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 hyperparameter tuning

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
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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.

microexcelanlyst

by George Taniwaki

While working toward my Microsoft Data Science Certificate (see Jul 2017 blog post), I also completed the Microsoft Excel for the Data Analyst XSeries Program sponsored by Microsoft and edX.

There are 3 classes in the program, two of which were also courses for the Microsoft Data Science Certificate.

DAT205x – Introduction to Data Analysis using Excel

This basic course on data analysis using Excel covers pivot tables, using SUMIF() and SUMIFS() functions to create dashboards and year-over-year comparison tables (something that is not possible using pivot tables alone), creating reports with hierarchal data, using Power Pivot, and creating multi-table reports using the data model and the More tables… feature.

Year-over-year comparison tables can also be created using the Excel data model and time intelligence functions. These are covered in the third course, DAT 206x.

Time: Since I am already an experienced Excel user, I skipped the videos and just did the homework. I covered the 8 modules in about 6 hours

Score:  I missed 1 quiz question and no lab questions for a combined score of 99%

image     image

DAT222x – Essential Statistics for Data Analysis using Excel

[I took DAT222x in order to earn the Microsoft Data Science Certificate. This section is copied from this  Jul 2017 blog post.]

This class is comprehensive and covers all the standard statistics and probability topics including descriptive statistics, Bayes rule, random variables, central limit theorem, sampling and confidence interval, and hypothesis testing. Most analysis is conducted using the Data analysis pack add-in for Excel.

Time: I used to work in market research, so I know my statistics. However, there are 36 homework assignments and it took me over 20 hours to complete the 5 modules.

Score: I missed 9 questions on the quizzes (88%) and six in the final exam (81%) for a combined score of 86%. (Despite the time it takes to complete, homework counts very little toward the final grade)

DAT222x-Score_thumb10     DAT222x-Certificate21

DAT206x – Analyzing and Visualizing Data with Excel

Topics include importing data and using queries with Excel, the Excel data model, using the M query language and DAX query language, creating dashboards and visualizations, and using Excel with Power BI.

Within the M language, topics include using the functions in the ribbon, including filtering rows, Table.Unpivot function.

Within the DAX language, topics include using the X functions like SUMX() and the CALCULATE() function, using Calendar table and time intelligence, and customize pivot tables and pivot charts using the CUBE functions from multidimensional expressions (MDX) language. The CUBE functions can also generate a table that can be used to create chart types that Excel does not support directly from a pivot table (for instance the new treemap, sunburst, and histogram charts).

Time: I am an experienced Excel user, but some of the advanced DAX functions were new to me. 6 hours for 8 modules

Score: I got a bit sloppy. I missed 2 lab questions and 1quiz question for a combined score of 95%

DAT206x Score     DAT206x Certificate

Final Certificate

Below is my certificate of completion for the Microsoft Excel for the Data Analyst XSeries Program.

ExcelXSeries Certificate

MsftBigData

by George Taniwaki

Big data and machine learning are all the rage now. Articles in the popular press inform us that anyone who can master the skills needed to turn giant piles of previously unexplored data into golden nuggets of business insight can write their own ticket to a fun and remunerative career (efinancialcareers May 2017).

Conversely, the press also tells us that if we don’t learn these skills a computer will take our job (USA Today Mar 2014). I will have a lot more to say about changes in employment and income during the industrial revolution in future blog posts.

But how do you learn to become a data scientist. And which software stack should one specialize in? There are many tools to choose from. Since I live in the Seattle area and do a lot of work for Microsoft, I decided to do take an online class developed and sponsored by Microsoft and edX. Completion of the course leads to a Microsoft Data Science Certificate.

The program consists of 10 courses with some choices, like conducting analysis using either Excel or Power BI, and programming using either R or Python. Other parts of the Microsoft stack you will learn include SQL Server for queries and Microsoft Azure Machine Learning (MAML) for analysis and visualization of results. The courses are priced about $99 each. You can audit them for free if you don’t care about the certificates.

I started the program in February and am about half way done. In case any clients or potential employers are interested in my credentials, my progress is shown below.

DAT101x – Data Science Orientation

If you haven’t been in college in a while or have never taken an online class, this is a good introduction to online learning. The homework consists of some simple statistics and visualization problems.

Time: 3 hours for 3 modules

Score: 100% on 3 assignments

DAT101x Score    DAT101x Certificate

DAT201x – Querying with Transact-SQL

I took a t-SQL class online at Bellevue College two years ago. Taking a class with a real teacher, even one you never meet, was a significantly better experience than a self-paced mooc. This course starts with the basics like select, subqueries, and variables. It also covers intermediate topics like programming, expressions, stored procedures, and error handling. I did my homework using both a local instance of SQL Server and on an Azure SQL database.

Time: 20 hours for 11 modules

Score: I missed one question in the homework and two in the final exam for a combined score of 94%

DAT201x Score     DAT201x Certificate

DAT207x – Analyzing and Visualizing Data with Power BI

I already have experience creating reports using Power BI. I also use Power Query (now called get and transform data) and M language and Power Pivot and DAX language, so this was an easy class.

The course covers data transforms, modeling, visualization, Power BI web service, organization packs, security and groups. It also touches on the developer API and building mobile apps.

Time: 12 hours for 9 modules

Score: I missed one lab question for a combined score of 98%

DAT207x Score     DAT207x Certificate

DAT222x – Essential Statistics for Data Analysis using Excel

This class is comprehensive and covers all the standard statistics and probability topics including descriptive statistics, Bayes rule, random variables, central limit theorem, sampling and confidence interval, and hypothesis testing. Most analysis is conducted using the Data analysis pack add-in for Excel.

Time: I used to work in market research, so I know my statistics. However, there are 36 homework assignments and it took me over 20 hours to complete the 5 modules.

Score: I missed 9 questions on the quizzes (88%) and six in the final exam (81%) for a combined score of 86%. (Despite the time it takes to complete, homework counts very little toward the final grade)

DAT222x Score     DAT222x Certificate

DAT204x – Introduction to R for Data Science

Now we are getting into the meat of the program. R is a functional language. In many ways it is similar to the M language used in Power Query. I was able to quickly learn the syntax and grasp the core concepts.

The course covers vectors, matrices, factors, lists, data frames, and simple graphics.

The lab assignments use DataCamp which has a script window where you write code and a console window that displays results. That makes it easy to debug programs as you write them.

The final exam used an unexpected format. It was timed and consisted of about 50 questions, mostly fill-in-the-blank responses that include code snippets. You are given 4 minutes per question. If you don’t answer within the time limit, it goes to the next question. I completed the test in about 70 minutes, but I ran out of time on several questions, and was exhausted at the end. I’m not convinced that a timed test is the best way to measure subject mastery by a beginning programmer. But maybe that is just rationalization on my part.

Time: 15 hours for 7 modules

Score: I got all the exercises (ungraded) and labs right and missed two questions in the quizzes. I only got 74% on the final, for a combined score of 88%

DAT204x Score     DAT204x Certificate

DAT203.1x Data Science Essentials

The first three modules in this course covered statistics and was mostly a repeat of the material introduced in DAT222x. But the rest of the course provides an excellent introduction to machine learning. You learn how to create a MAML instance, import a SQL query, manipulate it using R or Python, create a model, score it, publish it as a web service, and use the web service to append predictions as a column in Excel. I really like MAML. I will post a review of my experience in a future blog post.

The course was a little too cookbook-like for my taste. It consisted mostly of following directions to drag-drop boxes onto the canvas UI and copy-paste code snippets into the panels. However, if you want a quick introduction to machine learning without having to dig into the details of SQL, R, or Python, this is a great course.

Time: 10 hours for 6 modules

Score: 100% on the 6 labs and the final

DAT203.1x Score     DAT203.1x Certificate

I have now completed six out of the ten courses required for a certificate. I expect to finish the remaining 4 needed for a certificate by the end of the year. I will also probably take some of the other elective courses simply to learn more about Microsoft’s other machine learning and cloud services.

For my results in the remaining classes, see Microsoft Data Science Certificate-Part 2

Update: Modified the description of the final exam for DAT204x.

by George Taniwaki

Did you watch the debate on Monday night? I did. But I am also very interested in the post-debate media coverage and analysis. This morning, two articles that combine big data and the debate caught my eye. Both are novel and much more interesting than the tired stories that simply show changes in polls after a debate.

First, the New York Time reports that during the presidential debate (between 9:00 and 10:30 PM EDT) there is high correlation between the Betfair prediction market for who will win the presidential election and afterhours S&P 500 futures prices (see chart 1).

PresidentSandP500

Chart 1. Betfair prediction market for Mrs. Clinton compared to S&P 500 futures. Courtesy of New York Times

Correlation between markets is not a new phenomena. For several decades financial analysts have measured the covariance between commodity prices, especially crude oil, and equity indices. But this is the first time I have seen an article illustrating the covariance between a “fun” market for guessing who will become president against a “real” market. Check out the two graphs above, the similarity in shape is striking, including the fact that both continue to rise for about an hour after the debate ended.

In real-time, while the debate was being broadcast, players on Betfair believed the chance Mrs. Clinton will win the election rose by 5 percent. Meanwhile, the price of S&P 500 futures rose by 0.6%, meaning investors (who may be the same speculators who play on Betfair) believed the stock market prices in November were likely to be higher than before the debates started. There was no other surprise economic news that evening, so the debate is the most likely explanation for the surge. Pretty cool.

If the two markets are perfectly correlated (they aren’t) and markets are perfectly efficient (they aren’t), then one can estimate the difference in equity futures market value between the two candidates. If a 5% decrease in likelihood of a Trump win translates to a 0.6% increase in equity futures values, then the difference between Mr. Trump or Mrs. Clinton being elected (a 100% change in probability) results in about a 12% or $1.2 trillion (the total market cap of the S&P 500 is about $10 trillion) change in market value. (Note that I assume perfect correlation between the S&P 500 futures market and the actual market for the stocks used to calculate the index.)

Further, nearly all capital assets (stocks, bonds, commodities, real estate) in the US are now highly correlated. So the total difference is about $24 trillion (assuming total assets in the US are $200 trillion). Ironically, this probably means Donald Trump would be financially better off if he were to lose the election.

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The other article that caught my eye involves Google Trend data. According to the Washington Post, the phrase “registrarse para votar” was the third highest trending search term the day after the debate was broadcast. The number of searches is about four times higher than in the days prior to the debates (see chart 2). Notice the spike in searches matches a spike in Sep 2012 after the first Obama-Romney debate.

The article says that it is not clear if it was the debate itself that caused the increase or the fact that Google recently introduced Spanish-language voting guides to its automated Knowledge Box, which presumably led to more searches for “registrarse para votar”. (This is the problem with confounding events.)

After a bit of research, I discovered an even more interesting fact. The spike in searches did not stop on Sep 27. Today, on Sep 30, four days after the debates, the volume of searches is 10 times higher than on Sep 27, or a total of 40x higher than before the debate (see chart 3). The two charts are scaled to make the data comparable.

VotarWashPost

Chart 2. Searches for “registrarse para votar” past 5 years to Sep 27. Courtesy of Washington Post and Google Trends

VotarToday

Chart 3. Searches for “registrarse para votar” past 5 years to Sep 30. Courtesy of Google Trends

I wanted to see if the spike was due to the debate or due to the addition of Spanish voter information to the Knowledge Box. To do this, I compared “registrarse para votar” to “register to vote”. The red line in chart 4 shows Google Trend data for “register to vote” scaled so that the bump in Sept 2012 is the same height as in the charts above. I’d say the debate really had an unprecedented effect on interest in voting and the effect was probably bigger for Spanish speaking web users.

VoteToday

Chart 4. Searches for “register to vote” past 5 years to Sep 30. Courtesy of Google Trends

Finally, I wanted to see how the search requests were distributed geographically. The key here is that most Hispanic communities vote Democratic and many states with a large Hispanic population are already blue (such as California, Washington, New Mexico, New Jersey, and New York). The exception is Florida with a large population of Cuban immigrants who tend to vote Republican.

VotarRegionToday

Chart 5. Searches for “registrarse para votar” past 5 years to Sep 30 by county. Courtesy of Google Trends

If you are a supporter of Democrats like Mrs. Clinton, the good news is that a large number of queries are coming from Arizona, and Texas, two states where changes in demographics are slowly turning voting preferences from red to blue.

In Florida, it is not clear which candidate gains from increased number of Spanish-speaking voters. However, since the increase is a result of the debate (during which it was revealed that Mr. Trump had insulted and berated a beauty pageant winner from Venezuela, calling her “miss housekeeping”), I will speculate many newly registered voters are going to be Clinton supporters.

If the Google search trend continues, it may be driven by new reports that Mr. Trump may have violated the US sanctions forbidding business transactions in Cuba. Cuban-Americans searching for information on voter registration after hearing this story are more likely to favor Mrs. Clinton.

by George Taniwaki

Often times, one has lots of data to display that are grouped in pairs such as men vs. women. Further, we want to show the pairs but not compare them. Instead, we are more interested in comparing different groups within the pairs than between pairs within a group. For instance. our groups could be age and we are more interested in comparing 20-24 women to 25-29 women than we are between 20-24 women and 20-24 men.

The diverging stacked bar chart is a very good way to display a pair of values next to each other. To allow easier comparison of the length of adjacent bars, there is usually no white space between them. To allow easier comparison between the left and right bar, they usually have no space between them but are different colors. The values for the bars running to the left are not negative. They are positive, just like the values on the right. The left and right bars are paired and measure the values for two different related groups.

The most common use of the diverging stacked bar chart is to display age distribution of a population broken down by gender. This type of chart is often called a population pyramid.  An example of a population pyramid using data from the 2000 U.S. Census is shown in Figure 1.

PopulationPyramidUS2000

Figure 1. Population pyramid for the U.S. based on Census 2000 data. Image from Censusscope.

The population pyramid is a special case of the diverging stacked bar chart. Notice that  each of the horizontal bars is the same width and covers the same age range (except the oldest group). Thus, the height of each bar represents the same number of years and the stack of bars forms a vertical axis showing age. Similarly, the the area of each bar represents the proportion of the population in that age group and the area of all the bars shows the total size of the population. A well-drawn population pyramid shows three dimensions at once, age, gender, and counts.

The shape of a population pyramid tells a lot about the population growth (which itself is a result of economic and political conditions that affect fertility, infant survival, immigration and emigration, and longevity) of a group.Figure 2 shows the four commonly seen shapes for a population pyramid.

The two triangles at the right (labeled stage 1 and stage 2) describe a group with a combination of high birthrates, high emigration, and high mortality cause the number of young to greatly exceed the old. Several countries in Sub-Saharan Africa and India have population pyramids of this shape.

The flatter shape (labeled stage 3) describes a group where births, immigration/emigration, and mortality are in balance. Most of the developing countries and the U.S. have population pyramids of this shape.

Finally, the egg-shaped pyramid (labeled stage 4) has a base that is smaller than the center. This describes a group where a combination of low birth rate, high immigration rate, and low mortality causes a bulge in the middle. If the fertility rate is below the replacement rate (about 2.1 child per female lifetime) then the population is growing older and may even be shrinking. Nearly all of the developed countries and China have population pyramids of this shape.

PopulationPyramid

Figure 2. Four commonly seen shapes for population pyramid. Image from Wikipedia

If you would like to explore population pyramids on a national, state, and metro area basis, go to http://www.censusscope.org/us/chart_age.html

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Diverging stacked bar charts can be used in cases where there are more than two categories. In a paper presented at the 2011 Joint Statistical Meeting, Naomi Robbins and Richard Heiberger suggest that Lickert scale data should be presented using this method. If the questionnaire uses the standard 5 point scale, they argue that the  “Strongly disagree,” “Disagree,” and half the “Neither agree nor disagree” counts should be shown on the left bar. The counts for “Strongly agree,” “Agree,” and half of “Neither agree nor disagree” should be shown on the right bar. An example is shown in Figure 3.

image

Figure 3. Diverging stacked bar chart used to display Lickert scale data. Image from 2011 JSM

I’ve tried a bunch of different ways of presenting Lickert scale data (as well as other scaled data for importance, satisfaction, and other opinions) and have never been happy with my efforts. I really like this technique. If you review the paper, you will see eight common methods for displaying Lickert scale data that the authors label as “Not recommended.” I’ve used many of them.

For instance, I’ve used the standard colored bar chart like the one shown in Figure 4. The problem is that every bar is the same length so the ends of the bars, which your eyes are drawn to don’t convey any data. All of the data is conveyed at the interior points of the bars. By comparison, in Figure 3, the data is conveyed by the lengths of each bar and the proportion of each bar that is filled with the darker shade of color.

image

Figure 4. Standard bar chart to display Lickert scale data. Image from 2011 JSM

So how do you create your own diverging stacked bar charts? If you are an R language user, you can use functions available in the HH package and the latticeExtra package for the R language. These functions are also available in the RExcel for R add-in for Excel on Windows.

If you are not an R user, you can create diverging stacked bar charts manually using Excel or Tableau. For instructions using Excel, Amy Emery has a good tutorial on Slideshare.net.

Incidentally, if you have time, check out some of Ms. Emery’s other slide shows, they are quite good and cover a range of topics. There is even one to help R novices like me get started in learning the language.

Much thanks to my friend and colleague Carol Borthwick for pointing me to this new use for the diverging stacked bar chart.