Welcome to the first project of the Machine Learning Engineer Nanodegree! In this notebook, some template code has already been provided for you, and you will need to implement additional functionality to successfully complete this project. You will not need to modify the included code beyond what is requested. Sections that begin with 'Implementation' in the header indicate that the following block of code will require additional functionality which you must provide. Instructions will be provided for each section and the specifics of the implementation are marked in the code block with a 'TODO' statement. Please be sure to read the instructions carefully!
In addition to implementing code, there will be questions that you must answer which relate to the project and your implementation. Each section where you will answer a question is preceded by a 'Question X' header. Carefully read each question and provide thorough answers in the following text boxes that begin with 'Answer:'. Your project submission will be evaluated based on your answers to each of the questions and the implementation you provide.
Note: Code and Markdown cells can be executed using the Shift + Enter keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode.
In this project, you will evaluate the performance and predictive power of a model that has been trained and tested on data collected from homes in suburbs of Boston, Massachusetts. A model trained on this data that is seen as a good fit could then be used to make certain predictions about a home — in particular, its monetary value. This model would prove to be invaluable for someone like a real estate agent who could make use of such information on a daily basis.
The dataset for this project originates from the UCI Machine Learning Repository. The Boston housing data was collected in 1978 and each of the 506 entries represent aggregated data about 14 features for homes from various suburbs in Boston, Massachusetts. For the purposes of this project, the following preprocessing steps have been made to the dataset:
'MEDV' value of 50.0. These data points likely contain missing or censored values and have been removed.'RM' value of 8.78. This data point can be considered an outlier and has been removed.'RM', 'LSTAT', 'PTRATIO', and 'MEDV' are essential. The remaining non-relevant features have been excluded.'MEDV' has been multiplicatively scaled to account for 35 years of market inflation.Run the code cell below to load the Boston housing dataset, along with a few of the necessary Python libraries required for this project. You will know the dataset loaded successfully if the size of the dataset is reported.
In [1]:
# Import libraries necessary for this project
import numpy as np
import pandas as pd
from sklearn.cross_validation import ShuffleSplit
# Import supplementary visualizations code visuals.py
import visuals as vs
# Pretty display for notebooks
%matplotlib inline
# Load the Boston housing dataset
data = pd.read_csv('housing.csv')
prices = data['MEDV']
features = data.drop('MEDV', axis = 1)
# Success
print "Boston housing dataset has {} data points with {} variables each.".format(*data.shape)
In this first section of this project, you will make a cursory investigation about the Boston housing data and provide your observations. Familiarizing yourself with the data through an explorative process is a fundamental practice to help you better understand and justify your results.
Since the main goal of this project is to construct a working model which has the capability of predicting the value of houses, we will need to separate the dataset into features and the target variable. The features, 'RM', 'LSTAT', and 'PTRATIO', give us quantitative information about each data point. The target variable, 'MEDV', will be the variable we seek to predict. These are stored in features and prices, respectively.
For your very first coding implementation, you will calculate descriptive statistics about the Boston housing prices. Since numpy has already been imported for you, use this library to perform the necessary calculations. These statistics will be extremely important later on to analyze various prediction results from the constructed model.
In the code cell below, you will need to implement the following:
'MEDV', which is stored in prices.
In [2]:
# TODO: Minimum price of the data
minimum_price = np.min(prices)
# TODO: Maximum price of the data
maximum_price = np.max(prices)
# TODO: Mean price of the data
mean_price = np.mean(prices)
# TODO: Median price of the data
median_price = np.median(prices)
# TODO: Standard deviation of prices of the data
std_price = np.std(prices)
# Show the calculated statistics
print "Statistics for Boston housing dataset:\n"
print "Minimum price: ${:,.2f}".format(minimum_price)
print "Maximum price: ${:,.2f}".format(maximum_price)
print "Mean price: ${:,.2f}".format(mean_price)
print "Median price ${:,.2f}".format(median_price)
print "Standard deviation of prices: ${:,.2f}".format(std_price)
As a reminder, we are using three features from the Boston housing dataset: 'RM', 'LSTAT', and 'PTRATIO'. For each data point (neighborhood):
'RM' is the average number of rooms among homes in the neighborhood.'LSTAT' is the percentage of homeowners in the neighborhood considered "lower class" (working poor).'PTRATIO' is the ratio of students to teachers in primary and secondary schools in the neighborhood. Using your intuition, for each of the three features above, do you think that an increase in the value of that feature would lead to an increase in the value of 'MEDV' or a decrease in the value of 'MEDV'? Justify your answer for each.
Hint: This problem can phrased using examples like below.
'RM' value(number of rooms) of 6 be worth more or less than a home that has an 'RM' value of 7?'LSTAT' value(percent of lower class workers) of 15 have home prices be worth more or less than a neighborhood that has an 'LSTAT' value of 20?'PTRATIO' value(ratio of students to teachers) of 10 have home prices be worth more or less than a neighborhood that has an 'PTRATIO' value of 15?Answer: From the exploration of data we could say the impact of the features on MEDV is as below:
" RM " As the value of the RM increase the prices MEDV also increases.
" LSTAT " As the value of the RM increase the prices MEDV decreases.
" PTRATIO " As the value of the PTRATIO increase the prices MEDV decreases.
In [3]:
import matplotlib.pyplot as plt
plt.figure(figsize=(20, 5))
for i, col in enumerate(features.columns):
plt.subplot(1, 3, i+1)
plt.plot(data[col], prices, 'o')
plt.title(col)
plt.xlabel(col)
plt.ylabel('prices')
In this second section of the project, you will develop the tools and techniques necessary for a model to make a prediction. Being able to make accurate evaluations of each model's performance through the use of these tools and techniques helps to greatly reinforce the confidence in your predictions.
It is difficult to measure the quality of a given model without quantifying its performance over training and testing. This is typically done using some type of performance metric, whether it is through calculating some type of error, the goodness of fit, or some other useful measurement. For this project, you will be calculating the coefficient of determination, R2, to quantify your model's performance. The coefficient of determination for a model is a useful statistic in regression analysis, as it often describes how "good" that model is at making predictions.
The values for R2 range from 0 to 1, which captures the percentage of squared correlation between the predicted and actual values of the target variable. A model with an R2 of 0 is no better than a model that always predicts the mean of the target variable, whereas a model with an R2 of 1 perfectly predicts the target variable. Any value between 0 and 1 indicates what percentage of the target variable, using this model, can be explained by the features. A model can be given a negative R2 as well, which indicates that the model is arbitrarily worse than one that always predicts the mean of the target variable.
For the performance_metric function in the code cell below, you will need to implement the following:
r2_score from sklearn.metrics to perform a performance calculation between y_true and y_predict.score variable.
In [4]:
# TODO: Import 'r2_score'
from sklearn.metrics import r2_score
def performance_metric(y_true, y_predict):
""" Calculates and returns the performance score between
true and predicted values based on the metric chosen. """
# TODO: Calculate the performance score between 'y_true' and 'y_predict'
score = r2_score(y_true,y_predict)
# Return the score
return score
Assume that a dataset contains five data points and a model made the following predictions for the target variable:
| True Value | Prediction |
|---|---|
| 3.0 | 2.5 |
| -0.5 | 0.0 |
| 2.0 | 2.1 |
| 7.0 | 7.8 |
| 4.2 | 5.3 |
Run the code cell below to use the performance_metric function and calculate this model's coefficient of determination.
In [5]:
# Calculate the performance of this model
score = performance_metric([3, -0.5, 2, 7, 4.2], [2.5, 0.0, 2.1, 7.8, 5.3])
print "Model has a coefficient of determination, R^2, of {:.3f}.".format(score)
Hint: The R2 score is the proportion of the variance in the dependent variable that is predictable from the independent variable. In other words:
Answer:As the value of R^2 is near to 1 ,we can say that the variation is captured succesfully.
Even looking at the table we can see that the model is not highly deviated from its true value.
Your next implementation requires that you take the Boston housing dataset and split the data into training and testing subsets. Typically, the data is also shuffled into a random order when creating the training and testing subsets to remove any bias in the ordering of the dataset.
For the code cell below, you will need to implement the following:
train_test_split from sklearn.cross_validation to shuffle and split the features and prices data into training and testing sets.random_state for train_test_split to a value of your choice. This ensures results are consistent.X_train, X_test, y_train, and y_test.
In [6]:
# TODO: Import 'train_test_split'
from sklearn.cross_validation import train_test_split
# TODO: Shuffle and split the data into training and testing subsets
X_train, X_test, y_train, y_test = train_test_split(features, prices, test_size=0.2, random_state=42)
# Success
print "Training and testing split was successful."
Answer: Splitting the data will ensure that we are training our model on different data poins and we can use unseeen or test data points to evaluate the performance of model.
By using unseen data (Test Data) for evaluating the accuray of the model we can find out the undefitting(accuracy is low) and overfittingi.e., not able to generalize(accuracy is super high).
If we do not do split the data then we end up using the same data points for test and train. The r^2 value received can not be treated as the correct value if the data is not split.
In this third section of the project, you'll take a look at several models' learning and testing performances on various subsets of training data. Additionally, you'll investigate one particular algorithm with an increasing 'max_depth' parameter on the full training set to observe how model complexity affects performance. Graphing your model's performance based on varying criteria can be beneficial in the analysis process, such as visualizing behavior that may not have been apparent from the results alone.
The following code cell produces four graphs for a decision tree model with different maximum depths. Each graph visualizes the learning curves of the model for both training and testing as the size of the training set is increased. Note that the shaded region of a learning curve denotes the uncertainty of that curve (measured as the standard deviation). The model is scored on both the training and testing sets using R2, the coefficient of determination.
Run the code cell below and use these graphs to answer the following question.
In [7]:
# Produce learning curves for varying training set sizes and maximum depths
vs.ModelLearning(features, prices)
Hint: Are the learning curves converging to particular scores? Generally speaking, the more data you have, the better. But if your training and testing curves are converging with a score above your benchmark threshold, would this be necessary? Think about the pros and cons of adding more training points based on if the training and testing curves are converging.
Answer: I choose the model with maximum depth of "3"
The score of the training curve decrease and becomes saturated as we increase the data points. The score of the Testing curve saturated as we keep on increasing the data points .
No, having more training points does not benefit the model and model stopeed learning .
The following code cell produces a graph for a decision tree model that has been trained and validated on the training data using different maximum depths. The graph produces two complexity curves — one for training and one for validation. Similar to the learning curves, the shaded regions of both the complexity curves denote the uncertainty in those curves, and the model is scored on both the training and validation sets using the performance_metric function.
Run the code cell below and use this graph to answer the following two questions Q5 and Q6.
In [8]:
vs.ModelComplexity(X_train, y_train)
Hint: High bias is a sign of underfitting(model is not complex enough to pick up the nuances in the data) and high variance is a sign of overfitting(model is by-hearting the data and cannot generalize well). Think about which model(depth 1 or 10) aligns with which part of the tradeoff.
Answer: 1)Model at maximum depth of 1 suffers from high bias and low variance. As the depth is 1 , underlying pattern in the data is not found . By keeping the number of layers low we are constraining the complexity of the model. We can also see that the error at this point is large indicating that model is not able to learn the training data .
2)Model at maximum depth of 10 suffers from low bias and high variance.
When we train our model for 10 layers,we tend to make the deision based on even the small entropy values ,this will result in a tree which is higly complicated and cannot spilt the new data because it will fail to see high level patterns present in the new data and cannot classify accordingly.
when the depth of tree is =10 we can see that the training score is almost equal to 1.0 which means that the model has learnt all underlying patterns in training data so well that it perfectly predicts the output for all the data in training set. As the model memorizes all the underlying varaince it fits itself tightly to the training data points and creates a complicated model which is not open to understand any new patterns and cannot generalize it self to presict the unseen data.
The fact that the score of the training curve is too high when compared to the validation curve explains that the model has overfitted it self to the training data and unable to make predictions on the validation dataset.This is behavior of model with property of high variance.
Hint: Look at the graph above Question 5 and see where the validation scores lie for the various depths that have been assigned to the model. Does it get better with increased depth? At what point do we get our best validation score without overcomplicating our model? And remember, Occams Razor states "Among competing hypotheses, the one with the fewest assumptions should be selected."
Answer: Model Genralizes the unseen data at maximum depth of 3. Eventhought the score of the validation data increases beyond 3 upto 4 ,the difference between the training score and validaton score increases increases further(training graph deviates hugely from validation graph) . The fact that the training and validataion scores are mobing apart implies the model is becoming too complex to generalize the any unseen data(Overfitting occurs on training data)
Hint: When explaining the Grid Search technique, be sure to touch upon why it is used, what the 'grid' entails and what the end goal of this method is. To solidify your answer, you can also give an example of a parameter in a model that can be optimized using this approach.
Answer: GridSearch is am exhaustive searching technique which will fing the best hyperparameter that need to be used to train a model.
Gridsearch does this by taking the hyperparameters provided as inputs in the form of a dictionary containing tupples with various choices,and train the model with all the tuning parameters and returns the best parameter that tune the model bases upon the minimum error that was achieved by one of the combination.
Ex: we can find the best value of the depth of tree or minimum number of leaf or nodes that need to passed as hyper parameter.
parameter = {'max_depth':range(1,6) , 'min_samples_leaf' : range(1,3) }
What is the k-fold cross-validation training technique?
What benefit does this technique provide for grid search when optimizing a model?
Hint: When explaining the k-fold cross validation technique, be sure to touch upon what 'k' is, how the dataset is split into different parts for training and testing and the number of times it is run based on the 'k' value.
When thinking about how k-fold cross validation helps grid search, think about the main drawbacks of grid search which are hinged upon using a particular subset of data for training or testing and how k-fold cv could help alleviate that. You can refer to the docs for your answer.
Answer: K-fold cross-valiation split's the Data in K parts or subsets of equal lengths.K-1 subsets are treated as training data and the remaining 1 subset is treated as testing data.This process happends k number of times and every time new subset of data is treated as test data and the remaining subsets are treated as the training data. Machine learning algorithm repeatedly fits the data k number of times and final error = average of all the errors.
If we use only single subset for training there is a high possibilty that the model will train itself on the subset provided and predictions are highly accurate but when used the same model on unseen data the model fails to predict because the model got overfit. And there is also a probability that if the data is not split in random fashion and all the data of similar pattern lies in training set ,then model is highly biased to the training set we provided as input.
But when we use k-fold we are making sure that all the patterns are understood and the model is validataing it self for unseen data and improve the performence.
Cross-validation can detect overfit models by determining how well your model generalizes to other data sets by partitioning data. This process helps you assess how well the model fits new observations that weren't used in the model estimation process.
The varaince of the resulting estimate is decreased .And Gridsearch has the oppurtunity to test it's performance on all the the data by training k number of times.To further improve the model we should also split the data into 3 subcategories "test""validation""training".
Reference:http://blog.minitab.com/blog/adventures-in-statistics-2/the-danger-of-overfitting-regression-models
Your final implementation requires that you bring everything together and train a model using the decision tree algorithm. To ensure that you are producing an optimized model, you will train the model using the grid search technique to optimize the 'max_depth' parameter for the decision tree. The 'max_depth' parameter can be thought of as how many questions the decision tree algorithm is allowed to ask about the data before making a prediction. Decision trees are part of a class of algorithms called supervised learning algorithms.
In addition, you will find your implementation is using ShuffleSplit() for an alternative form of cross-validation (see the 'cv_sets' variable). While it is not the K-Fold cross-validation technique you describe in Question 8, this type of cross-validation technique is just as useful!. The ShuffleSplit() implementation below will create 10 ('n_splits') shuffled sets, and for each shuffle, 20% ('test_size') of the data will be used as the validation set. While you're working on your implementation, think about the contrasts and similarities it has to the K-fold cross-validation technique.
Please note that ShuffleSplit has different parameters in scikit-learn versions 0.17 and 0.18.
For the fit_model function in the code cell below, you will need to implement the following:
DecisionTreeRegressor from sklearn.tree to create a decision tree regressor object.'regressor' variable.'max_depth' with the values from 1 to 10, and assign this to the 'params' variable.make_scorer from sklearn.metrics to create a scoring function object.performance_metric function as a parameter to the object.'scoring_fnc' variable.GridSearchCV from sklearn.grid_search to create a grid search object.'regressor', 'params', 'scoring_fnc', and 'cv_sets' as parameters to the object. GridSearchCV object to the 'grid' variable.
In [9]:
# TODO: Import 'make_scorer', 'DecisionTreeRegressor', and 'GridSearchCV'
from sklearn.metrics import make_scorer
from sklearn.tree import DecisionTreeRegressor
from sklearn.grid_search import GridSearchCV
def fit_model(X, y):
""" Performs grid search over the 'max_depth' parameter for a
decision tree regressor trained on the input data [X, y]. """
# Create cross-validation sets from the training data
cv_sets = ShuffleSplit(X.shape[0], n_iter = 10, test_size = 0.20, random_state = 0)
# TODO: Create a decision tree regressor object
regressor = DecisionTreeRegressor(random_state = 42)
# TODO: Create a dictionary for the parameter 'max_depth' with a range from 1 to 10
params = {'max_depth':range(1,11)}
# TODO: Transform 'performance_metric' into a scoring function using 'make_scorer'
scoring_fnc = make_scorer(performance_metric)
# TODO: Create the grid search object
grid = GridSearchCV(estimator=regressor, param_grid=params, scoring=scoring_fnc, cv=cv_sets)
# Fit the grid search object to the data to compute the optimal model
grid = grid.fit(X, y)
# Return the optimal model after fitting the data
return grid.best_estimator_
Once a model has been trained on a given set of data, it can now be used to make predictions on new sets of input data. In the case of a decision tree regressor, the model has learned what the best questions to ask about the input data are, and can respond with a prediction for the target variable. You can use these predictions to gain information about data where the value of the target variable is unknown — such as data the model was not trained on.
In [10]:
# Fit the training data to the model using grid search
reg = fit_model(X_train, y_train)
# Produce the value for 'max_depth'
print "Parameter 'max_depth' is {} for the optimal model.".format(reg.get_params()['max_depth'])
Hint: The answer comes from the output of the code snipped above.
Answer: The result has selected max depth as 4 but where as i have manually selected from the graph the depth as 3. This could happen due to the fact the gridsearch is looking for the point at which the accuracy is maximum
Imagine that you were a real estate agent in the Boston area looking to use this model to help price homes owned by your clients that they wish to sell. You have collected the following information from three of your clients:
| Feature | Client 1 | Client 2 | Client 3 |
|---|---|---|---|
| Total number of rooms in home | 5 rooms | 4 rooms | 8 rooms |
| Neighborhood poverty level (as %) | 17% | 32% | 3% |
| Student-teacher ratio of nearby schools | 15-to-1 | 22-to-1 | 12-to-1 |
Hint: Use the statistics you calculated in the Data Exploration section to help justify your response. Of the three clients, client 3 has has the biggest house, in the best public school neighborhood with the lowest poverty level; while client 2 has the smallest house, in a neighborhood with a relatively high poverty rate and not the best public schools.
Run the code block below to have your optimized model make predictions for each client's home.
In [11]:
# Produce a matrix for client data
client_data = [[5, 17, 15], # Client 1
[4, 32, 22], # Client 2
[8, 3, 12]] # Client 3
# Show predictions
for i, price in enumerate(reg.predict(client_data)):
print "Predicted selling price for Client {}'s home: ${:,.2f}".format(i+1, price)
In [13]:
features.describe()
Out[13]:
Answer:
Price that I recommend is :$403,025.00, $237,478.72, $931,636.36. Note: As RM increases price increases. LSTAT increase price decreases. PTRATIO increase mostly price decreases.
Here we can see that the Client3 property is estimated at $931,636.36, it is because of the RM factor 8 and powerty level 3% and PTRATIO of 12 also contribute to higher price. All the factors are positively influencing the price calculated.
Here we can see that the Client2 property is estimated at $237,478.72, it is because of the RM factor 4 and powerty level 32% and PTRATIO of 22% also contribute to lower price. PTRATIO and LSTAT highly influence the price here and drops down the price down.
Here we can see that the Client1 property is estimated at $403,025.00, it is because of the RM factor 5 and powerty level 17% and PTRATIO of 15% also contribute to lower price. PTRATIO and LSTAT highly influence the price here and drops down the price down.
4 room's is estimated as 237,478.72 which is above the minimum. 5 room′s have is 403,025.00 which is similar to 4rooms Price + std. 8 room's have $931,636.36 which is great consider that the value is near to the maximum price and also follows the standard deviation.
An optimal model is not necessarily a robust model. Sometimes, a model is either too complex or too simple to sufficiently generalize to new data. Sometimes, a model could use a learning algorithm that is not appropriate for the structure of the data given. Other times, the data itself could be too noisy or contain too few samples to allow a model to adequately capture the target variable — i.e., the model is underfitted.
Run the code cell below to run the fit_model function ten times with different training and testing sets to see how the prediction for a specific client changes with respect to the data it's trained on.
In [12]:
vs.PredictTrials(features, prices, fit_model, client_data)
Hint: Take a look at the range in prices as calculated in the code snippet above. Some questions to answering:
Answer: This model cannot be used in real time due to the following reasosns 1)Information like the area avaiable as the swimming pool,Lawn,what are the different types of rooms available(like bedroom,hall,store room) also need to consider to provide the exact price. 2)This model cannot be used to estimated house pricing of the other cities 3)Data that is collected is from 1978 ,in order to make the model robust we need collect the fresh data inputs for Boston housing 4)As mentioned in the point 1 additional features are required to see the other patterns 5)yes, the model is robust enough to make predictions 6)Rural and urban cities have different pricing of the housing ,so we can not apply to the rurla cities
Note: Once you have completed all of the code implementations and successfully answered each question above, you may finalize your work by exporting the iPython Notebook as an HTML document. You can do this by using the menu above and navigating to
File -> Download as -> HTML (.html). Include the finished document along with this notebook as your submission.