Morten Hjorth-Jensen
419 lines
28 KiB
HTML
419 lines
28 KiB
HTML
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('And what about using neural networks?',
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('Why Linear Regression (aka Ordinary Least Squares and family)',
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('The code', 2, None, 'the-code'),
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('Splitting our Data in Training and Test data',
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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#textbooks" style="font-size: 80%;"><b>Textbooks</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs011.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-bs012.html#prerequisites" style="font-size: 80%;"><b>Prerequisites</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs013.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-bs014.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-bs015.html#machine-learning" style="font-size: 80%;"><b>Machine Learning</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs016.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-bs017.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-bs018.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-bs019.html#learning-outcomes" style="font-size: 80%;"><b>Learning outcomes</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs020.html#introduction" style="font-size: 80%;"><b>Introduction</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs021.html#ai-ml-and-some-statements-you-may-have-heard-and-what-do-they-mean" style="font-size: 80%;"><b>AI/ML and some statements you may have heard (and what do they mean?)</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs022.html#what-is-machine-learning" style="font-size: 80%;"><b>What is Machine Learning?</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs023.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-bs024.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-bs025.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-bs026.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="._week34-bs027.html#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-bs028.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-bs029.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-bs030.html#python-installers" style="font-size: 80%;"><b>Python installers</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs031.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-bs032.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-bs033.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="#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-bs035.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-bs036.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-bs037.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-bs038.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-bs038.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-bs038.html#organizing-our-data" style="font-size: 80%;"> Organizing our data</a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs038.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-bs038.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-bs039.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-bs040.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-bs041.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-bs042.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs043.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-bs044.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-bs045.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-bs047.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-bs047.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-bs048.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-bs049.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-bs050.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-bs054.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-bs054.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-bs053.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs054.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-bs055.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-bs056.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-bs062.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-bs062.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-bs062.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-bs062.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-bs062.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-bs062.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-bs063.html#fitting-an-equation-of-state-for-dense-nuclear-matter" style="font-size: 80%;"><b>Fitting an Equation of State for Dense Nuclear Matter</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs064.html#the-code" style="font-size: 80%;"><b>The code</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs065.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs066.html#exercises" style="font-size: 80%;"><b>Exercises</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs066.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs066.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
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<!-- navigation toc: --> <li><a href="._week34-bs066.html#exercise-3-split-data-in-test-and-training-data" style="font-size: 80%;"><b>Exercise 3: Split data in test and training data</b></a></li>
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</li>
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0034"></a>
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<!-- !split -->
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<h2 id="numpy-examples-and-important-matrix-and-vector-handling-packages" class="anchor">Numpy examples and Important Matrix and vector handling packages </h2>
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<p>There are several central software libraries for linear algebra and eigenvalue problems. Several of the more
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popular ones have been wrapped into ofter software packages like those from the widely used text <b>Numerical Recipes</b>. The original source codes in many of the available packages are often taken from the widely used
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software package LAPACK, which follows two other popular packages
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developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly here.
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</p>
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<ul>
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<li> LINPACK: package for linear equations and least square problems.</li>
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<li> LAPACK:package for solving symmetric, unsymmetric and generalized eigenvalue problems. From LAPACK's website <a href="http://www.netlib.org" target="_self"><tt>http://www.netlib.org</tt></a> it is possible to download for free all source codes from this library. Both C/C++ and Fortran versions are available.</li>
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<li> BLAS (I, II and III): (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. Blas I is vector operations, II vector-matrix operations and III matrix-matrix operations. Highly parallelized and efficient codes, all available for download from <a href="http://www.netlib.org" target="_self"><tt>http://www.netlib.org</tt></a>.</li>
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</ul>
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