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learning.jl
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import Base: getindex, copy;
export euclidean_distance, mean_square_error, root_mean_square_error,
mean_error, manhattan_distance, mean_boolean_error, hamming_distance, gaussian,
DataSet, set_problem, attribute_index, check_dataset_fields,
check_example, update_values, add_example, remove_examples, sanitize, summarize, copy,
classes_to_numbers, split_values_by_classes, find_means_and_deviations,
AbstractCountingProbabilityDistribution,
CountingProbabilityDistribution, add, smooth_for_observation, getindex, top, sample,
AbstractLearner, PluralityLearner, predict,
AbstractNaiveBayesModel, NaiveBayesLearner, NaiveBayesSimpleModel,
NaiveBayesDiscreteModel, NaiveBayesContinuousModel, NearestNeighborLearner,
AbstractDecisionTreeNode, DecisionLeafNode, DecisionForkNode, classify,
DecisionTreeLearner, plurality_value,
RandomForest, data_bagging, feature_bagging,
DecisionListLearner, decision_list_learning,
NeuralNetworkUnit, NeuralNetworkLearner, neural_network,
back_propagation_learning, random_weights,
PerceptronLearner, EnsembleLearner,
weighted_mode, AdaBoostLearner, adaboost!, weighted_replicate,
partition_dataset, cross_validation, cross_validation_wrapper,
RestaurantDataSet, SyntheticRestaurantDataSet,
MajorityDataSet, ParityDataSet, XorDataSet, ContinuousXorDataSet;
function euclidean_distance(X::AbstractVector, Y::AbstractVector)
return sqrt(sum(((x - y)^2) for (x, y) in zip(X, Y)));
end
function mean_square_error(X::AbstractVector, Y::AbstractVector)
return mean(((x - y)^2) for (x, y) in zip(X, Y));
end
function root_mean_square_error(X::AbstractVector, Y::AbstractVector)
return sqrt(mean_square_error(X, Y));
end
function mean_error(X::AbstractVector, Y::AbstractVector)
return mean(abs(x - y) for (x, y) in zip(X, Y));
end
function manhattan_distance(X::AbstractVector, Y::AbstractVector)
return sum(abs(x - y) for (x, y) in zip(X, Y));
end
function mean_boolean_error(X::AbstractVector, Y::AbstractVector)
return mean((x != y) for (x, y) in zip(X, Y));
end
function hamming_distance(X::AbstractVector, Y::AbstractVector)
return sum((x != y) for (x, y) in zip(X, Y));
end
"""
gaussian(mean::Float64, standard_deviation::Float64, x::Number)
Return the probability density of the gaussian distribution for variable 'x' given
the mean 'mean' and standard deviation 'standard_deviation'.
"""
function gaussian(mean::Number, standard_deviation::Number, x::Number)
return ((Float64(1)/(sqrt(2 * pi) * Float64(standard_deviation))) *
(e^(-0.5*((Float64(x) - Float64(mean))/Float64(standard_deviation))^2)));
end
#=
DataSet is a data set used by machine learning algorithms.
=#
mutable struct DataSet
name::String
source::String
examples::AbstractMatrix
attributes::AbstractVector
attributes_names::AbstractVector
values::AbstractVector
exclude::AbstractVector
distance::Function
inputs::AbstractVector
target::Int64
function DataSet(;name::String="", source::String="", attributes::Union{Void, AbstractVector}=nothing,
attributes_names::Union{Void, String, AbstractVector}=nothing,
examples::Union{Void, String, AbstractMatrix}=nothing,
values::Union{Void, AbstractVector}=nothing,
inputs::Union{Void, String, AbstractVector}=nothing, target::Union{Int64, String}=-1,
exclude::AbstractVector=[], distance::Function=mean_boolean_error)
# Use a matrix instead of array of arrays
local examples_array::AbstractMatrix;
if (typeof(examples) <: String)
examples_array = readcsv(examples);
elseif (typeof(examples) <: Void)
# 'name'.csv must be in current directory.
examples_array = readcsv(name*".csv");
else
examples_array = examples;
end
examples_array = map((function(element)
if (typeof(element) <: AbstractString)
return strip(element);
else
return element;
end
end),
examples_array);
local attributes_array::AbstractVector;
if (typeof(attributes) <: Void)
attributes_array = collect(1:getindex(size(examples_array), 2));
else
attributes_array = attributes;
end
local attributes_names_array::AbstractVector;
if (typeof(attributes_names) <: String)
attributes_names_array = map(String, split(attributes_names));
elseif (!(typeof(attributes_names) <: Void) && (length(attributes_names) != 0))
attributes_names_array = attributes_names;
else
attributes_names_array = attributes_array;
end
local values_is_set::Bool;
local new_values::AbstractVector;
if (typeof(values) <: Void)
values_is_set = false;
new_values = [];
else
values_is_set = true;
new_values = values;
end
# Construct new DataSet without 'inputs' and 'target' fields.
local ds::DataSet = new(name, source, examples_array, attributes_array, attributes_names_array,
new_values, exclude, distance);
# Set 'inputs' and 'target' fields of newly constructed DataSet.
set_problem(ds, target, inputs, exclude);
check_dataset_fields(ds, values_is_set);
return ds;
end
function DataSet(name::String,
source::String,
examples::AbstractMatrix,
attributes::AbstractVector,
attributes_names::AbstractVector,
values::AbstractVector,
exclude::AbstractVector,
distance::Function,
inputs::AbstractVector,
target::Int64)
return new(name, source, examples, attributes, attributes_names, values, exclude, distance, inputs, target);
end
end
function set_problem(ds::DataSet, target::Int64, inputs::Void, exclude::AbstractVector)
ds.target = attribute_index(ds, target);
local mapped_exclude::AbstractVector = map(attribute_index, (ds for i in exclude), exclude);
ds.inputs = collect(a for a in ds.attributes if ((a != ds.target) && (!(a in mapped_exclude))));
if (length(ds.values) == 0)
update_values(ds);
end
nothing;
end
function set_problem(ds::DataSet, target::Int64, inputs::AbstractVector, exclude::AbstractVector)
ds.target = attribute_index(ds, target);
ds.inputs = removeall(inputs, ds.target);
if (length(ds.values) == 0)
update_values(ds);
end
nothing;
end
function set_problem(ds::DataSet, target::String, inputs::Void, exclude::AbstractVector)
ds.target = attribute_index(ds, target);
local mapped_exclude::AbstractVector = map(attribute_index, (ds for i in exclude), exclude);
ds.inputs = collect(a for a in ds.attributes if ((a != ds.target) && (!(a in mapped_exclude))));
if (length(ds.values) == 0)
update_values(ds);
end
nothing;
end
function set_problem(ds::DataSet, target::String, inputs::AbstractVector, exclude::AbstractVector)
ds.target = attribute_index(ds, target);
ds.inputs = removeall(inputs, ds.target);
if (length(ds.values) == 0)
update_values(ds);
end
nothing;
end
function attribute_index(ds::DataSet, attribute::String)
return utils.index(ds.attributes_names, attribute);
end
function attribute_index(ds::DataSet, attribute::Int64)
# Julia counts from 1.
if (attribute < 0)
return length(ds.attributes) + attribute + 1;
elseif (attribute > 0)
return attribute;
else
error("attribute_index: \"", attribute, "\" is not a valid index for an array!");
end
end
function check_dataset_fields(ds::DataSet, values_bool::Bool)
if (length(ds.attributes_names) != length(ds.attributes))
error("check_dataset_fields(): The lengths of 'attributes_names' and 'attributes' must match!");
elseif (!(ds.target in ds.attributes))
error("check_dataset_fields(): The target attribute was not found in 'attributes'!");
elseif (ds.target in ds.inputs)
error("check_dataset_fields(): The target attribute should not be in the inputs!");
elseif (!issubset(Set(ds.inputs), Set(ds.attributes)))
error("check_dataset_fields(): The 'inputs' field must be a subset of 'attributes'!");
end
if (values_bool)
map(check_example, (ds for i in ds.examples), ds.examples);
end
nothing;
end
function check_example(ds::DataSet, example::AbstractVector)
if (length(ds.values) != 0)
for attribute in ds.attributes
if (!(example[attribute] in ds.values[attribute]))
error("check_example(): Found bad value ", example[attribute], " for attribute ",
ds.attribute_names[attribute], " in ", example, "!");
end
end
end
nothing;
end
function check_example(ds::DataSet, example::AbstractMatrix)
if (length(ds.values) != 0)
for attribute in ds.attributes
if (!(example[attribute, :] in ds.values[attribute]))
error("check_example(): Found bad value ", example[attribute, :], " for attribute ",
ds.attribute_names[attribute], " in ", example, "!");
end
end
end
nothing;
end
function update_values(ds::DataSet)
ds.values = collect(collect(Set(ds.examples[:, i])) for i in 1:size(ds.examples)[2]);
nothing;
end
function add_example(ds::DataSet, example::AbstractVector)
check_example(ds, example);
vcat(ds.examples, transpose(example));
nothing;
end
function remove_examples(ds::DataSet)
local updated_examples::AbstractVector = [];
for i in size(ds.examples)[1]
if (!("" in ds.examples[i, :]))
push!(update_examples, transpose(ds.examples[i, :]));
end
end
ds.examples = reduce(vcat, Array{Any, 2}(), updated_examples);
update_values(ds);
end
function remove_examples(ds::DataSet, value::String)
local updated_examples::AbstractVector = [];
for i in size(ds.examples)[1]
if (!(value in ds.examples[i, :]))
push!(update_examples, transpose(ds.examples[i, :]));
end
end
ds.examples = reduce(vcat, Array{Any, 2}(), updated_examples);
update_values(ds);
end
"""
sanitize(ds::DataSet, example::AbstractVector)
Return a copy of the given array 'example', such that non-input attributes are removed.
"""
function sanitize(ds::DataSet, example::AbstractVector)
local sanitized_example::AbstractVector = [];
for (i, example_item) in enumerate(example)
if (i in ds.inputs)
push!(sanitized_example, example_item);
end
end
return sanitized_example;
end
"""
classes_to_numbers(ds::DataSet, classes::Void)
classes_to_numbers(ds::DataSet, classes::AbstractVector)
Set the classifications of each example in ds.examples as numbers based on the given 'classes'.
"""
function classes_to_numbers(ds::DataSet, classes::Void)
local new_classes::AbstractVector = sort(ds.values[ds.target]);
for i in 1:size(ds.examples)[1]
local index_val::Int64 = utils.index(new_classes, ds.examples[i, ds.target]);
if (index_val == -1)
error("classes_to_numbers(): Could not find ", ds.examples[i, ds.target], " in ", new_classes, "!");
end
ds.examples[i, ds.target] = index_val;
end
nothing;
end
function classes_to_numbers(ds::DataSet, classes::AbstractVector)
local new_classes::AbstractVector;
if (length(classes) == 0)
new_classes = sort(ds.values[ds.target]);
else
new_classes = classes;
end
for i in 1:size(ds.examples)[1]
local index_val::Int64 = utils.index(new_classes, ds.examples[i, ds.target]);
if (index_val == -1)
error("classes_to_numbers(): Could not find ", ds.examples[i, ds.target], " in ", new_classes, "!");
end
ds.examples[i, ds.target] = index_val;
end
nothing;
end
function split_values_by_classes(ds::DataSet)
local buckets::Dict = Dict();
local target_names::AbstractVector = ds.values[ds.target];
for example in (ds.examples[i, :] for i in 1:size(ds.examples)[1])
local item::AbstractVector = collect(attribute for attribute in example
if (!(attribute in target_names)));
push!(get!(buckets, example[ds.target], []), item);
end
return buckets;
end
function find_means_and_deviations(ds::DataSet)
local target_names::AbstractVector = ds.values[ds.target];
local feature_numbers::Int64 = length(ds.inputs);
local item_buckets::Dict = split_values_by_classes(ds);
local means::Dict = Dict();
local deviations::Dict = Dict();
local key_initial_value::AbstractVector = collect(0.0 for i in 1:feature_numbers);
for target_name in target_names
local features = collect(Array{Float64, 1}() for i in 1:feature_numbers);
for item in item_buckets[target_name]
for i in 1:feature_numbers
push!(features[i], item[i]);
end
end
for i in 1:feature_numbers
get!(means, target_name, copy(key_initial_value))[i] = mean(features[i]);
get!(deviations, target_name, copy(key_initial_value))[i] = std(features[i]);
end
end
return means, deviations;
end
function summarize(ds::DataSet)
return @sprintf("<DataSet(%s): %d examples, %d attributes>", ds.name, length(ds.examples), length(ds.attributes));
end
copy(ds::DataSet) = DataSet(identity(ds.name),
identity(ds.source),
copy(ds.examples),
copy(ds.attributes),
copy(ds.attributes_names),
copy(ds.values),
copy(ds.exclude),
ds.distance,
copy(ds.inputs),
identity(ds.target));
abstract type AbstractCountingProbabilityDistribution end;
#=
CountingProbabilityDistribution is a probability distribution for counting
observations. Unlike the other implementations of AbstractProbabilityDistribution,
CountingProbabilityDistribution calculates the key's probability when
accessing the CountingProbabilityDistribution by the given key.
=#
mutable struct CountingProbabilityDistribution <: AbstractCountingProbabilityDistribution
dict::Dict
number_of_observations::Int64
default::Int64
sample_function::Nullable{Function}
function CountingProbabilityDistribution(observations::AbstractVector; default::Int64=0)
local cpd::CountingProbabilityDistribution = new(Dict(), 0, default, Nullable{Function}());
for observation in observations
add(cpd, observation);
end
return cpd;
end
function CountingProbabilityDistribution(; default::Int64=0)
local cpd::CountingProbabilityDistribution = new(Dict(), 0, default, Nullable{Function}());
return cpd;
end
end
"""
add{T <: AbstractCountingProbabilityDistribution}(cpd::T, observation)
Add observation 'observation' to the probability distribution 'cpd'.
"""
function add{T <: AbstractCountingProbabilityDistribution}(cpd::T, observation)
smooth_for_observation(cpd, observation);
cpd.dict[observation] = cpd.dict[observation] + 1;
cpd.number_of_observations = cpd.number_of_observations + 1;
cpd.sample_function = Nullable{Function}();
nothing;
end
"""
smooth_for_observation{T <: AbstractCountingProbabilityDistribution}(cpd::T, observation)
Initialize observation 'observation' in the distribution 'cpd' if the observation doesn't
exist in the distribution yet.
"""
function smooth_for_observation{T <: AbstractCountingProbabilityDistribution}(cpd::T, observation)
if (!(observation in keys(cpd.dict)))
cpd.dict[observation] = cpd.default;
cpd.number_of_observations = cpd.number_of_observations + cpd.default;
cpd.sample_function = Nullable{Function}();
end
nothing;
end
"""
getindex{T <: AbstractCountingProbabilityDistribution}(cpd::T, key)
Return the probability of the given 'key'.
"""
function getindex{T <: AbstractCountingProbabilityDistribution}(cpd::T, key)
smooth_for_observation(cpd, key);
return (Float64(cpd.dict[key]) / Float64(cpd.number_of_observations));
end
"""
top{T <: AbstractCountingProbabilityDistribution}(cpd::T, n::Int64)
Return an array of (observation_count, observation) tuples such that the array
does not exceed length 'n'.
"""
function top{T <: AbstractCountingProbabilityDistribution}(cpd::T, n::Int64)
local observations::AbstractVector = sort(collect(reverse((i...)) for i in cpd.dict),
lt=(function(p1::Tuple{Number, Any}, p2::Tuple{Number, Any})
return (p1[1] > p2[1]);
end));
if (length(observations) <= n)
return observations;
else
return observations[1:n];
end
end
"""
sample(cpd::CountingProbabilityDistribution)
Return a random sample from the probability distribution 'cpd'.
"""
function sample(cpd::CountingProbabilityDistribution)
if (isnull(cpd.sample_function))
cpd.sample_function = weighted_sampler(collect(keys(cpd.dict)), collect(values(cpd.dict)));
end
return get(cpd.sample_function)();
end
abstract type AbstractLearner end;
struct PluralityLearner{T} <: AbstractLearner
most_popular::T
function PluralityLearner{T}(mp::T) where T
return new(mp);
end
end
function PluralityLearner(ds::DataSet)
most_popular = mode(example[ds.target]
for example in (ds.examples[i, :] for i in 1:size(ds.examples)[1]));
return PluralityLearner{typeof(most_popular)}(most_popular);
end
function predict(pl::PluralityLearner, example::AbstractVector)
return pl.most_popular;
end
abstract type AbstractNaiveBayesModel end;
#=
NaiveBayesLearner is a learner that chooses to uses either a continuous model, discrete model,
or a conditional probability model (if 'simple' keyword is given as true).
=#
struct NaiveBayesLearner <: AbstractLearner
model::AbstractNaiveBayesModel
function NaiveBayesLearner(ds::DataSet; continuous::Bool=true)
if (continuous)
return new(NaiveBayesContinuousModel(ds));
else
return new(NaiveBayesDiscreteModel(ds));
end
end
# The expected type of distribution 'd' is Dict.
function NaiveBayesLearner(d::Dict; simple::Bool=false)
if (simple)
return new(NaiveBayesSimpleModel(d));
else
error("NaiveBayesLearner(): The values of 'simple' should be true! "*
"If the expected model is either continuous or discrete, try passing a DataSet rather than an Dict!");
end
end
end
function predict(nbl::NaiveBayesLearner, example::AbstractVector)
return predict(nbl.model, example);
end
function predict(nbl::NaiveBayesLearner, example::String)
return predict(nbl.model, example);
end
#=
NaiveBayesSimpleModel is a simple naive bayes classifier that is initialized with
a dictionary of classifications to CountingProbabilityDistributions.
Each key-value pair of the dictionary is in the form:
(classification, probability)=>CountingProbabilityDistribution
=#
struct NaiveBayesSimpleModel <: AbstractNaiveBayesModel
target_distribution::Dict
attributes_distributions::Dict
function NaiveBayesSimpleModel(distribution::Dict)
return new(Dict(collect((classification, p)
for (classification, p) in keys(distribution))),
Dict(collect((classification, cpd)
for ((classification, p), cpd) in distribution)));
end
end
function predict(nbsm::NaiveBayesSimpleModel, example::AbstractVector)
return argmax(collect(keys(nbsm.target_distribution)),
(function(target)
local attribute_distribution::AbstractCountingProbabilityDistribution = nbsm.attributes_distributions[target];
return (nbsm.target_distribution[target] * prod(attribute_distribution[attribute] for attribute in example));
end));
end
function predict(nbsm::NaiveBayesSimpleModel, example::String)
return argmax(collect(keys(nbsm.target_distribution)),
(function(target)
local attribute_distribution::AbstractCountingProbabilityDistribution = nbsm.attributes_distributions[target];
return (nbsm.target_distribution[target] * prod(attribute_distribution[attribute] for attribute in example));
end));
end
#=
NaiveBayesDiscreteModel contains the frequencies of the input attribute values depending
on their corresponding target value.
=#
mutable struct NaiveBayesDiscreteModel <: AbstractNaiveBayesModel
dataset::DataSet
target_values::AbstractVector
target_distribution::CountingProbabilityDistribution
attributes_distributions::Dict
function NaiveBayesDiscreteModel(ds::DataSet)
local nbdm::NaiveBayesDiscreteModel = new(ds,
ds.values[ds.target],
CountingProbabilityDistribution(ds.values[ds.target]));
nbdm.attributes_distributions = Dict(Pair((val, attribute), CountingProbabilityDistribution(ds.values[attribute]))
for val in nbdm.target_values
for attribute in ds.inputs);
for example in (ds.examples[i, :] for i in 1:size(ds.examples)[1])
target_value = example[ds.target];
add(nbdm.target_distribution, target_value);
for attribute in ds.inputs
add(nbdm.attributes_distributions[(target_value, attribute)], example[attribute]);
end
end
return nbdm;
end
end
function predict(nbdm::NaiveBayesDiscreteModel, example::AbstractVector)
return argmax(nbdm.target_values,
(function(target_value)
return (nbdm.target_distribution[target_value] *
prod(nbdm.attributes_distributions[(target_value, attribute)][example[attribute]]
for attribute in nbdm.dataset.inputs));
end));
end
#=
NaiveBayesContinuousModel contains the frequencies of the target values and the
mean and deviations for the input attribute values for each target value.
=#
mutable struct NaiveBayesContinuousModel <: AbstractNaiveBayesModel
dataset::DataSet
target_values::AbstractVector
target_distribution::CountingProbabilityDistribution
means::Dict
deviations::Dict
function NaiveBayesContinuousModel(ds::DataSet)
local nbcm::NaiveBayesContinuousModel = new(ds,
ds.values[ds.target],
CountingProbabilityDistribution(ds.values[ds.target]));
nbcm.means, nbcm.deviations = find_means_and_deviations(ds);
return nbcm;
end
end
function predict(nbcm::NaiveBayesContinuousModel, example::AbstractVector)
return argmax(nbcm.target_values,
(function(target_value)
local p::Float64 = nbcm.target_distribution[target_value];
for attribute in nbcm.dataset.inputs
p = p * gaussian(nbcm.means[target_value][attribute],
nbcm.deviations[target_value][attribute],
example[attribute]);
end
return p;
end));
end
#=
NearestNeighborLearner uses the k-nearest neighbors lookup for predictions.
=#
struct NearestNeighborLearner <: AbstractLearner
dataset::DataSet
k::Int64
function NearestNeighborLearner(ds::DataSet)
return new(ds, 1);
end
function NearestNeighborLearner(ds::DataSet, k::Int64)
return new(ds, k);
end
end
function nearest_neighbor_predict_isless(t1::Tuple, t2::Tuple)
return (t1[1] < t2[1]);
end
function predict(nnl::NearestNeighborLearner, example::AbstractVector)
local best_distances::AbstractVector = sort(collect((nnl.dataset.distance(dataset_example, example), dataset_example)
for dataset_example in (nnl.dataset.examples[i, :] for i in 1:size(nnl.dataset.examples)[1])),
lt=nearest_neighbor_predict_isless);
if (length(best_distances) > nnl.k)
best_distances = best_distances[1:nnl.k];
end
return mode(dataset_example[nnl.dataset.target] for (distance, dataset_example) in best_distances);
end
abstract type AbstractDecisionTreeNode end;
struct DecisionLeafNode{T} <: AbstractDecisionTreeNode
result::T
function DecisionLeafNode{T}(result::T) where T
return new(result);
end
end
function classify(dl::DecisionLeafNode, example::AbstractVector)
return dl.result;
end
DecisionLeafNode(result) = DecisionLeafNode{typeof(result)}(result);
struct DecisionForkNode <: AbstractDecisionTreeNode
attribute::Int64
attribute_name::Nullable
default_child::Nullable{DecisionLeafNode}
branches::Dict
function DecisionForkNode(attribute::Int64;
attribute_name::Union{Int64, String, Void}=nothing,
default_child::Union{DecisionLeafNode, Void}=nothing,
branches::Union{Dict, Void}=nothing)
local new_attribute_name::Nullable;
local new_branches::Dict;
if (typeof(attribute_name) <: Void)
new_attribute_name = Nullable(attribute);
else
new_attribute_name = Nullable(attribute_name);
end
if (typeof(branches) <: Void)
new_branches = Dict();
else
new_branches = branches;
end
return new(attribute, new_attribute_name, Nullable{DecisionLeafNode}(default_child), new_branches);
end
end
function classify(df::DecisionForkNode, example::AbstractVector)
attribute_value = example[df.attribute];
if (haskey(df.branches, attribute_value))
return classify(df.branches[attribute_value], example);
else
return classify(get(df.default_child), example);
end
end
function add(dfn::DecisionForkNode, key::Real, subtree)
dfn.branches[key] = subtree;
nothing;
end
function summarize(dfn::DecisionForkNode)
return @sprintf("DecisionForkNode(%s, %s, %s)", repr(dfn.attribute), repr(dfn.attribute_name), repr(dfn.branches));
end
"""
information_content(values::AbstractVector)
Return the number of bits that represent the probability distribution of non-zero values in 'values'.
"""
function information_content(values::AbstractVector)
local probabilities::Array{Float64, 1} = normalize(removeall(values, 0), 1);
if (length(probabilities) == 0)
return Float64(0);
else
return sum((-p * log2(p)) for p in probabilities);
end
end
function information_gain_content(dataset::DataSet, examples::AbstractMatrix)
return information_content(collect(count((function(example)
return (example[dataset.target] == value);
end), (examples[i,:] for i in 1:size(examples)[1]))
for value in dataset.values[dataset.target]));
end
"""
matrix_vcat(args::Vararg)
Returns an empty matrix when vcat() returns an empty vector, otherwise return vcat(args).
"""
function matrix_vcat(args::Vararg)
if (length(args) == 0)
return Array{Any, 2}(0, 0);
else
return vcat(args...);
end
end
"""
filter_examples_by_attribute(dataset::DataSet, attribute::Int64, examples::AbstractMatrix)
Return a Base.Generator of (value_i, examples_i) tuples for each value of 'attribute'.
"""
function filter_examples_by_attribute(dataset::DataSet, attribute::Int64, examples::AbstractMatrix)
return ((value, matrix_vcat((reshape(ex_i, (1, length(ex_i)))
for ex_i in (examples[i,:] for i in 1:size(examples)[1])
if (ex_i[attribute] == value))...))
for value in dataset.values[attribute]);
end
"""
information_gain(dataset::DataSet, attribute::Int64, examples::AbstractMatrix)
Return the expected reduction in entropy from testing the attribute 'attribute' given
the dataset 'dataset' and matrix 'examples'.
"""
function information_gain(dataset::DataSet, attribute::Int64, examples::AbstractMatrix)
local N::Float64 = Float64(size(examples)[1]);
local remainder::Float64 = Float64(sum(((size(examples_i)[1]/N)
* information_gain_content(dataset, examples_i)
for (value, examples_i) in filter_examples_by_attribute(dataset, attribute, examples))));
return (Float64(information_gain_content(dataset, examples)) - remainder);
end
"""
plurality_value(dataset::DataSet, examples::AbstractMatrix)
Return a DecisionLeafNode with the result field set to the most common output value
in the given matrix 'examples' (using argmax_random_tie()).
"""
function plurality_value(dataset::DataSet, examples::AbstractMatrix)
return DecisionLeafNode(argmax_random_tie(dataset.values[dataset.target],
(function(value)
return count((function(example::AbstractVector)
return (example[dataset.target] == value);
end), (examples[i,:] for i in 1:size(examples)[1]));
end)));
end
"""
decision_tree_learning(dataset::DataSet, examples::AbstractMatrix, attributes::AbstractVector; parent_examples::AbstractMatrix=Array{Any, 2}())
Return a decision tree as a DecisionLeafNode or a DecisionForkNode by applying the decision-tree
learning algorithm (Fig. 18.5) on the given dataset 'dataset', example matrix 'example', attributes
vector 'attributes', and parent examples 'parent_examples'.
"""
function decision_tree_learning(dataset::DataSet, examples::AbstractMatrix, attributes::AbstractVector; parent_examples::AbstractMatrix=Array{Any, 2}(0, 0))
# examples is empty
if (size(examples)[1] == 0)
return plurality_value(dataset, parent_examples);
# examples have the same classification
elseif (all((example[dataset.target] == examples[1, dataset.target])
for example in (examples[i, :] for i in 1:size(examples)[1])))
return DecisionLeafNode(examples[1, dataset.target]);
# attributes is empty
elseif (length(attributes) == 0)
return plurality_value(dataset, parent_examples);
else
local A::Int64 = argmax_random_tie(attributes,
(function(attribute)
return information_gain(dataset, attribute, examples);
end));
local tree::DecisionForkNode = DecisionForkNode(A,
attribute_name=dataset.attributes_names[A],
default_child=plurality_value(dataset, examples));
for (v_k, exs) in filter_examples_by_attribute(dataset, A, examples)
local subtree::AbstractDecisionTreeNode = decision_tree_learning(dataset, exs, removeall(attributes, A), parent_examples=examples);
add(tree, v_k, subtree);
end
return tree;
end
end
struct DecisionTreeLearner <: AbstractLearner
decision_tree::AbstractDecisionTreeNode
function DecisionTreeLearner(dataset::DataSet)
return new(decision_tree_learning(dataset, dataset.examples, dataset.inputs));
end
# The following constructor method for DecisionTreeLearner is to be used with
# cross_validation() for a decision tree constructed in a breadth-first fashion.
#
# The breadth-first decision_tree_learning() method is not implemented yet.
function DecisionTreeLearner(dataset::DataSet, node_count::Int64)
return new(decision_tree_learning(dataset, dataset.examples, dataset.inputs, node_count));
end
end
function predict(dtl::DecisionTreeLearner, example::AbstractVector)
return classify(dtl.decision_tree, example);
end
function data_bagging(dataset::DataSet)
local n::Int64 = size(dataset.examples)[1];
local sampled_examples::AbstractVector = weighted_sample_with_replacement(collect(dataset.examples[i, :]
for i in 1:size(dataset.examples)[1]), ones(n), n);
return reduce(vcat, (reshape(sample_example, (1, length(sample_example)))
for sample_example in sampled_examples));
end
function data_bagging(dataset::DataSet, m::Int64)
local n::Int64 = size(dataset.examples)[1];
local sampled_examples::AbstractVector = weighted_sample_with_replacement(collect(dataset.examples[i, :]
for i in 1:size(dataset.examples)[1]), ones(n), m);
return reduce(vcat, (reshape(sample_example, (1, length(sample_example)))
for sample_example in sampled_examples));
end
function feature_bagging(dataset::DataSet; p::Float64=0.7)
local inputs::AbstractVector = collect(i for i in dataset.inputs if (rand(RandomDeviceInstance) < p));
if (length(inputs) == 0)
return dataset.inputs;
else
return inputs;
end
end
struct RandomForest <: AbstractLearner
predictors::Array{DecisionTreeLearner, 1}
function RandomForest(dataset::DataSet; n::Int64=5)
local predictors::Array{DecisionTreeLearner, 1} = collect(DecisionTreeLearner(DataSet(examples=data_bagging(dataset),
attributes=dataset.attributes,
attributes_names=dataset.attributes_names,
target=dataset.target,
inputs=feature_bagging(dataset)))
for i in 1:n);
return new(predictors);
end
end
function predict(rf::RandomForest, example::AbstractVector)
return mode(predict(predictor, example) for predictor in rf.predictors);
end
function find_test_outcomes_from_examples(ds::DataSet, examples::Set)
println("find_test_outcomes_from_examples() is not yet implemented!");
nothing;
end
"""
decision_list_learning(ds::DataSet, examples::Set)
Return an array of (test::Function, outcome) tuples by using the decision list learning
algorithm (Fig. 18.11) on the given dataset 'ds' and a set of examples 'examples'.
"""
function decision_list_learning(ds::DataSet, examples::Set)
if (length(examples) == 0)
return [((function(examples::AbstractVector)
return true;
end), false)];
end
local t::Function;
local examples_t::Set;
t, output, examples_t = find_test_outcomes_from_examples(ds, examples);
if (typeof(t) <: Void)
error("decision_list_learning(): Could not find valid test 't'!");
end
return append!([(t, output)], decision_list_learning(ds, setdiff(examples, examples_t)));
end
struct DecisionListLearner <: AbstractLearner
decision_list::AbstractVector
function DecisionListLearner(dataset::DataSet)
return new(decision_list_learning(dataset, Set(dataset.examples[i, :]
for i in 1:size(dataset.examples)[1])));
end
end
function predict(dll::DecisionListLearner, examples::AbstractVector)
for (test, outcome) in dll.decision_list
if (test(examples))
return outcome;
end
end
error("predict(): All tests in the generated decision list failed for ", examples, "!");
end
#=
NeuralNetworkUnit is an unit (node) in a multilayer neural network.
=#
mutable struct NeuralNetworkUnit
weights::AbstractVector
inputs::AbstractVector
value::Nullable
activation::Function
function NeuralNetworkUnit()
return new([], [], Nullable(nothing), sigmoid);
end
function NeuralNetworkUnit(weights::AbstractVector, inputs::AbstractVector)
return new(weights, inputs, Nullable(nothing), sigmoid);
end
end
"""
neural_network(input_units::Int64, hidden_layers_sizes::Array{Int64, 1}, output_units::Int64)
Return an untrained neural network by using the given the number of input units 'input_units', the
hidden layers' sizes (the hidden layers should not include the input and output layers) in
'hidden_layers_sizes', and the number of output units 'output_units'.
"""
function neural_network(input_units::Int64, hidden_layers_sizes::Array{Int64, 1}, output_units::Int64)
local layers_sizes::AbstractVector = Array{Int64, 1}();
if (length(hidden_layers_sizes) == 0)
push!(layers_sizes, input_units);
push!(layers_sizes, output_units);
else
push!(layers_sizes, input_units);
append!(layers_sizes, hidden_layers_sizes);
push!(layers_sizes, output_units);