General Linear Models in Julia: Iris Study Case

In [55]:

    

using DataFrames, DataArrays, DataFramesMeta, RDatasets
using MLBase
using GLM
using Gadfly


    

In [2]:

    

iris = dataset("datasets", "iris");


    

In [3]:

    

showcols(iris)


    

    




150x5 DataFrames.DataFrame
| Col # | Name        | Eltype      | Missing |
|-------|-------------|-------------|---------|
| 1     | SepalLength | Float64     | 0       |
| 2     | SepalWidth  | Float64     | 0       |
| 3     | PetalLength | Float64     | 0       |
| 4     | PetalWidth  | Float64     | 0       |
| 5     | Species     | ASCIIString | 0       |

In [4]:

    

head(iris)


    

    
Out[4]:




SepalLength
SepalWidth
PetalLength
PetalWidth
Species
1
5.1
3.5
1.4
0.2
setosa
2
4.9
3.0
1.4
0.2
setosa
3
4.7
3.2
1.3
0.2
setosa
4
4.6
3.1
1.5
0.2
setosa
5
5.0
3.6
1.4
0.2
setosa
6
5.4
3.9
1.7
0.4
setosa

In [5]:

    

p1 = plot(iris, x="SepalLength", y="SepalWidth", color="Species")
p2 = plot(iris, x="PetalLength", y="PetalWidth", color="Species")
p3 = plot(iris, x="SepalLength", y="PetalLength", color="Species")
p4 = plot(iris, x="SepalWidth", y="PetalWidth", color="Species")
p = hstack(vstack(p1, p2), vstack(p3, p4))
draw(SVGJS(900px, 600px), p)


    

    




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In [6]:

    

df = copy(iris)
rename!(df, :SepalLength, :x1)
rename!(df, :SepalWidth, :x2)
rename!(df, :PetalLength, :x3)
rename!(df, :PetalWidth, :x4)
rename!(df, :Species, :y);


    

    




 in depwarn at deprecated.jl:73
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 in vstack at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:890
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 in execute_request_0x535c5df2 at /Users/diego/.julia/v0.4/IJulia/src/execute_request.jl:177
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 in call at /Users/diego/.julia/v0.4/Gadfly/src/varset.jl:53
 in render at /Users/diego/.julia/v0.4/Gadfly/src/geom/point.jl:35
 in render at /Users/diego/.julia/v0.4/Gadfly/src/geometry.jl:47
 in render_prepared at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:846
 in render at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:785
 in vstack at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:890
 in include_string at loading.jl:266
 in execute_request_0x535c5df2 at /Users/diego/.julia/v0.4/IJulia/src/execute_request.jl:177
 in eventloop at /Users/diego/.julia/v0.4/IJulia/src/IJulia.jl:141
 in anonymous at task.jl:447
while loading In[5], in expression starting on line 5
WARNING: Union(args...) is deprecated, use Union{args...} instead.
 in depwarn at deprecated.jl:73
 in call at deprecated.jl:50
 in call at /Users/diego/.julia/v0.4/Gadfly/src/coord.jl:46
 in call at /Users/diego/.julia/v0.4/Gadfly/src/coord.jl:43
 in render_prepare at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:507
 in render at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:781
 in vstack at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:890
 in include_string at loading.jl:266
 in execute_request_0x535c5df2 at /Users/diego/.julia/v0.4/IJulia/src/execute_request.jl:177
 in eventloop at /Users/diego/.julia/v0.4/IJulia/src/IJulia.jl:141
 in anonymous at task.jl:447
while loading In[5], in expression starting on line 5
WARNING: Union(args...) is deprecated, use Union{args...} instead.
 in depwarn at deprecated.jl:73
 in call at deprecated.jl:50
 in default_statistic at /Users/diego/.julia/v0.4/Gadfly/src/guide.jl:557
 in render_prepare at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:669
 in render at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:781
 in vstack at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:890
 in include_string at loading.jl:266
 in execute_request_0x535c5df2 at /Users/diego/.julia/v0.4/IJulia/src/execute_request.jl:177
 in eventloop at /Users/diego/.julia/v0.4/IJulia/src/IJulia.jl:141
 in anonymous at task.jl:447
while loading In[5], in expression starting on line 5
WARNING: Union(args...) is deprecated, use Union{args...} instead.
 in depwarn at deprecated.jl:73
 in call at deprecated.jl:50
 in default_statistic at /Users/diego/.julia/v0.4/Gadfly/src/guide.jl:738
 in render_prepare at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:669
 in render at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:781
 in vstack at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:890
 in include_string at loading.jl:266
 in execute_request_0x535c5df2 at /Users/diego/.julia/v0.4/IJulia/src/execute_request.jl:177
 in eventloop at /Users/diego/.julia/v0.4/IJulia/src/IJulia.jl:141
 in anonymous at task.jl:447
while loading In[5], in expression starting on line 5
WARNING: Union(args...) is deprecated, use Union{args...} instead.
 in depwarn at deprecated.jl:73
 in call at deprecated.jl:50
 in call at /Users/diego/.julia/v0.4/Gadfly/src/varset.jl:53
 in apply_scales at /Users/diego/.julia/v0.4/Gadfly/src/scale.jl:58
 in render_prepare at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:715
 in render at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:781
 in vstack at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:890
 in include_string at loading.jl:266
 in execute_request_0x535c5df2 at /Users/diego/.julia/v0.4/IJulia/src/execute_request.jl:177
 in eventloop at /Users/diego/.julia/v0.4/IJulia/src/IJulia.jl:141
 in anonymous at task.jl:447
while loading In[5], in expression starting on line 5
WARNING: Union(args...) is deprecated, use Union{args...} instead.
 in depwarn at deprecated.jl:73
 in call at deprecated.jl:50
 in call at /Users/diego/.julia/v0.4/Gadfly/src/varset.jl:53
 in concat at /Users/diego/.julia/v0.4/Gadfly/src/aesthetics.jl:243
 in render_prepare at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:738
 in render at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:781
 in vstack at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:890
 in include_string at loading.jl:266
 in execute_request_0x535c5df2 at /Users/diego/.julia/v0.4/IJulia/src/execute_request.jl:177
 in eventloop at /Users/diego/.julia/v0.4/IJulia/src/IJulia.jl:141
 in anonymous at task.jl:447
while loading In[5], in expression starting on line 5
WARNING: Union(args...) is deprecated, use Union{args...} instead.
 in depwarn at deprecated.jl:73
 in call at deprecated.jl:50
 in call at /Users/diego/.julia/v0.4/Gadfly/src/varset.jl:53
 in render at /Users/diego/.julia/v0.4/Gadfly/src/geom/point.jl:35
 in render at /Users/diego/.julia/v0.4/Gadfly/src/geometry.jl:47
 in render_prepared at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:846
 in render at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:785
 in vstack at /Users/diego/.julia/v0.4/Gadfly/src/Gadfly.jl:890
 in include_string at loading.jl:266
 in execute_request_0x535c5df2 at /Users/diego/.julia/v0.4/IJulia/src/execute_request.jl:177
 in eventloop at /Users/diego/.julia/v0.4/IJulia/src/IJulia.jl:141
 in anonymous at task.jl:447
while loading In[5], in expression starting on line 5

In [9]:

    

df_y1 = copy(df)
df_y2 = copy(df)
df_y3 = copy(df)

df_y1[:y] = DataArray{Int8}(df_y1[:y] .== "setosa")
df_y2[:y] = DataArray{Int8}(df_y2[:y] .== "versicolor")
df_y3[:y] = DataArray{Int8}(df_y3[:y] .== "virginica");


    

In [98]:

    

fit_model(df, formula) = glm(formula, df, Binomial())
function fit_models(df, formulas)
    linear_models = []
    for formula in formulas
        try 
            push!(linear_models, fit_model(df, formula)) 
        catch 
            LoadError 
        end
    end 
    return linear_models
end

predict_models(linear_models) = Array[GLM.predict(lm) for lm in linear_models]

binarize(vector) = map(x -> x >= .5? 1 : 0, vector)
evaluate_bin(y_real, y_pred) = calculate_accuracy(y_real, binarize(y_pred))
calculate_accuracy(y_real, y_pred) = round(sum(DataArray{Int8}(y_pred - y_real .== 0))/length(y_real), 4)
function max_label(y_preds, index)
    values = map(y -> y[index], y_preds)
    max_value = maximum(values)
    return findin(values, max_value)[1]
end

function evaluate(y_real, y_preds)
    y_pred = map(i -> max_label(y_preds, i), 1:length(y_real))
    acc = calculate_accuracy(y_real, y_pred)
    return acc, y_pred
end

function confusion_matrix(y_real, y_pred)
    size = max(length(Set(y_real)), length(Set(y_pred)))
    matrix = fill(0, (size, size))
    for i=1:length(y_real)
        matrix[y_real[i], y_pred[i]] += 1
    end
    return matrix
end


    

    
Out[98]:





confusion_matrix (generic function with 1 method)

In [23]:

    

formulas = [y ~ x1, y ~ x2, y ~ x3, y  ~ x4]


    

    
Out[23]:





4-element Array{DataFrames.Formula,1}:
 Formula: y ~ x1
 Formula: y ~ x2
 Formula: y ~ x3
 Formula: y ~ x4

In [62]:

    

lms = fit_models(df_y1, formulas);


    

In [73]:

    

map(y_pred -> evaluate_bin(df_y1[:y], y_pred), predict_models(lms))


    

    
Out[73]:





4-element Array{Float64,1}:
 0.666667
 0.46    
 0.646667
 0.666667

In [71]:

    

lms = fit_models(df_y2, formulas);


    

In [74]:

    

map(y_pred -> evaluate_bin(df_y2[:y], y_pred), predict_models(lms))


    

    
Out[74]:





4-element Array{Float64,1}:
 0.666667
 0.726667
 0.646667
 0.666667

In [152]:

    

lms = fit_models(df_y3, formulas);


    

In [76]:

    

map(y_pred -> evaluate_bin(df_y3[:y], y_pred), predict_models(lms))


    

    
Out[76]:





4-element Array{Float64,1}:
 0.666667
 0.593333
 0.686667
 0.666667

In [79]:

    

lms = fit_model(df_y1, formulas[1]), fit_model(df_y2, formulas[1]), fit_model(df_y3, formulas[4]);
df_y = copy(df)
df_y[:y] = df_y1[:y] + df_y2[:y]*2 + df_y3[:y]*3
acc, y_pred = evaluate(df_y[:y], predict_models(lms))
println("Acc: $acc")


    

    




Acc: 0.8466666666666667

In [80]:

    

formulas = [y ~ x1 + x2, y ~ x1 + x3, y ~ x1 + x4, y  ~ x2 + x3, y ~ x2 + x4, y ~ x3 + x4, 
            y ~ x1 + x2 + x3, y ~ x2 + x3 + x4, y ~ x1 + x3 + x4, y ~ x1 + x2 + x3 + x4]


    

    
Out[80]:





10-element Array{DataFrames.Formula,1}:
 Formula: y ~ x1 + x2          
 Formula: y ~ x1 + x3          
 Formula: y ~ x1 + x4          
 Formula: y ~ x2 + x3          
 Formula: y ~ x2 + x4          
 Formula: y ~ x3 + x4          
 Formula: y ~ x1 + x2 + x3     
 Formula: y ~ x2 + x3 + x4     
 Formula: y ~ x1 + x3 + x4     
 Formula: y ~ x1 + x2 + x3 + x4

In [99]:

    

lms = fit_models(df_y1, formulas)
acc_1 = map(y_pred -> evaluate_bin(df_y1[:y], y_pred), predict_models(lms))

lms = fit_models(df_y2, formulas)
acc_2 = map(y_pred -> evaluate_bin(df_y2[:y], y_pred), predict_models(lms))

lms = fit_models(df_y3, formulas)
acc_3 = map(y_pred -> evaluate_bin(df_y3[:y], y_pred), predict_models(lms))

println("Acc Y1: ", acc_1)
println("Acc Y2: ", acc_2)
println("Acc Y3: ", acc_3)


    

    




Acc Y1: Array[]
Acc Y2: [0.7133,0.62,0.6667,0.7267,0.7267,0.64,0.72,0.7467,0.7133,0.74]
Acc Y3: [0.8067,0.9667,0.96,0.9533,0.9533,0.96,0.9667,0.98,0.98,0.9867]

In [108]:

    

f1 = y ~ x1
f2 = y ~ x2 + x3 + x4
f3 = y ~ x1 + x2 + x3 + x4
lm1 = fit_model(df_y1, f1)
lm2 = fit_model(df_y2, f2)
lm3 = fit_model(df_y3, f3)
acc, y_pred = evaluate(df_y[:y], predict_models([lm1, lm2, lm3]))
println("Acc: $acc")
confusion_matrix(df_y[:y], y_pred)


    

    




Acc: 0.94






    
Out[108]:





3x3 Array{Int64,2}:
 50   0   0
  5  43   2
  1   1  48