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%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
# *k*-Nearest Neighbor # *k*-Nearest Neighbor
We'll implement *k*-Nearest Neighbor (*k*-NN) algorithm for this assignment. We recommend using [Madelon](https://archive.ics.uci.edu/ml/datasets/Madelon) dataset, although it is not mandatory. If you choose to use a different dataset, it should meet the following criteria: We'll implement *k*-Nearest Neighbor (*k*-NN) algorithm for this assignment. You can use data available in machine learning repositories such as [UCI Machine Learning Repository](https://archive.ics.uci.edu/ml/index.php) or a dataset related to your research. Your dataset should
* dependent variable should be binary (suited for binary classification) * have labels (suited for classification)
* number of features (attributes) should be at least 50 * ideally have between 1,000 - 5,000 examples
* number of examples (instances) should be between 1,000 - 5,000
A skeleton of a general supervised learning model is provided in "model.ipynb". The functions that will be implemented there will be indicated in this notebook. A skeleton of a general supervised learning model is provided in "model.ipynb". The functions that will be implemented there will be indicated in this notebook.
### Assignment Goals: ### Assignment Goals:
In this assignment, we will: In this assignment, we will:
* we'll implement 'Euclidean' and 'Manhattan' distance metrics * implement 'Euclidean' and 'Manhattan' distance metrics
* use the validation dataset to find a good value for *k* * use the validation dataset to find a good value for *k*
* evaluate our model with respect to performance measures: * evaluate our model with respect to performance measures:
* accuracy, generalization error and ROC curve * accuracy, generalization error and ROC curve
* try to assess if *k*-NN is suitable for the dataset you used * try to assess if *k*-NN is suitable for the dataset you used
### Note:
You are not required to follow this exact template. You can change what parameters your functions take or partition the tasks across functions differently. However, make sure there are outputs and implementation for items listed in the rubric for each task. Also, indicate in code with comments which task you are attempting.
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
# GRADING # GRADING
You will be graded on parts that are marked with **\#TODO** comments. Read the comments in the code to make sure you don't miss any. You will be graded on parts that are marked with **\#TODO** comments. Read the comments in the code to make sure you don't miss any.
### Mandatory for 478 & 878: ### Mandatory for 478 & 878:
| | Tasks | 478 | 878 | | | Tasks | 478 | 878 |
|---|----------------------------|-----|-----| |---|----------------------------|-----|-----|
| 1 | Implement `distance` | 10 | 10 | | 1 | Implement `distance` | 10 | 10 |
| 2 | Implement `k-NN` methods | 25 | 20 | | 2 | Implement `k-NN` methods | 25 | 20 |
| 3 | Model evaluation | 25 | 20 | | 3 | Model evaluation | 25 | 20 |
| 4 | Learning curve | 20 | 20 | | 4 | Learning curve | 20 | 20 |
| 6 | ROC curve analysis | 20 | 20 | | 6 | ROC curve analysis | 20 | 20 |
### Mandatory for 878, bonus for 478 ### Mandatory for 878, bonus for 478
| | Tasks | 478 | 878 | | | Tasks | 478 | 878 |
|---|----------------|-----|-----| |---|----------------|-----|-----|
| 5 | Optimizing *k* | 10 | 10 | | 5 | Optimizing *k* | 10 | 10 |
### Bonus for 478/878 ### Bonus for 478/878
| | Tasks | 478 | 878 | | | Tasks | 478 | 878 |
|---|----------------|-----|-----| |---|----------------|-----|-----|
| 7 | Assess suitability of *k*-NN | 10 | 10 | | 7 | Assess suitability of *k*-NN | 10 | 10 |
Points are broken down further below in Rubric sections. The **first** score is for 478, the **second** is for 878 students. There a total of 100 points in this assignment and extra 20 bonus points for 478 students and 10 bonus points for 878 students. Points are broken down further below in Rubric sections. The **first** score is for 478, the **second** is for 878 students. There are a total of 100 points in this assignment and extra 20 bonus points for 478 students and 10 bonus points for 878 students.
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
You can use numpy for array operations and matplotlib for plotting for this assignment. Please do not add other libraries. You can use numpy for array operations and matplotlib for plotting for this assignment. Please do not add other libraries.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
import numpy as np import numpy as np
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Following code makes the Model class and relevant functions available from model.ipynb. Following code makes the Model class and relevant functions available from model.ipynb.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
%run 'model.ipynb' %run 'model.ipynb'
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## TASK 1: Implement `distance` function ## TASK 1: Implement `distance` function
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Choice of distance metric plays an important role in the performance of *k*-NN. Let's start with implementing a distance method in the "distance" function in **model.ipynb**. It should take two data points and the name of the metric and return a scalar value. Choice of distance metric plays an important role in the performance of *k*-NN. Let's start with implementing a distance method in the "distance" function in **model.ipynb**. It should take two data points and the name of the metric and return a scalar value.
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Rubric: ### Rubric:
* Euclidean +5, +5 * Euclidean +5, +5
* Manhattan +5, +5 * Manhattan +5, +5
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Test `distance` ### Test `distance`
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
x = np.array(range(100)) x = np.array(range(100))
y = np.array(range(100, 200)) y = np.array(range(100, 200))
dist_euclidean = distance(x, y, 'Euclidean') dist_euclidean = distance(x, y, 'Euclidean')
dist_manhattan = distance(x, y, 'Manhattan') dist_manhattan = distance(x, y, 'Manhattan')
print('Euclidean distance: {}, Manhattan distance: {}'.format(dist_euclidean, dist_manhattan)) print('Euclidean distance: {}, Manhattan distance: {}'.format(dist_euclidean, dist_manhattan))
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## TASK 2: Implement $k$-NN Class Methods ## TASK 2: Implement $k$-NN Class Methods
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We can start implementing our *k*-NN classifier. *k*-NN class inherits Model class. Use the "distance" function you defined above. "fit" method takes *k* as an argument. "predict" takes as input an *mxd* array containing *d*-dimensional *m* feature vectors for examples and outputs the predicted class and the ratio of positive examples in *k* nearest neighbors. We can start implementing our *k*-NN classifier. *k*-NN class inherits Model class. Use the "distance" function you defined above. "fit" method takes *k* as an argument. "predict" takes as input an *mxd* array containing *d*-dimensional *m* feature vectors for examples and outputs the predicted class and the ratio of positive examples in *k* nearest neighbors.
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Rubric: ### Rubric:
* correct implementation of fit method +5, +5 * correct implementation of fit method +5, +5
* correct implementation of predict method +20, +15 * correct implementation of predict method +20, +15
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
class kNN(Model): class kNN(Model):
''' '''
Inherits Model class. Implements the k-NN algorithm for classification. Inherits Model class. Implements the k-NN algorithm for classification.
''' '''
def fit(self, training_features, training_labels, k, distance_f,**kwargs): def fit(self, training_features, training_labels, classes, k, distance_f,**kwargs):
''' '''
Fit the model. This is pretty straightforward for k-NN. Fit the model. This is pretty straightforward for k-NN.
Args: Args:
training_features: ndarray training_features: ndarray
training_labels: ndarray training_labels: ndarray
classes: ndarray
1D array containing unique classes in the dataset
k: int k: int
distance_f: function distance_f: function
kwargs: dict kwargs: dict
Contains keyword arguments that will be passed to distance_f Contains keyword arguments that will be passed to distance_f
''' '''
# TODO # TODO
# set self.train_features, self.train_labels, self.k, self.distance_f, self.distance_metric # set self.train_features, self.train_labels, self.classes, self.k, self.distance_f, self.distance_metric
raise NotImplementedError raise NotImplementedError
return return
def predict(self, test_features): def predict(self, test_features):
''' '''
Args: Args:
test_features: ndarray test_features: ndarray
mxd array containing features for the points to be predicted mxd array containing features for the points to be predicted
Returns: Returns:
ndarray ndarray
''' '''
raise NotImplementedError raise NotImplementedError
pred = [] pred = []
# TODO # TODO
# for each point in test_features # for each point in test_features
# use your implementation of distance function # use your implementation of distance function
# distance_f(..., distance_metric) # distance_f(..., distance_metric)
# to find the labels of k-nearest neighbors. # to find the labels of k-nearest neighbors.
# Find the ratio of the positive labels # you'll need proportion of the dominant class
# and append to pred with pred.append(ratio). # in k nearest neighbors
# when calculating learning curve you can make use of
# self.learning_curve and self.training_proportion
return np.array(pred) return np.array(pred)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## TASK 3: Build and Evaluate the Model ## TASK 3: Build and Evaluate the Model
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Rubric: ### Rubric:
* Reasonable accuracy values +10, +5 * Reasonable accuracy values +10, +5
* Reasonable confidence intervals on the error estimate +10, +10 * Reasonable confidence intervals on the error estimate +10, +10
* Reasonable confusion matrix +5, +5 * Reasonable confusion matrix +5, +5
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Preprocess the data files and partition the data. Preprocess the data files and partition the data.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# initialize the model # initialize the model
my_model = kNN() my_model = kNN()
# obtain features and labels from files # obtain features and labels from files
features, labels = preprocess(feature_file=..., label_file=...) features, labels = preprocess(feature_file=..., label_file=...)
# get class names (unique entries in labels)
classes = np.unique(labels)
# partition the data set # partition the data set
val_indices, test_indices, train_indices = partition(size=..., t = 0.3, v = 0.1) val_indices, test_indices, train_indices = partition(size=..., t = 0.3, v = 0.1)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Assign a value to *k* and fit the *k*-NN model. Assign a value to *k* and fit the *k*-NN model.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# pass the training features and labels to the fit method # pass the training features and labels to the fit method
kwargs_f = {'metric': 'Euclidean'} kwargs_f = {'metric': 'Euclidean'}
my_model.fit(training_features=..., training_labels-..., k=10, distance_f=..., **kwargs_f) my_model.fit(training_features=..., training_labels-..., classes, k=10, distance_f=..., **kwargs_f)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Computing the confusion matrix for *k* = 10 ### Computing the confusion matrix for *k* = 10
Now that we have the true labels and the predicted ones from our model, we can build a confusion matrix and see how accurate our model is. Implement the "conf_matrix" function (in model.ipynb) that takes as input an array of true labels (*true*) and an array of predicted labels (*pred*). It should output a numpy.ndarray. You do not need to change the value of the threshold parameter yet. Now that we have the true labels and the predicted ones from our model, we can build a confusion matrix and see how accurate our model is. Implement the "conf_matrix" function (in model.ipynb) that takes as input an array of true labels (*true*) and an array of predicted labels (*pred*). It should output a numpy.ndarray. You do not need to change the value of the threshold parameter yet.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# TODO # TODO
# get model predictions # get model predictions
pred_ratios = my_model.predict(my_model.features[my_model.test_indices]) pred_ratios = my_model.predict(features[test_indices])
# For now, we will consider a data point as predicted in the positive class if more than 0.5 # For now, we will consider a data point as predicted in a class if more than 0.5
# of its k-neighbors are positive. # of its k-neighbors are in that class.
threshold = 0.5 threshold = 0.5
# convert predicted ratios to predicted labels # convert predicted ratios to predicted labels
pred_labels = None pred_labels = None
# obtain true positive, true negative, # show the distribution of predicted and true labels in a confusion matrix
#false positive and false negative counts using conf_matrix confusion = conf_matrix(...)
tp,tn, fp, fn = conf_matrix(...) confusion
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Evaluate your model on the test data and report your **accuracy**. Also, calculate and report the 95% confidence interval on the generalization **error** estimate. Evaluate your model on the test data and report your **accuracy**. Also, calculate and report the 95% confidence interval on the generalization **error** estimate.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# TODO # TODO
# Calculate and report accuracy and generalization error with confidence interval here. Show your work in this cell. # Calculate and report accuracy and generalization error with confidence interval here. Show your work in this cell.
print('Accuracy: {}'.format(accuracy)) print('Accuracy: {}'.format(accuracy))
print('Confidence interval: {}-{}'.format(lower_bound, upper_bound)) print('Confidence interval: {}-{}'.format(lower_bound, upper_bound))
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## TASK 4: Plotting a learning curve ## TASK 4: Plotting a learning curve
A learning curve shows how error changes as the training set size increases. For more information, see [learning curves](https://www.dataquest.io/blog/learning-curves-machine-learning/). A learning curve shows how error changes as the training set size increases. For more information, see [learning curves](https://www.dataquest.io/blog/learning-curves-machine-learning/).
We'll plot the error values for training and validation data while varying the size of the training set. Report a good size for training set for which there is a good balance between bias and variance. We'll plot the error values for training and validation data while varying the size of the training set. Report a good size for training set for which there is a good balance between bias and variance.
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Rubric: ### Rubric:
* Correct training error calculation for different training set sizes +8, +8 * Correct training error calculation for different training set sizes +8, +8
* Correct validation error calculation for different training set sizes +8, +8 * Correct validation error calculation for different training set sizes +8, +8
* Reasonable learning curve +4, +4 * Reasonable learning curve +4, +4
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# train using %10, %20, %30, ..., 100% of training data # train using %10, %20, %30, ..., 100% of training data
training_proportions = np.arange(0.10, 1.01, 0.10) training_proportions = np.arange(0.10, 1.01, 0.10)
train_size = len(train_indices) train_size = len(train_indices)
training_sizes = np.int(np.ceil(size*proportion)) training_sizes = np.int(np.ceil(train_size*proportion))
# TODO # TODO
error_train = [] error_train = []
error_val = [] error_val = []
# For each size in training_sizes # For each size in training_sizes
for size in training_sizes: for size in training_sizes:
# fit the model using "size" data porint # fit the model using "size" data point
# Calculate error for training and validation sets # Calculate error for training and validation sets
# populate error_train and error_val arrays. # populate error_train and error_val arrays.
# Each entry in these arrays # Each entry in these arrays
# should correspond to each entry in training_sizes. # should correspond to each entry in training_sizes.
# plot the learning curve
plt.plot(training_sizes, error_train, 'r', label = 'training_error') plt.plot(training_sizes, error_train, 'r', label = 'training_error')
plt.plot(training_sizes, error_val, 'g', label = 'validation_error') plt.plot(training_sizes, error_val, 'g', label = 'validation_error')
plt.legend() plt.legend()
plt.show() plt.show()
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## TASK 5: Determining *k* ## TASK 5: Determining *k*
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Rubric: ### Rubric:
* Increased accuracy with new *k* +5, +5 * Accuracies reported with various *k* values +5, +5
* Improved confusion matrix +5, +5 * Confusion matrices shown for various *k* values +5, +5
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We can use the validation set to come up with a *k* value that results in better performance in terms of accuracy. We can use the validation set to come up with a *k* value that results in better performance in terms of accuracy.
Below calculate the accuracies for different values of *k* using the validation set. Report a good *k* value and use it in the analyses that follow this section. Report confusion matrix for the new value of *k*. Below calculate the accuracies for different values of *k* using the validation set. Report a good *k* value and use it in the analyses that follow this section. Report confusion matrix for the new value of *k*.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# TODO # TODO
# Change values of k. # Change values of k.
# Calculate accuracies for the validation set. # Calculate accuracies for the validation set.
# Report a good k value. # Report a good k value.
# Calculate the confusion matrix for new k. # Calculate the confusion matrix for new k.
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## TASK 6: ROC curve analysis ## TASK 6: ROC curve analysis
* Correct implementation +20, +20 * Correct implementation +20, +20
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### ROC curve and confusion matrix for the final model ROC curves are a good way to visualize sensitivity vs. 1-specificity for varying cut off points. Now, implement, in *model.ipynb*, a "ROC" function. "ROC" takes a list containing different threshold values to try and returns two arrays; one where each entry is the sensitivity at a given threshold and the other where entries are 1-specificities.
ROC curves are a good way to visualize sensitivity vs. 1-specificity for varying cut off points. Now, implement, in "model.ipynb", a "ROC" function that predicts the labels of the test set examples using different *threshold* values in "predict" and plot the ROC curve. "ROC" takes a list containing different *threshold* parameter values to try and returns two arrays; one where each entry is the sensitivity at a given threshold and the other where entries are 1-specificities.
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We can finally create the confusion matrix and plot the ROC curve for our optimal *k*-NN classifier. Use the *k* value you found above, if you completed TASK 5, else use *k* = 10. We'll plot the ROC curve for values between 0.1 and 1.0. Use the *k* value you found above, if you completed TASK 5, else use *k* = 10 to plot the ROC curve for values between 0.1 and 1.0.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# TODO # TODO
# ROC curve # ROC curve
roc_sens, roc_spec_ = ROC(my_model, my_model.test_indices, np.arange(0.1, 1.0, 0.1)) roc_sens, roc_spec_ = ROC(true_labels=..., preds=..., np.arange(0.1, 1.0, 0.1))
plt.plot(roc_sens, roc_spec_) plt.plot(roc_sens, roc_spec_)
plt.show() plt.show()
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## TASK 7: Assess suitability of *k*-NN to your dataset ## TASK 7: Assess suitability of *k*-NN to your dataset
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Use this cell to write about your understanding of why *k*-NN performed well if it did or why not if it didn't. What properties of the dataset affect the performance of the algorithm? Use this cell to write about your understanding of why *k*-NN performed well if it did or why not if it didn't. What properties of the dataset could have affected the performance of the algorithm?
......
ProgrammingAssignment_1/model.ipynb
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%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
# JUPYTER NOTEBOOK TIPS # JUPYTER NOTEBOOK TIPS
Each rectangular box is called a cell. Each rectangular box is called a cell.
* Ctrl+ENTER evaluates the current cell; if it contains Python code, it runs the code, if it contains Markdown, it returns rendered text. * Ctrl+ENTER evaluates the current cell; if it contains Python code, it runs the code, if it contains Markdown, it returns rendered text.
* Alt+ENTER evaluates the current cell and adds a new cell below it. * Alt+ENTER evaluates the current cell and adds a new cell below it.
* If you click to the left of a cell, you'll notice the frame changes color to blue. You can erase a cell by hitting 'dd' (that's two "d"s in a row) when the frame is blue. * If you click to the left of a cell, you'll notice the frame changes color to blue. You can erase a cell by hitting 'dd' (that's two "d"s in a row) when the frame is blue.
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
# Supervised Learning Model Skeleton # Supervised Learning Model Skeleton
We'll use this skeleton for implementing different supervised learning algorithms. We'll use this skeleton for implementing different supervised learning algorithms.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
class Model: class Model:
def fit(self): def fit(self):
raise NotImplementedError raise NotImplementedError
def predict(self, test_points): def predict(self, test_points):
raise NotImplementedError raise NotImplementedError
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def preprocess(feature_file, label_file): def preprocess(feature_file, label_file):
''' '''
Args: Args:
feature_file: str feature_file: str
file containing features file containing features
label_file: str label_file: str
file containing labels file containing labels
Returns: Returns:
features: ndarray features: ndarray
nxd features nxd features
labels: ndarray labels: ndarray
nx1 labels nx1 labels
''' '''
# read in features and labels # read in features and labels
features = np.genfromtxt(feature_file) features = np.genfromtxt(feature_file)
labels = np.genfromtxt(label_file) labels = np.genfromtxt(label_file)
return features, labels return features, labels
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def partition(size, t, v = 0): def partition(size, t, v = 0):
''' '''
Args: Args:
size: int size: int
number of examples in the whole dataset number of examples in the whole dataset
t: float t: float
proportion kept for test proportion kept for test
v: float v: float
proportion kept for validation proportion kept for validation
Returns: Returns:
test_indices: ndarray test_indices: ndarray
1D array containing test set indices 1D array containing test set indices
val_indices: ndarray val_indices: ndarray
1D array containing validation set indices 1D array containing validation set indices
''' '''
# number of test and validation examples # number of test and validation examples
t_size = np.int(np.ceil(size*t)) t_size = np.int(np.ceil(size*t))
v_size = np.int(np.ceil(size*v)) v_size = np.int(np.ceil(size*v))
# shuffle the indices # shuffle the indices
permuted = np.random.permutation(size) permuted = np.random.permutation(size)
# spare the first t_size for test # spare the first t_size for test
test_indices = permuted[:t_size] test_indices = permuted[:t_size]
# and the next v_size for validation # and the next v_size for validation
val_indices = permuted[t_size+1:t_size+v_size+1] val_indices = permuted[t_size+1:t_size+v_size+1]
train_indices = np.delete(np.arange(size), np.append(test_indices, val_indices), 0) train_indices = np.delete(np.arange(size), np.append(test_indices, val_indices), 0)
return test_indices, val_indices, train_indices return test_indices, val_indices, train_indices
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## TASK 1: Implement `distance` function ## TASK 1: Implement `distance` function
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
"distance" function will be used in calculating cost of *k*-NN. It should take two data points and the name of the metric and return a scalar value. "distance" function will be used in calculating cost of *k*-NN. It should take two data points and the name of the metric and return a scalar value.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
#TODO: Programming Assignment 1 #TODO: Programming Assignment 1
def distance(x, y, metric): def distance(x, y, metric):
''' '''
Args: Args:
x: ndarray x: ndarray
1D array containing coordinates for a point 1D array containing coordinates for a point
y: ndarray y: ndarray
1D array containing coordinates for a point 1D array containing coordinates for a point
metric: str metric: str
Euclidean, Manhattan Euclidean, Manhattan
Returns: Returns:
dist: float dist: float
''' '''
if metric == 'Euclidean': if metric == 'Euclidean':
raise NotImplementedError raise NotImplementedError
elif metric == 'Manhattan': elif metric == 'Manhattan':
raise NotImplementedError raise NotImplementedError
else: else:
raise ValueError('{} is not a valid metric.'.format(metric)) raise ValueError('{} is not a valid metric.'.format(metric))
return dist # scalar distance btw x and y return dist # scalar distance btw x and y
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## General supervised learning performance related functions ## General supervised learning performance related functions
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Implement the "conf_matrix" function that takes as input an array of true labels (*true*) and an array of predicted labels (*pred*). It should output a numpy.ndarray. Implement the "conf_matrix" function that takes as input an array of true labels (*true*) and an array of predicted labels (*pred*). It should output a numpy.ndarray.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# TODO: Programming Assignment 1 # TODO: Programming Assignment 1
def conf_matrix(true, pred): def conf_matrix(true, pred, n_classes):
''' '''
Args: Args:
true: ndarray true: ndarray
nx1 array of true labels for test set nx1 array of true labels for test set
pred: ndarray pred: ndarray
nx1 array of predicted labels for test set nx1 array of predicted labels for test set
n_classes: int
Returns: Returns:
ndarray result: ndarray
n_classes x n_classes array confusion matrix
''' '''
raise NotImplementedError raise NotImplementedError
result = np.ndarray([n_classes, n_classes])
tp = tn = fp = fn = 0
# calculate true positives (tp), true negatives(tn)
# false positives (fp) and false negatives (fn)
# returns the confusion matrix as numpy.ndarray # returns the confusion matrix as numpy.ndarray
return np.array([tp,tn, fp, fn]) return result
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
ROC curves are a good way to visualize sensitivity vs. 1-specificity for varying cut off points. "ROC" takes a list containing different *threshold* parameter values to try and returns two arrays; one where each entry is the sensitivity at a given threshold and the other where entries are 1-specificities. ROC curves are a good way to visualize sensitivity vs. 1-specificity for varying cut off points. "ROC" takes a list containing different *threshold* parameter values to try and returns two arrays; one where each entry is the sensitivity at a given threshold and the other where entries are 1-specificities.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# TODO: Programming Assignment 1 # TODO: Programming Assignment 1
def ROC(true_labels, preds, value_list): def ROC(true_labels, preds, value_list):
''' '''
Args: Args:
true_labels: ndarray true_labels: ndarray
1D array containing true labels 1D array containing true labels
preds: ndarray preds: ndarray
1D array containing thresholded value (e.g. proportion of positive neighbors in kNN) 1D array containing thresholded value (e.g. proportion of neighbors in kNN)
value_list: ndarray value_list: ndarray
1D array containing different threshold values 1D array containing different threshold values
Returns: Returns:
sens: ndarray sens: ndarray
1D array containing sensitivities 1D array containing sensitivities
spec_: ndarray spec_: ndarray
1D array containing 1-specifities 1D array containing 1-specifities
''' '''
# use conf_matrix to calculate tp, tn, fp, fn
# calculate sensitivity, 1-specificity # calculate sensitivity, 1-specificity
# return two arrays # return two arrays
raise NotImplementedError raise NotImplementedError
return sens, spec_ return sens, spec_
``` ```
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