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"""Learning from examples (Chapters 18)"""
import
copy
from
collections
import
defaultdict
from
statistics
import
stdev
from
qpsolvers
import
solve_qp
from
probabilistic_learning
import
NaiveBayesLearner
from
utils
import
*
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.attr_names 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.set_problem.
If not None, an erroneous value raises ValueError.
d.distance A function from a pair of examples to a non-negative 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 attr_names.
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
,
attr_names
=
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 .set_problem().
>>> DataSet(examples='1, 2, 3')
<DataSet(): 1 examples, 3 attributes>
"""
self
.
name
=
name
self
.
source
=
source
self
.
values
=
values
self
.
distance
=
distance
self
.
got_values_flag
=
bool
(
values
)
# 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
self
.
examples
is
not
None
and
attrs
is
None
:
attrs
=
list
(
range
(
len
(
self
.
examples
[
0
])))
self
.
attrs
=
attrs
# initialize .attr_names from string, list, or by default
if
isinstance
(
attr_names
,
str
):
self
.
attr_names
=
attr_names
.
split
()
else
:
self
.
attr_names
=
attr_names
or
attrs
self
.
set_problem
(
target
,
inputs
=
inputs
,
exclude
=
exclude
)
def
set_problem
(
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 attr_name.
Also computes the list of possible values, if that wasn't done yet.
"""
self
.
target
=
self
.
attr_num
(
target
)
exclude
=
list
(
map
(
self
.
attr_num
,
exclude
))
if
inputs
:
self
.
inputs
=
remove_all
(
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
.
attr_names
)
==
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
.
attr_names
[
a
],
example
))
def
attr_num
(
self
,
attr
):
"""Returns the number used for attr, which can be a name, or -n .. n-1."""
if
isinstance
(
attr
,
str
):
return
self
.
attr_names
.
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
]
*
feature_numbers
)
deviations
=
defaultdict
(
lambda
: [
0
]
*
feature_numbers
)
for
t
in
target_names
:
# find all the item feature values for item in class t
features
=
[[]
for
_
in
range
(
feature_numbers
)]
for
item
in
item_buckets
[
t
]:
for
i
in
range
(
feature_numbers
):
features
[
i
].
append
(
item
[
i
])
# 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
]
def
err_ratio
(
predict
,
dataset
,
examples
=
None
):
"""
Return the proportion of the examples that are NOT correctly predicted.
verbose - 0: No output; 1: Output wrong; 2 (or greater): Output correct
"""
examples
=
examples
or
dataset
.
examples
if
len
(
examples
)
==
0
:
return
0.0
right
=
0
for
example
in
examples
:
desired
=
example
[
dataset
.
target
]
output
=
predict
(
dataset
.
sanitize
(
example
))
if
output
==
desired
:
right
+=
1
return
1
-
(
right
/
len
(
examples
))
def
grade_learner
(
predict
,
tests
):
"""
Grades the given learner based on how many tests it passes.
tests is a list with each element in the form: (values, output).
"""
return
mean
(
int
(
predict
(
X
)
==
y
)
for
X
,
y
in
tests
)
def
train_test_split
(
dataset
,
start
=
None
,
end
=
None
,
test_split
=
None
):
"""
If you are giving 'start' and 'end' as parameters,
then it will return the testing set from index 'start' to 'end'
and the rest for training.
If you give 'test_split' as a parameter then it will return
test_split * 100% as the testing set and the rest as
training set.
"""
examples
=
dataset
.
examples
if
test_split
is
None
:
train
=
examples
[:
start
]
+
examples
[
end
:]
val
=
examples
[
start
:
end
]
else
:
total_size
=
len
(
examples
)
val_size
=
int
(
total_size
*
test_split
)
train_size
=
total_size
-
val_size
train
=
examples
[:
train_size
]
val
=
examples
[
train_size
:
total_size
]
return
train
,
val
def
cross_validation_wrapper
(
learner
,
dataset
,
k
=
10
,
trials
=
1
):
"""
[Figure 18.8]
Return the optimal value of size having minimum error on validation set.
errT: a training error array, indexed by size
errV: a validation error array, indexed by size
"""
errs
=
[]
size
=
1
while
True
:
errT
,
errV
=
cross_validation
(
learner
,
dataset
,
size
,
k
,
trials
)
# check for convergence provided err_val is not empty
if
errT
and
not
np
.
isclose
(
errT
[
-
1
],
errT
,
rtol
=
1e-6
):
best_size
=
0
min_val
=
np
.
inf
i
=
0
while
i
<
size
:
if
errs
[
i
]
<
min_val
:
min_val
=
errs
[
i
]
best_size
=
i
i
+=
1
return
learner
(
dataset
,
best_size
)
errs
.
append
(
errV
)
size
+=
1
def
cross_validation
(
learner
,
dataset
,
size
=
None
,
k
=
10
,
trials
=
1
):
"""
Do k-fold cross_validate and return their mean.
That is, keep out 1/k of the examples for testing on each of k runs.
Shuffle the examples first; if trials > 1, average over several shuffles.
Returns Training error, Validation error
"""
k
=
k
or
len
(
dataset
.
examples
)
if
trials
>
1
:
trial_errT
=
0
trial_errV
=
0
for
t
in
range
(
trials
):
errT
,
errV
=
cross_validation
(
learner
,
dataset
,
size
,
k
,
trials
)
trial_errT
+=
errT
trial_errV
+=
errV
return
trial_errT
/
trials
,
trial_errV
/
trials
else
:
fold_errT
=
0
fold_errV
=
0
n
=
len
(
dataset
.
examples
)
examples
=
dataset
.
examples
random
.
shuffle
(
dataset
.
examples
)
for
fold
in
range
(
k
):
train_data
,
val_data
=
train_test_split
(
dataset
,
fold
*
(
n
//
k
), (
fold
+
1
)
*
(
n
//
k
))
dataset
.
examples
=
train_data
h
=
learner
(
dataset
,
size
)
fold_errT
+=
err_ratio
(
h
,
dataset
,
train_data
)
fold_errV
+=
err_ratio
(
h
,
dataset
,
val_data
)
# reverting back to original once test is completed
dataset
.
examples
=
examples
return
fold_errT
/
k
,
fold_errV
/
k
def
leave_one_out
(
learner
,
dataset
,
size
=
None
):
"""Leave one out cross-validation over the dataset."""
return
cross_validation
(
learner
,
dataset
,
size
,
len
(
dataset
.
examples
))
def
learning_curve
(
learner
,
dataset
,
trials
=
10
,
sizes
=
None
):
if
sizes
is
None
:
sizes
=
list
(
range
(
2
,
len
(
dataset
.
examples
)
-
trials
,
2
))
def
score
(
learner
,
size
):
random
.
shuffle
(
dataset
.
examples
)
return
cross_validation
(
learner
,
dataset
,
size
,
trials
)
return
[(
size
,
mean
([
score
(
learner
,
size
)
for
_
in
range
(
trials
)]))
for
size
in
sizes
]
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
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
,
attr_name
=
None
,
default_child
=
None
,
branches
=
None
):
"""Initialize by saying what attribute this node tests."""
self
.
attr
=
attr
self
.
attr_name
=
attr_name
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."""
attr_val
=
example
[
self
.
attr
]
if
attr_val
in
self
.
branches
:
return
self
.
branches
[
attr_val
](
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
.
attr_name
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
.
attr_name
,
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
):
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
)
if
all_same_class
(
examples
):
return
DecisionLeaf
(
examples
[
0
][
target
])
if
len
(
attrs
)
==
0
:
return
plurality_value
(
examples
)
A
=
choose_attribute
(
attrs
,
examples
)
tree
=
DecisionFork
(
A
,
dataset
.
attr_names
[
A
],
plurality_value
(
examples
))
for
(
v_k
,
exs
)
in
split_by
(
A
,
examples
):
subtree
=
decision_tree_learning
(
exs
,
remove_all
(
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 example[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
=
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
(
remove_all
(
0
,
values
))
return
sum
(
-
p
*
np
.
log2
(
p
)
for
p
in
probabilities
)
def
DecisionListLearner
(
dataset
):
"""
[Figure 18.11]
A decision list implemented as a list of (test, value) pairs.
"""
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
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
LinearLearner
(
dataset
,
learning_rate
=
0.01
,
epochs
=
100
):
"""
[Section 18.6.3]
Linear classifier with hard threshold.
"""
idx_i
=
dataset
.
inputs
idx_t
=
dataset
.
target
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 weights
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
=
np
.
dot
(
w
,
x
)
t
=
example
[
idx_t
]
err
.
append
(
t
-
y
)
# update weights
for
i
in
range
(
len
(
w
)):
w
[
i
]
=
w
[
i
]
+
learning_rate
*
(
np
.
dot
(
err
,
X_col
[
i
])
/
num_examples
)
def
predict
(
example
):
x
=
[
1
]
+
example
return
np
.
dot
(
w
,
x
)
return
predict
def
LogisticLinearLeaner
(
dataset
,
learning_rate
=
0.01
,
epochs
=
100
):
"""
[Section 18.6.4]
Linear classifier with logistic regression.
"""
idx_i
=
dataset
.
inputs
idx_t
=
dataset
.
target
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 weights
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
=
[]
h
=
[]
# pass over all examples
for
example
in
examples
:
x
=
[
1
]
+
example
y
=
sigmoid
(
np
.
dot
(
w
,
x
))
h
.
append
(
sigmoid_derivative
(
y
))
t
=
example
[
idx_t
]
err
.
append
(
t
-
y
)
# update weights
for
i
in
range
(
len
(
w
)):
buffer
=
[
x
*
y
for
x
,
y
in
zip
(
err
,
h
)]
w
[
i
]
=
w
[
i
]
+
learning_rate
*
(
np
.
dot
(
buffer
,
X_col
[
i
])
/
num_examples
)
def
predict
(
example
):
x
=
[
1
]
+
example
return
sigmoid
(
np
.
dot
(
w
,
x
))
return
predict
def
NeuralNetLearner
(
dataset
,
hidden_layer_sizes
=
None
,
learning_rate
=
0.01
,
epochs
=
100
,
activation
=
sigmoid
):
"""
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
"""
if
hidden_layer_sizes
is
None
:
hidden_layer_sizes
=
[
3
]
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
,
activation
)
learned_net
=
BackPropagationLearner
(
dataset
,
raw_net
,
learning_rate
,
epochs
,
activation
)
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
=
dot_product
(
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
BackPropagationLearner
(
dataset
,
net
,
learning_rate
,
epochs
,
activation
=
sigmoid
):
"""
[Figure 18.23]
The back-propagation algorithm for multilayer networks.
"""
# 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
=
dot_product
(
inc
,
node
.
weights
)
node
.
value
=
node
.
activation
(
in_val
)
# initialize delta
delta
=
[[]
for
_
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
)]
# calculate delta at output
if
node
.
activation
==
sigmoid
:
delta
[
-
1
]
=
[
sigmoid_derivative
(
o_nodes
[
i
].
value
)
*
err
[
i
]
for
i
in
range
(
o_units
)]
elif
node
.
activation
==
relu
:
delta
[
-
1
]
=
[
relu_derivative
(
o_nodes
[
i
].
value
)
*
err
[
i
]
for
i
in
range
(
o_units
)]
elif
node
.
activation
==
tanh
:
delta
[
-
1
]
=
[
tanh_derivative
(
o_nodes
[
i
].
value
)
*
err
[
i
]
for
i
in
range
(
o_units
)]
elif
node
.
activation
==
elu
:
delta
[
-
1
]
=
[
elu_derivative
(
o_nodes
[
i
].
value
)
*
err
[
i
]
for
i
in
range
(
o_units
)]
elif
node
.
activation
==
leaky_relu
:
delta
[
-
1
]
=
[
leaky_relu_derivative
(
o_nodes
[
i
].
value
)
*
err
[
i
]
for
i
in
range
(
o_units
)]
else
:
return
ValueError
(
"Activation function unknown."
)
# 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
)]
if
activation
==
sigmoid
:
delta
[
i
]
=
[
sigmoid_derivative
(
layer
[
j
].
value
)
*
dot_product
(
w
[
j
],
delta
[
i
+
1
])
for
j
in
range
(
h_units
)]
elif
activation
==
relu
:
delta
[
i
]
=
[
relu_derivative
(
layer
[
j
].
value
)
*
dot_product
(
w
[
j
],
delta
[
i
+
1
])
for
j
in
range
(
h_units
)]
elif
activation
==
tanh
:
delta
[
i
]
=
[
tanh_derivative
(
layer
[
j
].
value
)
*
dot_product
(
w
[
j
],
delta
[
i
+
1
])
for
j
in
range
(
h_units
)]
elif
activation
==
elu
:
delta
[
i
]
=
[
elu_derivative
(
layer
[
j
].
value
)
*
dot_product
(
w
[
j
],
delta
[
i
+
1
])
for
j
in
range
(
h_units
)]
elif
activation
==
leaky_relu
:
delta
[
i
]
=
[
leaky_relu_derivative
(
layer
[
j
].
value
)
*
dot_product
(
w
[
j
],
delta
[
i
+
1
])
for
j
in
range
(
h_units
)]
else
:
return
ValueError
(
"Activation function unknown."
)
# 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
=
dot_product
(
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
,
activation
=
sigmoid
,
weights
=
None
,
inputs
=
None
):
self
.
weights
=
weights
or
[]
self
.
inputs
=
inputs
or
[]
self
.
value
=
None
self
.
activation
=
activation
def
network
(
input_units
,
hidden_layer_sizes
,
output_units
,
activation
=
sigmoid
):
"""
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
"""
layers_sizes
=
[
input_units
]
+
hidden_layer_sizes
+
[
output_units
]
net
=
[[
NNUnit
(
activation
)
for
_
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
,
e
in
enumerate
(
examples
):
# 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
(
max
(
nodes
,
key
=
lambda
node
:
node
.
value
))
class
SVC
:
def
__init__
(
self
,
kernel
=
linear_kernel
,
C
=
1.0
,
verbose
=
False
):
self
.
kernel
=
kernel
self
.
C
=
C
# hyper-parameter
self
.
sv_idx
,
self
.
sv
,
self
.
sv_y
=
np
.
zeros
(
0
),
np
.
zeros
(
0
),
np
.
zeros
(
0
)
self
.
alphas
=
np
.
zeros
(
0
)
self
.
w
=
None
self
.
b
=
0.0
# intercept
self
.
verbose
=
verbose
def
fit
(
self
,
X
,
y
):
"""
Trains the model by solving a quadratic programming problem.
:param X: array of size [n_samples, n_features] holding the training samples
:param y: array of size [n_samples] holding the class labels
"""
# In QP formulation (dual): m variables, 2m+1 constraints (1 equation, 2m inequations)
self
.
solve_qp
(
X
,
y
)
sv
=
self
.
alphas
>
1e-5
self
.
sv_idx
=
np
.
arange
(
len
(
self
.
alphas
))[
sv
]
self
.
sv
,
self
.
sv_y
,
self
.
alphas
=
X
[
sv
],
y
[
sv
],
self
.
alphas
[
sv
]
if
self
.
kernel
==
linear_kernel
:
self
.
w
=
np
.
dot
(
self
.
alphas
*
self
.
sv_y
,
self
.
sv
)
for
n
in
range
(
len
(
self
.
alphas
)):
self
.
b
+=
self
.
sv_y
[
n
]
self
.
b
-=
np
.
sum
(
self
.
alphas
*
self
.
sv_y
*
self
.
K
[
self
.
sv_idx
[
n
],
sv
])
self
.
b
/=
len
(
self
.
alphas
)
return
self
def
solve_qp
(
self
,
X
,
y
):
"""
Solves a quadratic programming problem. In QP formulation (dual):
m variables, 2m+1 constraints (1 equation, 2m inequations).
:param X: array of size [n_samples, n_features] holding the training samples
:param y: array of size [n_samples] holding the class labels
"""
m
=
len
(
y
)
# m = n_samples
self
.
K
=
self
.
kernel
(
X
)
# gram matrix
P
=
self
.
K
*
np
.
outer
(
y
,
y
)
q
=
-
np
.
ones
(
m
)
lb
=
np
.
zeros
(
m
)
# lower bounds
ub
=
np
.
ones
(
m
)
*
self
.
C
# upper bounds
A
=
y
.
astype
(
np
.
float64
)
# equality matrix
b
=
np
.
zeros
(
1
)
# equality vector
self
.
alphas
=
solve_qp
(
P
,
q
,
A
=
A
,
b
=
b
,
lb
=
lb
,
ub
=
ub
,
solver
=
'cvxopt'
,
sym_proj
=
True
,
verbose
=
self
.
verbose
)
def
predict_score
(
self
,
X
):
"""
Predicts the score for a given example.
"""
if
self
.
w
is
None
:
return
np
.
dot
(
self
.
alphas
*
self
.
sv_y
,
self
.
kernel
(
self
.
sv
,
X
))
+
self
.
b
return
np
.
dot
(
X
,
self
.
w
)
+
self
.
b
def
predict
(
self
,
X
):
"""
Predicts the class of a given example.
"""
return
np
.
sign
(
self
.
predict_score
(
X
))
class
SVR
:
def
__init__
(
self
,
kernel
=
linear_kernel
,
C
=
1.0
,
epsilon
=
0.1
,
verbose
=
False
):
self
.
kernel
=
kernel
self
.
C
=
C
# hyper-parameter
self
.
epsilon
=
epsilon
# epsilon insensitive loss value
self
.
sv_idx
,
self
.
sv
=
np
.
zeros
(
0
),
np
.
zeros
(
0
)
self
.
alphas_p
,
self
.
alphas_n
=
np
.
zeros
(
0
),
np
.
zeros
(
0
)
self
.
w
=
None
self
.
b
=
0.0
# intercept
self
.
verbose
=
verbose
def
fit
(
self
,
X
,
y
):
"""
Trains the model by solving a quadratic programming problem.
:param X: array of size [n_samples, n_features] holding the training samples
:param y: array of size [n_samples] holding the class labels
"""
# In QP formulation (dual): m variables, 2m+1 constraints (1 equation, 2m inequations)
self
.
solve_qp
(
X
,
y
)
sv
=
np
.
logical_or
(
self
.
alphas_p
>
1e-5
,
self
.
alphas_n
>
1e-5
)
self
.
sv_idx
=
np
.
arange
(
len
(
self
.
alphas_p
))[
sv
]
self
.
sv
,
sv_y
=
X
[
sv
],
y
[
sv
]
self
.
alphas_p
,
self
.
alphas_n
=
self
.
alphas_p
[
sv
],
self
.
alphas_n
[
sv
]
if
self
.
kernel
==
linear_kernel
:
self
.
w
=
np
.
dot
(
self
.
alphas_p
-
self
.
alphas_n
,
self
.
sv
)
for
n
in
range
(
len
(
self
.
alphas_p
)):
self
.
b
+=
sv_y
[
n
]
self
.
b
-=
np
.
sum
((
self
.
alphas_p
-
self
.
alphas_n
)
*
self
.
K
[
self
.
sv_idx
[
n
],
sv
])
self
.
b
-=
self
.
epsilon
self
.
b
/=
len
(
self
.
alphas_p
)
return
self
def
solve_qp
(
self
,
X
,
y
):
"""
Solves a quadratic programming problem. In QP formulation (dual):
m variables, 2m+1 constraints (1 equation, 2m inequations).
:param X: array of size [n_samples, n_features] holding the training samples
:param y: array of size [n_samples] holding the class labels
"""
#
m
=
len
(
y
)
# m = n_samples
self
.
K
=
self
.
kernel
(
X
)
# gram matrix
P
=
np
.
vstack
((
np
.
hstack
((
self
.
K
,
-
self
.
K
)),
# alphas_p, alphas_n
np
.
hstack
((
-
self
.
K
,
self
.
K
))))
# alphas_n, alphas_p
q
=
np
.
hstack
((
-
y
,
y
))
+
self
.
epsilon
lb
=
np
.
zeros
(
2
*
m
)
# lower bounds
ub
=
np
.
ones
(
2
*
m
)
*
self
.
C
# upper bounds
A
=
np
.
hstack
((
np
.
ones
(
m
),
-
np
.
ones
(
m
)))
# equality matrix
b
=
np
.
zeros
(
1
)
# equality vector
alphas
=
solve_qp
(
P
,
q
,
A
=
A
,
b
=
b
,
lb
=
lb
,
ub
=
ub
,
solver
=
'cvxopt'
,
sym_proj
=
True
,
verbose
=
self
.
verbose
)
self
.
alphas_p
=
alphas
[:
m
]
self
.
alphas_n
=
alphas
[
m
:]
def
predict
(
self
,
X
):
if
self
.
kernel
!=
linear_kernel
:
return
np
.
dot
(
self
.
alphas_p
-
self
.
alphas_n
,
self
.
kernel
(
self
.
sv
,
X
))
+
self
.
b
return
np
.
dot
(
X
,
self
.
w
)
+
self
.
b
class
MultiClassLearner
:
def
__init__
(
self
,
clf
,
decision_function
=
'ovr'
):
self
.
clf
=
clf
self
.
decision_function
=
decision_function
self
.
n_class
,
self
.
classifiers
=
0
, []
def
fit
(
self
,
X
,
y
):
"""
Trains n_class or n_class * (n_class - 1) / 2 classifiers
according to the training method, ovr or ovo respectively.
:param X: array of size [n_samples, n_features] holding the training samples
:param y: array of size [n_samples] holding the class labels
:return: array of classifiers
"""
labels
=
np
.
unique
(
y
)
self
.
n_class
=
len
(
labels
)
if
self
.
decision_function
==
'ovr'
:
# one-vs-rest method
for
label
in
labels
:
y1
=
np
.
array
(
y
)
y1
[
y1
!=
label
]
=
-
1.0
y1
[
y1
==
label
]
=
1.0
self
.
clf
.
fit
(
X
,
y1
)
self
.
classifiers
.
append
(
copy
.
deepcopy
(
self
.
clf
))
elif
self
.
decision_function
==
'ovo'
:
# use one-vs-one method
n_labels
=
len
(
labels
)
for
i
in
range
(
n_labels
):
for
j
in
range
(
i
+
1
,
n_labels
):
neg_id
,
pos_id
=
y
==
labels
[
i
],
y
==
labels
[
j
]
X1
,
y1
=
np
.
r_
[
X
[
neg_id
],
X
[
pos_id
]],
np
.
r_
[
y
[
neg_id
],
y
[
pos_id
]]
y1
[
y1
==
labels
[
i
]]
=
-
1.0
y1
[
y1
==
labels
[
j
]]
=
1.0
self
.
clf
.
fit
(
X1
,
y1
)
self
.
classifiers
.
append
(
copy
.
deepcopy
(
self
.
clf
))
else
:
return
ValueError
(
"Decision function must be either 'ovr' or 'ovo'."
)
return
self
def
predict
(
self
,
X
):
"""
Predicts the class of a given example according to the training method.
"""
n_samples
=
len
(
X
)
if
self
.
decision_function
==
'ovr'
:
# one-vs-rest method
assert
len
(
self
.
classifiers
)
==
self
.
n_class
score
=
np
.
zeros
((
n_samples
,
self
.
n_class
))
for
i
in
range
(
self
.
n_class
):
clf
=
self
.
classifiers
[
i
]
score
[:,
i
]
=
clf
.
predict_score
(
X
)
return
np
.
argmax
(
score
,
axis
=
1
)
elif
self
.
decision_function
==
'ovo'
:
# use one-vs-one method
assert
len
(
self
.
classifiers
)
==
self
.
n_class
*
(
self
.
n_class
-
1
)
/
2
vote
=
np
.
zeros
((
n_samples
,
self
.
n_class
))
clf_id
=
0
for
i
in
range
(
self
.
n_class
):
for
j
in
range
(
i
+
1
,
self
.
n_class
):
res
=
self
.
classifiers
[
clf_id
].
predict
(
X
)
vote
[
res
<
0
,
i
]
+=
1.0
# negative sample: class i
vote
[
res
>
0
,
j
]
+=
1.0
# positive sample: class j
clf_id
+=
1
return
np
.
argmax
(
vote
,
axis
=
1
)
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