June 2018


NepalEarthquake3

Town of Barpak after Gorkha earthquake. Image from The Telegraph (UK)

 

by George Taniwaki

This is the final set of my notes from a machine learning class offered by edX. Part 1 of this blog entry is posted in June 2018.

Step 7: Optimize model

At the end of step 6, I discovered that none of my three models met the minimum F score (at least 0.60) needed to pass the class. Starting with the configuration shown in Figure 5, I modified my experiment by replacing the static data split with partition and sampling using 10 evenly split folds. I used a random seed of 123 to ensure reproducibility.

I added both a cross-validation step and a hyperparameter tuning step to optimize results. To improve performance, I added a Convert to indicator values module. This converts the categorical variables into dummy binary variables before running the model.

Unfortunately, the MAML ordinal regression module does not support hyperparameter tuning. So I replaced it with the one-vs-all multiclass classifier. The new configuration is shown in Figure 6 below. (Much thanks to my classmate Robert Ritz for sharing his model.)

Figure 6. Layout of MAML Studio experiment with partitioning and hyperparameter tuning steps

Fig6MamlConfig2

For an explanation of how hyperparameter tuning works, see Microsoft documentation and MSDN blog post.

Model 5 – One-vs-all multiclass model using logistic regression classifier

In the earlier experiments, the two-class logistic regression classifier gave the best results. I will use it again with the one-vs-all multiclass model. The default parameter ranges for the two-class logistic regression classifier are: Optimization tolerance = 1E-4, 1E-7, L1 regularization weight = 0 .01, 0.1, 1.0, L2 regularization weight = 0.01, 0.1, 1.0, and memory size for L-BFGS = 5, 20, 50.

Table 12a. Truth table for one-vs-all multiclass model using logistic regression classifier

Truth table Is 1 Is 2 Is 3 TOTAL
Predict 1 296 156 20 472
Predict 2 621 4633 1651 6905
Predict 3 21 847 1755 2623
TOTAL 936 5636 3426 10000

 

Table 12b. Performance measures for one-vs-all multiclass model using logistic regression classifier

Performance Value
Avg Accuracy 0.76
F1 Score 0.64
F1 Score (test data) Not submitted

 

The result is disappointing. The new model has an F1 score of 0.64, which is lower than the F1 score of the ordinal regression model using the logistic regression classifier.

Model 6 – Add geo_level_2 to model

Originally, I excluded geo_level_2 from the model even though the Chi-square test was significant because it consumed too many degrees of freedom. I rerun the experiment with the variable and keeping all other variables and parameters the same.

Table 13a. Truth table for one-vs-all multiclass model using logistic regression classifier and including geo_level_2

Truth table Is 1 Is 2 Is 3 TOTAL
Predict 1 355 218 27 600
Predict 2 564 4662 1446 6672
Predict 3 19 756 1953 2728
TOTAL 938 5636 3426 10000

 

Table 13b. Performance measures for one-vs-all multiclass model using logistic regression classifier and including geo_level_2

Performance Value
Avg Accuracy 0.80
F1 Score 0.70
F1 Score (test data) Not submitted

 

The resulting F1 score using the test dataset is 0.70, which is better than any prior experiments and meets our target of 0.70 exactly.

Model 7 – Add height/floor to the model

I will try to improve the model by adding a variable measuring height/floor. This variable is always positive, skewed toward zero and has a long tail. To normalize it, I apply the natural log transform and name the variable ln_height_per_floor. Table 14 and Figure 7 show the summary statistics.

Table 14. Descriptive statistics for ln_height_per_floor

Variable name Min Median Max Mean Std dev
ln_height_per_floor -1.79 0.69 2.30 0.76 0.25

 

Figure 7. Histogram of ln_height_per_floor

Fig7HistLn_height_per_floor

I run the model again with no other changes.

Table 15a. Truth table for one-vs-all multiclass model using logistic regression classifier, including geo_level_2, height/floor

Truth table Is 1 Is 2 Is 3 TOTAL
Predict 1 366 227 28 621
Predict 2 557 4640 1436 6633
Predict 3 15 769 1962 2746
TOTAL 938 5636 3426 10000

 

Table 15b. Performance measures for one-vs-all multiclass model using logistic regression classifier, including geo_level_2, height/floor

Performance Value
Avg Accuracy 0.80
F1 Score 0.70
F1 Score (test data) Not submitted

 

The accuracy of predicting damage_level = 1 or 3 increases, but the accuracy of 2 decreases. Resulting in no change in average accuracy or the F1 score.

Model 8 – Go back to ordinal regression

The accuracy of the one-vs-all multiclass model was significantly improved by adding geo_level_2. Let’s see what happens if I add this variable to the ordinal regression model which produced a higher F1 score than the one-vs-all model.

Table 16a. Truth table for ordinal regression model using logistic regression classifier, including geo_level_2, height/floor

Truth table Is 1 Is 2 Is 3 TOTAL
Predict 1 80 59 1 140
Predict 2 227 1557 542 2326
Predict 3 3 246 585 834
TOTAL 310 1862 1128 3300

 

Table 16b. Performance measures for ordinal regression model using logistic regression classifier, including geo_level_2, height/floor

Performance Value
Avg Accuracy 0.78
F1 Score 0.67
F1 Score (test data) Not submitted

 

Surprisingly, ordinal regression produces worse results when the geo_level_2 variable is included than without it.

Model 9 – Convert numeric to categorical

I spent a lot of effort adjusting and normalizing my numeric variables. They were mostly integer values with small range and did not appear to be correlated to damage_grade. Could the model be improved by treating them as categorical? Let’s find out.

First I perform a Chi Square test to confirm all of the variables are significant. Then run the model after converting all the values from numeric to strings, and converting all the variables from numeric to categorical.

Table 17. Chi-square results of numerical values to damage_grade

Variable name Chi-square Deg. of freedom P value
count_floor_pre_eq 495 14 < 2.2E-16*
height 367 37 < 2.2e-16*
age 690 60 < 2.2e-16*
area 738 314 < 2.2e-16*
count_families 76 14 1.3e-10*
count_superstructure 104 14 7.1e-16*
count_secondary_use 79 4 3.6e-16*

*One or more enums have sample sizes too small to use Chi-square approximation
[ ] P value greater than 0.05 significance level

Table 18a. Truth table for ordinal regression model using logistic regression classifier, including geo_level_2, height/floor, and converting numeric to categorical

Truth table Is 1 Is 2 Is 3 TOTAL
Predict 1 83 62 3 148
Predict 2 224 1544 540 2308
Predict 3 3 256 585 844
TOTAL 310 1862 1128 3300

 

Table 18b. Performance measures for ordinal regression model using logistic regression classifier, including geo_level_2, height/floor, and converting numeric to categorical

Performance Value
Avg Accuracy 0.78
F1 Score 0.67
F1 Score (test data) Not submitted

 

Changing the integer variables to categorical has almost no impact on the F1 score.

Conclusion

Table 19 below summarizes all nine models I built. Six of them achieved an F1 score of 0.60 or higher on the training data, which would probably have been sufficient to pass the class. Two of them had F1 score of 0.70 which would be a grade of 95 out of 100.

I was unable to run most of these models on the test dataset and submit the results to the data science capstone website. Thus, I do not know what my leaderboard F1 score would be. It is possible that I overfit my model to the training data and my leaderboard F1 score might be lower.

Finding the best combination of variables, models, and model hyperparameters is difficult to do manually. It took me several hours to build the nine models described in this blog post. Machine learning automation tools exist but are not yet robust, nor built into platforms like MAML Studio. (Much thanks again to Robert Ritz who pointed me to TPOT, a Python-based tool for auto ML.)

Table 19. Summary of models. Green indicates differences from base case, model 2

Model Variables Algorithm Training data F1 score (test data)
1 None Naïve guess = 2 None 0.56
3 27 from Table 5 Ordinal regression with decision forest 0.67 split 0.64
4 27 from Table 5 Ordinal regression with SVM 0.67 split 0.57 (0.5644)
2 27 from Table 5 Ordinal regression with logistic regression 0.67 split 0.68 (0.5687)
5 27 from Table 5 One-vs-all multiclass with logistic regression, hyperparameter tuning 10-fold partition 0.64
6 27 from Table 5, geo_level_2 One-vs-all multiclass with logistic regression, hyperparameter tuning 10-fold partition 0.70
7 27 from Table 5, geo_level_2, height/floor One-vs-all multiclass with logistic regression, hyperparameter tuning 10-fold partition 0.70
8 27 from Table 5, geo_level_2, height/floor Ordinal regression with logistic regression 0.67 split 0.67
9 27 from Table 5, convert numeric to categorical, geo_level_2, height/floor Ordinal regression with logistic regression 0.67 split 0.67

NepalEarthquake2

Damage caused by Gorkha earthquake. Image by Prakash Mathema/AFP/Getty Images

by George Taniwaki

This is a continuation of my notes for a machine learning class offered by edX. Part 1 of this blog entry is posted in June 2018.

Step 4: Multivariate analysis

Pairwise scatterplots of the numerical variables after adjusting and normalizing are shown in Figure 4 below. The dependent variable (damage_grade) does not appear to be correlated with any of the numerical independent variables. Despite the lack of correlation, I included all the numeric variables when building the model. If I have time, I will convert these numerical variables into categorical ones.

Among the independent variables, covariance is highest between count_floors_pre_eq and height highlighted in green. This makes sense, taller buildings are likely to have more floors. If I have time, I will add a new variable height_per_floor (= height / count_floors_pre_eq).

Figure 4. Pairwise scatterplots of all numerical parameters. Correlations highlighted in green

Fig4Scatterplot

There are 11 categorical and 23 binary parameters. I used the Chi-square test to compare distributions of these to the distribution of the dependent variable damage_grade, treated as categorical. The results are shown in Table 5 below.

All are statistically significant at 0.05 level, except for the 5 highlighted in red brackets. They will be excluded from the model. Two of the geo_level variables consume too many degrees of freedom given our sample size. (Even big datasets have limitations.) They are highlighted in orange and will be excluded from the model. If I have time, I will add a new custom geo_level variable with about 1000 degrees of freedom. The remaining 27 variables will be retained for use in the model.

Table 5. Chi-square results of categorical and Boolean values to damage_grade

Variable name Chi-square Deg. of freedom P value
geo_level_1_id 2746 60 < 2.2e-16*
geo_level_2_id 6592 2272 < 2.2e-16*
geo_level_3_id 13039 10342 < 2.2e-16*
land_surface_condition 15.9 4 0.0032
foundation_type 1857 8 < 2.2e-16*
roof_type 1122 4 < 2.2e-16
ground_floor_type 1347 8 < 2.2e-16*
other_floor_type 1117 6 < 2.2e-16
position 47.3 6 1.6e-08
plan_configuration 46.5 16 8.0e-05*
legal_ownership_status 80.2 6 3.2e-15
has_superstructure_adobe_mud 50.3 2 1.1e-11
has_superstructure_mud_mortar_stone 1053 2 < 2.2e-16
has_superstructure_stone_flag 28.6 2 6.2e-07
has_superstructure_cement_mortar_stone 53.8 2 2.1e-12
has_superstructure_mud_mortar_brick 37.5 2 7.3e09
has_superstructure_cement_mortar_brick 632 2 < 2.2e-16
has_superstructure_timber 64.9 2 8.0e-15
has_superstructure_bamboo 55.1 2 1.1e-12
has_superstructure_rc_non_engineered 296 2 < 2.2e-16
has_superstructure_rc_engineered 603 2 < 2.2e-16*
has_superstructure_other 9.8 2 0.0072
has_secondary_use 76.2 2 < 2.2e-16
has_secondary_use_agriculture 25.0 2 3.8e-06
has_secondary_use_hotel 90.9 2 < 2.2e-16
has_secondary_use_rental 49.4 2 1.9e-11
has_secondary_use_institution 10.8 2 0.0046*
has_secondary_use_school 32.1 2 1.1e-07*
has_secondary_use_industry 2.3 2 [ 0.31 ]*
has_secondary_use_health_post 1.5 2 [ 0.46 ]*
has_secondary_use_gov_office 4.2 2 [ 0.12 ]*
has_secondary_use_use_police 0.8 2 [ 0.68 ]*
has_secondary_use_other 15.3 2 0.00049*
has_missing_age 3.1 2 [ 0.21 ]*

*One or more enums have sample sizes too small to use Chi-square approximation
[ ] P value greater than 0.05 significance level

Step 5: Building the model

The dependent variable can take on the value 1, 2, or 3. I could use a classification method like multi-class logistic regression to create our model. However, there is a better way. I will use the ordinal regression algorithm available from Microsoft Azure Machine Learning (MAML).

Ordinal regression requires a binary classifier method. For this project, I will try three classifiers available in MAML, two-class logistic regression, two-class decision forest, and two-class support vector machine (SVM). I will use the default parameters for each classifier and submit all three models as entries in the contest. (This is sort of a cheat to improve the F1 score and my grade. In practice, you should only submit the results using the best model based on the training data.)

A simple model configuration using a static data split and without either a cross-validation step or a hyperparameter tuning step to optimize results is shown in Figure 5 below. I will add these steps later if the simple model does not meet the performance goals.

Figure 5. Layout of a simple MAML Studio experiment

Fig5MamlConfig1

I used a data split of 0.67, meaning 6,700 records were used to train the model and the remaining 3,300 were used to score and evaluate it. I used a random number seed of 123 to ensure every run of my experiment used the same split and produced replicable results.

Step 6: Measuring performance and testing results

A generic truth table for an experiment with 3 outcomes is shown in Table 6a below. Using data from the truth table, four performance metrics can be calculated, average accuracy, micro-average precision , micro-average recall, and geometric average F1 score. The calculation of the performance metrics is shown in Table 6b. Note that since all combinations are measured, recall, precision, and F1 score are all equal. Perhaps the contest should have used the macro-average recall and precision to calculate the F1 score.

Table 6a. Generic truth table for case with 3 outcomes

Truth table Is 1 Is 2 Is 3 TOTAL
Predict 1 TP1|TN2|TN3 FP1|FN2|TN3 FP1|TN2|FN3 TP1+FP1
Predict 2 FN1|FP2|TN3 TN1|TP2|TN3 TN1|FP2|FN3 TP2+FP2
Predict 3 FN1|TN2|FP3 TN1|FN2|FP3 TN1|TN2|TP3 TP3+FP3
TOTAL TP1+FN1 TP2+FN2 TP3+FN3 Pop

 

Table 6b. Performance measures for case with 3 outcomes

Performance Calculation
Avg Accuracy ∑((TP + TN) / Pop) / 3
Avg Precision (micro) P = ∑TP / ∑(TP + FP)) = ∑TP / Pop
Avg Recall (micro) R = ∑TP / ∑(TP + FN)) = ∑TP / Pop
F1 Score (2 * P * R) / (P + R) = ∑TP / Pop

 

Grading for the course is based on the F1 score for a hidden subset of the test dataset as shown in Table 7 below. F1 scores between these points will receive linearly proportional grades. For instance,  an F1 score of 0.65 would earn a grade of 75.

Table 7. Grading of project based on F1 score (test data)

F1 Score Grade
< 0.60 1 out of 100
0.60 60/100
0.64 70/100
0.66 80/100
0.70 95/100

 

Below are the results of my models.

Model 1 – Naïve guessing

The most common value for damage_grade is 2. Any prediction model should perform better than the naïve guess of predicting the damage is 2 for all buildings.

Table 8a. Truth table for naive guess of damage_grade = 2

Truth table Is 1 Is 2 Is 3 TOTAL
Predict 1 0 0 0 0
Predict 2 310 1862 1128 3300
Predict 3 0 0 0 0
TOTAL 310 1862 1128 3300

 

Table 8b. Performance measures for naive guess of damage_grade = 2

Performance Value
Avg Accuracy 0.71
F1 Score 0.56
F1 Score (test data) Not submitted

 

Model 2 – Ordinal regression model using 2-class logistic regression classifier

The default parameters for the 2-class logistic regression classifier are: Optimization tolerance = 1E-07, L1 regularization weight = 1, L2 regularization weight = 1. Notice in Table 9b the large gap between the F1 score using the training data and the test data. This indicates the model is overfitted.

Table 9a. Truth table for ordinal regression model using 2-class logistic regression classifier

Truth table Is 1 Is 2 Is 3 TOTAL
Predict 1 84 52 1 137
Predict 2 223 1567 536 2326
Predict 3 3 243 591 837
TOTAL 310 1862 1128 3300

 

Table 9b. Performance measures for ordinal regression model using 2-class logistic regression classifier

Performance Value
Avg Accuracy 0.79
F1 Score 0.68
F1 Score (test data) 0.5687

 

Model 3 – Ordinal regression model using 2-class decision forest classifier

The default parameter settings are: Resampling method = Bagging, Trainer mode = Single parameter, Number of decision trees = 8, Maximum depth of trees = 32, Number of random splits per need = 128, minimum number of samples per node = 1.

Table 10a. Truth table for ordinal regression model using decision forest classifier

Truth table Is 1 Is 2 Is 3 TOTAL
Predict 1 85 55 1 144
Predict 2 218 1335 432 1985
Predict 3 7 472 692 1171
TOTAL 310 1862 1128 3300

 

Table 10b. Performance measures for ordinal regression model using decision forest classifier

Performance Value
Avg Accuracy 0.76
F1 Score 0.64
F1 Score (test data) Not submitted

 

Model 4 – Ordinal regression model using 2-class support vector machine (SVM) classifier

The default parameter settings are: Number of iterations = 1, Lambda = 0.001.

Table 11a. Truth table for ordinal regression model using SVM classifier

Truth table Is 1 Is 2 Is 3 TOTAL
Predict 1 31 21 3 55
Predict 2 273 1667 932 2872
Predict 3 6 174 193 373
TOTAL 310 1862 1128 3300

 

Table 11b. Performance measures for ordinal regression model using SVM classifier
Avg F1 Score0.

Performance Value
Avg Accuracy 0.72
F1 Score 0.57
F1 Score (test data) 0.5644

 

Summary of models in step 6

Unfortunately, none of my initial models performed well. The F1 score never meets the target of 0.70. In fact, in some cases my model don’t do much better than just guessing. (Note: You can see my scores on the contest leaderboard.)  In the next section, we will add a cross-validation step and an hyperparameter tuning step to optimize the models and and see if that improves them.

This completes steps 4 to 6 of building a machine learning model. The remaining optimization step and the results are posted at How to create a machine learning model – Part 3.

NepalEarthquake1

Damage caused by Gorkha earthquake. Image from The Guardian

by George Taniwaki

At the beginning of each quarter edX and Microsoft offer a one-month long course called DAT 102x, Data Science Capstone. The class consists of a single machine learning project using real-world data. The class this past April used data collected by the Nepal government after the Gorkha earthquake in 2015. The earthquake killed nearly 9,000 people and left over 100,000 homeless.

The assignment was to predict damage level for individual buildings based on building characteristics such as age, height, location, construction materials, and use type. Below are the steps I used to solve this problem. The solution is general enough to apply to any machine learning problem. My description is a bit lengthy but shows the iterative nature of tuning a machine learning model.

About machine learning contests

The class project is operated as a contest. Students download training and test datasets, create a model using the training dataset, use the model to make predictions for the test dataset, submit their predictions, and see their scored results on a leaderboard.

As is common for machine learning contests, the training data consists of two files. The first file includes a large number of records (for the earthquake project, there were 10,000). Each record consists of an index and the independent variables (38 building parameters). A separate label file contains only two columns, the index and and their associated dependent variable(s) (in the earthquake project, there is only one, called damage_grade). The two files must be joined before creating a model.

The test file (10,000 more records of building indexes and parameters) has the same format as the training file. You use your model to create an output file consisting of the index and the predicted values of the dependent variable(s). You submit the file to a web service which then scores your results.

You can submit multiple predictions to be scored, adjusting your model after each submission in an attempt to improve your score. Your final score is based on the highest score achieved. To reduce the chance that competitors (students) overfit their model to the test data, the score is based on an undisclosed subset of records in the test file.

Approach to model building

The general approach to building a machine learning model is to first examine the dependent variables using univariate methods (step 1). Repeat for the independent variables (step 2). Normalize the variables (step 3). Examine correlations using multivariate methods (step 4).  Select the relevant variables, choose a model, and build it (step 5). Evaluate and test the model (step 6) and tune the parameters (step 7) to get the best fit without overfitting. Some iteration may be required.

Step 1: Univariate statistics for the dependent variable

There is one dependent variable, damage_grade, labeled with an integer from 1 to 3. Higher values mean worse damage. However, the intervals between each class are not constant, so the scale is ordinal not interval. Descriptive statistics are shown in Table 1 and Figure 1 below.

Table 1. Descriptive statistics for dependent variable

Variable name Min Median Max Mean Std dev
damage_grade 1 2 3 2.25 0.61

 

Figure 1. Histogram of dependent variable

Fig1HistDep

Step 2: Univariate statistics for the independent variables

As mentioned above, there are 38 building parameters. Details of the variables are given at Data Science Capstone. The 38 independent variables can be divided into 4 classes, binary, interval integer, float, and categorical as shown in Table 2 below. Notice that the parameter count_families is defined as a float even though it only takes on integer values.

Table 2. Summary of independent variables

Variable type Quantity Examples
Binary (Boolean) 22 has_superstructure_XXXX, has_secondary_use, has_secondary_use_XXXX
Integer, interval 4 count_floors_pre_eq, height, age, area
Float 1 count_families
Categorical 11 geo_level_1_id, geo_level_2_id, geo_level_3_id, land_surface_condition, foundation type, roof_type, ground_floor_type, other_floor_type, position, plan_configuration, legal_ownership_status

 

The binary variables fall into three groups. First is has_superstructure_XXXX, where XXXX can be 11 possible materials used to produce the building superstructure such as adobe mud, timber, bamboo, etc. The second is has_secondary_use_XXXX, where XXXX can be 10 possible secondary uses for the building such as agriculture, hotel, school, etc. Finally, has_secondary_use indicates if any has_secondary_use_XXXX variables is true.

Whenever I have groups of binary variables, I like to create new interval integer variables based on them. In this case, they are named count_superstructure and count_secondary_use which are a count of the number of true values for each. count_superstructure can vary from 0 to 11 while count_secondary_use can vary from 0 to 10.

For the 7 numerical parameters, their minimum, median, maximum, mean, standard deviation, and histogram are shown in Table 3 and Figure 2 below. Possible outliers, which occur in all 7 numerical variables, are highlighted in red.

Table 3. Descriptive statistics for the 7 numerical variables. Red indicates possible outliers

Variable name Min Median Max Mean Std dev
count_floors_pre_eq 1 2 9 2.15 0.74
height 1 5 30 4.65 1.79
age 0 15 995 25.39 64.48
area 6 34 425 38.44 21.27
count_families 0 1 7 0.98 0.42
count_superstructure 1 1 8 1.45 0.78
count_secondary_use 0 0 2 0.11 0.32

 

 

Figure 2. Histograms for the 7 numerical variables. Red indicates possible outliers

Fig2HistIndep

Upon inspection of the dataset, none of the numerical variables have missing values. However, it appears that for 40 records, age has an outlier values of 995. The next highest value is 200. Further, the lowest age value is zero, which does not work well with the log transform. To clean the data, I created a new binary variable named has_missing_age, with value = 1 if age = 995, else = 0 otherwise. I also created a new numerical variable named adjust_age, with value = 1 if age = 0, else = 15 (the median) if age = 995, else = age otherwise.

The variable area has a wide range, but does not appear to contain any outliers.

The variables count_families, count_superstructure, and count_secondary_use do not seem to have any outliers. They also do not need to be normalized.

For the 11 categorical variables, the number of categories (enums), and the names of the enums with the largest and smallest counts are shown in Table 4 below.

Table 4. Descriptive statistics for the 11 categorical variables. Red indicates one or more enums has fewer than 10 recorded instances

Variable name Count enums Max label / count Min label / count Comments
geo_level_1_id 31 0 / 903 30 / 7 hierarchical
geo_level_2_id 1137 0 / 157 tie / 1 hierarchical
geo_level_3_id 5172 7 / 24 tie / 1 hierarchical
land_surface_condition 3 d502 / 8311 2f15 / 347
foundation type 5 337f / 8489 bb5f / 48
roof_type 3 7g76 / 7007 67f9 / 579
ground_floor_type 5 b1b4 / 8118 bb5f / 10
other_floor_type 4 f962 / 6412 67f9 / 415 correlated with ground_floor_type
position 4 3356 / 7792 bcab / 477
plan_configuration 9 a779 / 9603 cb88 / 1 lumpy distribution
legal_ownership_status 4 c8e1 / 9627 bb5f / 61 lumpy distribution

 

None of the categorical or binary variables have missing values. None of the enums are empty, though some of the enums (highlighted in red in Table 4 above) have fewer than 10 recorded instance, so may bias the model. Unfortunately, we do not have any information about the meaning of the enum labels, so do not have a good way to group the sparse enums into larger categories. If this were a real-world problem I would take time to investigate this issue.

Step 3: Normalize the numerical variables

As can be seen in Figure 2 above, some of the independent numerical variables are skewed toward low values and have long tails. I normalized the distributions by creating new variables using the log transform function. The resulting variables have names prefixed with ln_. The descriptive statistics of the normalized variables are shown in Table 5 and Figure 3 below.

Table 5. Descriptive statistics for adjusted and normalized numerical parameters

Variable name Min Median Max Mean Std dev
ln_count_floors_pre_eq 0 0.69 2.19 0.70 0.36
ln_height 0 1.61 3.40 1.46 0.40
ln_adjust_age 0 2.71 5.30 2.61 1.12
ln_area 1.79 3.53 6.05 3.54 0.46

 

Figure 3. Histograms of adjusted and normalized numerical parameters

Fig3HistIndep

This completes the first 3 steps of building a machine learning model. Steps 4 to 6 to solve this contest problem are posted at How to create a machine learning model – Part 2. The final optimization step 7 is posted at Part 3.