Morten Hjorth-Jensen
423 lines
28 KiB
HTML
423 lines
28 KiB
HTML
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<a class="navbar-brand" href="week34-bs.html">Week 34: Introduction to the course, Logistics and Practicalities</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week34-bs001.html#overview-of-first-week" style="font-size: 80%;"><b>Overview of first week</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs002.html#schedule-first-week" style="font-size: 80%;"><b>Schedule first week</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs003.html#lectures-and-computerlab" style="font-size: 80%;"><b>Lectures and ComputerLab</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs004.html#communication-channels" style="font-size: 80%;"><b>Communication channels</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs005.html#course-format" style="font-size: 80%;"><b>Course Format</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs006.html#teachers" style="font-size: 80%;"><b>Teachers</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs007.html#deadlines-for-projects-tentative" style="font-size: 80%;"><b>Deadlines for projects (tentative)</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs008.html#grading" style="font-size: 80%;"><b>Grading</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs009.html#reading-material" style="font-size: 80%;"><b>Reading material</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs010.html#main-textbooks" style="font-size: 80%;"><b>Main textbooks</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs011.html#other-popular-texts" style="font-size: 80%;"><b>Other popular texts</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs012.html#reading-suggestions-week-34" style="font-size: 80%;"><b>Reading suggestions week 34</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs013.html#prerequisites" style="font-size: 80%;"><b>Prerequisites</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs014.html#topics-covered-in-this-course-statistical-analysis-and-optimization-of-data" style="font-size: 80%;"><b>Topics covered in this course: Statistical analysis and optimization of data</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs015.html#statistical-analysis-and-optimization-of-data" style="font-size: 80%;"><b>Statistical analysis and optimization of data</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs016.html#machine-learning" style="font-size: 80%;"><b>Machine Learning</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs017.html#deep-learning-methods" style="font-size: 80%;"><b>Deep learning methods</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs018.html#extremely-useful-tools-strongly-recommended" style="font-size: 80%;"><b>Extremely useful tools, strongly recommended</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs019.html#other-courses-on-data-science-and-machine-learning-at-uio" style="font-size: 80%;"><b>Other courses on Data science and Machine Learning at UiO</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs020.html#other-courses-on-data-science-and-machine-learning-at-uio-contn" style="font-size: 80%;"><b>Other courses on Data science and Machine Learning at UiO, contn</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs021.html#learning-outcomes" style="font-size: 80%;"><b>Learning outcomes</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs022.html#types-of-machine-learning" style="font-size: 80%;"><b>Types of Machine Learning</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs023.html#essential-elements-of-ml" style="font-size: 80%;"><b>Essential elements of ML</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs024.html#an-optimization-minimization-problem" style="font-size: 80%;"><b>An optimization/minimization problem</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs025.html#the-plethora-of-machine-learning-algorithms-methods" style="font-size: 80%;"><b>The plethora of machine learning algorithms/methods</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs026.html#what-is-generative-modeling" style="font-size: 80%;"><b>What Is Generative Modeling?</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs027.html#example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster-https-www-oreilly-com-library-view-generative-deep-learning-9781098134174-ch01-html" style="font-size: 80%;"><b>Example of generative modeling, "taken from Generative Deep Learning by David Foster":"https://www.oreilly.com/library/view/generative-deep-learning/9781098134174/ch01.html"</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs028.html#generative-versus-discriminative-modeling" style="font-size: 80%;"><b>Generative Versus Discriminative Modeling</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs029.html#example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster-https-www-oreilly-com-library-view-generative-deep-learning-9781098134174-ch01-html" style="font-size: 80%;"><b>Example of discriminative modeling, "taken from Generative Deep Learning by David Foster":"https://www.oreilly.com/library/view/generative-deep-learning/9781098134174/ch01.html"</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs030.html#discriminative-modeling" style="font-size: 80%;"><b>Discriminative Modeling</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs031.html#a-frequentist-approach-to-data-analysis" style="font-size: 80%;"><b>A Frequentist approach to data analysis</b></a></li>
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<!-- navigation toc: --> <li><a href="#what-is-a-good-model" style="font-size: 80%;"><b>What is a good model?</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs033.html#what-is-a-good-model-can-we-define-it" style="font-size: 80%;"><b>What is a good model? Can we define it?</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs034.html#software-and-needed-installations" style="font-size: 80%;"><b>Software and needed installations</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs035.html#python-installers" style="font-size: 80%;"><b>Python installers</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs036.html#useful-python-libraries" style="font-size: 80%;"><b>Useful Python libraries</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs037.html#installing-r-c-cython-or-julia" style="font-size: 80%;"><b>Installing R, C++, cython or Julia</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs038.html#installing-r-c-cython-numba-etc" style="font-size: 80%;"><b>Installing R, C++, cython, Numba etc</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs039.html#numpy-examples-and-important-matrix-and-vector-handling-packages" style="font-size: 80%;"><b>Numpy examples and Important Matrix and vector handling packages</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs040.html#numpy-and-arrays" style="font-size: 80%;"><b>Numpy and arrays</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs041.html#matrices-in-python" style="font-size: 80%;"><b>Matrices in Python</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs042.html#meet-the-pandas" style="font-size: 80%;"><b>Meet the Pandas</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs043.html#pandas-ai" style="font-size: 80%;"><b>Pandas AI</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs044.html#simple-linear-regression-model-using-scikit-learn" style="font-size: 80%;"> Simple linear regression model using <b>scikit-learn</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs044.html#to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies" style="font-size: 80%;"> To our real data: nuclear binding energies. Brief reminder on masses and binding energies</a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs044.html#organizing-our-data" style="font-size: 80%;"> Organizing our data</a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs044.html#and-what-about-using-neural-networks" style="font-size: 80%;"> And what about using neural networks?</a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs044.html#a-first-summary" style="font-size: 80%;"><b>A first summary</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs045.html#why-linear-regression-aka-ordinary-least-squares-and-family" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family)</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs046.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs047.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs048.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs049.html#general-linear-models-and-linear-algebra" style="font-size: 80%;"><b>General linear models and linear algebra</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs050.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs051.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs053.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs053.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs054.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs055.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs056.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs059.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs059.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs059.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs060.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs061.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs067.html#the-chi-2-function" style="font-size: 80%;"><b>The \( \chi^2 \) function</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs067.html#the-chi-2-function" style="font-size: 80%;"><b>The \( \chi^2 \) function</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs067.html#the-chi-2-function" style="font-size: 80%;"><b>The \( \chi^2 \) function</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs067.html#the-chi-2-function" style="font-size: 80%;"><b>The \( \chi^2 \) function</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs067.html#the-chi-2-function" style="font-size: 80%;"><b>The \( \chi^2 \) function</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs067.html#the-chi-2-function" style="font-size: 80%;"><b>The \( \chi^2 \) function</b></a></li>
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0032"></a>
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<!-- !split -->
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<h2 id="what-is-a-good-model" class="anchor">What is a good model? </h2>
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<p>In science and engineering we often end up in situations where we want to infer (or learn) a
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quantitative model \( M \) for a given set of sample points \( \boldsymbol{X} \in [x_1, x_2,\dots x_N] \).
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</p>
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<p>As we will see repeatedely in these lectures, we could try to fit these data points to a model given by a
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straight line, or if we wish to be more sophisticated to a more complex
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function.
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</p>
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<p>The reason for inferring such a model is that it
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serves many useful purposes. On the one hand, the model can reveal information
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encoded in the data or underlying mechanisms from which the data were generated. For instance, we could discover important
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corelations that relate interesting physics interpretations.
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</p>
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<p>In addition, it can simplify the representation of the given data set and help
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us in making predictions about future data samples.
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</p>
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<p>A first important consideration to keep in mind is that inferring the <em>correct</em> model
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for a given data set is an elusive, if not impossible, task. The fundamental difficulty
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is that if we are not specific about what we mean by a <em>correct</em> model, there
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could easily be many different models that fit the given data set <em>equally well</em>.
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