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Logistic Regression · Flux
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Logistic Regression
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Logistic Regression
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<h1>
<a class="nav-anchor" id="Logistic-Regression-with-MNIST-1" href="#Logistic-Regression-with-MNIST-1">
Logistic Regression with MNIST
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<p>
This walkthrough example will take you through writing a multi-layer perceptron that classifies MNIST digits with high accuracy.
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<p>
First, we load the data using the MNIST package:
</p>
<pre><code class="language-julia">using Flux, MNIST
data = [(trainfeatures(i), onehot(trainlabel(i), 0:9)) for i = 1:60_000]
train = data[1:50_000]
test = data[50_001:60_000]</code></pre>
<p>
The only Flux-specific function here is
<code>onehot</code>
, which takes a class label and turns it into a one-hot-encoded vector that we can use for training. For example:
</p>
<pre><code class="language-julia">julia&gt; onehot(:b, [:a, :b, :c])
3-element Array{Int64,1}:
0
1
0</code></pre>
<p>
Otherwise, the format of the data is simple enough, it&#39;s just a list of tuples from input to output. For example:
</p>
<pre><code class="language-julia">julia&gt; data[1]
([0.0,0.0,0.0, … 0.0,0.0,0.0],[0,0,0,0,0,1,0,0,0,0])</code></pre>
<p>
<code>data[1][1]</code>
is a
<code>28*28 == 784</code>
length vector (mostly zeros due to the black background) and
<code>data[1][2]</code>
is its classification.
</p>
<p>
Now we define our model, which will simply be a function from one to the other.
</p>
<pre><code class="language-julia">m = Chain(
Input(784),
Affine(128), relu,
Affine( 64), relu,
Affine( 10), softmax)
model = tf(model)</code></pre>
<p>
We can try this out on our data already:
</p>
<pre><code class="language-julia">julia&gt; model(data[1][1])
10-element Array{Float64,1}:
0.10614
0.0850447
0.101474
...</code></pre>
<p>
The model gives a probability of about 0.1 to each class – which is a way of saying, &quot;I have no idea&quot;. This isn&#39;t too surprising as we haven&#39;t shown it any data yet. This is easy to fix:
</p>
<pre><code class="language-julia">Flux.train!(model, train, test, η = 1e-4)</code></pre>
<p>
The training step takes about 5 minutes (to make it faster we can do smarter things like batching). If you run this code in Juno, you&#39;ll see a progress meter, which you can hover over to see the remaining computation time.
</p>
<p>
Towards the end of the training process, Flux will have reported that the accuracy of the model is now about 90%. We can try it on our data again:
</p>
<pre><code class="language-julia">10-element Array{Float32,1}:
...
5.11423f-7
0.9354
3.1033f-5
0.000127077
...</code></pre>
<p>
Notice the class at 93%, suggesting our model is very confident about this image. We can use
<code>onecold</code>
to compare the true and predicted classes:
</p>
<pre><code class="language-julia">julia&gt; onecold(data[1][2], 0:9)
5
julia&gt; onecold(model(data[1][1]), 0:9)
5</code></pre>
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