$F_{\beta} = (1 + \beta^2) \cdot = \frac {precision \cdot recall}{(\beta^2 \cdot precision) + recall}$
In particular, when $\beta = 0.5$ , more emphasis is placed on precision. This is called the $F_{0.5}$ score (or F-score for simplicity).
This can greatly affect accuracy, since we could simply say "this person does not make more than 50,000 USD" and generally be right, without ever looking at the data!
Making such a statement would be called naive, since we have not considered any information to substantiate the claim.
It is always important to consider the naive prediction for your data, to help establish a benchmark for whether a model is performing well.
That been said, using that prediction would be pointless: If we predicted all people made less than 50,000 USD, CharityML would identify no one as donors.
Note: Recap of accuracy, precision, recall.
Accuracy measures how often the classifier makes the correct prediction.
It’s the ratio of the number of correct predictions to the total number of predictions (the number of test data points).
$accuracy = \frac {number \ of \ correct \ predictions}{total \ number \ of \ predictions}$
Precision tells us what proportion of data points we classified as individuals making more than 50,000 USD, actually made more than 50,000 USD.
It is a ratio of true positives to all positives (all points classified as individuals making more than 50,000 USD, irrespective of whether that was the correct classification),
in other words it is the ratio of
$precision = \frac {true \ positives}{true \ positives + false \ positives}$
Recall (sensitivity) tells us what proportion of individuals that actually made more than 50,000 USD were classified by us as individuals making more than 50,000 USD.
It is a ratio of true positives to all individuals that actually made more than 50,000 USD, in other words it is the ratio of
$recall = \frac {true \ positives}{true \ positives + false \ negatives}$
For classification problems that are skewed in their classification distributions like in our case, accuracy by itself is not a very good metric.
Precision and recall help a lot and can be combined to get the F1 score, which is the weighted average (harmonic mean) of the precision and recall scores.
This score can range from 0 to 1, with 1 being the best possible F1 score (we take the harmonic mean as we are dealing with ratios).
Question 1 - Naive Predictor Performace
If we chose a model that always predicted an individual made more than 50,000 USD, what would that model's accuracy and F-score be on this dataset?
Answer 1
The code cell below displays both indicators in the output.
Supervised Learning Models
The following supervised learning models are currently available in scikit-learn that you may choose from:
- Gaussian Naive Bayes (GaussianNB)
- Decision Trees
- Ensemble Methods (Bagging, AdaBoost, Random Forest, Gradient Boosting)
- K-Nearest Neighbors (KNeighbors)
- Stochastic Gradient Descent Classifier (SGDC)
- Support Vector Machines (SVM)
- Logistic Regression
Question 2 - Model Application
List three of the supervised learning models above that are appropriate for this problem that you will test on the census data.
For each model chosen:
- Describe one real-world application in industry where the model can be applied. (You may need to do research for this — give references!)
- What are the strengths of the model; when does it perform well?
- What are the weaknesses of the model; when does it perform poorly?
- What makes this model a good candidate for the problem, given what you know about the data?
Answer 2
I have chosen the following models: GradientBoostingClassifier(); RandomForestClassifier(); AdaBoostClassifier().
All of them are ensemble methods and combine the predictions of several base estimators to improve generalizability / robustness over a single estimator.
Let's have a look at their applications and characteristics:
1) GradientBoostingClassifier.
Applications: in the field of learning to rank (for example, web-seach), in ecology, etc.
🕸Web-Search Ranking with Initialized Gradient Boosted Regression Trees
🕸Gradient boosting machines, a tutorial
The advantages and the disadvantages (Gradient Tree Boosting).
Strengths: natural handling of data of mixed type (= heterogeneous features), predictive power, robustness to outliers in output space (via robust loss functions).
Weaknesses: scalability, due to the sequential nature of boosting it can hardly be parallelized.
2) RandomForestClassifier.
Applications: in ecology, bioinformatics, etc.
🕸Random Forests for Classification in Ecology
🕸Random Forest for Bioinformatics
The advantages and the disadvantages (Random Forests).
Strengths: runs efficiently on large data bases; gives estimates of what variables are important in the classification;
maintains accuracy when a large proportion of the data are missing; high prediction accuracy.
Weaknesses: difficult to interpret, can be slow to evaluate.
3) AdaBoostClassifier.
Applications: the problem of face detection, text classification, etc.
🕸AdaBoost-based face detection for embedded systems
🕸Text Classification by Boosting Weak Learners based on Terms and Concepts
The advantages and the disadvantages (Ada Boost).
Strengths: can be used with data that is textual, numeric, discrete, etc.; can be combined with any other learning algorithm, not prone to overfitting; simple to implement.
Weaknesses: can be sensitive to noisy data and outliers; the performance depends on data and weak learner (can fail if weak classifiers too complex).
The outputs in our case are the variant of social ranking and it's a well-known fact that ensemble classifiers tend to be a better choice for this ranking.
All these algorithms will produce enough good predictions because of some reasons:
- they usually demonstrate high performance in practical tasks;
- do not so prone to overfitting;
- work well with mixed types of features (categorical and numeric).
Implementation: Creating a Training and Predicting Pipeline
To properly evaluate the performance of each model we've chosen, it's important that we create a training and predicting pipeline
that allows us to quickly and effectively train models using various sizes of training data and perform predictions on the testing data.
The implementation here will be used in the following section.
We will do the following points:
- Import fbeta_score and accuracy_score from sklearn.metrics.
- Fit the learner to the sampled training data and record the training time.
- Perform predictions on the test data X_test, and also on the first 300 training points X_train[:300].
- Record the total prediction time.
- Calculate the accuracy score for both the training subset and testing set.
- Calculate the F-score for both the training subset and testing set.
- Make sure that you set the beta parameter!
Implementation: Initial Model Evaluation
Next steps are the following:
Import the three supervised learning models you've discussed in the previous section.
Initialize the three models and store them in clf_A, clf_B, and clf_C.
Use the random_state parameter for each model you use, if provided.
Note: Use the default settings for each model — you will tune one specific model in a later section.
Calculate the number of records equal to 1%, 10%, and 100% of the training data.
Store those values in samples_1, samples_10, and samples_100 respectively.
Improving Results
In this final section, we will choose from the three supervised learning models the best model to use on the student data.
We will then perform a grid search optimization for the model over the entire training set (X_train and y_train)
by tuning at least one parameter to improve upon the untuned model's F-score.
Question 3 - Choosing the Best Model
Based on the evaluation you performed earlier, in one to two paragraphs, explain to CharityML which of the three models you believe
to be most appropriate for the task of identifying individuals that make more than 50,000 USD.
Answer 3
I think that for this case, we need to choose the GradientBoostingClassifier algorithm as it showed the highest accuracy and F-score for the testing set and escaped overfitting.
The algorithm is proved to be very time-consuming in the training process, but it can be ignored since the amount of data is not very big.
The confusion matrix can be used to evaluate the quality of the output for the chosen classifier.
Question 4 - Describing the Model in Layman's Terms
In one to two paragraphs, explain to CharityML, in layman's terms, how the final model chosen is supposed to work.
Be sure that you are describing the major qualities of the model, such as how the model is trained and how the model makes a prediction.
Avoid using advanced mathematical or technical jargon, such as describing equations or discussing the algorithm implementation.
Answer 4
Let's describe the mechanism of the model with three important component:
- the measurement for checking how well our model predicts the outputs based on input values,
- the algorithm from the certain group (for examples, decision trees) for making predictions,
- the additive mechanism for algorithms for minimizing the measure function.
At first, we set up the most important component (a measurement) that maps every event onto a real number intuitively representing some "cost" associated with this event.
The goal of estimation for supervised learning is to find the measure function that models all inputs (events) well:
if it were applied to the training set, it should predict the output values enough well.
Then we check the model effectiveness applied it to the testing set.
The measurement quantifies the amount by which the predictions deviate from the actual output values. Naturally, our task is to reach the minimum "cost".
At each particular Gradient Boosting iteration, a new algorithm (in practice, it's almost always from a tree-based group) is trained with respect to the error that was learned so far.
This procedure has the following steps:
- add one algorithm that can reduce the loss based on the current estimates (existing algorithms in the model are not changed);
- use an effective procedure called gradient descent to minimize the loss:
- fit a new model to the data;
- choose the directions for changing the measure function by finding the negative moving rates of this function, it helps to get a lower cost on the next iteration;
- find the best step-size in the chosen directions, the step magnitude is multiplied by a factor between 0 and 1 called a learning rate;
- update the measure function;
- repeat till the fixed number of algorithms are added or the loss reaches an acceptable level or the loss no longer improves on an external validation dataset.
The result of the model training should be that predictions slowly converge toward observed values.
The model for the CharityML is trained to produce the best predictions for the income categorical variable,
and the loss function evaluates how these predictions deviate from the actual values.
Implementation: Model Tuning
We will tune the chosen model and use grid search (GridSearchCV) with at least one important parameter tuned with at least 3 different values.
We will need to use the entire training set for this.
Our steps:
Import sklearn.grid_search.GridSearchCV and sklearn.metrics.make_scorer.
Initialize the classifier you've chosen and store it in clf.
Set a random_state if one is available to the same state you set before.
Create a dictionary of parameters you wish to tune for the chosen model.
Example: parameters = {'parameter' : [list of values]}.
Note: Avoid tuning the max_features parameter of your learner if that parameter is available!
Use make_scorer to create a fbeta_score scoring object (with $\beta=0.5$).
Perform grid search on the classifier clf using scorer, and store it in grid_obj.
Fit the grid search object to the training data (X_train, y_train), and store it in grid_fit.
Question 5 - Final Model Evaluation
What is your optimized model's accuracy and F-score on the testing data? Are these scores better or worse than the unoptimized model?
How do the results from your optimized model compare to the naive predictor benchmarks you found earlier in Question 1?
Answer 5
Final accuracy score and F-score on the testing data are represented in the last column.
These indicators are better than for the non-optimized model and they are 4-5 times greater than the initial prediction indicators for the naive predictor benchmarks.
Feature Importance
An important task when performing supervised learning on a dataset like the census data we study here is determining which features provide the most predictive power.
By focusing on the relationship between only a few crucial features and the target label we simplify our understanding of the phenomenon, which is most always a useful thing to do.
In the case of this project, that means we wish to identify a small number of features that most strongly predict whether an individual makes at most or more than 50,000 USD.
We will choose a scikit-learn classifier (e.g., Ada Boost, Random Forest) that has the feature_importance_ attribute,
which is a function that ranks the importance of features according to the chosen classifier,
in the next python cell fit this classifier to training set and use this attribute to determine the top 5 most important features for the census dataset.
Question 6 - Feature Relevance Observation
In Exploring the Data, it was shown there are thirteen available features for each individual on record in the census data.
Of these thirteen records, which five features do you believe to be most important for prediction, and in what order would you rank them and why?
Answer 6
For me, the variables “age”, “education-num”, “occupation”, “relationship”, “hours-per-week” look like the most influential.
Of course, it's expected to receive a higher pay if the person has studied longer, has a high paying occupation, is older and more experienced,
has a longtime relationship and works more hours per week.
I would rank them in the following order:
1) education-num; 2) age; 3) hours-per-week; 4) occupation; 5) relationship.
Implementation: Extracting Feature Importance
We will choose a scikit-learn supervised learning algorithm that has a feature_importance_ attribute availble for it.
This attribute is a function that ranks the importance of each feature when making predictions based on the chosen algorithm.
We will need to implement the following:
Import a supervised learning model from sklearn if it is different from the three used earlier.
Train the supervised model on the entire training set.
Extract the feature importances using .feature_importances_.
Question 7 - Extracting Feature Importance
Observe the visualization created above which displays the five most relevant features for predicting if an individual makes at most or above 50,000 USD.
How do these five features compare to the five features you discussed in Question 6? If you were close to the same answer, how does this visualization confirm your thoughts?
If you were not close, why do you think these features are more relevant?
Answer 7
This visualization confirms my thoughts about the most influential features but, in many cases, does not confirm the order which I predicted and include the features capital-gain and capital-loss.
I think it happens because the age in practice has more meaning than I expected.
And the capital gain and capital loss variables show a high correlation to income levels so these variables can be used for prediction.
Implementation: Feature Selection
How does a model perform if we only use a subset of all the available features in the data?
With less features required to train, the expectation is that training and prediction time is much lower — at the cost of performance metrics.
From the visualization above, we see that the top five most important features contribute more than half of the importance of all features present in the data.
This hints that we can attempt to reduce the feature space and simplify the information required for the model to learn.
The code cell below will use the same optimized model we found earlier, and train it on the same training set with only the top five important features.
Question 8 - Effects of Feature Selection
How does the final model's F-score and accuracy score on the reduced data using only five features compare to those same scores when all features are used?
If training time was a factor, would you consider using the reduced data as your training set?
Answer 8
The final model's F-score and accuracy score on the reduced data does not decrease a lot.
This means we can confirm the use of the reduced data with a high level of confidence if training time is an important factor.
Conclusion
In this project, models of classifiers and their application to predict categorical variables were discussed in detail.
We studied the methods of data preparing and model optimizing as well.
For Additional Code Experiments