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using Plots
using RDatasets
using Convex
using SCS</code></pre><p>This is an example logistic regression using <code>RDatasets</code>'s iris data. Our goal is to gredict whether the iris species is versicolor using the sepal length and width and petal length and width.</p><pre><code class="language-julia">iris = dataset("datasets", "iris");
iris[1:10,:]</code></pre><p>10 rows × 5 columns</p><table class="data-frame"><thead><tr><th></th><th>SepalLength</th><th>SepalWidth</th><th>PetalLength</th><th>PetalWidth</th><th>Species</th></tr><tr><th></th><th>Float64</th><th>Float64</th><th>Float64</th><th>Float64</th><th>Categorical…</th></tr></thead><tbody><tr><th>1</th><td>5.1</td><td>3.5</td><td>1.4</td><td>0.2</td><td>setosa</td></tr><tr><th>2</th><td>4.9</td><td>3.0</td><td>1.4</td><td>0.2</td><td>setosa</td></tr><tr><th>3</th><td>4.7</td><td>3.2</td><td>1.3</td><td>0.2</td><td>setosa</td></tr><tr><th>4</th><td>4.6</td><td>3.1</td><td>1.5</td><td>0.2</td><td>setosa</td></tr><tr><th>5</th><td>5.0</td><td>3.6</td><td>1.4</td><td>0.2</td><td>setosa</td></tr><tr><th>6</th><td>5.4</td><td>3.9</td><td>1.7</td><td>0.4</td><td>setosa</td></tr><tr><th>7</th><td>4.6</td><td>3.4</td><td>1.4</td><td>0.3</td><td>setosa</td></tr><tr><th>8</th><td>5.0</td><td>3.4</td><td>1.5</td><td>0.2</td><td>setosa</td></tr><tr><th>9</th><td>4.4</td><td>2.9</td><td>1.4</td><td>0.2</td><td>setosa</td></tr><tr><th>10</th><td>4.9</td><td>3.1</td><td>1.5</td><td>0.1</td><td>setosa</td></tr></tbody></table><p>We'll define <code>Y</code> as the outcome variable: +1 for versicolor, -1 otherwise.</p><pre><code class="language-julia">Y = [species == "versicolor" ? 1.0 : -1.0 for species in iris.Species]</code></pre><pre><code class="language-none">150-element Array{Float64,1}:
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
⋮
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0</code></pre><p>We'll create our data matrix with one column for each feature (first column corresponds to offset).</p><pre><code class="language-julia">X = hcat(ones(size(iris, 1)), iris.SepalLength, iris.SepalWidth, iris.PetalLength, iris.PetalWidth);</code></pre><p>Now to solve the logistic regression problem.</p><pre><code class="language-julia">n, p = size(X)
beta = Variable(p)
problem = minimize(logisticloss(-Y.*(X*beta)))
solve!(problem, () -> SCS.Optimizer(verbose=false))</code></pre><p>Let's see how well the model fits.</p><pre><code class="language-julia">using Plots
logistic(x::Real) = inv(exp(-x) + one(x))
perm = sortperm(vec(X*beta.value))
plot(1:n, (Y[perm] .+ 1)/2, st=:scatter)
plot!(1:n, logistic.(X*beta.value)[perm])</code></pre><svg height="400" viewBox="0 0 2400 1600" width="600" xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><defs><clipPath id="clip0100"><rect height="1600" width="2400" x="0" y="0"></rect></clipPath></defs><path clip-path="url(#clip0100)" d="
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