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<section id="title-slide" class="quarto-title-block center">
  <h1 class="title">Advanced Machine Learning</h1>
  <p class="subtitle">Neural Networks, Deep Learning and Artificial Intelligence</p>

<div class="quarto-title-authors">
</div>

</section>
<section>
<section id="from-artificial-neural-networks-to-artifial-intelligence" class="title-slide slide level1 center">
<h1>From Artificial Neural Networks to Artifial Intelligence</h1>

</section>
<section id="historical-background-1" class="slide level2">
<h2>Historical Background (1)</h2>
<ul>
<li><p>In the post-pandemic world, a lightning rise of AI, with a mess of realities and promises is impacting society.</p></li>
<li><p>Since ChatGPT entered the scene everybody has an experience, an opinion, or a fear on the topic.</p></li>
</ul>

<img data-src="https://bernardmarr.com/wp-content/uploads/2022/04/The-Dangers-Of-Not-Aligning-Artificial-Intelligence-With-Human-Values.jpg" class="quarto-figure quarto-figure-center r-stretch" style="width:100.0%"></section>
<section id="is-it-just-machine-learning" class="slide level2">
<h2>Is it just machine learning?</h2>
<ul>
<li><p>Most tasks performed by AI can be described as Classification or Prediction used in applications as:</p>
<ul>
<li>Recommendation systems,</li>
<li>Image recognition, Image generation</li>
<li>Natural language processing</li>
</ul></li>
<li><p>AI relies on machine learning algorithms, to make predictions based on large amounts of data.</p></li>
<li><p>AI has far-reaching implications beyond its predictive capabilities, including ethical, social or technological.</p></li>
</ul>
</section>
<section id="ai-anns-and-deep-learning" class="slide level2">
<h2>AI, ANNs and Deep learning</h2>
<ul>
<li><p>In many contexts, talking about AI means talking about <em>Deep Learning (DL)</em>.</p></li>
<li><p>DL is a successful AI model which has powered many application such as <em>self-driving cars, voice assistants, and medical diagnosis systems</em>.</p></li>
<li><p>DL originates in the field of <em>Artificial Neural Networks</em></p></li>
<li><p>But DL extends the basic principles of ANNs by:</p>
<ul>
<li>Adding complex architectures and algorithms and</li>
<li>At the same time becoming more automatic</li>
</ul></li>
</ul>
</section>
<section id="the-early-history-of-ai-1" class="slide level2">
<h2>The early history of AI (1)</h2>

<img data-src="images/AIHistory1.jpg" style="width:90.0%" class="r-stretch quarto-figure-center"><p class="caption"><a href="https://nerdyelectronics.com/a-quick-history-of-ai-ml-and-dl/">A Quick History of AI, ML and DL</a></p></section>
<section id="milestones-in-the-history-of-dl" class="slide level2">
<h2>Milestones in the history of DL</h2>
<p>We can see several hints worth to account for:</p>
<ul>
<li><p>The <strong>Perceptron</strong> and the first <strong>Artificial Neural Network</strong> where the basic building block was introduced.</p></li>
<li><p>The <strong>Multilayered perceptron</strong> and back-propagation where complex architectures were suggested to improve the capabilities.</p></li>
<li><p><strong>Deep Neural Networks</strong>, with many hidden layers, and auto-tunability capabilities.</p></li>
</ul>
</section>
<section id="from-ann-to-deep-learning" class="slide level2">
<h2>From ANN to Deep learning</h2>

<img data-src="images/WhyDLNow.png" class="quarto-figure quarto-figure-center r-stretch" style="width:100.0%"><p class="caption">Why Deep Learning Now?</p><div class="font90">
<p>Source: <a href="introtodeeplearning.com">Alex Amini’s MIT Introduction to Deep Learning’ course</a></p>
</div>
</section>
<section id="success-stories" class="slide level2">
<h2>Success stories</h2>
<p>Success stories such as</p>
<ul>
<li><p>the development of self-driving cars,</p></li>
<li><p>the use of AI in medical diagnosis, and</p></li>
<li><p>online shopping personalized recommendations</p></li>
</ul>
<p>have also contributed to the widespread adoption of AI.</p>
</section>
<section id="not-to-talk-abou-the-fears" class="slide level2">
<h2>Not to talk abou the fears</h2>
<div class="columns">
<div class="column" style="width:60%;">
<ul>
<li><p>AI also comes with fears from multiple sources from science fiction to religion</p>
<ul>
<li><p>Mass unemployment</p></li>
<li><p>Loss of privacity</p></li>
<li><p>AI bias</p></li>
<li><p>AI fakes</p></li>
<li><p>Or, simply, AI takeover</p></li>
</ul></li>
</ul>
</div><div class="column" style="width:40%;">
<p><br></p>
<p><img data-src="images/2.1-Introduction_to_ANN-Slides_insertimage_2.png"></p>
</div>
</div>
</section>
<section id="back-to-science" class="slide level2">
<h2>Back to science</h2>
<p>Where/How does it all fit?</p>

<img data-src="images/AI-ML-DL-1.jpg" class="quarto-figure quarto-figure-center r-stretch" style="width:100.0%"></section>
<section id="ai-ml-dl" class="slide level2">
<h2>AI, ML, DL …</h2>
<ul>
<li><p><strong>Artificial intelligence</strong>: Ability of a computer to perform tasks commonly associated with intelligent beings.</p></li>
<li><p><strong>Machine learning</strong>: study of algorithms that learn from examples and experience instead of relying on hard-coded rules and make predictions on new data</p></li>
<li><p><strong>Deep learning</strong>: sub field of ML focusing on learning data representations as successive successive layers of increasingly meaningful representations.</p></li>
</ul>
</section>
<section id="how-does-dl-improve" class="slide level2">
<h2>How does DL improve</h2>

<img data-src="images/ML_vs_DL-2.png" class="quarto-figure quarto-figure-center r-stretch" style="width:100.0%"><p class="caption"><a href="https://ieeexplore.ieee.org/document/9363896">ML and DL Approaches for Brain Disease Diagnosis</a></p><aside class="notes">
<ul>
<li>DNN: feature extraction and classification without (or with much les) human intervention.</li>
<li>DNN improves with data availability, without seemingly reaching plateaus.</li>
</ul>
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</section>
<section id="size-does-matter" class="slide level2">
<h2>Size does matter!</h2>

<img data-src="images/PerformanceVsAmountOfData.png" class="quarto-figure quarto-figure-center r-stretch" style="width:100.0%"><p class="caption">An illustration of the performance comparison between deep learning (DL) and other machine learning (ML) algorithms, where DL modeling from large amounts of data can increase the performance</p></section>
<section id="the-impact-of-deep-learning" class="slide level2 smaller">
<h2>The impact of Deep learning</h2>
<ul>
<li><p>Near-human-level image classification</p></li>
<li><p>Near-human-level speech transcription</p></li>
<li><p>Near-human-level handwriting transcription</p></li>
<li><p>Dramatically improved machine translation</p></li>
<li><p>Dramatically improved text-to-speech conversion</p></li>
<li><p>Digital assistants such as Google Assistant and Amazon Alexa</p></li>
<li><p>Near-human-level autonomous driving</p></li>
<li><p>Improved ad targeting, as used by Google, Baidu, or Bing</p></li>
<li><p>Improved search results on the web</p></li>
<li><p>Ability to answer natural language questions</p></li>
<li><p>Superhuman Go playing</p></li>
</ul>
</section>
<section id="not-all-that-glitters-is-gold" class="slide level2">
<h2>Not all that glitters is gold …</h2>
<ul>
<li><p>According to F. Chollet, the developer of Keras,</p>
<ul>
<li>“<em>we shouldn’t believe the short-term hype, but should believe in the long-term vision</em>.</li>
<li><em>It may take a while for AI to be deployed to its true potential—a potential the full extent of which no one has yet dared to dream</em></li>
<li><em>but AI is coming, and it will transform our world in a fantastic way</em>”.</li>
</ul></li>
</ul>
</section></section>
<section>
<section id="the-artificial-neurone-an" class="title-slide slide level1 center">
<h1>The Artificial Neurone (AN)</h1>

</section>
<section id="emulating-biological-neurons" class="slide level2">
<h2>Emulating biological neurons</h2>
<div class="columns">
<div class="column" style="width:50%;">
<div class="cell" data-layout-align="center">
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure>
<p><img data-src="images/NaturalNeuron.png" class="quarto-figure quarto-figure-center" style="width:100.0%"></p>
<figcaption><a href="">A biological Neuron</a></figcaption>
</figure>
</div>
</div>
</div>
</div><div class="column" style="width:50%;">
<div class="cell" data-layout-align="center">
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure>
<p><img data-src="images/MacCulloghPitts-Neuron.png" class="quarto-figure quarto-figure-center" style="width:100.0%"></p>
<figcaption><a href="">MuCulloch &amp; Pitts proposal</a></figcaption>
</figure>
</div>
</div>
</div>
</div>
</div>
<ul>
<li>The first model of an artifial neurone was proposed by Mc Cullough &amp; Pitts in 1943</li>
</ul>
</section>
<section id="mc-culloughs-neuron" class="slide level2">
<h2>Mc Cullough’s neuron</h2>
<ul>
<li>It may be divided into 2 parts.
<ul>
<li>The first part, <span class="math inline">\(g\)</span>,takes an input (as the dendrites of a neuron would do),</li>
<li>It performs an aggregation and</li>
<li>based on the aggregated value the second part, <span class="math inline">\(f\)</span>, makes a decision.</li>
</ul></li>
</ul>
<p>See <a href="https://towardsdatascience.com/mcculloch-pitts-model-5fdf65ac5dd1">the source of this picture</a> for an illustration on how this can be used to emulate logical operations such as AND, OR or NOT, but not XOR.</p>
</section>
<section id="limitations" class="slide level2">
<h2>Limitations</h2>
<p>This first attempt to emulate neurons succeeded but with limitations:</p>
<ul>
<li><p>What about non-Boolean (say, real) inputs?</p></li>
<li><p>What if all inputs are not equal?</p></li>
<li><p>What if we want to assign more importance to some inputs?</p></li>
<li><p>What about functions which are not linearly separable? Say XOR function</p></li>
</ul>
</section>
<section id="overcoming-the-limitations" class="slide level2">
<h2>Overcoming the limitations</h2>
<ul>
<li><p>To overcome these limitations Rosenblatt, proposed the perceptron model, or <em>artificial neuron</em>, in 1958.</p></li>
<li><p>Generalizes McCullough-Pitts neuron in that <em>weights and thresholds can be learnt over time</em>.</p>
<ul>
<li>It takes a weighted sum of the inputs and</li>
<li>It sets the output to iff the sum is more than an arbitrary threshold (<strong><span class="math inline">\(\theta\)</span></strong>).</li>
</ul></li>
</ul>
</section>
<section id="rosenblatts-perceptron" class="slide level2">
<h2>Rosenblatt’s perceptron</h2>
<p><a href="https://towardsdatascience.com/perceptron-the-artificial-neuron-4d8c70d5cc8d"><img data-src="images/RosenblattPerceptron1.png" style="width:100.0%"></a></p>
</section>
<section id="rosenblatts-perceptron-1" class="slide level2">
<h2>Rosenblatt’s perceptron</h2>
<div class="font80">
<ul>
<li>Instead of hand coding the thresholding parameter <span class="math inline">\(\theta\)</span>,</li>
<li>It is added as one of the inputs, with the weight <span class="math inline">\(w_0=-\theta\)</span>.</li>
</ul>
</div>
<p><a href="https://towardsdatascience.com/perceptron-the-artificial-neuron-4d8c70d5cc8d"><img data-src="images/RosenblattPerceptron2.png" style="width:100.0%"></a></p>
</section>
<section id="comparison-between-the-two" class="slide level2">
<h2>Comparison between the two</h2>
<p><a href="https://towardsdatascience.com/perceptron-the-artificial-neuron-4d8c70d5cc8d"><img data-src="images/McCullaughVSRosenblattPerceptron.png" style="width:100.0%"></a></p>
</section>
<section id="comparison-between-the-two-1" class="slide level2">
<h2>Comparison between the two</h2>
<ul>
<li><p>This is an improvement because</p>
<ul>
<li>both, weights and threshold, can be learned and</li>
<li>the inputs can be real values</li>
</ul></li>
<li><p>But there is still a drawback in that a single perceptron can only be used to implement linearly separable functions.</p></li>
<li><p>Artificial Neural Networks improve on this by introducing <em>Activation Functions</em></p></li>
</ul>
</section>
<section id="activation-in-biological-neurons" class="slide level2">
<h2>Activation in biological neurons</h2>
<ul>
<li>Biological neurons are specialized cells that transmit signals to communicate with each other.</li>
<li>Neuron’s activation is based on releasing <em>neurotransmitters</em>, chemicals that transmit signals between nerve cells.
<ul>
<li>When the signal reaching the neuron exceeds a certain threshold, it releases neurotransmitters to continue the communication process.</li>
</ul></li>
</ul>
</section>
<section id="activation-functions-in-an" class="slide level2">
<h2>Activation functions in AN</h2>
<ul>
<li>Analogously, <em>activation functions</em> in AN are functions to decide if the AN it is activated or not.</li>
<li>AN’s activation function is a mathematical function applied to the neuron’s input to produce an output.
<ul>
<li>In practice it extends to complicated functions that can learn complex patterns in the data.</li>
<li>Activation functions can incorporate non-linearity, improving over linear classifiers.</li>
</ul></li>
</ul>
</section>
<section id="activation-function" class="slide level2">
<h2>Activation function</h2>

<img data-src="images/ActivationFunction0.png" class="quarto-figure quarto-figure-center r-stretch" style="width:100.0%"></section>
<section id="artificial-neuron" class="slide level2">
<h2>Artificial Neuron</h2>
<p>With all these ideas in mind we can now define an Artificial Neuron as a <em>computational unit</em> that :</p>
<ul>
<li><p>takes as input <span class="math inline">\(x=(x_0,x_1,x_2,x_3),\ (x_0 = +1 \equiv bias)\)</span>,</p></li>
<li><p>outputs <span class="math inline">\(h_{\theta}(x) = f(\theta^\intercal x) = f(\sum_i \theta_ix_i)\)</span>,</p></li>
<li><p>where <span class="math inline">\(f:\mathbb{R}\mapsto \mathbb{R}\)</span> is called the <strong>activation function</strong>.</p></li>
</ul>
</section>
<section id="activation-functions" class="slide level2">
<h2>Activation functions</h2>
<div class="font90">
<ul>
<li><p>Goal of activation function is to provide the neuron with <em>the capability of producing the required outputs</em>.</p></li>
<li><p>Flexible enough to produce</p>
<ul>
<li>Either linear or non-linear transformations.</li>
<li>Output in the desired range ([0,1], {-1,1}, <span class="math inline">\(\mathbb{R}^+\)</span>…)</li>
</ul></li>
<li><p>Usually chosen from a (small) set of possibilities.</p>
<ul>
<li>Sigmoid function</li>
<li>Hyperbolic tangent, or <code>tanh</code>, function</li>
<li>ReLU</li>
</ul></li>
</ul>
</div>
</section>
<section id="the-sigmoid-function" class="slide level2 smaller">
<h2>The sigmoid function</h2>
<div class="columns">
<div class="column" style="width:50%;">
<p><span class="math display">\[
f(z)=\frac{1}{1+e^{-z}}
\]</span></p>
<ul>
<li><p>Output real values <span class="math inline">\(\in (0,1)\)</span>.</p></li>
<li><p>Natural interpretations as <em>probability</em></p></li>
</ul>
<div class="cell" data-layout-align="center">
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure>
<p><img data-src="images/sigmoidFunction.png" class="quarto-figure quarto-figure-center" style="width:100.0%"></p>
</figure>
</div>
</div>
</div>
</div><div class="column" style="width:50%;">
<div class="cell" data-layout-align="center">
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure>
<p><img data-src="images/sigmoidFunctionDerivative.png" class="quarto-figure quarto-figure-center" style="width:100.0%"></p>
</figure>
</div>
</div>
</div>
</div>
</div>
</section>
<section id="the-hyperbolic-tangent" class="slide level2 smaller">
<h2>the hyperbolic tangent</h2>
<div class="columns">
<div class="column" style="width:50%;">
<p>Also called <code>tanh</code>, function:</p>
<p><span class="math display">\[
f(z)=\frac{e^{z}-e^{-z}}{e^{z}+e^{-z}}
\]</span></p>
<ul>
<li><p>outputs are zero-centered and bounded in −1,1</p></li>
<li><p>scaled and shifted Sigmoid</p></li>
<li><p>stronger gradient but still has vanishing gradient problem</p></li>
<li><p>Its derivative is <span class="math inline">\(f'(z)=1-(f(z))^2\)</span>.</p></li>
</ul>
</div><div class="column" style="width:50%;">
<div class="cell" data-layout-align="center">
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure>
<p><img data-src="images/TanhFunction.png" class="quarto-figure quarto-figure-center" style="width:100.0%"></p>
</figure>
</div>
</div>
</div>
</div>
</div>
</section>
<section id="the-relu" class="slide level2 smaller">
<h2>The ReLU</h2>
<div class="columns">
<div class="column" style="width:50%;">
<ul>
<li><p><em>rectified linear unit</em>: <span class="math inline">\(f(z)=\max\{0,z\}\)</span>.</p></li>
<li><p>Close to a linear: piece-wise <em>linear</em> function with two linear pieces.</p></li>
<li><p>Outputs are in %(0,)$ , thus not bounded</p></li>
<li><p>Half rectified: activation threshold at 0</p></li>
<li><p>No vanishing gradient problem</p></li>
</ul>
</div><div class="column" style="width:50%;">
<div class="cell" data-layout-align="center">
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure>
<p><img data-src="images/ReLUFunction.png" class="quarto-figure quarto-figure-center" style="width:100.0%"></p>
</figure>
</div>
</div>
</div>
</div>
</div>
</section>
<section id="more-activation-functions" class="slide level2">
<h2>More activation functions</h2>
<p><img data-src="images/ActivationFunctions.png" style="width:100.0%">.</p>
</section>
<section id="putting-it-all-together" class="slide level2">
<h2>Putting it all together</h2>

<img data-src="images/ArtificialNeuron.png" class="quarto-figure quarto-figure-center r-stretch" style="width:100.0%"></section>
<section id="in-words" class="slide level2 smaller">
<h2>In words</h2>
<ul>
<li><p>An ANN takes a vector of input values <span class="math inline">\(x_{1}, \ldots, x_{d}\)</span> and combines it with some weights that are local to the neuron <span class="math inline">\(\left(w_{0}, w_{1}, . ., w_{d}\right)\)</span> to compute a net input <span class="math inline">\(w_{0}+\sum_{i=1}^{d} w_{i} \cdot x_{i}\)</span>.</p></li>
<li><p>To compute its output, it then passes the net input through a possibly non-linear univariate activation function <span class="math inline">\(g(\cdot)\)</span>, usually vchosen from a set of options such as <em>Sigmoid</em>, <em>Tanh</em> or <em>ReLU</em> functions</p></li>
<li><p>To deal with the <em>bias</em>, we create an extra input variable <span class="math inline">\(x_{0}\)</span> with value always equal to 1 , and so the function computed by a single artificial neuron (parameterized by its weights <span class="math inline">\(\mathbf{w}\)</span> ) is:</p></li>
</ul>
<p><span class="math display">\[
y(\mathbf{x})=g\left(w_{0}+\sum_{i=1}^{d} w_{i} x_{i}\right)=g\left(\sum_{i=0}^{d} w_{i} x_{i}\right)=g\left(\mathbf{w}^{\mathbf{T}} \mathbf{x}\right)
\]</span></p>
</section></section>
<section>
<section id="from-neurons-to-neural-networks" class="title-slide slide level1 center">
<h1>From neurons to neural networks</h1>

</section>
<section id="the-basic-neural-network" class="slide level2 smaller">
<h2>The basic neural network</h2>
<p>Following with the brain analogy one can combine (artificial) neurons to create better learners.</p>
<p>A simple artificial neural network is usually created by combining two types of modifications to the basic perceptron (AN).</p>
<ul>
<li>Stacking several neurons insteads of just one.</li>
<li>Adding an additional layer of neurons, which is call a <em>hidden</em> layer,</li>
</ul>
<p>This yields a system where the output of a can be the input of another in many different ways.</p>
</section>
<section id="an-artificial-neural-network" class="slide level2">
<h2>An Artificial Neural network</h2>

<img data-src="images/nn.jpg" class="quarto-figure quarto-figure-center r-stretch" style="width:90.0%"></section>
<section id="the-architecture-of-ann" class="slide level2 smaller">
<h2>The architecture of ANN</h2>
<p>In this figure, we have used circles to also denote the inputs to the network.</p>
<ul>
<li><p>Circles labeled +1 are <em>bias units</em>, and correspond to the intercept term.</p></li>
<li><p>The leftmost layer of the network is called the <em>input layer</em>.</p></li>
<li><p>The rightmost layer of the network is called the <em>output</em> layer.</p></li>
<li><p>The middle layer of nodes is called the <em>hidden layer</em>, because its values are not observed in the training set.</p></li>
</ul>
<p>Bias nodes are not counted when stating the neuron size.</p>
<p>With all this in mind our example neural network has three layers with:</p>
<ul>
<li>3 input units (not counting the bias unit),</li>
<li>3 hidden units,<br>
</li>
<li>1 output unit.</li>
</ul>
</section>
<section id="how-an-ann-works" class="slide level2">
<h2>How an ANN works</h2>
<p>An ANN is a predictive model (a <em>learner</em>) whose properties and behaviour can be well characterized.</p>
<!-- In practice this means: -->
<ul>
<li><p>It operates through a process known as <em>forward propagation</em>, which encompasses the information flow from the input layer to the output layer.</p></li>
<li><p>Forward propagation is performed by composing a series of linear and non-linear (activation) functions.</p></li>
<li><p>These are characterized (parametrized) by their <em>weights</em> and <em>biases</em>, that need to be <em>learnt</em>.</p>
<ul>
<li>This is done by <em>training the ANN</em>.</li>
</ul></li>
</ul>
</section>
<section id="training-the-ann" class="slide level2 smaller">
<h2>Training the ANN</h2>
<ul>
<li><p>In order for the ANN to perform well, the training process aims at finding the best possible parameter values for the learning task defined by the fnctions. This is done by</p>
<ul>
<li>Selecting an appropriate (convex) loss function,</li>
<li>Finding those weights that minimize a the total <em>cost</em> function (avg. loss).</li>
</ul></li>
<li><p>This is usually done using some iterative optimization procedure such as <em>gradient descent</em>.</p>
<ul>
<li>This requires evaluating derivatives in a huge number of points.</li>
<li>Such high number may be reduced by <em>Stochastic Gradient Descent</em>.</li>
<li>The evaluation of derivatives is simplified thanks to <em>Backpropagation</em>.</li>
</ul></li>
</ul>
</section>
<section id="forward-propagation" class="slide level2 smaller">
<h2>Forward propagation</h2>
<p>As described above the process that encompasses the computations required to go from the input values to the final output is known as <em>forward propagation</em>.</p>
<p>The weights are combined with the input to produce the final output.</p>
<p>Each node, <span class="math inline">\(a_i^{(2)}\)</span> of the hidden layer opperates on all nodes of the input values</p>
<p><span class="math display">\[\begin{eqnarray}
a_1^{(2)}&amp;=&amp;f(\theta_{10}^{(1)}+\theta_{11}^{(1)}x_1+\theta_{12}^{(1)}x_2+\theta_{13}^{(1)}x_3)\\
a_2^{(2)}&amp;=&amp;f(\theta_{20}^{(1)}+\theta_{21}^{(1)}x_1+\theta_{22}^{(1)}x_2+\theta_{23}^{(1)}x_3)\\
a_3^{(2)}&amp;=&amp;f(\theta_{30}^{(1)}+\theta_{31}^{(1)}x_1+\theta_{32}^{(1)}x_2+\theta_{33}^{(1)}x_3))
\end{eqnarray}\]</span></p>
<p>The output of the hidden layer is transformed through the activation function:</p>
<p><span class="math display">\[
h_{\Theta}(x)=a_1^{(3)}=f(\theta_{10}^{(2)}+\theta_{11}^{(2)}a_1^{(2)}+\theta_{12}^{(2)}a_2^{(2)}+\theta_{13}^{(2)}a_3^{(2)}
\]</span></p>
</section>
<section id="eficient-forward-propagation" class="slide level2">
<h2>Eficient Forward propagation</h2>
<ul>
<li><p>The way input data is transformed, through a series of weightings and transformations, until the ouput layer is called <em>forward propagation</em>.</p></li>
<li><p>By organizing parameters in matrices, and using matrix-vector operations, fast linear algebra routines can be used to perform the required calculations in a fast efficent way.</p></li>
</ul>
</section>
<section id="multiple-architectures-for-ann" class="slide level2">
<h2>Multiple architectures for ANN</h2>
<ul>
<li><p>We have so far focused on a single hidden layer neural network of the example.</p></li>
<li><p>One can. however build neural networks with many distinct architectures (meaning patterns of connectivity between neurons), including ones with multiple hidden layers.</p></li>
<li><p>See <a href="https://www.asimovinstitute.org/neural-network-zoo/">here the Neural Network Zoo</a>.</p></li>
</ul>
</section>
<section id="multiple-architectures-for-ann-1" class="slide level2 smaller">
<h2>Multiple architectures for ANN</h2>
<div class="columns">
<div class="column" style="width:50%;">
<ul>
<li><p>We have so far focused on a single hidden layer neural network of the example</p></li>
<li><p>One can build neural networks with many distinct architectures (meaning patterns of connectivity between neurons), including ones with multiple hidden layers.</p></li>
</ul>
</div><div class="column" style="width:50%;">
<p><img data-src="images/2.1-Introduction_to_ANN-Slides_insertimage_3.png"> <a href="https://www.asimovinstitute.org/neural-network-zoo/">The Neural Network Zoo</a></p>
</div>
</div>
</section>
<section id="multiple-layer-dense-networks" class="slide level2">
<h2>Multiple layer dense Networks</h2>
<ul>
<li>Most common choice is a <span class="math inline">\(n_l\)</span>-layered network:
<ul>
<li>layer 1 is the input layer,</li>
<li>layer <span class="math inline">\(n_l\)</span> is the output layer,</li>
<li>and each layer <span class="math inline">\(l\)</span> is densely connected to layer <span class="math inline">\(l+1\)</span>.</li>
</ul></li>
<li>In this setting, to compute the output of the network, we can compute all the activations in layer <span class="math inline">\(L_2\)</span>, then layer <span class="math inline">\(L_3\)</span>, and so on, up to layer <span class="math inline">\(L_{nl}\)</span>, using equations seen previously.</li>
</ul>
</section>
<section id="feed-forward-nns" class="slide level2">
<h2>Feed Forward NNs</h2>
<ul>
<li>The type of NN described is called feed-forward <em>neural network (FFNN)</em>, since
<ul>
<li>All computations are done by Forward propagation</li>
<li>The connectivity graph does not have any directed loops or cycles.</li>
</ul></li>
</ul>
</section></section>
<section>
<section id="an-example-using-r" class="title-slide slide level1 center">
<h1>An example using R</h1>

</section>
<section id="a-predictive-ann" class="slide level2">
<h2>A predictive ANN</h2>
<p>We use the <code>neuralnet</code> package to build a simple neural network to predict if a type of stock pays dividends or not.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href=""></a><span class="cf">if</span> (<span class="sc">!</span><span class="fu">require</span>(neuralnet)) </span>
<span id="cb1-2"><a href=""></a>  <span class="fu">install.packages</span>(<span class="st">"neuralnet"</span>, <span class="at">dep=</span><span class="cn">TRUE</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="data-for-the-example" class="slide level2">
<h2>Data for the example</h2>
<p>And use the <code>dividendinfo.csv</code> dataset from <a href="https://github.com/MGCodesandStats/datasets" class="uri">https://github.com/MGCodesandStats/datasets</a></p>
<div class="cell">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href=""></a>mydata <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="st">"https://raw.githubusercontent.com/MGCodesandStats/datasets/master/dividendinfo.csv"</span>)</span>
<span id="cb2-2"><a href=""></a><span class="fu">str</span>(mydata)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>'data.frame':   200 obs. of  6 variables:
 $ dividend       : int  0 1 1 0 1 1 1 0 1 1 ...
 $ fcfps          : num  2.75 4.96 2.78 0.43 2.94 3.9 1.09 2.32 2.5 4.46 ...
 $ earnings_growth: num  -19.25 0.83 1.09 12.97 2.44 ...
 $ de             : num  1.11 1.09 0.19 1.7 1.83 0.46 2.32 3.34 3.15 3.33 ...
 $ mcap           : int  545 630 562 388 684 621 656 351 658 330 ...
 $ current_ratio  : num  0.924 1.469 1.976 1.942 2.487 ...</code></pre>
</div>
</div>
</section>
<section id="data-pre-processing" class="slide level2">
<h2>Data pre-processing</h2>
<div class="cell">
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href=""></a>normalize <span class="ot">&lt;-</span> <span class="cf">function</span>(x) {</span>
<span id="cb4-2"><a href=""></a>  <span class="fu">return</span> ((x <span class="sc">-</span> <span class="fu">min</span>(x)) <span class="sc">/</span> (<span class="fu">max</span>(x) <span class="sc">-</span> <span class="fu">min</span>(x)))</span>
<span id="cb4-3"><a href=""></a>}</span>
<span id="cb4-4"><a href=""></a>normData <span class="ot">&lt;-</span> <span class="fu">as.data.frame</span>(<span class="fu">lapply</span>(mydata, normalize))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="test-and-training-sets" class="slide level2">
<h2>Test and training sets</h2>
<p>Finally we break our data in a test and a training set:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href=""></a>perc2Train <span class="ot">&lt;-</span> <span class="dv">2</span><span class="sc">/</span><span class="dv">3</span></span>
<span id="cb5-2"><a href=""></a>ssize <span class="ot">&lt;-</span> <span class="fu">nrow</span>(normData)</span>
<span id="cb5-3"><a href=""></a><span class="fu">set.seed</span>(<span class="dv">12345</span>)</span>
<span id="cb5-4"><a href=""></a>data_rows <span class="ot">&lt;-</span> <span class="fu">floor</span>(perc2Train <span class="sc">*</span>ssize)</span>
<span id="cb5-5"><a href=""></a>train_indices <span class="ot">&lt;-</span> <span class="fu">sample</span>(<span class="fu">c</span>(<span class="dv">1</span><span class="sc">:</span>ssize), data_rows)</span>
<span id="cb5-6"><a href=""></a>trainset <span class="ot">&lt;-</span> normData[train_indices,]</span>
<span id="cb5-7"><a href=""></a>testset <span class="ot">&lt;-</span> normData[<span class="sc">-</span>train_indices,]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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</section>
<section id="training-a-neural-network" class="slide level2">
<h2>Training a neural network</h2>
<p>We train a simple NN with two hidden layers, with 4 and 2 neurons respectively.</p>
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<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href=""></a><span class="co">#Neural Network</span></span>
<span id="cb6-2"><a href=""></a><span class="fu">library</span>(neuralnet)</span>
<span id="cb6-3"><a href=""></a>nn <span class="ot">&lt;-</span> <span class="fu">neuralnet</span>(dividend <span class="sc">~</span> fcfps <span class="sc">+</span> earnings_growth <span class="sc">+</span> de <span class="sc">+</span> mcap <span class="sc">+</span> current_ratio, </span>
<span id="cb6-4"><a href=""></a>                <span class="at">data=</span>trainset, </span>