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Copy file name to clipboardExpand all lines: docs/01-Problem-Setup.html
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<li><ahref="#population-and-sample" id="toc-population-and-sample" class="nav-link active" data-scroll-target="#population-and-sample"><spanclass="header-section-number">2.1</span> Population and Sample</a></li>
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<li><ahref="#how-to-pick-a-model" id="toc-how-to-pick-a-model" class="nav-link" data-scroll-target="#how-to-pick-a-model"><spanclass="header-section-number">2.2</span> How to pick a model?</a></li>
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<li><ahref="#how-to-evaluate-a-model" id="toc-how-to-evaluate-a-model" class="nav-link" data-scroll-target="#how-to-evaluate-a-model"><spanclass="header-section-number">2.3</span> How to evaluate a model?</a></li>
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<li><ahref="#preview-linear-regression" id="toc-preview-linear-regression" class="nav-link" data-scroll-target="#preview-linear-regression"><spanclass="header-section-number">2.4</span> Preview: linear regression</a></li>
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<li><ahref="#how-to-evaluate-and-pick-a-model" id="toc-how-to-evaluate-and-pick-a-model" class="nav-link" data-scroll-target="#how-to-evaluate-and-pick-a-model"><spanclass="header-section-number">2.2</span> How to evaluate and pick a model?</a></li>
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<li><ahref="#preview-linear-regression" id="toc-preview-linear-regression" class="nav-link" data-scroll-target="#preview-linear-regression"><spanclass="header-section-number">2.3</span> Preview: linear regression</a></li>
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</ul>
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<divclass="toc-actions"><ul><li><ahref="https://github.com/ottrproject/OTTR_Quarto/edit/main/01-Problem-Setup.qmd" class="toc-action"><iclass="bi bi-github"></i>Edit this page</a></li><li><ahref="https://docs.google.com/forms/d/e/1FAIpQLSfBvVELBg8lcynKj0TrzMlov1zil-Sbkh9VhMKRcSpeo1xo6g/viewform" class="toc-action"><iclass="bi empty"></i>Report an issue</a></li></ul></div></nav>
<p>Where <spanclass="math inline">\(f(Age, BMI, Income, ...)\)</span> is a machine learning model that takes in the clinical and demographic variables and make a prediction on the <spanclass="math inline">\(BloodPressure\)</span>. This model is not perfect to give a perfect, correct prediction, so there is an “error term” <spanclass="math inline">\(\epsilon\)</span> that captures the imperfectness of the model.</p>
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<p>Where <spanclass="math inline">\(f(Age, BMI, Income, ...)\)</span> is a machine learning model that takes in the clinical and demographic variables and make a prediction on the <spanclass="math inline">\(BloodPressure\)</span>. This model is not perfect to give the correct prediction, so there is an “error term” <spanclass="math inline">\(\epsilon\)</span> (Greek letter epsilon) that captures the imperfectness of the model.</p>
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<p>A machine learning model, such as the one described above, has <em>two main uses:</em></p>
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<oltype="1">
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<li><p><strong>Prediction:</strong> How accurately can we predict outcomes?</p>
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<ul>
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<li><p><strong>Prediction:</strong> How accurately can we predict outcomes?</p></li>
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<li><p><strong>Inference:</strong> Which predictors are associated with the response, and how strong is the association?</p></li>
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</ul>
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<li>Given a new person’s <spanclass="math inline">\(Age, BMI, Income, …\)</span> , predict the person’s <spanclass="math inline">\(BloodPressure\)</span> and compare it to the true value.</li>
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</ul></li>
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<li><p><strong>Inference:</strong> Which predictors are associated with the response, and how strong is the association?</p>
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<ul>
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<li>Suppose the model is described as <spanclass="math inline">\(BloodPressure = f(Age,BMI,Income,…)=20 + 3 \cdot Age - .2 \cdot BMI + .00015 \cdot Income\)</span>. Each variable has a relationship to the outcome: an increase of <spanclass="math inline">\(Age\)</span> by 1 will lead to an increase of <spanclass="math inline">\(BloodPressure\)</span> by 3. This measures the strength of association between a variable and the outcome.</li>
<h2data-number="2.1" class="anchored" data-anchor-id="population-and-sample"><spanclass="header-section-number">2.1</span> Population and Sample</h2>
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<p>The way we formulate machine learning model is based on some fundamental concepts in inferential statistics. We will refresh this quickly in the context of our problem. Recall the following definitions:</p>
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<p><strong>Population:</strong> The entire collection of individual units that a researcher is interested to study. For NHANES, this could be the entire US population.</p>
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<p><strong>Sample:</strong> A smaller collection of individual units that the researcher has selected to study. For NHANES, this could be a random sampling of the US population.</p>
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<p>In Machine Learning problems, we often like to take two, non-overlapping samples from the population: the <strong>Training Set</strong>, and the <strong>Test Set</strong>. We <strong>train</strong> our model using the Training Set, which gives us a function <spanclass="math inline">\(f()\)</span> that relates the predictors to the outcome. Then, for our main use cases:</p>
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<oltype="1">
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<li><strong>Prediction:</strong> We use the trained model to predict the outcome using predictors from the Test Set and compare the predicted outcome to the true value in the Test Set.</li>
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<li><strong>Inference</strong>: We examine the function <spanclass="math inline">\(f()\)</span>’s trained values, which are called <strong>parameters</strong>. For instance, <spanclass="math inline">\(f(Age,BMI,Income,…)=20 + 3 \cdot Age - .2 \cdot BMI + .00015 \cdot Income\)</span>, the values <spanclass="math inline">\(20\)</span>, <spanclass="math inline">\(3\)</span>, <spanclass="math inline">\(-.2\)</span>, and <spanclass="math inline">\(.00015\)</span> are the parameters. Because these parameters are derived from the Training Set, they are an <em>estimated</em> quantity from a sample, similar to other summary statistics like the mean of a sample. Therefore, to say anything about the true population, we have to use statistical tools such as p-values and confidence intervals.</li>
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</ol>
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<p>If the concepts of population, sample, estimation, p-value, and confidence interval is new to you, we recommend do a bit of reading here [todo].</p>
<h2data-number="2.3" class="anchored" data-anchor-id="how-to-evaluate-a-model"><spanclass="header-section-number">2.3</span> How to evaluate a model?</h2>
<h2data-number="2.2" class="anchored" data-anchor-id="how-to-evaluate-and-pick-a-model"><spanclass="header-section-number">2.2</span> How to evaluate and pick a model?</h2>
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<p>The little example model we showcased above is an example of a <strong>linear model</strong>, but we will look at several types of models in this course. In order to decide how to evaluate and pick a model, we will need to develop a framework to assess a model.</p>
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"href": "01-Problem-Setup.html",
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"title": "2 Problem Set-Up",
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"section": "",
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"text": "2.1 Population and Sample",
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"text": "2.1 Population and Sample\nThe way we formulate machine learning model is based on some fundamental concepts in inferential statistics. We will refresh this quickly in the context of our problem. Recall the following definitions:\nPopulation: The entire collection of individual units that a researcher is interested to study. For NHANES, this could be the entire US population.\nSample: A smaller collection of individual units that the researcher has selected to study. For NHANES, this could be a random sampling of the US population.\nIn Machine Learning problems, we often like to take two, non-overlapping samples from the population: the Training Set, and the Test Set. We train our model using the Training Set, which gives us a function \\(f()\\) that relates the predictors to the outcome. Then, for our main use cases:\nIf the concepts of population, sample, estimation, p-value, and confidence interval is new to you, we recommend do a bit of reading here [todo].",
"text": "Prediction: We use the trained model to predict the outcome using predictors from the Test Set and compare the predicted outcome to the true value in the Test Set.\nInference: We examine the function \\(f()\\)’s trained values, which are called parameters. For instance, \\(f(Age,BMI,Income,…)=20 + 3 \\cdot Age - .2 \\cdot BMI + .00015 \\cdot Income\\), the values \\(20\\), \\(3\\), \\(-.2\\), and \\(.00015\\) are the parameters. Because these parameters are derived from the Training Set, they are an estimated quantity from a sample, similar to other summary statistics like the mean of a sample. Therefore, to say anything about the true population, we have to use statistical tools such as p-values and confidence intervals.",
"section": "2.2 How to evaluate and pick a model?",
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"text": "2.2 How to evaluate and pick a model?\nThe little example model we showcased above is an example of a linear model, but we will look at several types of models in this course. In order to decide how to evaluate and pick a model, we will need to develop a framework to assess a model.",
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