m |
|
| (153 intermediate revisions not shown.) |
| Line 1: |
Line 1: |
| | + | <!-- {{Unreleased}} --> |
| | __TOC__ | | __TOC__ |
| | | | |
| - | This lab is due by Friday, October 21 at 10:00pm.
| + | {{Lab_Due|when=Thursday, October 29}} |
| | | | |
| - | (todo put code online)
| + | {{Get_Code|lab=6}} |
| - | <!--
| + | |
| - | To work on this lab, you will need to get the code, much like you did for the previous labs. You can:
| + | |
| - | * Use Git on your computer: <tt>git clone username@athena.dialup.mit.edu:/mit/6.034/www/labs/lab5</tt>
| + | |
| - | * Use Git on Athena: <tt>git clone /mit/6.034/www/labs/lab5</tt>
| + | |
| - | * Download it as a ZIP file: http://web.mit.edu/6.034/www/labs/lab5/lab5.zip
| + | |
| - | * View the files individually: http://web.mit.edu/6.034/www/labs/lab5/
| + | |
| - | -->
| + | |
| - | Your answers for this lab belong in the main file <tt>lab5.py</tt>. This lab will cover identification trees as well as k-nearest neighbors.
| + | |
| | | | |
| | + | == Breaking down a problem into smaller sub-problems == |
| | | | |
| - | == Identification Trees ==
| + | For your convenience, we have split this lab into two sections. Part 1 covers the topic of [[Lab_5:_Identification_Trees | identification trees]], and Part 2 covers [[Lab_5:_k-Nearest_Neighbors | k-nearest neighbors]]. |
| - | In this section of the lab, we will first warm up by using an ID tree to classify points. Then, we will learn how to construct new ID trees from raw data, using the techniques we learned in class.
| + | |
| | | | |
| - | === Using an ID Tree to classify unknown points ===
| + | We strongly suggest that you complete [[Lab_6:_Identification_Trees | Part 1 (ID Trees)]] by '''Thursday, October 15'''. |
| - | In this lab, we will represent an ID tree recursively as a tree of <tt>IdentificationTreeNode</tt> objects. For more information, see the [[#IdentificationTreeNode | API]] below.
| + | |
| | | | |
| - | For the ID trees section, we will represent a data point as a dictionary mapping attributes to values. For example:
| + | We strongly suggest that you then complete [[Lab_6:_k-Nearest_Neighbors | Part 2 (kNN)]] by '''Tuesday, October 20'''. |
| - | point = {"X": 1, "Y": 2, "Angel": True} ##(jmn todo: use a better example that matches the test data)
| + | |
| | | | |
| - | To begin, let's use an ID tree to classify a point! Classifying a point using an ID tree is straight-forward. We recursively apply the current node's classifier to the data point, using the result to choose which branch to take to the child node. If a "leaf" node is ever encountered, that node gives the final classification of the point.
| + | The final deadline to complete Lab 6 (both [[Lab_6:_Identification_Trees | Part 1 (ID Trees)]] and [[Lab_6:_k-Nearest_Neighbors | Part 2 (kNN)]]) is '''Thursday, October 29'''. |
| | | | |
| - | Write a function <tt>id_tree_classify_point</tt> that takes in a point (represented as a dictionary) and an ID tree (represented as a <tt>IdentificationTreeNode</tt>) and uses the ID tree to classify the point (even if the point already has a classification defined), returning the final classification:
| + | Note that if you submit online after completing Part 1 (but before completing Part 2), the tester will fail as expected for kNN tests. Don't fret! '''As long as you submit and pass all online tests by Thursday, October 29, you will be awarded full lab credit.''' |
| | | | |
| - | def id_tree_classify_point(point, id_tree):
| + | {{Survey}} |
| - | | + | |
| - | This function can be written cleanly in 3-4 lines, either iteratively or recursively.
| + | |
| - | If you're not sure how, check out the available methods in the [[#IdentificationTreeNode | <tt>IdentificationTreeNode</tt> API]]. In particular, the methods <tt>.apply_classifier(point)</tt> and <tt>.get_node_classification()</tt> may be useful.
| + | |
| - | | + | |
| - | === Calculating Disorder ===
| + | |
| - | Now that we're able to classify points, it's time to actually construct an ID tree! We'll start by coding the information-disorder equations to calculate the disorder of a branch or test. These equations are explained in more detail on page 429 of [http://courses.csail.mit.edu/6.034f/ai3/ch21.pdf the reading].
| + | |
| - | | + | |
| - | (todo provide equations here & explain disorder)
| + | |
| - | | + | |
| - | branch_disorder should take in a branch (of a decision stump), represented as a list of classifications (such as <tt>["Oak", "Oak", "Maple"]</tt>), and return the disorder of the branch (a number):
| + | |
| - | | + | |
| - | def branch_disorder(branch):
| + | |
| - | | + | |
| - | The following Python tricks and shortcuts may be useful here and/or later in the lab:
| + | |
| - | * <tt>log2</tt>: We've defined a function <tt>log2</tt> that takes in a single number and returns log<sub>2</sub> of the number.
| + | |
| - | * <tt>INF</tt>: As in previous labs, we've defined the constant <tt>INF</tt>, which is a float representing infinity
| + | |
| - | * <tt>list.count</tt>: <tt>.count</tt> is a built-in list method that counts how many times an item occurs in a list. For example, <tt>[10, 20, 20, 30].count(20)</tt> -> <tt>2</tt>.
| + | |
| - | * <tt>float</tt>: Recall that if you divide two ints in Python2, it rounds down to the nearest int, so you'll need to cast one of them to a float if you want to perform normal division.
| + | |
| - | * <tt>set</tt>: Recall from Lab 0 that a set is handy way to count or enumerate the unique items in a list.
| + | |
| - | | + | |
| - | | + | |
| - | average_test_disorder should take in a decision stump (a.k.a. a "test"), represented as a list of branches (such as <tt>[["Oak", "Oak", "Maple"], ["Maple", "Maple"]]</tt>), and return the disorder of the entire stump (a number):
| + | |
| - | | + | |
| - | def average_test_disorder(stump):
| + | |
| - | | + | |
| - | === Constructing an ID Tree ===
| + | |
| - | In order to actually construct an ID tree, we'll need to work directly with classifiers, also known as tests. (todo explain further)
| + | |
| - | | + | |
| - | We will represent each classifier as a <tt>Classifier</tt> object, described in the [[#Classifier | API]] below.
| + | |
| - | | + | |
| - | Using the disorder functions you defined above, implement a function to select the best classifier. The function should take in some data (as a list of point dictionaries), a list of Classifiers, and the attribute you want your ID tree to ultimately classifying by (e.g. "tree_type"). It should return the Classifier that has the lowest disorder.
| + | |
| - | | + | |
| - | Edge cases:
| + | |
| - | * If two Classifiers are tied for lowest disorder, break ties by preferring classifiers that occur earlier in the list.
| + | |
| - | * If the Classifier with lowest disorder is no good (that is, it doesn't separate the data at all), raise the exception <tt>NoGoodClassifiersError</tt> instead of returning a Classifier.
| + | |
| - | | + | |
| - | def find_best_classifier(data, possible_classifiers, classification_key):
| + | |
| - | | + | |
| - | | + | |
| - | Next, we will incorporate the ID tree. Use <tt>find_best_classifier</tt> to implement the next function, which should take in an incomplete tree (as an IdentificationTreeNode object) and a list of possible classifiers. The function should perform one of three actions:
| + | |
| - | * If the node is homogeneous (you can use the function is_homogeneous(data, classification_key) to check this), then it should be a leaf node, so add the classification to the node.
| + | |
| - | * If the node is not homogeneous and the data can be divided further, add the best classifier to the node.
| + | |
| - | * If the node is not homogeneous but there are no good classifiers left, raise a <tt>NoGoodClassifiersError</tt>.
| + | |
| - | | + | |
| - | The function should either modify and return the original IdentificationTreeNode, or raise an exception. Implement add_best_classifier_to_tree:
| + | |
| - | | + | |
| - | def add_best_classifier_to_tree(id_tree_node, possible_classifiers):
| + | |
| - | | + | |
| - | | + | |
| - | Now, you can implement the function finish_greedy_subtree, which takes in an incomplete tree (represented as an IndentificationTreeNode) and a list of possible classifiers, and adds classifiers to the tree until either perfect classification has been achieved, or there are no good classifiers left. If a branch cannot become homogeneous, leave its classification unassigned (which defaults to None). We recommend implementing this function recursively.
| + | |
| - | | + | |
| - | def finish_greedy_subtree(id_tree_node, possible_classifiers):
| + | |
| - | | + | |
| - | Finally, to put it all together, we've provided a function that calls your functions to construct a complete ID tree:
| + | |
| - | | + | |
| - | <pre>
| + | |
| - | def construct_greedy_identification_tree(data, possible_classifiers, classification_key):
| + | |
| - | id_tree = IdentificationTreeNode(data, classification_key)
| + | |
| - | return finish_greedy_subtree(id_tree, possible_classifiers)
| + | |
| - | </pre>
| + | |
| - | | + | |
| - | We've also provided some datasets from past quizzes, so you can now use your ID tree builder to solve problems! For example, if you run:
| + | |
| - | print construct_greedy_identification_tree(tree_data, tree_classifiers, "tree_type")
| + | |
| - | ...it should compute and print the solution to the tree-identification problem from 2014 Q2.
| + | |
| - | | + | |
| - | You can also try:
| + | |
| - | print construct_greedy_identification_tree(angel_data, angel_classifiers, "Classification") #from 2012 Q2
| + | |
| - | print construct_greedy_identification_tree(numeric_data, numeric_classifiers, "class") #from 2013 Q2
| + | |
| - | | + | |
| - | You can also change the classification_key attribute to, for example, use tree_type to predict what type of bark_texture a tree has:
| + | |
| - | print construct_greedy_identification_tree(tree_data, tree_classifiers_reverse, "bark_texture") #build an ID tree to predict bark_texture
| + | |
| - | | + | |
| - | === Conceptual questions ===
| + | |
| - | todo
| + | |
| - | | + | |
| - | == k-Nearest Neighbors ==
| + | |
| - | | + | |
| - | === Multiple Choice ===
| + | |
| - | todo: something about drawing 1NN boundaries
| + | |
| - | | + | |
| - | === Python warm-up: Distance metrics ===
| + | |
| - | k-nearest neighbors can use many different distance metrics. In 6.034, we cover four of them:
| + | |
| - | * Euclidean distance: the straight-line distance between two points (todo add formula)
| + | |
| - | * Manhattan distance: todo explain (todo add formula)
| + | |
| - | * Hamming distance: todo explain (todo add formula)
| + | |
| - | * Cosine distance: todo explain (todo add formula) (todo note about cosine_distance being negated, b/c it's a similarity metric where 1 = most similar, 0 = not similar)
| + | |
| - | | + | |
| - | It's also possible to transform data instead of using a different metric -- for instance, transforming to polar coordinates -- but in this lab we will only work with distance metrics in Cartesian coordinates.
| + | |
| - | | + | |
| - | We'll start with some basic functions for manipulating vectors, which may be useful for <tt>cosine_distance</tt>. For these, we will represent an ''n''-dimensional vector as a list or tuple of ''n'' coordinates.
| + | |
| - | <tt>dot_product</tt> should compute the dot product of two vectors, while <tt>norm</tt> computes the length of a vector. (There is a simple implementation of <tt>norm</tt> that uses <tt>dot_product</tt>.) Implement both functions:
| + | |
| - | | + | |
| - | def dot_product(u, v):
| + | |
| - | | + | |
| - | def norm(v):
| + | |
| - | | + | |
| - | | + | |
| - | Next, you'll implement each of the four distance metrics. For the rest of the k-nearest neighbors portion of this lab, we will represent data points as [[#Point_(for_kNN)|Point]] objects (described below in the API). Each distance function should take in two Points and return the distance between them as a float or int. Implement each distance function:
| + | |
| - | | + | |
| - | def euclidean_distance(point1, point2):
| + | |
| - | | + | |
| - | def manhattan_distance(point1, point2):
| + | |
| - | | + | |
| - | def hamming_distance(point1, point2):
| + | |
| - | | + | |
| - | def cosine_distance(point1, point2):
| + | |
| - | | + | |
| - | === Classifying Points with k-Nearest Neighbors ===
| + | |
| - | | + | |
| - | We've provided a function: (todo explain)
| + | |
| - | | + | |
| - | <pre>
| + | |
| - | def get_k_closest_points(point, data, k, distance_metric):
| + | |
| - | "return list of k points closest to input point, based on metric"
| + | |
| - | if k >= len(data):
| + | |
| - | return data
| + | |
| - | sorted_points = sorted(data, key=lambda p2: distance_metric(point, p2))
| + | |
| - | return sorted_points[:k]
| + | |
| - | </pre>
| + | |
| - | | + | |
| - | Your task is to use that to write a function that classifies a point, given a set of data (as a list of Points), a value of k, and a distance metric (a function):
| + | |
| - | def knn_classify_point(point, data, k, distance_metric):
| + | |
| - | | + | |
| - | todo hint: to get the mode of a list, do: max(set(my_list), key=my_list.count)
| + | |
| - | | + | |
| - | === Cross-validation: Choosing the best k and distance metric ===
| + | |
| - | | + | |
| - | todo explain functions
| + | |
| - | | + | |
| - | todo clarify different definitions of cross-validation; we're using leave-one-out
| + | |
| - | | + | |
| - | def cross_validate(data, k, distance_metric):
| + | |
| - | | + | |
| - | | + | |
| - | def find_best_k_and_metric(data):
| + | |
| - | | + | |
| - | === More multiple choice ===
| + | |
| - | todo something about overfitting, underfitting, running classify and find_best_k... on some data to see what happens
| + | |
| - | | + | |
| - | | + | |
| - | == Survey ==
| + | |
| - | Please answer these questions at the bottom of your <tt>lab5.py</tt> file:
| + | |
| - | | + | |
| - | * <tt>NAME</tt>: What is your name? (string)
| + | |
| - | | + | |
| - | * <tt>COLLABORATORS</tt>: Other than 6.034 staff, with whom did you work on this lab? (string, or empty string if you worked alone)
| + | |
| - | | + | |
| - | * <tt>HOW_MANY_HOURS_THIS_LAB_TOOK</tt>: Approximately how many hours did you spend on this lab? (number or string)
| + | |
| - | | + | |
| - | * <tt>WHAT_I_FOUND_INTERESTING</tt>: Which parts of this lab, if any, did you find interesting? (string)
| + | |
| - | | + | |
| - | * <tt>WHAT_I_FOUND_BORING</tt>: Which parts of this lab, if any, did you find boring or tedious? (string)
| + | |
| - | | + | |
| - | * (optional) <tt>SUGGESTIONS</tt>: What specific changes would you recommend, if any, to improve this lab for future years? (string)
| + | |
| - | | + | |
| - | | + | |
| - | (We'd ask which parts you find confusing, but if you're confused you should really ask a TA.)
| + | |
| - | | + | |
| - | When you're done, run the online tester to submit your code. <!--(The online tester for Lab 5 will be made available by ___.)-->
| + | |
| - | | + | |
| - | == API Reference Documentation ==
| + | |
| - | The file <tt>api.py</tt> defines the <tt>Classifier</tt>, <tt>IdentificationTreeNode</tt>, and <tt>Point</tt> classes, as well as some helper functions for ID trees, all described below. (todo: describe helper functions)
| + | |
| - | | + | |
| - | === Classifier ===
| + | |
| - | <tt>Classifier</tt> objects are used for constructing and manipulating ID trees.
| + | |
| - | | + | |
| - | A <tt>Classifier</tt> has the following attributes:
| + | |
| - | *<b><tt>classifier</tt></b><tt>.name</tt>, the name of the classifier.
| + | |
| - | *<b><tt>classifier</tt></b><tt>.classify</tt>, a function that takes in a point and returns a value.
| + | |
| - | | + | |
| - | In our ID trees, a point is represented as a dict mapping attribute names to their values.
| + | |
| - | | + | |
| - | === IdentificationTreeNode ===
| + | |
| - | In this lab, an ID tree is represented ''recursively'' as a tree of <tt>IdentificationTreeNode</tt> objects. In particular, an <tt>IdentificationTreeNode</tt> object fully represents an entire ID tree rooted at that node.
| + | |
| - | | + | |
| - | For example, suppose we have an <tt>IdentificationTreeNode</tt> called <tt>id_tree_node</tt> Then, <tt>id_tree_node</tt>'s children are themselves <tt>IdentificationTreeNode</tt> objects, each fully describing the sub-trees of <tt>id_tree_node</tt>. However, if <tt>id_tree_node</tt> has no children, then <tt>id_tree_node</tt> is a leaf, meaning that it represents a homogeneous (by classification) set of data points. Furthermore, any datum at this node is definitively classified by that leaf's classification.
| + | |
| - | | + | |
| - | As such, in a completed ID tree, each node is either
| + | |
| - | * a leaf node with a ''classification'' such as <tt>"Yes"</tt> (is a vampire) or <tt>"No"</tt> (is not a vampire) in the vampires example; or
| + | |
| - | * a non-leaf node with a ''classifier'' (such as <tt>"Accent"</tt> in the vampires example), with branches (one per classifier result, e.g. <tt>"Heavy"</tt>, <tt>"Odd"</tt>, and <tt>"None"</tt>) leading to child nodes.
| + | |
| - | | + | |
| - | An <tt>IdentificationTreeNode</tt> has the following attributes and methods:
| + | |
| - | *<b><tt>id_tree_node</tt></b><tt>.data</tt>, the list of training points at this node in the tree.
| + | |
| - | *<b><tt>id_tree_node</tt></b><tt>.classification_key</tt>, the single attribute by which the tree classifies points (e.g. <tt>"Vampire?"</tt> for the vampires example, or <tt>"Classification"</tt> for the angel data).
| + | |
| - | *<b><tt>id_tree_node</tt></b><tt>.get_parent_branch_name()</tt>: returns the name of the branch leading to this node, or <tt>"ID Tree"</tt> if this is a root node.
| + | |
| - | *<b><tt>id_tree_node</tt></b><tt>.is_leaf()</tt>: returns <tt>True</tt> if the node is a leaf (has a classification), otherwise <tt>False</tt>.
| + | |
| - | *<b><tt>id_tree_node</tt></b><tt>.set_classifier(classifier)</tt>: Uses the specified <tt>[[#Classifier | Classifier]]</tt> object to add branches below the current node. Modifies and returns the original <tt>id_tree_node</tt>. May print warnings if the specified classifier is inadvisable.
| + | |
| - | *<b><tt>id_tree_node</tt></b><tt>.apply_classifier(point)</tt>: Applies this node's classifier to a given data point by following the appropriate branch of the tree, then returns the ''child'' node. If this node is a leaf node (and thus doesn't have a classifier), raises a <tt>RuntimeError</tt>.
| + | |
| - | *<b><tt>id_tree_node</tt></b><tt>.get_classifier()</tt>: returns the [[#Classifier | classifier]] associated with this node, if it has one. Otherwise, returns <tt>None</tt>.
| + | |
| - | *<b><tt>id_tree_node</tt></b><tt>.set_node_classification(classification)</tt>: Sets this node's classification, thus defining this node as a leaf node. Modifies and returns the original <tt>id_tree_node</tt>. May print warnings if the node already has branches defined.
| + | |
| - | *<b><tt>id_tree_node</tt></b><tt>.get_node_classification()</tt>: returns this node's classification, if it has one. Otherwise, returns <tt>None</tt>.
| + | |
| - | *<b><tt>id_tree_node</tt></b><tt>.get_branches()</tt>: returns a dictionary mapping this node's child branches to the nodes at the end of them. <!--todo explain better-->
| + | |
| - | *<b><tt>id_tree_node</tt></b><tt>.describe_type()</tt>: returns a human-readable string describing the node type (e.g. leaf, subtree, etc.).
| + | |
| - | | + | |
| - | === Point (for kNN) ===
| + | |
| - | <tt>Point</tt> objects are used in the k-nearest neighbors section only.
| + | |
| - | | + | |
| - | A <tt>Point</tt> has the following attributes:
| + | |
| - | *<b><tt>point</tt></b><tt>.name</tt>, the name of the point (a string), if defined.
| + | |
| - | *<b><tt>point</tt></b><tt>.coords</tt>, the coordinates of the point, represented as a vector (a tuple or list of numbers).
| + | |
| - | *<b><tt>point</tt></b><tt>.classification</tt>, the classification of the point, if known.
| + | |
Before working on the lab, you will need to get the code. You can...
Note that if you submit online after completing Part 1 (but before completing Part 2), the tester will fail as expected for kNN tests. Don't fret! As long as you submit and pass all online tests by Thursday, October 29, you will be awarded full lab credit.
