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"""Learn to estimate functions from examples. (Chapters 18, 20)"""
from
utils
import
(
removeall
,
unique
,
product
,
mode
,
argmax
,
argmax_random_tie
,
isclose
,
gaussian
,
dotproduct
,
vector_add
,
scalar_vector_product
,
weighted_sample_with_replacement
,
weighted_sampler
,
num_or_str
,
normalize
,
clip
,
sigmoid
,
print_table
,
open_data
,
sigmoid_derivative
,
probability
,
norm
,
matrix_multiplication
)
import
copy
import
heapq
import
math
import
random
from
statistics
import
mean
,
stdev
from
collections
import
defaultdict
# ______________________________________________________________________________
def
euclidean_distance
(
X
,
Y
):
return
math
.
sqrt
(
sum
([(
x
-
y
)
**
2
for
x
,
y
in
zip
(
X
,
Y
)]))
def
rms_error
(
X
,
Y
):
return
math
.
sqrt
(
ms_error
(
X
,
Y
))
def
ms_error
(
X
,
Y
):
return
mean
([(
x
-
y
)
**
2
for
x
,
y
in
zip
(
X
,
Y
)])
def
mean_error
(
X
,
Y
):
return
mean
([
abs
(
x
-
y
)
for
x
,
y
in
zip
(
X
,
Y
)])
def
manhattan_distance
(
X
,
Y
):
return
sum
([
abs
(
x
-
y
)
for
x
,
y
in
zip
(
X
,
Y
)])
def
mean_boolean_error
(
X
,
Y
):
return
mean
(
int
(
x
!=
y
)
for
x
,
y
in
zip
(
X
,
Y
))
def
hamming_distance
(
X
,
Y
):
return
sum
(
x
!=
y
for
x
,
y
in
zip
(
X
,
Y
))
# ______________________________________________________________________________
class
DataSet
:
"""A data set for a machine learning problem. It has the following fields:
d.examples A list of examples. Each one is a list of attribute values.
d.attrs A list of integers to index into an example, so example[attr]
gives a value. Normally the same as range(len(d.examples[0])).
d.attrnames Optional list of mnemonic names for corresponding attrs.
d.target The attribute that a learning algorithm will try to predict.
By default the final attribute.
d.inputs The list of attrs without the target.
d.values A list of lists: each sublist is the set of possible
values for the corresponding attribute. If initially None,
it is computed from the known examples by self.setproblem.
If not None, an erroneous value raises ValueError.
d.distance A function from a pair of examples to a nonnegative number.
Should be symmetric, etc. Defaults to mean_boolean_error
since that can handle any field types.
d.name Name of the data set (for output display only).
d.source URL or other source where the data came from.
d.exclude A list of attribute indexes to exclude from d.inputs. Elements
of this list can either be integers (attrs) or attrnames.
Normally, you call the constructor and you're done; then you just
access fields like d.examples and d.target and d.inputs."""
def
__init__
(
self
,
examples
=
None
,
attrs
=
None
,
attrnames
=
None
,
target
=
-
1
,
inputs
=
None
,
values
=
None
,
distance
=
mean_boolean_error
,
name
=
''
,
source
=
''
,
exclude
=
()):
"""Accepts any of DataSet's fields. Examples can also be a
string or file from which to parse examples using parse_csv.
Optional parameter: exclude, as documented in .setproblem().
>>> DataSet(examples='1, 2, 3')
<DataSet(): 1 examples, 3 attributes>
"""
self
.
name
=
name
self
.
source
=
source
self
.
values
=
values
self
.
distance
=
distance
if
values
is
None
:
self
.
got_values_flag
=
False
else
:
self
.
got_values_flag
=
True
# Initialize .examples from string or list or data directory
if
isinstance
(
examples
,
str
):
self
.
examples
=
parse_csv
(
examples
)
elif
examples
is
None
:
self
.
examples
=
parse_csv
(
open_data
(
name
+
'.csv'
).
read
())
else
:
self
.
examples
=
examples
# Attrs are the indices of examples, unless otherwise stated.
if
attrs
is
None
and
self
.
examples
is
not
None
:
attrs
=
list
(
range
(
len
(
self
.
examples
[
0
])))
self
.
attrs
=
attrs
# Initialize .attrnames from string, list, or by default
if
isinstance
(
attrnames
,
str
):
self
.
attrnames
=
attrnames
.
split
()
else
:
self
.
attrnames
=
attrnames
or
attrs
self
.
setproblem
(
target
,
inputs
=
inputs
,
exclude
=
exclude
)
def
setproblem
(
self
,
target
,
inputs
=
None
,
exclude
=
()):
"""Set (or change) the target and/or inputs.
This way, one DataSet can be used multiple ways. inputs, if specified,
is a list of attributes, or specify exclude as a list of attributes
to not use in inputs. Attributes can be -n .. n, or an attrname.
Also computes the list of possible values, if that wasn't done yet."""
self
.
target
=
self
.
attrnum
(
target
)
exclude
=
list
(
map
(
self
.
attrnum
,
exclude
))
if
inputs
:
self
.
inputs
=
removeall
(
self
.
target
,
inputs
)
else
:
self
.
inputs
=
[
a
for
a
in
self
.
attrs
if
a
!=
self
.
target
and
a
not
in
exclude
]
if
not
self
.
values
:
self
.
update_values
()
self
.
check_me
()
def
check_me
(
self
):
"""Check that my fields make sense."""
assert
len
(
self
.
attrnames
)
==
len
(
self
.
attrs
)
assert
self
.
target
in
self
.
attrs
assert
self
.
target
not
in
self
.
inputs
assert
set
(
self
.
inputs
).
issubset
(
set
(
self
.
attrs
))
if
self
.
got_values_flag
:
# only check if values are provided while initializing DataSet
list
(
map
(
self
.
check_example
,
self
.
examples
))
def
add_example
(
self
,
example
):
"""Add an example to the list of examples, checking it first."""
self
.
check_example
(
example
)
self
.
examples
.
append
(
example
)
def
check_example
(
self
,
example
):
"""Raise ValueError if example has any invalid values."""
if
self
.
values
:
for
a
in
self
.
attrs
:
if
example
[
a
]
not
in
self
.
values
[
a
]:
raise
ValueError
(
'Bad value {} for attribute {} in {}'
.
format
(
example
[
a
],
self
.
attrnames
[
a
],
example
))
def
attrnum
(
self
,
attr
):
"""Returns the number used for attr, which can be a name, or -n .. n-1."""
if
isinstance
(
attr
,
str
):
return
self
.
attrnames
.
index
(
attr
)
elif
attr
<
0
:
return
len
(
self
.
attrs
)
+
attr
else
:
return
attr
def
update_values
(
self
):
self
.
values
=
list
(
map
(
unique
,
zip
(
*
self
.
examples
)))
def
sanitize
(
self
,
example
):
"""Return a copy of example, with non-input attributes replaced by None."""
return
[
attr_i
if
i
in
self
.
inputs
else
None
for
i
,
attr_i
in
enumerate
(
example
)]
def
classes_to_numbers
(
self
,
classes
=
None
):
"""Converts class names to numbers."""
if
not
classes
:
# If classes were not given, extract them from values
classes
=
sorted
(
self
.
values
[
self
.
target
])
for
item
in
self
.
examples
:
item
[
self
.
target
]
=
classes
.
index
(
item
[
self
.
target
])
def
remove_examples
(
self
,
value
=
""
):
"""Remove examples that contain given value."""
self
.
examples
=
[
x
for
x
in
self
.
examples
if
value
not
in
x
]
self
.
update_values
()
def
split_values_by_classes
(
self
):
"""Split values into buckets according to their class."""
buckets
=
defaultdict
(
lambda
: [])
target_names
=
self
.
values
[
self
.
target
]
for
v
in
self
.
examples
:
item
=
[
a
for
a
in
v
if
a
not
in
target_names
]
# Remove target from item
buckets
[
v
[
self
.
target
]].
append
(
item
)
# Add item to bucket of its class
return
buckets
def
find_means_and_deviations
(
self
):
"""Finds the means and standard deviations of self.dataset.
means : A dictionary for each class/target. Holds a list of the means
of the features for the class.
deviations: A dictionary for each class/target. Holds a list of the sample
standard deviations of the features for the class."""
target_names
=
self
.
values
[
self
.
target
]
feature_numbers
=
len
(
self
.
inputs
)
item_buckets
=
self
.
split_values_by_classes
()
means
=
defaultdict
(
lambda
: [
0
for
i
in
range
(
feature_numbers
)])
deviations
=
defaultdict
(
lambda
: [
0
for
i
in
range
(
feature_numbers
)])
for
t
in
target_names
:
# Find all the item feature values for item in class t
features
=
[[]
for
i
in
range
(
feature_numbers
)]
for
item
in
item_buckets
[
t
]:
features
=
[
features
[
i
]
+
[
item
[
i
]]
for
i
in
range
(
feature_numbers
)]
# Calculate means and deviations fo the class
for
i
in
range
(
feature_numbers
):
means
[
t
][
i
]
=
mean
(
features
[
i
])
deviations
[
t
][
i
]
=
stdev
(
features
[
i
])
return
means
,
deviations
def
__repr__
(
self
):
return
'<DataSet({}): {:d} examples, {:d} attributes>'
.
format
(
self
.
name
,
len
(
self
.
examples
),
len
(
self
.
attrs
))
# ______________________________________________________________________________
def
parse_csv
(
input
,
delim
=
','
):
r"""Input is a string consisting of lines, each line has comma-delimited
fields. Convert this into a list of lists. Blank lines are skipped.
Fields that look like numbers are converted to numbers.
The delim defaults to ',' but '\t' and None are also reasonable values.
>>> parse_csv('1, 2, 3 \n 0, 2, na')
[[1, 2, 3], [0, 2, 'na']]"""
lines
=
[
line
for
line
in
input
.
splitlines
()
if
line
.
strip
()]
return
[
list
(
map
(
num_or_str
,
line
.
split
(
delim
)))
for
line
in
lines
]
# ______________________________________________________________________________
class
CountingProbDist
:
"""A probability distribution formed by observing and counting examples.
If p is an instance of this class and o is an observed value, then
there are 3 main operations:
p.add(o) increments the count for observation o by 1.
p.sample() returns a random element from the distribution.
p[o] returns the probability for o (as in a regular ProbDist)."""
def
__init__
(
self
,
observations
=
[],
default
=
0
):
"""Create a distribution, and optionally add in some observations.
By default this is an unsmoothed distribution, but saying default=1,
for example, gives you add-one smoothing."""
self
.
dictionary
=
{}
self
.
n_obs
=
0.0
self
.
default
=
default
self
.
sampler
=
None
for
o
in
observations
:
self
.
add
(
o
)
def
add
(
self
,
o
):
"""Add an observation o to the distribution."""
self
.
smooth_for
(
o
)
self
.
dictionary
[
o
]
+=
1
self
.
n_obs
+=
1
self
.
sampler
=
None
def
smooth_for
(
self
,
o
):
"""Include o among the possible observations, whether or not
it's been observed yet."""
if
o
not
in
self
.
dictionary
:
self
.
dictionary
[
o
]
=
self
.
default
self
.
n_obs
+=
self
.
default
self
.
sampler
=
None
def
__getitem__
(
self
,
item
):
"""Return an estimate of the probability of item."""
self
.
smooth_for
(
item
)
return
self
.
dictionary
[
item
]
/
self
.
n_obs
# (top() and sample() are not used in this module, but elsewhere.)
def
top
(
self
,
n
):
"""Return (count, obs) tuples for the n most frequent observations."""
return
heapq
.
nlargest
(
n
, [(
v
,
k
)
for
(
k
,
v
)
in
self
.
dictionary
.
items
()])
def
sample
(
self
):
"""Return a random sample from the distribution."""
if
self
.
sampler
is
None
:
self
.
sampler
=
weighted_sampler
(
list
(
self
.
dictionary
.
keys
()),
list
(
self
.
dictionary
.
values
()))
return
self
.
sampler
()
# ______________________________________________________________________________
def
PluralityLearner
(
dataset
):
"""A very dumb algorithm: always pick the result that was most popular
in the training data. Makes a baseline for comparison."""
most_popular
=
mode
([
e
[
dataset
.
target
]
for
e
in
dataset
.
examples
])
def
predict
(
example
):
"""Always return same result: the most popular from the training set."""
return
most_popular
return
predict
# ______________________________________________________________________________
def
NaiveBayesLearner
(
dataset
,
continuous
=
True
,
simple
=
False
):
if
simple
:
return
NaiveBayesSimple
(
dataset
)
if
(
continuous
):
return
NaiveBayesContinuous
(
dataset
)
else
:
return
NaiveBayesDiscrete
(
dataset
)
def
NaiveBayesSimple
(
distribution
):
"""A simple naive bayes classifier that takes as input a dictionary of
CountingProbDist objects and classifies items according to these distributions.
The input dictionary is in the following form:
(ClassName, ClassProb): CountingProbDist"""
target_dist
=
{
c_name
:
prob
for
c_name
,
prob
in
distribution
.
keys
()}
attr_dists
=
{
c_name
:
count_prob
for
(
c_name
,
_
),
count_prob
in
distribution
.
items
()}
def
predict
(
example
):
"""Predict the target value for example. Calculate probabilities for each
class and pick the max."""
def
class_probability
(
targetval
):
attr_dist
=
attr_dists
[
targetval
]
return
target_dist
[
targetval
]
*
product
(
attr_dist
[
a
]
for
a
in
example
)
return
argmax
(
target_dist
.
keys
(),
key
=
class_probability
)
return
predict
def
NaiveBayesDiscrete
(
dataset
):
"""Just count how many times each value of each input attribute
occurs, conditional on the target value. Count the different
target values too."""
target_vals
=
dataset
.
values
[
dataset
.
target
]
target_dist
=
CountingProbDist
(
target_vals
)
attr_dists
=
{(
gv
,
attr
):
CountingProbDist
(
dataset
.
values
[
attr
])
for
gv
in
target_vals
for
attr
in
dataset
.
inputs
}
for
example
in
dataset
.
examples
:
targetval
=
example
[
dataset
.
target
]
target_dist
.
add
(
targetval
)
for
attr
in
dataset
.
inputs
:
attr_dists
[
targetval
,
attr
].
add
(
example
[
attr
])
def
predict
(
example
):
"""Predict the target value for example. Consider each possible value,
and pick the most likely by looking at each attribute independently."""
def
class_probability
(
targetval
):
return
(
target_dist
[
targetval
]
*
product
(
attr_dists
[
targetval
,
attr
][
example
[
attr
]]
for
attr
in
dataset
.
inputs
))
return
argmax
(
target_vals
,
key
=
class_probability
)
return
predict
def
NaiveBayesContinuous
(
dataset
):
"""Count how many times each target value occurs.
Also, find the means and deviations of input attribute values for each target value."""
means
,
deviations
=
dataset
.
find_means_and_deviations
()
target_vals
=
dataset
.
values
[
dataset
.
target
]
target_dist
=
CountingProbDist
(
target_vals
)
def
predict
(
example
):
"""Predict the target value for example. Consider each possible value,
and pick the most likely by looking at each attribute independently."""
def
class_probability
(
targetval
):
prob
=
target_dist
[
targetval
]
for
attr
in
dataset
.
inputs
:
prob
*=
gaussian
(
means
[
targetval
][
attr
],
deviations
[
targetval
][
attr
],
example
[
attr
])
return
prob
return
argmax
(
target_vals
,
key
=
class_probability
)
return
predict
# ______________________________________________________________________________
def
NearestNeighborLearner
(
dataset
,
k
=
1
):
"""k-NearestNeighbor: the k nearest neighbors vote."""
def
predict
(
example
):
"""Find the k closest items, and have them vote for the best."""
best
=
heapq
.
nsmallest
(
k
, ((
dataset
.
distance
(
e
,
example
),
e
)
for
e
in
dataset
.
examples
))
return
mode
(
e
[
dataset
.
target
]
for
(
d
,
e
)
in
best
)
return
predict
# ______________________________________________________________________________
def
truncated_svd
(
X
,
num_val
=
2
,
max_iter
=
1000
):
"""Computes the first component of SVD"""
def
normalize_vec
(
X
,
n
=
2
):
"""Normalizes two parts (:m and m:) of the vector"""
X_m
=
X
[:
m
]
X_n
=
X
[
m
:]
norm_X_m
=
norm
(
X_m
,
n
)
Y_m
=
[
x
/
norm_X_m
for
x
in
X_m
]
norm_X_n
=
norm
(
X_n
,
n
)
Y_n
=
[
x
/
norm_X_n
for
x
in
X_n
]
return
Y_m
+
Y_n
def
remove_component
(
X
):
"""Removes components of already obtained eigen vectors from X"""
X_m
=
X
[:
m
]
X_n
=
X
[
m
:]
for
eivec
in
eivec_m
:
coeff
=
dotproduct
(
X_m
,
eivec
)
X_m
=
[
x1
-
coeff
*
x2
for
x1
,
x2
in
zip
(
X_m
,
eivec
)]
for
eivec
in
eivec_n
:
coeff
=
dotproduct
(
X_n
,
eivec
)
X_n
=
[
x1
-
coeff
*
x2
for
x1
,
x2
in
zip
(
X_n
,
eivec
)]
return
X_m
+
X_n
m
,
n
=
len
(
X
),
len
(
X
[
0
])
A
=
[[
0
for
_
in
range
(
n
+
m
)]
for
_
in
range
(
n
+
m
)]
for
i
in
range
(
m
):
for
j
in
range
(
n
):
A
[
i
][
m
+
j
]
=
A
[
m
+
j
][
i
]
=
X
[
i
][
j
]
eivec_m
=
[]
eivec_n
=
[]
eivals
=
[]
for
_
in
range
(
num_val
):
X
=
[
random
.
random
()
for
_
in
range
(
m
+
n
)]
X
=
remove_component
(
X
)
X
=
normalize_vec
(
X
)
for
_
in
range
(
max_iter
):
old_X
=
X
X
=
matrix_multiplication
(
A
, [[
x
]
for
x
in
X
])
X
=
[
x
[
0
]
for
x
in
X
]
X
=
remove_component
(
X
)
X
=
normalize_vec
(
X
)
# check for convergence
if
norm
([
x1
-
x2
for
x1
,
x2
in
zip
(
old_X
,
X
)])
<=
1e-10
:
break
projected_X
=
matrix_multiplication
(
A
, [[
x
]
for
x
in
X
])
projected_X
=
[
x
[
0
]
for
x
in
projected_X
]
eivals
.
append
(
norm
(
projected_X
,
1
)
/
norm
(
X
,
1
))
eivec_m
.
append
(
X
[:
m
])
eivec_n
.
append
(
X
[
m
:])
return
(
eivec_m
,
eivec_n
,
eivals
)
# ______________________________________________________________________________
class
DecisionFork
:
"""A fork of a decision tree holds an attribute to test, and a dict
of branches, one for each of the attribute's values."""
def
__init__
(
self
,
attr
,
attrname
=
None
,
default_child
=
None
,
branches
=
None
):
"""Initialize by saying what attribute this node tests."""
self
.
attr
=
attr
self
.
attrname
=
attrname
or
attr
self
.
default_child
=
default_child
self
.
branches
=
branches
or
{}
def
__call__
(
self
,
example
):
"""Given an example, classify it using the attribute and the branches."""
attrvalue
=
example
[
self
.
attr
]
if
attrvalue
in
self
.
branches
:
return
self
.
branches
[
attrvalue
](
example
)
else
:
# return default class when attribute is unknown
return
self
.
default_child
(
example
)
def
add
(
self
,
val
,
subtree
):
"""Add a branch. If self.attr = val, go to the given subtree."""
self
.
branches
[
val
]
=
subtree
def
display
(
self
,
indent
=
0
):
name
=
self
.
attrname
print
(
'Test'
,
name
)
for
(
val
,
subtree
)
in
self
.
branches
.
items
():
print
(
' '
*
4
*
indent
,
name
,
'='
,
val
,
'==>'
,
end
=
' '
)
subtree
.
display
(
indent
+
1
)
def
__repr__
(
self
):
return
(
'DecisionFork({0!r}, {1!r}, {2!r})'
.
format
(
self
.
attr
,
self
.
attrname
,
self
.
branches
))
class
DecisionLeaf
:
"""A leaf of a decision tree holds just a result."""
def
__init__
(
self
,
result
):
self
.
result
=
result
def
__call__
(
self
,
example
):
return
self
.
result
def
display
(
self
,
indent
=
0
):
print
(
'RESULT ='
,
self
.
result
)
def
__repr__
(
self
):
return
repr
(
self
.
result
)
# ______________________________________________________________________________
def
DecisionTreeLearner
(
dataset
):
"""[Figure 18.5]"""
target
,
values
=
dataset
.
target
,
dataset
.
values
def
decision_tree_learning
(
examples
,
attrs
,
parent_examples
=
()):
if
len
(
examples
)
==
0
:
return
plurality_value
(
parent_examples
)
elif
all_same_class
(
examples
):
return
DecisionLeaf
(
examples
[
0
][
target
])
elif
len
(
attrs
)
==
0
:
return
plurality_value
(
examples
)
else
:
A
=
choose_attribute
(
attrs
,
examples
)
tree
=
DecisionFork
(
A
,
dataset
.
attrnames
[
A
],
plurality_value
(
examples
))
for
(
v_k
,
exs
)
in
split_by
(
A
,
examples
):
subtree
=
decision_tree_learning
(
exs
,
removeall
(
A
,
attrs
),
examples
)
tree
.
add
(
v_k
,
subtree
)
return
tree
def
plurality_value
(
examples
):
"""Return the most popular target value for this set of examples.
(If target is binary, this is the majority; otherwise plurality.)"""
popular
=
argmax_random_tie
(
values
[
target
],
key
=
lambda
v
:
count
(
target
,
v
,
examples
))
return
DecisionLeaf
(
popular
)
def
count
(
attr
,
val
,
examples
):
"""Count the number of examples that have attr = val."""
return
sum
(
e
[
attr
]
==
val
for
e
in
examples
)
def
all_same_class
(
examples
):
"""Are all these examples in the same target class?"""
class0
=
examples
[
0
][
target
]
return
all
(
e
[
target
]
==
class0
for
e
in
examples
)
def
choose_attribute
(
attrs
,
examples
):
"""Choose the attribute with the highest information gain."""
return
argmax_random_tie
(
attrs
,
key
=
lambda
a
:
information_gain
(
a
,
examples
))
def
information_gain
(
attr
,
examples
):
"""Return the expected reduction in entropy from splitting by attr."""
def
I
(
examples
):
return
information_content
([
count
(
target
,
v
,
examples
)
for
v
in
values
[
target
]])
N
=
float
(
len
(
examples
))
remainder
=
sum
((
len
(
examples_i
)
/
N
)
*
I
(
examples_i
)
for
(
v
,
examples_i
)
in
split_by
(
attr
,
examples
))
return
I
(
examples
)
-
remainder
def
split_by
(
attr
,
examples
):
"""Return a list of (val, examples) pairs for each val of attr."""
return
[(
v
, [
e
for
e
in
examples
if
e
[
attr
]
==
v
])
for
v
in
values
[
attr
]]
return
decision_tree_learning
(
dataset
.
examples
,
dataset
.
inputs
)
def
information_content
(
values
):
"""Number of bits to represent the probability distribution in values."""
probabilities
=
normalize
(
removeall
(
0
,
values
))
return
sum
(
-
p
*
math
.
log2
(
p
)
for
p
in
probabilities
)
# ______________________________________________________________________________
def
RandomForest
(
dataset
,
n
=
5
):
"""An ensemble of Decision Trees trained using bagging and feature bagging."""
def
data_bagging
(
dataset
,
m
=
0
):
"""Sample m examples with replacement"""
n
=
len
(
dataset
.
examples
)
return
weighted_sample_with_replacement
(
m
or
n
,
dataset
.
examples
, [
1
]
*
n
)
def
feature_bagging
(
dataset
,
p
=
0.7
):
"""Feature bagging with probability p to retain an attribute"""
inputs
=
[
i
for
i
in
dataset
.
inputs
if
probability
(
p
)]
return
inputs
or
dataset
.
inputs
def
predict
(
example
):
print
([
predictor
(
example
)
for
predictor
in
predictors
])
return
mode
(
predictor
(
example
)
for
predictor
in
predictors
)
predictors
=
[
DecisionTreeLearner
(
DataSet
(
examples
=
data_bagging
(
dataset
),
attrs
=
dataset
.
attrs
,
attrnames
=
dataset
.
attrnames
,
target
=
dataset
.
target
,
inputs
=
feature_bagging
(
dataset
)))
for
_
in
range
(
n
)]
return
predict
# ______________________________________________________________________________
# A decision list is implemented as a list of (test, value) pairs.
def
DecisionListLearner
(
dataset
):
"""[Figure 18.11]"""
def
decision_list_learning
(
examples
):
if
not
examples
:
return
[(
True
,
False
)]
t
,
o
,
examples_t
=
find_examples
(
examples
)
if
not
t
:
raise
Exception
return
[(
t
,
o
)]
+
decision_list_learning
(
examples
-
examples_t
)
def
find_examples
(
examples
):
"""Find a set of examples that all have the same outcome under
some test. Return a tuple of the test, outcome, and examples."""
raise
NotImplementedError
def
passes
(
example
,
test
):
"""Does the example pass the test?"""
raise
NotImplementedError
def
predict
(
example
):
"""Predict the outcome for the first passing test."""
for
test
,
outcome
in
predict
.
decision_list
:
if
passes
(
example
,
test
):
return
outcome
predict
.
decision_list
=
decision_list_learning
(
set
(
dataset
.
examples
))
return
predict
# ______________________________________________________________________________
def
NeuralNetLearner
(
dataset
,
hidden_layer_sizes
=
[
3
],
learning_rate
=
0.01
,
epochs
=
100
):
"""Layered feed-forward network.
hidden_layer_sizes: List of number of hidden units per hidden layer
learning_rate: Learning rate of gradient descent
epochs: Number of passes over the dataset
"""
i_units
=
len
(
dataset
.
inputs
)
o_units
=
len
(
dataset
.
values
[
dataset
.
target
])
# construct a network
raw_net
=
network
(
i_units
,
hidden_layer_sizes
,
o_units
)
learned_net
=
BackPropagationLearner
(
dataset
,
raw_net
,
learning_rate
,
epochs
)
def
predict
(
example
):
# Input nodes
i_nodes
=
learned_net
[
0
]
# Activate input layer
for
v
,
n
in
zip
(
example
,
i_nodes
):
n
.
value
=
v
# Forward pass
for
layer
in
learned_net
[
1
:]:
for
node
in
layer
:
inc
=
[
n
.
value
for
n
in
node
.
inputs
]
in_val
=
dotproduct
(
inc
,
node
.
weights
)
node
.
value
=
node
.
activation
(
in_val
)
# Hypothesis
o_nodes
=
learned_net
[
-
1
]
prediction
=
find_max_node
(
o_nodes
)
return
prediction
return
predict
def
random_weights
(
min_value
,
max_value
,
num_weights
):
return
[
random
.
uniform
(
min_value
,
max_value
)
for
i
in
range
(
num_weights
)]
def
BackPropagationLearner
(
dataset
,
net
,
learning_rate
,
epochs
):
"""[Figure 18.23] The back-propagation algorithm for multilayer network"""
# Initialise weights
for
layer
in
net
:
for
node
in
layer
:
node
.
weights
=
random_weights
(
min_value
=
-
0.5
,
max_value
=
0.5
,
num_weights
=
len
(
node
.
weights
))
examples
=
dataset
.
examples
'''
As of now dataset.target gives an int instead of list,
Changing dataset class will have effect on all the learners.
Will be taken care of later
'''
o_nodes
=
net
[
-
1
]
i_nodes
=
net
[
0
]
o_units
=
len
(
o_nodes
)
idx_t
=
dataset
.
target
idx_i
=
dataset
.
inputs
n_layers
=
len
(
net
)
inputs
,
targets
=
init_examples
(
examples
,
idx_i
,
idx_t
,
o_units
)
for
epoch
in
range
(
epochs
):
# Iterate over each example
for
e
in
range
(
len
(
examples
)):
i_val
=
inputs
[
e
]
t_val
=
targets
[
e
]
# Activate input layer
for
v
,
n
in
zip
(
i_val
,
i_nodes
):
n
.
value
=
v
# Forward pass
for
layer
in
net
[
1
:]:
for
node
in
layer
:
inc
=
[
n
.
value
for
n
in
node
.
inputs
]
in_val
=
dotproduct
(
inc
,
node
.
weights
)
node
.
value
=
node
.
activation
(
in_val
)
# Initialize delta
delta
=
[[]
for
i
in
range
(
n_layers
)]
# Compute outer layer delta
# Error for the MSE cost function
err
=
[
t_val
[
i
]
-
o_nodes
[
i
].
value
for
i
in
range
(
o_units
)]
# The activation function used is the sigmoid function
delta
[
-
1
]
=
[
sigmoid_derivative
(
o_nodes
[
i
].
value
)
*
err
[
i
]
for
i
in
range
(
o_units
)]
# Backward pass
h_layers
=
n_layers
-
2
for
i
in
range
(
h_layers
,
0
,
-
1
):
layer
=
net
[
i
]
h_units
=
len
(
layer
)
nx_layer
=
net
[
i
+
1
]
# weights from each ith layer node to each i + 1th layer node
w
=
[[
node
.
weights
[
k
]
for
node
in
nx_layer
]
for
k
in
range
(
h_units
)]
delta
[
i
]
=
[
sigmoid_derivative
(
layer
[
j
].
value
)
*
dotproduct
(
w
[
j
],
delta
[
i
+
1
])
for
j
in
range
(
h_units
)]
# Update weights
for
i
in
range
(
1
,
n_layers
):
layer
=
net
[
i
]
inc
=
[
node
.
value
for
node
in
net
[
i
-
1
]]
units
=
len
(
layer
)
for
j
in
range
(
units
):
layer
[
j
].
weights
=
vector_add
(
layer
[
j
].
weights
,
scalar_vector_product
(
learning_rate
*
delta
[
i
][
j
],
inc
))
return
net
def
PerceptronLearner
(
dataset
,
learning_rate
=
0.01
,
epochs
=
100
):
"""Logistic Regression, NO hidden layer"""
i_units
=
len
(
dataset
.
inputs
)
o_units
=
len
(
dataset
.
values
[
dataset
.
target
])
hidden_layer_sizes
=
[]
raw_net
=
network
(
i_units
,
hidden_layer_sizes
,
o_units
)
learned_net
=
BackPropagationLearner
(
dataset
,
raw_net
,
learning_rate
,
epochs
)
def
predict
(
example
):
o_nodes
=
learned_net
[
1
]
# Forward pass
for
node
in
o_nodes
:
in_val
=
dotproduct
(
example
,
node
.
weights
)
node
.
value
=
node
.
activation
(
in_val
)
# Hypothesis
return
find_max_node
(
o_nodes
)
return
predict
class
NNUnit
:
"""Single Unit of Multiple Layer Neural Network
inputs: Incoming connections
weights: Weights to incoming connections
"""
def
__init__
(
self
,
weights
=
None
,
inputs
=
None
):
self
.
weights
=
[]
self
.
inputs
=
[]
self
.
value
=
None
self
.
activation
=
sigmoid
def
network
(
input_units
,
hidden_layer_sizes
,
output_units
):
"""Create Directed Acyclic Network of given number layers.
hidden_layers_sizes : List number of neuron units in each hidden layer
excluding input and output layers
"""
# Check for PerceptronLearner
if
hidden_layer_sizes
:
layers_sizes
=
[
input_units
]
+
hidden_layer_sizes
+
[
output_units
]
else
:
layers_sizes
=
[
input_units
]
+
[
output_units
]
net
=
[[
NNUnit
()
for
n
in
range
(
size
)]
for
size
in
layers_sizes
]
n_layers
=
len
(
net
)
# Make Connection
for
i
in
range
(
1
,
n_layers
):
for
n
in
net
[
i
]:
for
k
in
net
[
i
-
1
]:
n
.
inputs
.
append
(
k
)
n
.
weights
.
append
(
0
)
return
net
def
init_examples
(
examples
,
idx_i
,
idx_t
,
o_units
):
inputs
=
{}
targets
=
{}
for
i
in
range
(
len
(
examples
)):
e
=
examples
[
i
]
# Input values of e
inputs
[
i
]
=
[
e
[
i
]
for
i
in
idx_i
]
if
o_units
>
1
:
# One-Hot representation of e's target
t
=
[
0
for
i
in
range
(
o_units
)]
t
[
e
[
idx_t
]]
=
1
targets
[
i
]
=
t
else
:
# Target value of e
targets
[
i
]
=
[
e
[
idx_t
]]
return
inputs
,
targets
def
find_max_node
(
nodes
):
return
nodes
.
index
(
argmax
(
nodes
,
key
=
lambda
node
:
node
.
value
))
# ______________________________________________________________________________
def
LinearLearner
(
dataset
,
learning_rate
=
0.01
,
epochs
=
100
):
"""Define with learner = LinearLearner(data); infer with learner(x)."""
idx_i
=
dataset
.
inputs
idx_t
=
dataset
.
target
# As of now, dataset.target gives only one index.
examples
=
dataset
.
examples
num_examples
=
len
(
examples
)
# X transpose
X_col
=
[
dataset
.
values
[
i
]
for
i
in
idx_i
]
# vertical columns of X
# Add dummy
ones
=
[
1
for
_
in
range
(
len
(
examples
))]
X_col
=
[
ones
]
+
X_col
# Initialize random weigts
num_weights
=
len
(
idx_i
)
+
1
w
=
random_weights
(
min_value
=
-
0.5
,
max_value
=
0.5
,
num_weights
=
num_weights
)
for
epoch
in
range
(
epochs
):
err
=
[]
# Pass over all examples
for
example
in
examples
:
x
=
[
1
]
+
example
y
=
dotproduct
(
w
,
x
)
t
=
example
[
idx_t
]
err
.
append
(
t
-
y
)
# update weights
for
i
in
range
(
len
(
w
)):
w
[
i
]
=
w
[
i
]
+
learning_rate
*
(
dotproduct
(
err
,
X_col
[
i
])
/
num_examples
)
def
predict
(
example
):
x
=
[
1
]
+
example
return
dotproduct
(
w
,
x
)
return
predict
# ______________________________________________________________________________
def
EnsembleLearner
(
learners
):
"""Given a list of learning algorithms, have them vote."""
def
train
(
dataset
):
predictors
=
[
learner
(
dataset
)
for
learner
in
learners
]
def
predict
(
example
):
return
mode
(
predictor
(
example
)
for
predictor
in
predictors
)
return
predict
return
train
# ______________________________________________________________________________
def
AdaBoost
(
L
,
K
):
"""[Figure 18.34]"""
def
train
(
dataset
):
examples
,
target
=
dataset
.
examples
,
dataset
.
target
N
=
len
(
examples
)
epsilon
=
1.
/
(
2
*
N
)
w
=
[
1.
/
N
]
*
N
h
,
z
=
[], []
for
k
in
range
(
K
):
h_k
=
L
(
dataset
,
w
)
h
.
append
(
h_k
)
error
=
sum
(
weight
for
example
,
weight
in
zip
(
examples
,
w
)
if
example
[
target
]
!=
h_k
(
example
))
# Avoid divide-by-0 from either 0% or 100% error rates:
error
=
clip
(
error
,
epsilon
,
1
-
epsilon
)
for
j
,
example
in
enumerate
(
examples
):
if
example
[
target
]
==
h_k
(
example
):
w
[
j
]
*=
error
/
(
1.
-
error
)
w
=
normalize
(
w
)
z
.
append
(
math
.
log
((
1.
-
error
)
/
error
))
return
WeightedMajority
(
h
,
z
)
return
train
def
WeightedMajority
(
predictors
,
weights
):
"""Return a predictor that takes a weighted vote."""
def
predict
(
example
):
return
weighted_mode
((
predictor
(
example
)
for
predictor
in
predictors
),
weights
)
return
predict
def
weighted_mode
(
values
,
weights
):
"""Return the value with the greatest total weight.
>>> weighted_mode('abbaa', [1,2,3,1,2])
'b'
"""
totals
=
defaultdict
(
int
)
for
v
,
w
in
zip
(
values
,
weights
):
totals
[
v
]
+=
w
return
max
(
list
(
totals
.
keys
()),
key
=
totals
.
get
)
# _____________________________________________________________________________
# Adapting an unweighted learner for AdaBoost
def
WeightedLearner
(
unweighted_learner
):
"""Given a learner that takes just an unweighted dataset, return
one that takes also a weight for each example. [p. 749 footnote 14]"""
def
train
(
dataset
,
weights
):
return
unweighted_learner
(
replicated_dataset
(
dataset
,
weights
))
return
train
def
replicated_dataset
(
dataset
,
weights
,
n
=
None
):
"""Copy dataset, replicating each example in proportion to its weight."""
n
=
n
or
len
(
dataset
.
examples
)
result
=
copy
.
copy
(
dataset
)
result
.
examples
=
weighted_replicate
(
dataset
.
examples
,
weights
,
n
)
return
result
def
weighted_replicate
(
seq
,
weights
,
n
):
"""Return n selections from seq, with the count of each element of
seq proportional to the corresponding weight (filling in fractions
randomly).
>>> weighted_replicate('ABC', [1,2,1], 4)
['A', 'B', 'B', 'C']
"""
assert
len
(
seq
)
==
len
(
weights
)
weights
=
normalize
(
weights
)
wholes
=
[
int
(
w
*
n
)
for
w
in
weights
]
fractions
=
[(
w
*
n
)
%
1
for
w
in
weights
]
return
(
flatten
([
x
]
*
nx
for
x
,
nx
in
zip
(
seq
,
wholes
))
+
weighted_sample_with_replacement
(
n
-
sum
(
wholes
),
seq
,
fractions
))
def
flatten
(
seqs
):
return
sum
(
seqs
, [])
# _____________________________________________________________________________
# Functions for testing learners on examples
def
err_ratio
(
predict
,
dataset
,
examples
=
None
,
verbose
=
0
):
"""Return the proportion of the examples that are NOT correctly predicted.
verbose - 0: No output; 1: Output wrong; 2 (or greater): Output correct"""
if
examples
is
None
:
examples
=
dataset
.
examples
if
len
(
examples
)
==
0
:
return
0.0
right
=
0.0
for
example
in
examples
:
desired
=
example
[
dataset
.
target
]
output
=
predict
(
dataset
.
sanitize
(
example
))
if
output
==
desired
:
right
+=
1
if
verbose
>=
2
:
print
(
' OK: got {} for {}'
.
format
(
desired
,
example
))
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