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</head>
<body class="quarto-light">
<div class="reveal">
<div class="slides">
<section id="title-slide" class="quarto-title-block center">
<h1 class="title">Introduction to ANN and Deep Learning</h1>
<div class="quarto-title-authors">
<div class="quarto-title-author">
<div class="quarto-title-author-name">
A. Sanchez, F. Reverter and E. Vegas
</div>
</div>
</div>
</section>
<section>
<section id="overview-of-deep-learning" class="title-slide slide level1 center">
<h1>Overview of Deep Learning</h1>
</section>
<section id="historical-background-1" class="slide level2">
<h2>Historical Background (1)</h2>
<ul>
<li><p>Today, in April 2023, our world is convulsed by the explosion of Artificial Intelligence.</p></li>
<li><p>It has probably been in the last months (weeks), since ChatGPT has arrived, that everybody has 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" style="width:100.0%" class="r-stretch quarto-figure-center"></section>
<section id="historical-background-2" class="slide level2">
<h2>Historical Background (2)</h2>
<ul>
<li><p>AI use statistical learning methods, such as machine learning algorithms, to make predictions based on large amounts of data.</p></li>
<li><p>Prediction is a fundamental capability of AI and is used in a wide range of applications.</p></li>
<li><p>However, it is important to keep in mind that AI has far-reaching implications beyond its predictive capabilities, including ethical, social or technological.</p></li>
</ul>
</section>
<section id="deep-learning" class="slide level2">
<h2>Deep learning</h2>
<ul>
<li><p>Deep learning 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>Essentially, deep learning extends the basic principles of artificial neural networks by</p>
<ul>
<li>Adding complex architectures and algorithms and</li>
<li>At the same time becoming more automatic</li>
</ul></li>
<li><p>We won’t delve into the history of ANN, but a quick look at it may help fully grasp its current capabilities.</p></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:100.0%" class="r-stretch quarto-figure-center"><p class="caption">A Brief History of AI from 1940s till Today</p><ul>
<li>The origins of AI, and as such of DL can be traced almost one century backwards;</li>
<li><a href="https://nerdyelectronics.com/a-quick-history-of-ai-ml-and-dl/" id="AIHistory">A Quick History of AI, ML and DL</a></li>
</ul>
</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-artificial-neural-networks-to-deep-learning" class="slide level2">
<h2>From Artificial Neural Networks to Deep learning</h2>
<p><img data-src="images/WhyDLNow.png" style="width:100.0%" data-fig-align="center" alt="Why Deep Learning Now?"> Source: Alex Amini’s ‘MIT Introduction to Deep Learning’ course (introtodeeplearning.com)</p>
</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>the creation of personalized recommendations in online shopping</p></li>
</ul>
<p>have also contributed to the widespread adoption of AI.</p>
</section>
<section id="ai-ml-dl" class="slide level2">
<h2>AI, ML, DL …</h2>
<img data-src="images/AI-ML-DL-1.jpg" style="width:100.0%" class="r-stretch quarto-figure-center"></section>
<section id="ai-ml-dl-1" class="slide level2">
<h2>AI, ML, DL …</h2>
<ul>
<li><p>Artificial intelligence: Ability of a computer to perform tasks commonly associated with intelligent beings.</p></li>
<li><p>Machine learning: 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>Deep learning: sub field of ML focusing on learning data representations as successive successive layers of increasingly meaningful representations.</p></li>
</ul>
</section>
<section id="machine-vs-deep-learning" class="slide level2">
<h2>Machine vs Deep Learning</h2>
<div class="columns">
<div class="column" style="width:40%;">
<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>
</div><div class="column" style="width:60%;">
<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/ML_vs_DL-2.png" style="width:100.0%"></p>
</figure>
</div>
</div>
</div>
</div>
</div>
</section>
<section id="size-does-matter" class="slide level2">
<h2>Size does matter!</h2>
<img data-src="images/PerformanceVsAmountOfData.png" style="width:100.0%" class="r-stretch quarto-figure-center"><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="artificial-neural-networks" class="title-slide slide level1 center">
<h1>Artificial Neural Networks</h1>
</section>
<section id="the-perceptron-the-building-block" class="slide level2">
<h2>The perceptron, the building block</h2>
<ul>
<li><p>The perceptron, was introduced in the 50’s (one version of the perceptron at least), as a mathematical model that might emulate a neuron.</p></li>
<li><p>The idea was <em>trying</em> <em>to produce a model that, given some inputs, and an appropriate set of examples, learn to produce the desired output</em>.</p></li>
</ul>
</section>
<section id="mc-culloughs-neuron" class="slide level2">
<h2>Mc Cullough’s neuron</h2>
<ul>
<li>The first computational model of a neuron was proposed by Warren MuCulloch (neuroscientist) and Walter Pitts (logician) in 1943.</li>
</ul>
<img data-src="images/MacCulloghPitts-Neuron.png" style="width:93.0%" class="r-stretch quarto-figure-center"></section>
<section id="mc-culloughs-neuron-1" 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 (ahem dendrite ahem),</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 Frank Rosenblatt, proposed the classical perception model, the <em>artificial neuron</em>, in 1958.</p></li>
<li><p>It is more generalized computational model than the McCullough-Pitts neuron where weights and thresholds can be learnt over time.</p></li>
<li><p>Rosenblatt’s perceptron is very similar to an M-P neuron but</p>
<ul>
<li>It takes a weighted sum of the inputs and</li>
<li>It sets the output as one only when the sum is more than an arbitrary threshold (<strong><em>theta</em></strong>).</li>
</ul></li>
</ul>
</section>
<section id="rosenblatts-perceptron" class="slide level2">
<h2>Rosenblatt’s perceptron</h2>
<img data-src="images/RosenblattPerceptron1.png" style="width:100.0%" class="r-stretch quarto-figure-center"></section>
<section id="rosenblatts-perceptron-1" class="slide level2">
<h2>Rosenblatt’s perceptron (1)</h2>
<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>
<img data-src="images/RosenblattPerceptron2.png" style="width:100.0%" class="r-stretch quarto-figure-center"></section>
<section id="comparison-between-the-two" class="slide level2">
<h2>Comparison between the two</h2>
<img data-src="images/McCullaughVSRosenblattPerceptron.png" style="width:100.0%" class="r-stretch quarto-figure-center"></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 in the CNS that transmit electrical and chemical signals to communicate with each other.</li>
<li>The neuron’s activation is based on the release of neurotransmitters, chemical substances that transmit signals between nerve cells.
<ul>
<li>When the signal reaching the neuron exceeds a certain threshold, the neuron 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>In AN, the 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" style="width:100.0%" class="r-stretch quarto-figure-center"></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">\(x=(x_0,x_1,x_2,x_3)\)</span> (<span class="math inline">\(x_0\)</span> = +1, called bias),</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>
<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>
</section>
<section id="the-sigmoid-function" class="slide level2 smaller">
<h2>The sigmoid function</h2>
<div class="columns">
<div class="column" style="width:40%;">
<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> of an event</p></li>
<li><p><em>vanishing gradient</em> problem</p></li>
<li><p>Its derivative is: <span class="math inline">\(f'(z)=f(z)(1-f(z))\)</span>.</p></li>
</ul>
</div><div class="column" style="width:60%;">
<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" 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:40%;">
<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:60%;">
<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" 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:40%;">
<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:60%;">
<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" 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" style="width:100.0%" class="r-stretch quarto-figure-center"><p><span class="math inline">\(\Sigma=\left\langle w_{j}, x\right\rangle+ b_{j}\)</span></p>
</section>
<section id="multilayer-perceptrons" class="slide level2 smaller">
<h2>Multilayer perceptrons</h2>
<ul>
<li>A Multilayer Perceptron or Artificial Neural Network (ANN) is a computational model that mimics the structure and function of the human brain.</li>
<li>It is composed of interconnected nodes, called neurons, that are organized into layers.</li>
<li>Neurons in each layer are connected to neurons in the next layer, forming a directed graph-like structure.</li>
<li>The first layer (input layer) receives input data.</li>
<li>Last layer produces the final prediction</li>
<li>Intermediate (hidden) layers perform intermediate calculations.</li>
</ul>
</section>
<section id="an-artificial-neural-network" class="slide level2">
<h2>An Artificial Neural network</h2>
<img data-src="images/MultiLayer1.png" style="width:100.0%" class="r-stretch quarto-figure-center"></section>
<section id="the-architecture-of-ann" class="slide level2">
<h2>The architecture of ANN</h2>
<ul>
<li><p>Multilayers perceptrons have a basic architecture:</p>
<ul>
<li>each unit (or neuron) of a layer is linked to all the units of the next layer</li>
<li>but has no link with the neurons of the same layer.</li>
</ul></li>
<li><p>This basic architecture can changes in many possible ways</p>
<ul>
<li>There may be links between neurons in same layer,</li>
<li>Missing links between two layers …</li>
</ul></li>
</ul>
</section>
<section id="the-architecture-of-an-ann" class="slide level2">
<h2>The architecture of an ANN</h2>
<ul>
<li><p>The architecture of a multilayer perceptron is defined by:</p>
<ul>
<li>The number of hidden layers and</li>
<li>The number of neurons in each layer</li>
</ul></li>
<li><p>Activation functions are important in the definition of the ANN, but not relevant for the architecture.</p></li>
</ul>
</section>
<section id="activation-functions-for-ann-1" class="slide level2">
<h2>Activation functions for ANN (1)</h2>
<ul>
<li>For the output layer, the activation function is generally different from the one used on the hidden layers.
<ul>
<li>For <strong>regression</strong>, we apply no activation function on the output layer.</li>
<li>For <strong>binary</strong> classification, where output is a prediction of <span class="math inline">\(\mathbb{P}(Y=1 /X) \in [0,1]\)</span>
<ul>
<li>The <em>sigmoid</em> activation function is used.</li>
</ul></li>
<li>For <strong>multi-class classification</strong>, where there is one neuron per class giving a prediction of <span class="math inline">\(\mathbb{P}(Y=i / X)\)</span>.
<ul>
<li>The soft-max activation function is common</li>
</ul></li>
</ul></li>
</ul>
</section>
<section id="the-soft-max-activation-function" class="slide level2">
<h2>The soft-max activation function</h2>
<p><span class="math display">\[
\operatorname{softmax}(z)_{i}=\frac{\exp \left(z_{i}\right)}{\sum_{j} \exp \left(z_{j}\right)}
\]</span></p>
</section></section>
<section>
<section id="an-example" class="title-slide slide level1 center">
<h1>An example</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="#cb1-1"></a><span class="cf">if</span> (<span class="sc">!</span><span class="fu">require</span>(neuralnet)) </span>
<span id="cb1-2"><a href="#cb1-2"></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="#cb2-1"></a>mydata <span class="ot"><-</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="#cb2-2"></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="#cb4-1"></a>normalize <span class="ot"><-</span> <span class="cf">function</span>(x) {</span>
<span id="cb4-2"><a href="#cb4-2"></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="#cb4-3"></a>}</span>
<span id="cb4-4"><a href="#cb4-4"></a>normData <span class="ot"><-</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="#cb5-1"></a>perc2Train <span class="ot"><-</span> <span class="dv">2</span><span class="sc">/</span><span class="dv">3</span></span>
<span id="cb5-2"><a href="#cb5-2"></a>ssize <span class="ot"><-</span> <span class="fu">nrow</span>(normData)</span>
<span id="cb5-3"><a href="#cb5-3"></a><span class="fu">set.seed</span>(<span class="dv">12345</span>)</span>
<span id="cb5-4"><a href="#cb5-4"></a>data_rows <span class="ot"><-</span> <span class="fu">floor</span>(perc2Train <span class="sc">*</span>ssize)</span>
<span id="cb5-5"><a href="#cb5-5"></a>train_indices <span class="ot"><-</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="#cb5-6"></a>trainset <span class="ot"><-</span> normData[train_indices,]</span>
<span id="cb5-7"><a href="#cb5-7"></a>testset <span class="ot"><-</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>
</div>
</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>
<div class="cell">
<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="#cb6-1"></a><span class="co">#Neural Network</span></span>
<span id="cb6-2"><a href="#cb6-2"></a><span class="fu">library</span>(neuralnet)</span>
<span id="cb6-3"><a href="#cb6-3"></a>nn <span class="ot"><-</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="#cb6-4"></a> <span class="at">data=</span>trainset, </span>
<span id="cb6-5"><a href="#cb6-5"></a> <span class="at">hidden=</span><span class="fu">c</span>(<span class="dv">2</span>,<span class="dv">1</span>), </span>
<span id="cb6-6"><a href="#cb6-6"></a> <span class="at">linear.output=</span><span class="cn">FALSE</span>, </span>
<span id="cb6-7"><a href="#cb6-7"></a> <span class="at">threshold=</span><span class="fl">0.01</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="network-plot" class="slide level2">
<h2>Network plot</h2>
<p>The output of the procedure is a neural network with estimated weights</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1"></a><span class="fu">plot</span>(nn, <span class="at">rep =</span> <span class="st">"best"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<img data-src="Introduction_to_Deep_Learning-Slides_files/figure-revealjs/unnamed-chunk-14-1.png" width="960" class="r-stretch"></section>
<section id="predictions" class="slide level2">
<h2>Predictions</h2>
<div class="cell">
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1"></a>temp_test <span class="ot"><-</span> <span class="fu">subset</span>(testset, <span class="at">select =</span></span>
<span id="cb8-2"><a href="#cb8-2"></a> <span class="fu">c</span>(<span class="st">"fcfps"</span>,<span class="st">"earnings_growth"</span>, </span>
<span id="cb8-3"><a href="#cb8-3"></a> <span class="st">"de"</span>, <span class="st">"mcap"</span>, <span class="st">"current_ratio"</span>))</span>
<span id="cb8-4"><a href="#cb8-4"></a>nn.results <span class="ot"><-</span> <span class="fu">compute</span>(nn, temp_test)</span>
<span id="cb8-5"><a href="#cb8-5"></a>results <span class="ot"><-</span> <span class="fu">data.frame</span>(<span class="at">actual =</span> </span>
<span id="cb8-6"><a href="#cb8-6"></a> testset<span class="sc">$</span>dividend, </span>
<span id="cb8-7"><a href="#cb8-7"></a> <span class="at">prediction =</span> nn.results<span class="sc">$</span>net.result)</span>
<span id="cb8-8"><a href="#cb8-8"></a><span class="fu">head</span>(results)</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> actual prediction
9 1 0.9919213885
19 1 0.9769206123
22 0 0.0002187144
26 0 0.6093330933
27 1 0.7454164893
29 1 0.9515431416</code></pre>
</div>
</div>
</section>
<section id="model-evaluation" class="slide level2">
<h2>Model evaluation</h2>
<div class="cell">
<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1"></a>roundedresults<span class="ot"><-</span><span class="fu">sapply</span>(results,round,<span class="at">digits=</span><span class="dv">0</span>)</span>
<span id="cb10-2"><a href="#cb10-2"></a>roundedresultsdf<span class="ot">=</span><span class="fu">data.frame</span>(roundedresults)</span>
<span id="cb10-3"><a href="#cb10-3"></a><span class="fu">attach</span>(roundedresultsdf)</span>
<span id="cb10-4"><a href="#cb10-4"></a><span class="fu">table</span>(actual,prediction)</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> prediction
actual 0 1
0 33 3
1 4 27</code></pre>
</div>
</div>
</section></section>
<section>
<section id="some-mathematics-behind-ann" class="title-slide slide level1 center">
<h1>Some mathematics behind ANN</h1>
</section>
<section id="training-an-ann" class="slide level2 smaller">
<h2>Training an ANN</h2>
<ul>
<li><p>An ANN is a predictive model whose properties and behaviour can be mathematically characterized.</p></li>
<li><p>In practice this means:</p>
<ul>
<li>The ANN acts by composing a series of linear and non-linear (activation) functions.</li>
<li>These are characterized by their <em>weights</em> and <em>biases</em>, that need to be <em>learnt</em> .</li>
</ul></li>
<li><p><em>Training</em> the network 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>
</ul>
</section>
<section id="the-tools-for-training" class="slide level2">
<h2>The tools for training</h2>
<ul>
<li><p>Training an ANN is usually done using some iterative optimization procedure such as <em>Gradient Descent</em>.</p></li>
<li><p>This requires evaluating derivatives in a huge number of points.</p>
<ul>
<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="a-guiding-example" class="slide level2">
<h2>A guiding example</h2>
<p>Consider a toy ANN to illustrate the concepts</p>
<div class="columns">
<div class="column" style="width:50%;">
<ul>
<li>Input layer with 3 input units (plus bias unit),</li>
<li>1 hidden layer with 3 hidden units,</li>
<li>Output layer with 1 output unit.</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/nn.jpg" style="width:100.0%"></p>
</figure>
</div>
</div>
</div>
</div>
</div>
</section>
<section id="a-logistic-regression-ann" class="slide level2">
<h2>A logistic regression ANN</h2>
<ul>
<li><p>From input layer to layer 2: A non-linear transformation yields new set of complex features.</p></li>
<li><p>From layer 2 to output layer: New features are transformed, using a sigmoid activation function.</p></li>
</ul>
<p><span class="math display">\[
\mbox{The final output is: }h_{\theta}(x)=\frac{1}{1+e^{-\theta^\intercal x}}
\]</span></p>
</section>
<section id="logistic-regression-1" class="slide level2">
<h2>Logistic regression (1)</h2>
<p>Recall that, the logistic regression model is:</p>
<p><span class="math display">\[
\log\frac{p(Y=1|x)}{1-p(Y=1|x)}=\theta^\intercal x
\]</span></p>
<p>Isolating <span class="math inline">\(p(Y=1|x)\)</span> and taking logs in both sides:</p>
<p><span class="math display">\[
\frac{p(Y=1|x)}{1-p(Y=1|x)}=e^{\theta^\intercal x}
\]</span></p>