Yesterday we had a look at Julia’s regression model capabilities. A natural counterpart to these are models which perform classification. We’ll be looking at the GLM and DecisionTree packages. But, before I move on to that, I should mention the MLBase package which provides a load of functionality for data preprocessing, performance evaluation, cross-validation and model tuning.

## Logistic Regression

Logistic regression lies on the border between the regression techniques we considered yesterday and the classification techniques we’re looking at today. In effect though it’s really a classification technique. We’ll use some data generated in yesterday’s post to illustrate. Specifically we’ll look at the relationship between the Boolean field `valid`

and the three numeric fields.

```
julia> head(points)
6x4 DataFrame
| Row | x | y | z | valid |
|-----|----------|---------|---------|-------|
| 1 | 0.867859 | 3.08688 | 6.03142 | false |
| 2 | 9.92178 | 33.4759 | 2.14742 | true |
| 3 | 8.54372 | 32.2662 | 8.86289 | true |
| 4 | 9.69646 | 35.5689 | 8.83644 | true |
| 5 | 4.02686 | 12.4154 | 2.75854 | false |
| 6 | 6.89605 | 27.1884 | 6.10983 | true |
```

To further refresh your memory, the plot below shows the relationship between `valid`

and the variables `x`

and `y`

. We’re going to attempt to capture this relationship in our model.

Logistic regression is also applied with the `glm()`

function from the GLM package. The call looks very similar to the one used for linear regression except that the error family is now `Binomial()`

and we’re using a logit link function.

```
julia> model = glm(valid ~ x + y + z, points, Binomial(), LogitLink())
DataFrameRegressionModel{GeneralizedLinearModel{GlmResp{Array{Float64,1},Binomial,LogitLink},
DensePredChol{Float64,Cholesky{Float64}}},Float64}:
Coefficients:
Estimate Std.Error z value Pr(>|z|)
(Intercept) -23.1457 3.74348 -6.18295 <1e-9
x -0.260122 0.269059 -0.966786 0.3337
y 1.36143 0.244123 5.5768 <1e-7
z 0.723107 0.14739 4.90606 <1e-6
```

According to the model there is a significant relationship between `valid`

and both `y`

and `z`

but not `x`

. Looking at the plot above we can see that `x`

does have an influence on `valid`

(there is a gradual transition from false to true with increasing `x`

), but that this effect is rather “fuzzy”, hence the large p-value. By comparison there is a very clear and abrupt change in `valid`

at `y`

values of around 15. The effect of `y`

is also about twice as strong as that of `z`

. All of this makes sense in light of the way that the data were constructed.

## Decision Trees

Now we’ll look at another classification technique: decision trees. First load the required packages and then grab the iris data.

```
julia> using MLBase, DecisionTree
julia> using RDatasets, Distributions
julia> iris = dataset("datasets", "iris");
julia> iris[1:5,:]
5x5 DataFrame
| Row | 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" |
```

We’ll also define a Boolean variable to split the data into training and testing sets.

`julia> train = rand(Bernoulli(0.75), nrow(iris)) .== 1;`

We split the data into features and labels and then feed those into `build_tree()`

. In this case we are building a classifier to identify whether or not a particular iris is of the versicolor variety.

```
julia> features = array(iris[:,1:4]);
julia> labels = [n == "versicolor" ? 1 : 0 for n in iris[:Species]];
julia> model = build_tree(labels[train], features[train,:]);
```

Let’s have a look at the product of a labours.

```
julia> print_tree(model)
Feature 3, Threshold 3.0
L-> 0 : 36/36
R-> Feature 3, Threshold 4.8
L-> Feature 4, Threshold 1.7
L-> 1 : 38/38
R-> 0 : 1/1
R-> Feature 3, Threshold 5.1
L-> Feature 1, Threshold 6.7
L-> Feature 2, Threshold 3.2
L-> Feature 4, Threshold 1.8
L-> Feature 1, Threshold 6.3
L-> 0 : 1/1
R-> 1 : 1/1
R-> 0 : 5/5
R-> 1 : 1/1
R-> 1 : 2/2
R-> 0 : 29/29
```

The textual representation of the tree above breaks the decision process down into a number of branches where the model decides whether to go to the left (L) or right (R) branch according to whether or not the value of a given feature is above or below a threshold value. So, for example, on the third line of the output we must decide whether to move to the left or right depending on whether feature 3 (PetalLength) is less or greater than 4.8.

We can then apply the decision tree model to the testing data and see how well it performs using standard metrics.

```
julia> predictions = apply_tree(model, features[!train,:]);
julia> ROC = roc(labels[!train], convert(Array{Int32,1}, predictions))
ROCNums{Int64}
p = 8
n = 28
tp = 7
tn = 28
fp = 0
fn = 1
julia> precision(ROC)
1.0
julia> recall(ROC)
0.875
```

A true positive rate of 87.5% and true negative rate of 100% is not too bad at all!

The DecisionTree package also implements random forest and boosting models. Other related packages are:

- SVM (support vector machines);
- kNN (k-nearest neighbours);
- GradientBoost (gradient boosting);
- XGBoost (extreme gradient boosting);
- Orchestra (ensemble learning).

Definitely worth checking out if you have the time. My time is up though. Come back soon to hear about what Julia provides for evolutionary programming.