. By specifying a parameter distribution containing ranges or distributions for hyperparameters such as the number of estimators Nov 18, 2019 · Decision Tree’s are an excellent way to classify classes, unlike a Random forest they are a transparent or a whitebox classifier which means we can actually find the logic behind decision tree Aug 28, 2021 · Grid Search. GS is a tuning technique that allows users to select which Dec 21, 2021 · Unlike grid and random search, informed search learns from its previous iterations through the following process. Aug 13, 2021 · In this Scikit-Learn learn tutorial I've talked about hyperparameter tuning with grid search. [2]. T == Average Temperature (°C) TM == Maximum temperature (°C) Tm == Minimum temperature (°C) SLP == Atmospheric pressure at sea level (hPa) Oct 31, 2020 · Apologies, but something went wrong on our end. The class allows you to: Apply a grid search to an array of hyper-parameters, and. grid_search. Feb 28, 2024 · Random search. Oct 5, 2022 · Use random search on a broad range of values if you don’t already have an idea of the parameters that will perform well on your model. The grid search algorithm exhaustively searches through all possible combinations of hyperparameters specified in the param_grid dictionary and evaluates the model’s performance using the Feb 21, 2019 · I want to create a Decision Tree and do hyperparameter tuning on the parameters and have the model output what the optimal hyperparameters are. Aug 30, 2023 · 4. Sep 29, 2020 · What is Grid Search? Grid search is a technique for tuning hyperparameter that may facilitate build a model and evaluate a model for every combination of algorithms parameters per grid. For example, if you want to tune the learning_rate and the max_depth, you need to specify all the values you think will be relevant for the search. One of the popular hyperparameter methodologies is Grid Search. A model hyperparameter is a characteristic of a model that is external to the model and whose value cannot be estimated from data. hyperparameter tuning) An important task in ML is model selection, or using data to find the best model or parameters for a given task. The small population Dec 21, 2021 · Thank you for reading! These are 5 hyperparameters that I normally tweak when I develop decision trees. model_selection import GridSearchCV def dtree_grid_search(X,y,nfolds): #create a dictionary of all values we want to test param_grid = { 'criterion':['gini','entropy'],'max_depth': np. 615). Next, we’ll define our data. 5, you may wish you limit the range. STEP 4: Building and optimising xgboost model using Hyperparameter tuning (Random Search) STEP 5: Make predictions on the final xgboost model. The value of the hyperparameter has to be set before the learning process begins. Mar 20, 2020 · params_grid: the dictionary object that holds the hyperparameters you want to try scoring : evaluation metric that you want to use, you can simply pass a valid string/ object of evaluation metric cv : number of cross-validation you have to try for each selected set of hyperparameters Manual tuning. #machinelearning #decisiontree #datascienceDecision Tree if built without hyperparameter optimization tends to overfit the model. e. This can be done using a dictionary, where the keys are the hyperparameters and the values are the ranges of Oct 12, 2020 · Here’s how we can speed up hyperparameter tuning using 1) Bayesian optimization with Hyperopt and Optuna, running on… 2) the Ray distributed machine learning framework, with a unified API to many hyperparameter search algos and early stopping schedulers, and… 3) a distributed cluster of cloud instances for even faster tuning. You might consider some iterative grid search. STEP 3: Train Test Split. For regularization parameters, it’s common to use exponential scale: 1e-5, 1e-4, 1e-3, …, 1. Oct 22, 2023 · Step 3: Fit GridSearchCV to the Data. Random search; Find areas with good score; Run grid search in a smaller area; Continue until the optimal solution is obtained; Genetic algorithm is a method of informed hyperparameter tuning which is based upon the real-world Jan 31, 2024 · 5. Oct 17, 2022 · First and foremost, we’ll need to import the necessary libraries. Let’s demonstrate Grid Search using the diamonds dataset and target variable “carat”. The parameter grid. Hyperopt is one of the most popular hyperparameter tuning packages available. 3 and 4, respectively. Grid Search Grid search is a popular hyperparameter optimization (GSHO) technique that, given a limited range of values, thoroughly assesses all possible combinations of hyperparameters. Cross-validate your model using k-fold cross validation. We might use 10 fold cross-validation to search the best value for that tuning hyperparameter. fit(X_train, y_train) Finally, get your results. Aug 28, 2021 · Gradient boosting “Gradient boosting is a machine learning technique for regression, classification and other tasks, which produces a prediction model in the form of an ensemble of weak prediction models, typically decision trees. The Titanic dataset is a csv file that we can load using the read. choose the “optimal” model across these parameters. Applying a randomized search. Both techniques evaluate models for a given hyperparameter vector using cross-validation, hence the “ CV ” suffix of each class name. In this post, we will go through Decision Tree model building. J. Searching for optimal parameters with successive halving# Jun 10, 2020 · Here is the code for decision tree Grid Search. We’ll be using Sklearn for this example, so we’ll need to import the “ StackingClassifier ” module from Sklearn. Apr 6, 2021 · Grid-Search (GS) can be used on a by-model basis, as each type of machine learning model has different catalogue of hyperparameters. min_sample_split – a parameter that tells the decision tree in a random forest the minimum required number of observations in any given node in order to split it. This will save a lot of time. n_estimators = [int(x) for x in np. In this article, we will explore the differences between grid search and random search and provide insights The grid search algorithm then performs the search, training and evaluating the model with different hyperparameter combinations using cross-validation. 2021, 11, x FOR PEER REVIEW 7 of 17 . We investigated hyperparameter tuning by: Obtaining a baseline accuracy on our dataset with no hyperparameter tuning — this value became our score to beat. Grid search does the heavy lifting and identifies the best combination of hyperparameters to Nov 27, 2023 · Basic Hyperparameter Tuning Techniques. This article explains the differences between these approaches The model to be used: a DecisionTreeClassifier with a random_state parameter of 42. This can save us a bit of time when creating our model. The more hyperparameters of an algorithm that you need to tune, the slower the tuning process. You'll be able to find the optimal set of hyperparameters for a Pros and Cons of Grid Search . Learning decision trees was essential in my studies on DS and ML — it was the algorithm that helped me to grasp the huge impact that hyperparameters can have in your algo’s performance and how they can be key for the failure or success of a project. First, we will use the trainControl() function to define the method of cross validation to be carried out and search type i. Grid Search For anyone who’s unfamiliar with the term, grid search involves running a model many times with combinations of various hyperparameters. Hyperopt. The approach is broken down into two parts: Evaluate an ARIMA model. LightGBM utilizes gradient-boosting decision trees for both classification and regression tasks. Bergstra, J. Evaluate sets of ARIMA parameters. linspace(start = 200, stop = 2000, num = 10)] # Number of features to consider at every split. Grid search is a popular hyperparameter optimisation technique. Scikit-learn provides these two methods for algorithm parameter tuning and examples of each are provided below. The number of cross-folds: cv=3. Apr 17, 2022 · Because of this, scaling or normalizing data isn’t required for decision tree algorithms. Oct 20, 2021 · Photo by Roberta Sorge on Unsplash. Print the best parameters identified by the grid search using the best_params_ attribute of the Dec 7, 2023 · Hyperparameter tuning is the process of selecting the optimal values for a machine learning model’s hyperparameters. Also you can change the Grid Search Hyperparameter Tuning on Classification Algorithm with XGBoost model gets the best value while the Decision tree has the lowest value. Tuning may be done for individual Estimator s such as LogisticRegression, or for entire Pipeline s which include multiple algorithms, featurization, and Aug 21, 2019 · Phrased as a search problem, you can use different search strategies to find a good and robust parameter or set of parameters for an algorithm on a given problem. difficulty of finding a good combination with a coarse standard grid search. , Random search for hyper-parameter optimization, The Journal of Machine Learning Research (2012) 3. You predefine a grid of potential values for each hyperparameter, and the All parameters in the grid search that don't start with base_estimator__ are Adaboost's, and the others are 'forwarded' to the object we pass as base_estimator argument (DTC in the sample). Popular methods are Grid Search, Random Search and Bayesian Optimization. , the AUC) is the sum of the green and yellow areas, and the contribution to the score is the height of the areas, so basically only the green one is significant for the score. STEP 2: Read a csv file and explore the data. An optimal model can then be selected from the various different attempts, using any relevant metrics. Hyperparameters are settings that control the learning process of the model, such as the learning rate, the number of neurons in a neural network, or the kernel size in a support vector machine. Mar 1, 2019 · The principle of grid search is exhaustive searching. 01; Automated tuning. fit(X_train, y_train) In this example, svm_clf is the SVM classifier that we defined in step 1, param_grid is the hyperparameter space that we defined in step 2, and cv is the cross-validation scheme that we defined in step 3. The point is to identify which hyperparameters are likely to work best. Refresh the page, check Medium ’s site status, or find something interesting to read. A simple yet surprisingly effective alternative to performing a grid search is to train and assess candidate models by using random combinations of hyperparameter values. When a decision tree is the weak learner, the resulting algorithm is called gradient boosted trees, which usually You can specify how the hyperparameter tuning is performed. If optimized the model perf Aug 28, 2020 · Typically, it is challenging to know what values to use for the hyperparameters of a given algorithm on a given dataset, therefore it is common to use random or grid search strategies for different hyperparameter values. Parameters like in decision criterion, max_depth, min_sample Decision Tree Regression With Hyper Parameter Tuning. rpart. 2. Hyperparameter Tuning for Decision Tree Classifiers in Sklearn. from sklearn. Depending on the application though, this could be a significant benefit. STEP 1: Importing Necessary Libraries. In contrast to Grid Search, not all given parameter values are tried out in Randomized Search. Aug 1, 2021 · Compare the accuracy score from the first Decision Tree to the accuracy score after you performed the grid search. plotly for 3-D plots. Is the optimal parameter 15, go on with [11,13,15,17,19]. Initial random forest classifier with default hyperparameter values reached 81% accuracy on the test. Set and get hyperparameters in scikit-learn; 📝 Exercise M3. Example: In a linear Feb 22, 2023 · Grid search. The complete code can be found at this GitHub repository. May 17, 2021 · In this tutorial, you learned the basics of hyperparameter tuning using scikit-learn and Python. 692–0. The hyperparameter verbose=1. So in general I'd suggest you carefully look at what each of them does, and follow suggestions from reliable resources. Play with your data. Utilizing an exhaustive grid search. Grid Search using Cross Validation provides convenience in testing each model parameter without having to do manual validation one by one. The structure of decision trees resembles the flowchart of decisions helps us to interpret and explain easily. The first step is to set up a study function. Dec 29, 2018 · 4. 01; Quiz M3. Model Parameters In a machine learning model, training data is used to learn the weights of the model. Aug 25, 2023 · Random Forest Hyperparameter #2: min_sample_split. Feb 13, 2021 · I added a very broad range for your tuning grid, but since the optimal model had a mincriterion of 0. It is also a good idea to use both random search and grid search to get the best possible results. I will use a 3-fold CV because the data set is relatively small and run 200 random combinations. criterion: Decides the measure of the quality of a split based on criteria Nov 2, 2022 · Grid Search and Randomized Search are two widely used techniques in Hyperparameter Tuning. Call the fit() method to perform the grid search using 3-fold cross-validation. If “sqrt”, then max_features=sqrt (n_features). The lesson also demonstrates the usage of Explore and run machine learning code with Kaggle Notebooks | Using data from multiple data sources Jan 21, 2023 · For machine learning algorithms, fine-tuning hyperparameters is a computational challenge due to the large size of the problem space. The iris dataset consists of 150 samples of different Table of Contents. May 24, 2021 · GridSearchCV: scikit-learn’s implementation of a grid search for hyperparameter tuning. These weights are the Model parameters. 4%. Oct 28, 2021 · Optimizing hyper-parameters with Optuna follows a similar process regardless of the model you are using. datasets IRIS dataset. and Bengio, Y. It elucidates two primary hyperparameters: `max_depth` and `min_samples_split`, explaining their significance and how improper tuning can lead to underfitting or overfitting. Hyperparameter tuning by grid-search; Hyperparameter tuning by randomized-search; 🎥 Analysis of hyperparameter search results; Analysis of hyperparameter search results; Evaluation and Machine learning models are used today to solve problems within a broad span of disciplines. The default value of the minimum_sample_split is assigned to 2. Currently, three algorithms are implemented in hyperopt. It features an imperative, define-by-run style user API. In machine learning, hyperparameter tuning is the process of optimizing a model’s hyperparameters to improve its performance on a given dataset. However, even these methods are relatively inefficient because they do not choose the next Comparing randomized search and grid search for hyperparameter estimation compares the usage and efficiency of randomized search and grid search. If you are familiar with machine learning, you may have worked with algorithms like Linear Regression, Logistic Regression, Decision Trees, Support Vector Machines, etc. estimator – A scikit-learn model. Random Search . Grid Search: Grid search is like having a roadmap for your hyperparameters. a. frame() with tuneLength = 100 for example for caret to pick a grid of 100 automatically where you dont need to specify the mincriterion numbers. Using grid search for hyperparameter tuning has the following advantages: Grid search explores all specified combinations, ensuring you don't miss the best hyperparameters within the defined search space. Dec 10, 2016 · @drsimonj here to share a tidyverse method of grid search for optimizing a model’s hyperparameters. A more technical definition from Wikipedia, grid search is: an Oct 10, 2021 · Hyperparameters of Decision Tree. 01; 📃 Solution for Exercise M3. There are several different techniques for accomplishing this task. 1. If “log2”, then max_features=log2 (n_features). Is that what you had expected? We perform a round of grid searching in order to elucidate the optimal hyperparameter values. Random search is faster than grid search and should always be used when you have a large parameter space. k. csv function. Oct 16, 2022 · In this blog post, we will tune the hyperparameters of a Decision Tree Classifier using Grid Search. These figures show the predictive performance in terms of BAC values averaged over the 30 repetitions (y-axis), for each tuning technique and default values over all datasets (x-axis) presented in Sep 18, 2020 · Specifically, it provides the RandomizedSearchCV for random search and GridSearchCV for grid search. Using grid search we were able to tune selected hyperparameters in 247 seconds and increased accuracy to 88%. It is a powerful approach for finding the optimal set of hyperparameter values. Med. In this paper, a comprehensive comparative analysis of various hyperparameter tuning techniques is performed; these are Grid Search, Random Search, Bayesian Optimization Oct 6, 2023 · The decision tree hyperparameters are defined as the decision tree is a machine learning algorithm used for two tasks: classification and regression. Hyperparameters are the parameters that control the model’s architecture and therefore have a Jun 24, 2021 · Grid Layouts. Some of the key advantages of LightGBM include: Optuna is an automatic hyperparameter optimization software framework, particularly designed for machine learning. . For this example, we’ll be using the Sklearn. Using the previously created grid, we can find the best hyperparameters for our Random Forest Regressor. Nov 5, 2021 · Grid Search is exhaustive and Random Search, is well… random, so could miss the most important values. In addition, the decision tree is used for building trees in ensemble learning algorithms, and the hyperparameter is a parameter in which its value is used to control the learning process. Sep 29, 2021 · In this article, we used a random forest classifier to predict “type of glass” using 9 different attributes. For example, you can change the optimization method to grid search or limit the training time. time: Used to time how long the grid search takes. Sep 17, 2023 · # Fit the grid search to the training data grid_search. Next, we have our command line arguments: A hyperparameter is a parameter that controls the learning process of the machine learning algorithm. The technique involves creating a grid out of Sep 29, 2021 · Grid search parameter tuning (hyperparameters tuned are shown in Table 5) for SVM, NB, and ANN-MLP reported notably lower accuracy performance compared to the accuracy achieved in the TPOT optimization model (accuracy of 0. configuration from grid search hyperparameter tuning method. Model selection (a. You can also replace tuneGrid = data. Side note: AdaBoost always uses another classifier as a base estimator : it's a 'meta classifier' that works by fitting several version of the 'base Apr 15, 2020 · If “auto”, then max_features=sqrt (n_features). 1 Is hyperparameter tuning necessary for decision trees? Tuning results for J48 and CART algorithms are depicted in Figs. tree import DecisionTreeClassifier from sklearn. The code in this tutorial makes use of the scikit-learn, Pandas, and the statsmodels Python libraries. Pers. Grid search trains a machine learning model with each combination of possible values of hyperparameters on the training set and evaluates the performance according to a predefined metric on a cross validation set. Grid and random search are hands-off, but Sep 21, 2023 · rpart to fit decision trees without tuning. Now let’s create our grid! This grid will be a dictionary, where the keys are the names of the hyperparameters we want to focus on, and the values will be lists containing Mar 20, 2024 · Decision trees are powerful models extensively used in machine learning for classification and regression tasks. Hyperparameter Tuning for Random Forest. SVC: Our Support Vector Machine (SVM) used for classification (SVC) paths: Grabs the paths of all images in our input dataset directory. Hyperopt allows the user to describe a search space in which the user expects the best results allowing the algorithms in hyperopt to search more efficiently. After doing this, I would like to fit the model using these parameters. arange(3, 15)} # decision tree model dtree_model=DecisionTreeClassifier() #use gridsearch to test all We will use caret package to perform Cross Validation and Hyperparameter tuning (nround- Number of trees and max_depth) using grid search technique. Grid Search exhaustively searches through every combination of the hyperparameter values specified. On the flip side, however: Tuning hyperparameter is an architecture of deep learning to improve the performance of predictive models. The app opens a dialog box in which you can select optimization options. As demonstrated in Bergstra and 5. For example, if the hyperparameter is the number of leaves in a decision tree, then the grid could be 10, 20, 30, …, 100. For example, instead of setting 'n_estimators' to np. This tutorial won’t go into the details of k-fold cross validation. Random Search. Two simple and easy search strategies are grid search and random search. However, the performance of decision trees highly relies on the hyperparameters, selecting the optimal hyperparameter can sign Jan 9, 2018 · To use RandomizedSearchCV, we first need to create a parameter grid to sample from during fitting: from sklearn. fit(X_train, y_train) Step 4: Access the Best Parameters and Model. evaluate, using resampling, the effect of model tuning parameters on performance. This code snippet demonstrates the utilization of RandomizedSearchCV to perform hyperparameter tuning for the Gradient Boosting Classifier on the Titanic dataset. ggplot2 for general plots we will do. the search for the hyperparameter combination for which the trained model shows the best performance for the given data set. Grid Search Cross-Validation is a popular tuning technique that chooses the best set of hyperparameters for a model by iterating and evaluating through all possible combinations of given parameters. Both classes require two arguments. References. estimator, param_grid, cv, and scoring. It is a brute-force exhaustive search The lesson centers on understanding and applying hyperparameter tuning to decision trees, a crucial machine learning algorithm for classification and regression tasks. Jan 17, 2017 · In this tutorial, we will develop a method to grid search ARIMA hyperparameters for a one-step rolling forecast. 3. # Access the best hyperparameters Nov 8, 2020 · This article introduces the idea of Grid Search for hyperparameter tuning. Common Approaches to Hyperparameter Tuning . The caret package has several functions that attempt to streamline the model building and evaluation process. How does it differ? It is most likely that you will find the accuracy score has decreased. Coming from a Python background, GridSearchCV was very straightforward and does exactly this. On the Learn tab, in the Options section, click Optimizer. Manual tuning takes time away from important steps of the machine learning pipeline like feature engineering and interpreting results. An efficient strategy for adjusting hyperparameters can be established with the use of the greedy search and Swarm intelligence algorithms. The above picture represents how Grid and Randomized Grid Search might perform trying to optimize a model which scoring function (e. Recipe Objective. It is engineered for speed and efficiency, providing faster training times and better performance than older boosting algorithms like XGBoost. The description of the arguments is as follows: 1. Snippets of code are provided to help understanding the implementation. Aug 6, 2020 · Let’s see how the Randomised Grid Search Cross-Validation is used. arange (10,30), set it to [10,15,20,25,30]. Three of the most popular approaches for hyperparameter tuning include Grid Search, Randomised Search, and Bayesian Search. Hyperparameter Tuning is choosing the best set of hyperparameters that gives the maximum performance for the learning model. Grid Search with Cross Validation Jun 24, 2018 · Grid search and random search are slightly better than manual tuning because we set up a grid of model hyperparameters and run the train-predict -evaluate cycle automatically in a loop while we do more productive things (like feature engineering). Finally, grid search outputs hyperparameters that achieve the best performance. The outcomes of hyperparameter tuning for a Decision Tree in classification scenarios using random search are shown in Table 7. Sep 29, 2021 · decision tree algorithm by using grid search estimator. This dataset contains May 7, 2021 · Hyperparameter Grid. Tuning machine learning hyperparameters is a tedious yet crucial task, as the performance of an algorithm can be highly dependent on the choice of hyperparameters. We will use air quality data. For example, c in Support Vector Machines, k in k-Nearest Neighbors, the number of hidden layers in Neural Networks. It is a good choice for exploring smaller hyperparameter spaces. Sep 12, 2021 · In this work, we propose hyperparameters optimization using grid search to optimize the parameters of eight existing models and apply the best parameters to predict the outcomes of HIV tests from In this video, we will use a popular technique called GridSeacrhCV to do Hyper-parameter tuning in Decision Tree About CampusX:CampusX is an online mentorshi Jul 9, 2024 · clf = GridSearchCv(estimator, param_grid, cv, scoring) Primarily, it takes 4 arguments i. You will find a way to automate this process. Jun 8, 2022 · rpart to fit decision trees without tuning. plot to plot our decision trees. 1 Model Training and Parameter Tuning. g. "grid" or "random". Here is the link to data. This means that if any terminal node has more than two Feb 29, 2024 · Hyperparameter Tuning using Randomized Search CV. A hyperparameter grid in the form of a Python dictionary with names and values of parameter names must be passed as Dec 23, 2017 · Typically, a machine learning engineer or data scientist will perform some form of manual parameter tuning (grid search or random search) for a few models — like decision tree, support vector Jun 18, 2023 · Grid search and random search are two popular techniques used for hyperparameter tuning. You will learn how a Grid Search works, and how to implement it to optimize the performance of your Machine Learning Method. The Random Search and Grid Search optimization techniques show promise and efficiency for this task. 2. Keywords: Machine Learning, See full list on towardsdatascience. May 10, 2023 · The next step is to define the hyperparameter space that you want to search over. We can further improve our results by using grid search to focus on the most promising hyperparameters ranges found in the random search. However, there is a superior method available through the Hyperopt package! Hyperopt is an open source hyperparameter tuning library that uses a Bayesian approach to find the best values for the hyperparameters. Feb 1, 2022 · The search for optimal hyperparameters is called hyperparameter optimization, i. This article covers the comparison and implementation of random search, grid search, and Bayesian optimization methods using Sci-kit learn and HyperOpt libraries for hyperparameter tuning of the…. Two of the key challenges in machine learning are finding the right algorithm to use and optimizing your model. Jul 3, 2018 · 23. Then, when we run the hyperparameter tuning, we try all the combinations from both May 10, 2023 · Here's an example of how to use it: grid_search = GridSearchCV(svm_clf, param_grid, cv=cv) grid_search. This dataset contains Jun 12, 2023 · Grid Search Cross-Validation. Figure 4. # Fit GridSearchCV to the training data. qk lz qt kt rr lc kf dk dn le