{ "cells": [ { "cell_type": "markdown", "id": "ce8ae0bf", "metadata": {}, "source": [ "# Linear regresion\n", "\n", "This is modeled after **Morten Hjorth-Jensen** \n", "\n", "Please see his lecture notes and get deeper into Machine Learning." ] }, { "cell_type": "markdown", "id": "afdac614", "metadata": {}, "source": [ "Linear regresion is a low level (or first step in) machine learning (ML), but all equations can be derived analytically and important concepts for ML can be introduced, such as, the choice of model, assumptions of error, cost function, regularizations, correlations, etc." ] }, { "cell_type": "markdown", "id": "a7a6a140", "metadata": {}, "source": [ "Some of the important concepts are:\n", "\n", "* **Data input and output**, which we will denote by $D$:\n", "\\begin{equation}\n", "D=\\{ (x_0,y_0),(x_1,y_1),...(x_{n-1},y_{n-1})\\}\n", "\\end{equation}\n", "Here $x_i$ is the input and $y_i$ is the onput. $x_i$ can be scalar or large vector of data. Similarly, $y_i$ might be a number, or, classification. \n", "\n", "Examples: i) credit card information for customers: $x_i$ is the amount of loan, the income, the marriage status, etc. The ouput is the prediction that the customer will default, i.e., true/false. ii) handwriting recognition: The input $x_i$ are the pixels of the image, the output is a number or a letter. iii) cancer data: The input $x_i$ are characteristics of the tumor such as its size, radius, smoothness, symmetry, fractal dimension, etc., the output is $M$=malignant, $B$=benign.\n", "\n", "\n", "* **Model**: basic assumption about the data to be fit. \n", "\n", "For linear regression we assume that the data can be fit with continuous function $\\widetilde{y}(x)$, which is deterministic, and the data has some extra random noise, normally distributed, i.e., \n", "\n", "$$y_i = \\widetilde{y}(x_i) + \\varepsilon_i$$\n", "\n", "where $\\widetilde{y}(x)$ can be expanded in terms of some continuous functions, and $\\varepsilon = \\eta N(0,\\sigma^2)$, where $\\eta$ is some small number, and $N$ is normal (gaussian) distribution with vanishing mean and width $\\sigma$.\n", "\n", "* **Cost function** (functional to be minimized):\n", "\n", "The simplest is the mean average error (MAE), which is equivalent to $\\chi^2$:\n", "\n", "$$C = \\frac{1}{n} \\sum_i (\\widetilde{y}(x_i)-y_i)^2$$\n", "\n", "but different cost functions, such as **Ridge** regression and **Lasso** regression are often used. \n", "\n", "The cross-entropy is used for binary models (discrete with two outcomes):\n", "\n", "$$C=\\sum_i y_i \\log(p(y_i=1|x_i))+(1-y_i) \\log(1-p(y_i=1|x_i))$$\n", "\n", "* **Covariance and Correlation matrix**:\n", "It meassures correlation between different features in data. It can be used to eliminate irrelevant parameters from the model or those that are almost linearly dependent.\n", "\n", "The **covariance** $cov(\\vec{x}_i,\\vec{x}_j)$ is defined for two vectors that have many components $\\vec{x}_i=x_{n,i}$ and $\\vec{x}_j=x_{n,j}$ and takes the form\n", "\\begin{eqnarray}\n", "&& cov(\\vec{x}_i,\\vec{x}_j)= \\frac{1}{n} \\sum_n (x_{n,i}-)(x_{n,j}-)\\\\\n", "&& =\\frac{1}{n}\\sum_n x_{n,i}\\\\\n", "\\end{eqnarray}\n", "\n", "The diagonal parts of the covariance is the variance, i.e., \n", "\\begin{eqnarray}\n", "cov(\\vec{x}_i,\\vec{x}_i) \\equiv \\sigma^2_i = \\frac{1}{n} \\sum_n (x_{n,i}-)^2,\n", "\\end{eqnarray}\n", "which can be \"taken out\" of covariance matrix to define correlation matrix. The matrix elements of the correlation matrix are simply given by\n", "\\begin{eqnarray}\n", "&& corr(\\vec{x}_i,\\vec{x}_j)= \\frac{cov(\\vec{x}_i,\\vec{x}_j)}{\\sqrt{cov(\\vec{x}_i,\\vec{x}_i)\\; cov(\\vec{x}_j,\\vec{x}_j)}}\\\\\n", "&& corr(\\vec{x}_i,\\vec{x}_j)=\\frac{1}{\\sigma_i \\sigma_j} \\frac{1}{n}\\sum_n (x_{n,i}-)(x_{n,j}-)\\\\\n", "\\end{eqnarray}" ] }, { "cell_type": "markdown", "id": "b64533e2", "metadata": {}, "source": [ "### Linear regression details\n", "\n", "In linear regression we try to represent the continuous function $\\widetilde{y}(x)$ as a linear superposition of known functions $g_j(x)$ with $j\\in[0,...p-1]$. We want to find the coefficients $\\beta_j$ of the linear superposition, i.e., \n", "\n", "\\begin{eqnarray}\n", "\\widetilde{y}(x_i) = \\sum_{j=0}^{p-1} g_j(x_i) \\beta_j\n", "\\end{eqnarray}\n", "\n", "The functions $g_j(x)$ can be a polynomial $g_j(x)=x^j$ or the Fourier components $g_j(x)=e^{2\\pi j x}$ or Legendre, Chebyshev polynomials, or any other complete set of functions." ] }, { "cell_type": "markdown", "id": "58401ff9", "metadata": {}, "source": [ "Next we define the **Design** matrix $\\mathbf{X}$, which is a rectangular matrix with $\\mathbb{R}^{n\\times p}$, where $n$ is the dimension of the input data components, and $p$ is the number of functions we will use in the expansion\n", "\n", "\\begin{equation}\n", "\\mathbf{X} =\n", "\\begin{bmatrix} g_0(x_0) & g_1(x_0) & \\cdots & g_{p-1}(x_0) \\\\\n", " g_0(x_1) & g_1(x_1) & \\cdots & g_{p-1}(x_1) \\\\\n", " \\cdots\\\\\n", " g_0(x_{n-1}) & g_1(x_{n-1}) &\\cdots & g_{p-1}(x_{n-1})\n", "\\end{bmatrix}\n", "\\end{equation}\n", "Normaly we expect $n0} U_{il} U^T_{lj} y_j.$$\n", "\n", "Note that $U U^T=1$, but the sum above runs only over components for which $\\sigma_l>0$, hence $\\sum'_l U_{il} U^T_{lj}$ above is a projection and not unity. Only if $X$ is a square non-singular matrix than $\\sum'_l U_{il} U^T_{lj}$ is unity and $\\widetilde{y}=y$.\n", "\n" ] }, { "cell_type": "markdown", "id": "22b41262", "metadata": {}, "source": [ "As mentioned above, different types of cost functions exist, which regularize the singularity of $\\mathbf{X}^T X$ in different ways. The most famous are **Ridge** regression and **Lasso** regression.\n", "\n", "In **Ridge** regression we add lagrange multiplayer $\\lambda$ such that $\\sum_j \\beta_j^2$ (or equivalently $||\\boldsymbol{\\beta}||_2^2$) does not explode. At the same time, it also regularizes the inverse, and hence allows one to avoid pseudo-inverse.\n", "\n", "The **Ridge** cost function is \n", "$$C(\\beta)=\\frac{1}{n} \\sum_{i=0}^{n-1} (y_i-\\widetilde{y}_i)^2 +\\lambda \\frac{1}{n}\\sum_{j=0}^{p-1}\\beta_j^2$$\n", "which is a constrained optimization that requires $||\\boldsymbol{\\beta}||_2^2$ to be as small as possible ($\\lambda>0$), hence the purpose of such regularization is to prohibit the parameters $\\beta$ to become too large. In ML we typically not optimize $C$ with respect to $\\lambda$, but we rather keep it is hyperparameter, which is another parameter of the model that allows one to tune the model to best describe the data.\n", "\n", "We can take the derivative of the cost function as before, to obtain\n", "\\begin{eqnarray}\n", "\\frac{\\partial C(\\beta)}{\\partial \\beta_l}=\\frac{1}{n}\\sum_i 2(y_i-X_{ij}\\beta_j)(-1)X_{il} +\\frac{2}{n}\\lambda \\beta_l= 2 \\frac{1}{n} (\\mathbf{X}^T(\\mathbf{X} \\boldsymbol{\\beta}-\\boldsymbol{y})+\\lambda \\boldsymbol{\\beta})_l\n", "\\end{eqnarray}\n", "which has a minimum at\n", "$$(\\mathbf{X}^T \\mathbf{X}+\\lambda) \\boldsymbol{\\beta}^*=\\mathbf{X}^T y$$\n", "or\n", "$$\\boldsymbol{\\beta}^*=(\\mathbf{X}^T \\mathbf{X}+\\lambda)^{-1}\\mathbf{X}^T y$$\n", "which clearly avoids singularity of the inverse $\\mathbf{X}^T \\mathbf{X}$ because $\\lambda>0$ and $\\mathbf{X}^T \\mathbf{X}$ is positive definite matrix.\n", "\n", "The parameter $\\lambda$ is also called shrinkage parameter, because it removes singular values which are small, i.e., removes less important degrees of freeedom.\n", "\n", "To see that, we use SVD decomposition of $\\mathbf{X}=U \\sigma V^T$ as before, and we see that $\\mathbf{X}^T \\mathbf{X}+\\lambda=V (\\sigma^2+\\lambda) V^T$, hence \n", "$$\\beta^*_{Ridge}=(\\mathbf{X}^T \\mathbf{X}+\\lambda)^{-1} \\mathbf{X}^T y=V \\frac{1}{\\sigma^2+\\lambda} V^T V\\sigma U^T y = V \\frac{\\sigma}{\\sigma^2+\\lambda} U^T y$$\n", "hence when compared to regular linear regression, Ridge regression replaces $$\\frac{1}{\\sigma}\\rightarrow \\frac{\\sigma}{\\sigma^2+\\lambda}$$\n", "which essentially removes singular values which are much smaller than $\\lambda$, i.e., we keep only singular values which are comparable or larger than $\\lambda$ in the final result, shrinking the set of parameters $\\beta$." ] }, { "cell_type": "markdown", "id": "298aeb2f", "metadata": {}, "source": [ "Another type of regression is called **Lasso** regression, which adds absolute values of parameters $\\beta$ to cost function, i.e., \n", "$$C(\\beta)=\\frac{1}{n} \\sum_{i=0}^{n-1} (y_i-\\widetilde{y}_i)^2 +\\lambda \\frac{1}{n}\\sum_{j=0}^{p-1}|\\beta_j|$$\n", "which gives derivative\n", "\\begin{eqnarray}\n", "\\frac{\\partial C(\\beta)}{\\partial \\beta_l}=\\frac{1}{n}\\sum_i 2(y_i-X_{ij}\\beta_j)(-1)X_{il} +\\frac{1}{n}\\lambda\\; \\mathrm{sign}(\\beta_l)= 2 \\frac{1}{n} (\\mathbf{X}^T(\\mathbf{X} \\boldsymbol{\\beta}-\\boldsymbol{y})+\\frac{\\lambda}{2} \\mathrm{sign}(\\boldsymbol{\\beta}))_l\n", "\\end{eqnarray}\n", "and requires one to solve\n", "\\begin{eqnarray}\n", "\\mathbf{X}^T \\mathbf{y}=\\mathbf{X}^T\\mathbf{X} \\boldsymbol{\\beta}^* + \\frac{\\lambda}{2} \\mathrm{sign}(\\boldsymbol{\\beta}^*)\n", "\\end{eqnarray}\n", "No close analytical solution for $\\beta^*$ exists for this equation, and only numerical solution can be found." ] }, { "cell_type": "markdown", "id": "2328a9eb", "metadata": {}, "source": [ "### Simple linear regression model using **scikit-learn**\n", "\n", "We start with comparing our linear regression results with those of **Scikit-Learn** library. \n", "\n", "To demonstrate capabilities, we will solve the problem of nuclear binding energies.\n", "\n", "\n", "A popular and physically intuitive model which can be used to parametrize \n", "the experimental binding energies of all nucleai in periodic table is the so-called \n", "**liquid drop model**. The ansatz is based on the following expression\n", "$$BE(N,Z) = a_0 + a_1 A-a_2 A^{2/3}-a_3\\frac{Z^2}{A^{1/3}}-a_4\\frac{(N-Z)^2}{A},$$\n", "where $A$ stands for the number of nucleons and the $a_i$s are parameters which are determined by a fit to the experimental data. \n", "\n", "To arrive at the above expression we have assumed that we can make the following assumptions:\n", "\n", " * There is a volume term $a_1A$ proportional with the number of nucleons (the energy is also an extensive quantity). When an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has a certain number of other nucleons in contact with it. This contribution is proportional to the volume.\n", "\n", " * There is a surface energy term $a_2A^{2/3}$. The assumption here is that a nucleon at the surface of a nucleus interacts with fewer other nucleons than one in the interior of the nucleus and hence its binding energy is less. This surface energy term takes that into account and is therefore negative and is proportional to the surface area.\n", "\n", " * There is a Coulomb energy term $a_3\\frac{Z^2}{A^{1/3}}$. The electric repulsion between each pair of protons in a nucleus yields less binding. \n", "\n", " * There is an asymmetry term $a_4\\frac{(N-Z)^2}{A}$. This term is associated with the Pauli exclusion principle and reflects the fact that the proton-neutron interaction is more attractive on the average than the neutron-neutron and proton-proton interactions.\n", "\n", "\n", "We will fit the binding energy $BE$ as a function of $A$ with functions \n", "$g_0(x)=1$, $g_1(x)=x$, $g_2(x)=x^{2/3}$, $g_3(x)=x^{-1/3}$, $g_4(x)=1/x$. \n", "\n", "The binding energies are in file \"NucleousEnergy.dat\".\n", "The Python code follows here." ] }, { "cell_type": "code", "execution_count": 6, "id": "c5ddca15", "metadata": {}, "outputs": [ { "data": { "image/png": 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ZP0auuBjlpyaoMM1lQvXAyESLxRDrCYb0Xnlvi8WSqVmakTfG3IIAC0tyxujmS8ee8XhPMKTNR5r13uFG+Tt7tLvaq/cON6miqV0VTe16+7RWxZIMl8ZnJikrOV6Lx6dr0fh0FvACLhL/C4qS3dU++QM9csfHaGqux+xygFEpxmHXwpI0LSxJCz/W2BrQoeNtOtzQqvcPN+tgvV+d3SEdOt6qQ8fbdOh4/+6UNFecZuR5NH9cmjLdTuWOSdDcwhRmdgHniWARJW8fapAkLRiXxsAxYBhJS3IqLcmpecWpuvWygvDjvs5ulR1qVJ2vUwfrW/X6R/U61tyhxrYuvbnvuN7cdzx87JjEWM0tTFFBqktzClN0WVGKMtxOZqUAZ0GwiIK/fVitX71+UJK0eHy6ydUAOB/J8bFaMjU7fP9HN0vejm4daWjT+4ebtONYi3wd3dpd7VNTW5fW7a2XJP3ft3tX03XG2DUxy62FJWkqTndp7JgEzStOZRE8jHoRBYuenh7df//9+tOf/qTa2lrl5OTojjvu0L/+67/Kbh+dzYRvHTiue57aLkm6YkK6Pjc33+SKAFwoT0KsZub3DvDs0xMMaevRZh2ob9XB+la9e6hR++r8CvSEtLPKq51V3vCxSc4YLSpJ05TcZM0tTNXcohSCBkadiILFz372M/3mN7/RH/7wB02dOlVbtmzRnXfeKY/Ho29961uDVeOwZBiGbDab/lRWIUm65dJc/cfnLqUbBLCYGIdd88elaf64k+M2Aj1B1bR0antlszYfaVadt1O7q32q9XXqtT11em1PnSQp1mFTVnK8xmUk6coJ6ZqSk6zM5HiNS3exiigsK6Jg8e677+rmm2/WjTfeKEkqKirS008/rS1btgxKccPVz9d8pD9vOaZf3T5Lb+zrbR792pUlhApglHDGOFSU7lJRukt/NytPUu/KuzuOtWjb0Wbtrvbp7YMNqvcHdKy5Q8eaO7Rx/8kxGxlupxaPT1dRmktTcpM1rzhVngQ2YIM1RBQsFi9erN/85jfav3+/Jk6cqA8++ECbNm3SL37xiwFfEwgEFAgEwvd9Pt8FFztcvLCjWsf9Ad35+GZ19YQ0ITNJl+S4zS4LgInsdptmF6RodkHvSruGYaiqpUO13k59cMyrTQeOq7K5Q1XNHTruD+i57VXh19psUkpinHLHxOuaSZlaMC5NOZ54Faa5+IMFI05EweJ73/uevF6vJk+eLIfDoWAwqAceeEC33377gK8pLS3Vj370o4sudKjV+Tr1zOZK3T6vQBluZ/jxzu6gqlo6JEkd3UFJ0i2zxjI6HEA/NptNeSmJyktJ1NyiVP3j4mJJvd0o75U36YPKFh1tate2o80qb2hTU1uXmtq6tKvKp1+90TsYfExirBYUp6kgLVHjM5J0xcR05XgSzPxYwMeKKFg888wzevLJJ/XUU09p6tSp2rFjh1auXKnc3FwtX778rK9ZtWqV7rvvvvB9n8+n/PzhP8DxdxvL9dimw2rvCur7SyeHHz/S2KbT1yr91MzcIa4OwEjljHHoyokZunJiRvixprYu1fs7tbfGp7V76rS/rlVVzR1qae/Wq7tr+70+xm5TYpyjd9xHcaqS42M1PitJM8Z6WGsDw0JEweK73/2uvv/97+u2226TJE2fPl1Hjx5VaWnpgMHC6XTK6XSe9bnh7GB9qyRpT03/rpvyE4vpzMjz6PpLsjQmMZZ9CABclFRXnFJdcZqcnRwes9EdDOmDyhZtr2hRjbdTOyqbtaOyRT0hQ77OHq3dU6e1JwaJSr0zUjLcTmUkOTWnKEX5KYly2KWpuR5NyUlmsCiGTETBor29/YxppQ6HQ6FQaIBXjFwVTe2SpAN1/n6Plx/vDRwlGUn65nUThrwuAKNDrMOuuUWpmlt0cr+htkCPWgM9qvcF9Oa+eu2v88vX2aMdFc3ydfY+d7ihTe8faer3b7mdMUpOiFVWslOX5CQr1RUnlzNGU3KSNS7DpbgYu9Jc7AqL6IgoWNx000164IEHVFBQoKlTp2r79u166KGH9OUvf3mw6jNFTzCkyhPBosbbKW9Hd3jEdl+Lxbh0Ni8CMLRczhi5nDHKSo7X9LyTWwcEQ4YOHW9VS3u3jjS2acuRJjW3d6ujK6htFc3yB3rkD/SoqqVD2ypazvpvu+NjNLsgRWlJcUpPcmpytluFaS5lup3KcDtZjwPnLaJg8atf/Uo/+MEP9I1vfEP19fXKzc3V17/+df3bv/3bYNVniuqWTvWcskPigTp/+K+GQye2aR6XkWRKbQBwOofdpolZvTPT5hWn9luor6snpIqmNvk7e1TZ3KF9tT61dvaoqb1bH1S2qNbbqe5QSP7OHm04ZUrs6dzxvV0tl+aP0V1XlYTfDzhdRMHC7XbrF7/4xTmnl1rBkca2fvf3nQgWhmGEu0LGZdBiAWD4i4uxa3xmbwiYVZAinWWweU8wpL01fu2s8srX2a1ab6f21PhU4+1QvS+gQE9v8PB39qj8eJue3ValBeNSdeOMXH1qZi5rcKAf9go5i6MnukH6HKjrDRMNrV3yd/bIZpOK6QoBYBExDrum53n6da/0MQxD/kCPjvsDqmru0NPvV+iVXbUqK29SWXmTfvrSXi2dlq1F49N17eRMpbriTPgEGE4IFmdx9ER3R6orTk1tXdpX2zuAs6+1IteTQH8jgFHBZrMpOT5WyfGxKslI0pUTM1TZ1K5XdtXof7Ye0/66Vj27vUrPbq9SXIxdy6bn6KpJGVowLk1ZyfFmlw8TECzO4khjb4vFdZMz9Zetx7Svzq91e+r0RNlRSXSDABjd8lMT9bUrS/TVK8bp/cNNenPfcW3Yf1x7a3zhkGG3SZ+Ylq1Pz8rTZSxZPqoQLM6ioqm3xeK6S7L0P9uOqamtS1954uR+KAtO2YwIAEYrm80W3qDte5+YpB2VLXrxg2ptOdKsnVVevbyzVi/vrJXdJl0+Pl03Ts/RpGy3LslJptXXwggWpwmFDB090WJxSY5bU3KStbvap5TEWN0ya6z+19RszS9O/Zh/BQBGF5vNplkFKb0DRCV9VOvTk2VH9c7BRpU3tOmtAw1660CDpN7FvG6amauFJWmampusEmbZWYrNME5foHpw+Xw+eTweeb1eJScnD+Vbn5cab4cWlr4hh92mj378CdV6O7W/zq/Lx6eTsAHgAhxtbNNz26tUVt6og/Wtamjt6vf85Gy3bpiSpcnZybqsKEWZjM0Yls73+j2qWywCPUH98d2jumJChiZl907HOnxiAay8lATFOuzKT01kyW4AuAiFaS6tvH6ipN5W4bLDjfrbhzX6qManXVU+fVTr10e1J1c5viQnWZOyknRJTrJumJLFukEjzKgOFhv3N+gnL+3VgnF1Wv21hZKkHcdaJElTc4dfawoAjHR2u02LStK1qCRdkuRt79Yru2q0vaJFu2u82lXl096a3tvzO6pV+spHSnPFaVyGSwtL0rV4fLpKMlxKdcWxq/QwNaqDRUNrQJK0q8qnUMiQ3W7TjhPL3V6aP8a8wgBglPAkxuq2eQW6bV6BJOm4P6AtR5p0uLFNZeVNeudggxrbutTY1qXNR5r1n68fkCTleuJ1+fh0FaW7lJeSoEUl6cpwj7wNL61oVAeLtkCPJKk10KNjzR3KT03QjsoWSdKl+SkmVgYAo1OG26ml03MkSd+4uvf/pw83tGl3tVfr9x3XB5UtqvZ2qtrbqb9sPdbvtYVpiSpITdSs/DGaPy5NBamJyvbEK5bt5IfUqA4WrSeChdS7PXqMw6Z6f0AOu03Tx565Ah0AYGi5nDGaNtajaWM9uvWy3laN9q4ebT7SrC1HmlTr7dTe2t6xGkcb23W0sb139skbByVJ8bF2zS1M1aRst/JTEnRZcaouyWYb+cE0qoNF2ynBYm+NT6ETE2QmZbmVEMcMEAAYjhLjYnTVxAxdNTEj/Fhja0AH6lt16Hirysqb9OGx3g3WOrtD2nSwQZsONoSPdcfHqCQjSdPHejSvOFXF6S4VpCUqOZ5FvKJhVAeL1kAw/PveGp86unvvX1owxqSKAAAXIi3JqbQkpxaMS9Pn5xdK6t3nZH9dq94/0qTKpnYdqPPrvcNN8nf2aEdli3ZUtuiPJ1ZUttmkS7KTNX2sRwVpiZpdkKI5hSmKi6EbJVKjPFic0mJR61NLe7ckBm4CgBXYbDZNynaHlxOQereRP9zQpgP1fm050qztlS2qau5QQ2tAe2p82lPjCx8bF2PXuHSXpuQka05RikoykpSXkqCxYxKYkXIOozpYnNoVUtnUoeqWTknS7AIGbgKAFcXF2MNhY9mMk1vI1/s79f7hJh2q7w0dZeWNamjtCq+x8ez2qvCxWclOzcpPUWFaombmj9HlJenyJNKN0mdUB4tTWywkKRgy9KmZuRqfyWIsADCaZLrj+wUNwzBU2dShA/V+fXDMq+0VzTrW3KFjze2q8wX06u7a8LE2mzR2TIImZ7t1WVGqpuZ6VJiWqLyU0dmyMaqDRV+LhTPGrkBPSCUZLpV+errJVQEAzGaz2VSQlqiCtERdd0lW+PHO7qC2VTRrX61f5cfb9O6JZcp7Q0eH1u2tDx+bnRyvhSVpKslwadpYjxaMSxsVW0MQLCStvH6idla16J+WTJLLOapPCQDgHOJjHf1WDpWkprYuHaxv1YfHWnq7U463qrKpQ7W+Tj13ShdKQqxDk7LdmpiVpLlFqVo8Pl25YxLM+BiDalRvQjb3J+vU0BrQy9+8QlNYwhsAECWd3UFtPtKkDypbVH68Te8calStr/OM42bmeXT1pExdOTFDcwqH9/g+NiE7D30tFkm0UgAAoig+1qErJmToigm9a20YhqGD9a06UN+qXVVelZU3antliz445tUHx7z65esH9INlU/SPi4tNrvzijdorajBkhNetcDmt3+cFADCPzWbThCy3JmS59ckTS5Yf9we0bm+d3vyoXq/tqdPPXv1IcQ6bHn3rsKaNTVbp380YkbNNRu3KH6fOCGFcBQBgqGW4nbp9XoF++8U5umpihrp6QvrBC7tV0dSul3fW6qaHN+m98kazy4zYqA0Wfd0gsQ6bnKysBgAwic1m04Ofma7k+N4/cj87J0/5qQmqaGrXrb8r01ef2KLy460mV3n+Ru2f6n3BwuWMGZXzjAEAw0eOJ0EvffMKtbR3a3qeRy3tXfo/r+3T0+9Xau2e3u6SuUUpSnLGqLM7JGeMXTfPGqtPTM0edsuOj9pg0dcV4oobtacAADCM5KcmKj+19/cxiXH6yS3TdceiIj34ykdat7deZeVN/Y5//aN6pSc5dfu8fP3D/ALleIbH1NVRe1VtO7EBGTNCAADD1fhMt/57+WXaecyr8oZWtXcFFR9r1+GGdq1+v0L1/oB+9cZB/df6Q5pfnKruYEj1/oDWrLzStMW4Ru1VNdxiwYwQAMAwNz3Po+l5nn6P3XvteL22u05PvHtE7x1u0juHTg70bGgNKC8lcajLlDSKg8WpYywAABhpYh123TgjRzfOyNH+Or82H2lSSmKcMtxOpSc5Tatr1F5V27pYHAsAYA0Ts9yamOX++AOHwPAaSjqE/J0ECwAAom3UBgu6QgAAiL5RHyxosQAAIHpGbbBoDfTtE0KwAAAgWiIKFkVFRbLZbGfcVqxYMVj1RcX2imYdrO+/HOrJFgummwIAEC0R/bm+efNmBYPB8P1du3bphhtu0Gc/+9moFxYt3vZufe637yo9yal3V10XfrxvVggtFgAARE9EV9WMjIx+9x988EGVlJToqquuimpR0dTU3qXuoKEab6e6gyHFOnobaVoZvAkAQNRd8FW1q6tLTz75pO67775zbuIVCAQUCATC930+34W+5QXp6gmdfO+ObqWdWDSkryvETbAAACBqLnjw5vPPP6+Wlhbdcccd5zyutLRUHo8nfMvPz7/Qt7wg3cGTwcLb0R3+vbWTFgsAAKLtgoPFY489pqVLlyo3N/ecx61atUperzd8q6ysvNC3vCCBU1ssToQJia4QAAAGwwVdVY8ePap169bp2Wef/dhjnU6nnE7z1iw/tSukr8XCMAy1dbG7KQAA0XZBLRaPP/64MjMzdeONN0a7nqjrCvYfYyFJnd0hBUOGJCkpnmABAEC0RBwsQqGQHn/8cS1fvlwxMcP/ony2FouG1t7BpHExdrniWMcCAIBoiThYrFu3ThUVFfryl788GPVE3amDN32d/YNFRpLznDNaAABAZCJucliyZIkMwxiMWgbF2VssuiRJaUlxptQEAIBVWX6vkP7rWPTOBOlrsUhPMm9QKQAAVmT5YBE4W1eIvy9Y0GIBAEA0WT5YdPecOSuEFgsAAAaH5YPF2aab9o2xIFgAABBd1g8WZxm8ebyvxcJNsAAAIJpGVbDoW9K7sZUxFgAADAbrB4vTNiEzDCPcFZJBVwgAAFFl/WBxSotFMGTI29Ed7hJhjAUAANFl/WBxSouFJJU3tEmSYuw2eRJizSgJAADLsn6w6OkfLA7Vt0rqXXXTbmc5bwAAomnUBYu+Fgu6QQAAiL5RFyz6WiwIFgAARJ/lg0X3AGMs2IAMAIDos3ywOGPw5vHeFgummgIAEH2WDxaBE10hKYm9M0BCJ3Z8pysEAIDos3yw6BtjkXHa8t15KQlmlAMAgKVZPlj0jbFIdZ0cU3Ht5ExdPyXLrJIAALAsyweLvhaLKyZkyBXn0O3z8vXbL85RrMPyHx0AgCEXY3YBg61v8OaCcam666r/JQeLYgEAMGgs/2d7X4tFnMNBqAAAYJCNnmARY/mPCgCA6Sx/te3rCol10FoBAMBgs36woMUCAIAhY+mrrWEY4RYLggUAAIPP0lfbnpAh48RKm06Hw9xiAAAYBSwdLE7d2TQ2hjEWAAAMNksHi1N3No1jQSwAAAadpa+2fS0WdpsUQ7AAAGDQWfpqG2BGCAAAQ8rSV9zwjBBaKwAAGBKWvuJ2M9UUAIAhZekr7sl9Qiz9MQEAGDYsfcVl1U0AAIZWxFfcqqoqfeELX1BaWpoSExN16aWXauvWrYNR20UjWAAAMLRiIjm4ublZl19+ua655hq98soryszM1KFDhzRmzJhBKu/iBMIbkBEsAAAYChEFi5/97GfKz8/X448/Hn6sqKgo2jVFTTctFgAADKmIrrgvvvii5s6dq89+9rPKzMzUrFmz9Oijj57zNYFAQD6fr99tqDDdFACAoRXRFbe8vFyPPPKIJkyYoDVr1uiuu+7SN7/5TT3xxBMDvqa0tFQejyd8y8/Pv+iizxdjLAAAGFoRXXFDoZBmz56tn/70p5o1a5a+/vWv66tf/aoeeeSRAV+zatUqeb3e8K2ysvKiiz5fTDcFAGBoRXTFzcnJ0ZQpU/o9dskll6iiomLA1zidTiUnJ/e7DZUuFsgCAGBIRXTFvfzyy7Vv375+j+3fv1+FhYVRLSpa6AoBAGBoRXTF/fa3v62ysjL99Kc/1cGDB/XUU0/pd7/7nVasWDFY9V0UBm8CADC0IrriXnbZZXruuef09NNPa9q0afrxj3+sX/ziF/r85z8/WPVdFFosAAAYWhGtYyFJy5Yt07JlywajlqjrCxYskAUAwNCw9BW3b3dTJy0WAAAMCUtfcekKAQBgaFn6isvgTQAAhpalr7iBvjEWtFgAADAkLH3FZeVNAACGlqWvuN2svAkAwJCy9BWXwZsAAAwtS19xGbwJAMDQsvQVlxYLAACGlqWvuAzeBABgaFn6itvZTYsFAABDybJXXMMwVN3SIUnKHRNvcjUAAIwOlg0WTW1d8gd6ZLNJeSmJZpcDAMCoYLlgUe/rVEdXUEca2yVJuZ4Excc6TK4KAIDRIeJt04ezen+n5v30deWnJujb10+UJBWm0VoBAMBQsVSLxe4qnySpsqlDO6u8kqTCNJeZJQEAMKpYKlh4EmPDv7/0YY0kqYgWCwAAhoylgkUoZIR/r/cHJNEVAgDAULJWsDDOfIyuEAAAho7FgsWZyYIWCwAAho6lg0Wm26nEOEtNfAEAYFizVrAI9b9fRDcIAABDylrB4rQWC7pBAAAYWpbqJ+gLFmMSY7V4fLq+duU4kysCAGB0sWSwKEhN1MP/MNvkagAAGH2s1RVyYoyF3WYztxAAAEYpawWLEy0WdnIFAACmsFiw6P1JiwUAAOawWLDoa7EgWAAAYAZrBgtLfSoAAEYOS12C6QoBAMBclgoWBl0hAACYylLBIniiyYJcAQCAOSIKFvfff79sNlu/W3Z29mDVFrG+rhAH800BADBFxCtvTp06VevWrQvfdzgcUS3oYjArBAAAc0UcLGJiYoZVK8WpDBbIAgDAVBGPsThw4IByc3NVXFys2267TeXl5ec8PhAIyOfz9bsNluCJJb1ttFgAAGCKiILF/Pnz9cQTT2jNmjV69NFHVVtbq0WLFqmxsXHA15SWlsrj8YRv+fn5F130QPq6QhwECwAATBFRsFi6dKk+85nPaPr06br++uv10ksvSZL+8Ic/DPiaVatWyev1hm+VlZUXV/E5GCyQBQCAqS5q23SXy6Xp06frwIEDAx7jdDrldDov5m3OW9+sELpCAAAwx0X9bR8IBLR3717l5OREq56L0reOBbNCAAAwR0TB4p/+6Z+0YcMGHT58WO+9957+/u//Xj6fT8uXLx+s+iJycoyFyYUAADBKRdQVcuzYMd1+++1qaGhQRkaGFixYoLKyMhUWFg5WfREx2CsEAABTRRQsVq9ePVh1REXQ6FvSm2ABAIAZLDV/ItwVYqlPBQDAyGGpSzBdIQAAmMtSwSIUoisEAAAzWSpYBNkrBAAAU1kqWLBtOgAA5rJUsDDYNh0AAFNZKliEwtNNTS4EAIBRylLBom/bdFosAAAwh6WChRFex4JgAQCAGSwVLOgKAQDAXBYLFr0/6QoBAMAclgoWJ7dNN7kQAABGKUsFi/AYC1osAAAwhaWCRV9XCEt6AwBgDosFCxbIAgDATBYNFiYXAgDAKGWtYNG3QBbJAgAAU1grWNAVAgCAqSwVLNg2HQAAc1kqWBgskAUAgKksFSzCXSE0WQAAYAqLBYven+QKAADMYa1gEWLwJgAAZrJWsKArBAAAU1kzWJArAAAwhcWCRe9PukIAADCHtYIF26YDAGAqawULVt4EAMBUFgsWvT8JFgAAmMNiwaJvVojJhQAAMEpZ6hJMVwgAAOayVrDo2zadYAEAgCmsFSxosQAAwFQXFSxKS0tls9m0cuXKKJVzcQz2CgEAwFQXHCw2b96s3/3ud5oxY0Y067kowRPJwkaLBQAAprigYNHa2qrPf/7zevTRR5WSkhLtmi5YX1eIgyYLAABMcUHBYsWKFbrxxht1/fXXf+yxgUBAPp+v322wsG06AADmion0BatXr9a2bdu0efPm8zq+tLRUP/rRjyIu7EKwbToAAOaKqMWisrJS3/rWt/Tkk08qPj7+vF6zatUqeb3e8K2ysvKCCj0fofAYi0F7CwAAcA4RtVhs3bpV9fX1mjNnTvixYDCojRs36uGHH1YgEJDD4ej3GqfTKafTGZ1qP0ZfVwhjLAAAMEdEweK6667Tzp07+z125513avLkyfre9753RqgYagbrWAAAYKqIgoXb7da0adP6PeZyuZSWlnbG42YIhugKAQDATJZcedNBsgAAwBQRzwo53fr166NQRnSEV95kjAUAAKawZIsFuQIAAHNYKliwpDcAAOayVLDo2zadMRYAAJjDUsGC6aYAAJjLUsGib4EscgUAAOawVLAI0mIBAICpLBUsDLZNBwDAVJYKFmybDgCAuSwWLJhuCgCAmSwVLPr2CqHFAgAAc1gqWBhsmw4AgKksFSxCzAoBAMBUlgoWbJsOAIC5LBUswrubkiwAADCFpYJFiHUsAAAwlSWDBQ0WAACYwzLBwjCMUxbIIlkAAGAGCwWLk7+zbToAAOawTLAInZIsaLEAAMAcFgoWJ3+3WeZTAQAwsljmEkyLBQAA5rNksGCMBQAA5rBQsDj5O7kCAABzWChY0BUCAIDZrBMsQqcGCxMLAQBgFLNOsDh1HQuSBQAAprBQsDiZLGx0hQAAYArLBQsaKwAAMI91gkWo9ycDNwEAMI91gkVfiwVNFgAAmMZ6wYJcAQCAaSwTLAy2TAcAwHSWCRbBUF+LBcECAACzRBQsHnnkEc2YMUPJyclKTk7WwoUL9corrwxWbRGhKwQAAPNFFCzy8vL04IMPasuWLdqyZYuuvfZa3Xzzzdq9e/dg1Xfe+hbIYvAmAADmiYnk4Jtuuqnf/QceeECPPPKIysrKNHXq1KgWFqmTLRYECwAAzBJRsDhVMBjUX/7yF7W1tWnhwoUDHhcIBBQIBML3fT7fhb7lOREsAAAwX8SDN3fu3KmkpCQ5nU7dddddeu655zRlypQBjy8tLZXH4wnf8vPzL6rggZxcIGtQ/nkAAHAeIg4WkyZN0o4dO1RWVqa7775by5cv1549ewY8ftWqVfJ6veFbZWXlRRU8EFosAAAwX8RdIXFxcRo/frwkae7cudq8ebN++ctf6re//e1Zj3c6nXI6nRdX5XlgVggAAOa76HUsDMPoN4bCLMwKAQDAfBG1WPzzP/+zli5dqvz8fPn9fq1evVrr16/Xq6++Olj1nTe6QgAAMF9EwaKurk5f/OIXVVNTI4/HoxkzZujVV1/VDTfcMFj1nTeDrhAAAEwXUbB47LHHBquOixZk23QAAExnmb1C2DYdAADzWS9YkCsAADCNZYIF26YDAGA+ywSLvm3TbQQLAABMY5lg0dcV4rDMJwIAYOSxzGWYrhAAAMxnmWDR12JBVwgAAOaxTLDoG2PBrBAAAMxjmWDRt1eIgxYLAABMY5lgYbBXCAAAprNMsAiGx1iYXAgAAKOYZYJFuCuEQRYAAJjGMsGCrhAAAMxnmWARoisEAADTWSZYsG06AADms0ywOLmkN8ECAACzWCZYGGybDgCA6SwTLPpmhbCkNwAA5rFMsGBJbwAAzGeZYGEwxgIAANNZJljQFQIAgPksFCxYIAsAALNZJlgwxgIAAPNZJlgYbJsOAIDpLBMsTi7pTbAAAMAsFgoWvT/pCgEAwDwWChYM3gQAwGzWCRZ9gzdpsgAAwDTWCRZ0hQAAYDrLBIsgXSEAAJjOMsGC3U0BADCfZYJFePAmyQIAANNYKFj0/qQrBAAA80QULEpLS3XZZZfJ7XYrMzNTt9xyi/bt2zdYtUUkxJLeAACYLqJgsWHDBq1YsUJlZWVau3atenp6tGTJErW1tQ1WfeeNrhAAAMwXE8nBr776ar/7jz/+uDIzM7V161ZdeeWVUS0sUnSFAABgvoiCxem8Xq8kKTU1dcBjAoGAAoFA+L7P57uYtxxQiFkhAACY7oIHbxqGofvuu0+LFy/WtGnTBjyutLRUHo8nfMvPz7/Qtzynk2MsSBYAAJjlgoPFPffcow8//FBPP/30OY9btWqVvF5v+FZZWXmhb3lOdIUAAGC+C+oKuffee/Xiiy9q48aNysvLO+exTqdTTqfzgoqLBJuQAQBgvoiChWEYuvfee/Xcc89p/fr1Ki4uHqy6IsZeIQAAmC+iYLFixQo99dRTeuGFF+R2u1VbWytJ8ng8SkhIGJQCzxe7mwIAYL6Ixlg88sgj8nq9uvrqq5WTkxO+PfPMM4NV33mjKwQAAPNF3BUyXNEVAgCA+SyzV4hBiwUAAKazTLAInggW5AoAAMxjmWDR1xXioC8EAADTWChY0BUCAIDZrBMs2DYdAADTWSdYhMdYkCwAADCLhYJF70/GWAAAYB7LBAuDbdMBADCdZYJFMERXCAAAZrNMsAh3hRAsAAAwjYWCRd8mZCYXAgDAKGaZy7AR3iuEFgsAAMximWDBGAsAAMxnmWDR1xXCGAsAAMxjmWBhsG06AACms0ywYOVNAADMZ5lgEWSBLAAATGeZYMGS3gAAmM8ywcJg23QAAExnmWBxcoyFyYUAADCKWSZYBEO9P2mxAADAPJYJFn1dIYyxAADAPJYJFnSFAABgPssEi74lvekKAQDAPJYJFmxCBgCA+SwTLMJ7hVjmEwEAMPJY5jLct0AWS3oDAGAeywQLxlgAAGA+ywQLg23TAQAwnWWCxcmuEHPrAABgNLNQsKArBAAAs8WYXUC03Hl5sVoD3Up3x5ldCgAAo5ZlgsXdV5eYXQIAAKNexF0hGzdu1E033aTc3FzZbDY9//zzg1AWAAAYiSIOFm1tbZo5c6YefvjhwagHAACMYBF3hSxdulRLly4djFoAAMAIN+hjLAKBgAKBQPi+z+cb7LcEAAAmGfTppqWlpfJ4POFbfn7+YL8lAAAwyaAHi1WrVsnr9YZvlZWVg/2WAADAJIPeFeJ0OuV0Ogf7bQAAwDBgmZU3AQCA+SJusWhtbdXBgwfD9w8fPqwdO3YoNTVVBQUFUS0OAACMLBEHiy1btuiaa64J37/vvvskScuXL9fvf//7qBUGAABGnoiDxdVXXx3eohwAAOBUjLEAAABRQ7AAAABRM+S7m/Z1o7ACJwAAI0ffdfvjhkMMebDw+/2SxAqcAACMQH6/Xx6PZ8DnbcYQj8QMhUKqrq6W2+2WzWaL6LU+n0/5+fmqrKxUcnLyIFU4unBOo49zGn2c0+jifEbfaDinhmHI7/crNzdXdvvAIymGvMXCbrcrLy/vov6N5ORky/6HMwvnNPo4p9HHOY0uzmf0Wf2cnqulog+DNwEAQNQQLAAAQNSMqGDhdDr1wx/+kE3NoohzGn2c0+jjnEYX5zP6OKcnDfngTQAAYF0jqsUCAAAMbwQLAAAQNQQLAAAQNQQLAAAQNSMqWPzXf/2XiouLFR8frzlz5uitt94yu6QR4f7775fNZut3y87ODj9vGIbuv/9+5ebmKiEhQVdffbV2795tYsXDz8aNG3XTTTcpNzdXNptNzz//fL/nz+ccBgIB3XvvvUpPT5fL5dKnPvUpHTt2bAg/xfDycef0jjvuOON7u2DBgn7HcE5PKi0t1WWXXSa3263MzEzdcsst2rdvX79j+J5G5nzOKd/TM42YYPHMM89o5cqV+pd/+Rdt375dV1xxhZYuXaqKigqzSxsRpk6dqpqamvBt586d4ef+/d//XQ899JAefvhhbd68WdnZ2brhhhvC+7pAamtr08yZM/Xwww+f9fnzOYcrV67Uc889p9WrV2vTpk1qbW3VsmXLFAwGh+pjDCsfd04l6ROf+ES/7+3LL7/c73nO6UkbNmzQihUrVFZWprVr16qnp0dLlixRW1tb+Bi+p5E5n3Mq8T09gzFCzJs3z7jrrrv6PTZ58mTj+9//vkkVjRw//OEPjZkzZ571uVAoZGRnZxsPPvhg+LHOzk7D4/EYv/nNb4aowpFFkvHcc8+F75/POWxpaTFiY2ON1atXh4+pqqoy7Ha78eqrrw5Z7cPV6efUMAxj+fLlxs033zzgazin51ZfX29IMjZs2GAYBt/TaDj9nBoG39OzGREtFl1dXdq6dauWLFnS7/ElS5bonXfeMamqkeXAgQPKzc1VcXGxbrvtNpWXl0uSDh8+rNra2n7n1ul06qqrruLcnqfzOYdbt25Vd3d3v2Nyc3M1bdo0zvM5rF+/XpmZmZo4caK++tWvqr6+Pvwc5/TcvF6vJCk1NVUS39NoOP2c9uF72t+ICBYNDQ0KBoPKysrq93hWVpZqa2tNqmrkmD9/vp544gmtWbNGjz76qGpra7Vo0SI1NjaGzx/n9sKdzzmsra1VXFycUlJSBjwG/S1dulR/+tOf9MYbb+g//uM/tHnzZl177bUKBAKSOKfnYhiG7rvvPi1evFjTpk2TxPf0Yp3tnEp8T89myHc3vRinb7NuGEbEW6+PRkuXLg3/Pn36dC1cuFAlJSX6wx/+EB5kxLm9eBdyDjnPA7v11lvDv0+bNk1z585VYWGhXnrpJX36058e8HWcU+mee+7Rhx9+qE2bNp3xHN/TCzPQOeV7eqYR0WKRnp4uh8NxRrqrr68/I33j47lcLk2fPl0HDhwIzw7h3F648zmH2dnZ6urqUnNz84DH4NxycnJUWFioAwcOSOKcDuTee+/Viy++qDfffFN5eXnhx/meXriBzunZ8D0dIcEiLi5Oc+bM0dq1a/s9vnbtWi1atMikqkauQCCgvXv3KicnR8XFxcrOzu53bru6urRhwwbO7Xk6n3M4Z84cxcbG9jumpqZGu3bt4jyfp8bGRlVWVionJ0cS5/R0hmHonnvu0bPPPqs33nhDxcXF/Z7nexq5jzunZ8P3VCNnVsjq1auN2NhY47HHHjP27NljrFy50nC5XMaRI0fMLm3Y+853vmOsX7/eKC8vN8rKyoxly5YZbrc7fO4efPBBw+PxGM8++6yxc+dO4/bbbzdycnIMn89ncuXDh9/vN7Zv325s377dkGQ89NBDxvbt242jR48ahnF+5/Cuu+4y8vLyjHXr1hnbtm0zrr32WmPmzJlGT0+PWR/LVOc6p36/3/jOd75jvPPOO8bhw4eNN99801i4cKExduxYzukA7r77bsPj8Rjr1683ampqwrf29vbwMXxPI/Nx55Tv6dmNmGBhGIbx61//2igsLDTi4uKM2bNn95vyg4HdeuutRk5OjhEbG2vk5uYan/70p43du3eHnw+FQsYPf/hDIzs723A6ncaVV15p7Ny508SKh58333zTkHTGbfny5YZhnN857OjoMO655x4jNTXVSEhIMJYtW2ZUVFSY8GmGh3Od0/b2dmPJkiVGRkaGERsbaxQUFBjLly8/43xxTk8627mUZDz++OPhY/ieRubjzinf07Nj23QAABA1I2KMBQAAGBkIFgAAIGoIFgAAIGoIFgAAIGoIFgAAIGoIFgAAIGoIFgAAIGoIFgAAIGoIFgAAIGoIFgAAIGoIFgAAIGoIFgAAIGr+HxbaAIx4ohOAAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Binding energy in terms of nucleous weight A==x, is in this file\n", "from numpy import *\n", "from pylab import *\n", "\n", "na_data = loadtxt('NucleousEnergy.dat').T\n", "x,y = na_data\n", "plot(x,y)\n", "show()" ] }, { "cell_type": "code", "execution_count": 7, "id": "f4f5f696", "metadata": {}, "outputs": [], "source": [ "# Seeting up the Design matrix\n", "X=zeros((len(x),5))\n", "X[:,0]=1 # all functions we need\n", "X[:,1]=x\n", "X[:,2]=x**(2/3)\n", "X[:,3]=x**(-1/3)\n", "X[:,4]=1./x" ] }, { "cell_type": "code", "execution_count": 8, "id": "02e41e58", "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import LinearRegression\n", "\n", "# Using scikit to get coefficients\n", "lg = LinearRegression()\n", "clf=lg.fit(X,y)\n", "yt=clf.predict(X) # widetilde(y)" ] }, { "cell_type": "markdown", "id": "e18116a7", "metadata": {}, "source": [ "This is an equivalent code, but using our own equations derived above." ] }, { "cell_type": "code", "execution_count": 9, "id": "7b10dfe7", "metadata": {}, "outputs": [], "source": [ "# matrix inversion to find beta\n", "Beta = dot(linalg.inv(X.T @ X) @ X.T, y)\n", "# and then make the prediction\n", "ytilde = X @ Beta" ] }, { "cell_type": "code", "execution_count": 10, "id": "a63e7159", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# comparing the regression with data and our regression with those from the library \n", "\n", "plot(x,yt,label='Regression library')\n", "plot(x,y, label='Data')\n", "plot(x,ytilde,label='Regression ours')\n", "xlabel('A')\n", "ylabel('Binding Energy')\n", "legend(loc='best')\n", "show()" ] }, { "cell_type": "code", "execution_count": 11, "id": "6786b653", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The intercept alpha: \n", " 5.294399745619717\n", "Coefficient beta : \n", " [ 0.00000000e+00 -2.96611194e-02 2.01719003e-01 1.08078025e+01\n", " -4.03097597e+01]\n", "Our coefficients: \n", " [ 5.29439975e+00 -2.96611194e-02 2.01719003e-01 1.08078025e+01\n", " -4.03097597e+01]\n", "Mean squared error: 0.02\n", "Variance score: 0.95\n", "Mean squared log error: 0.00\n", "Mean absolute error: 0.05\n" ] } ], "source": [ "from sklearn.metrics import mean_squared_error, r2_score, mean_squared_log_error, mean_absolute_error\n", "\n", "# more information from library\n", "print('The intercept alpha: \\n', lg.intercept_)\n", "print('Coefficient beta : \\n', lg.coef_)\n", "print('Our coefficients: \\n', Beta)\n", "# The mean squared error \n", "print(\"Mean squared error: %.2f\" % mean_squared_error(y, yt))\n", "# Explained variance score: 1 is perfect prediction \n", "print('Variance score: %.2f' % r2_score(y, yt))\n", "# Mean squared log error \n", "print('Mean squared log error: %.2f' % mean_squared_log_error(y, yt) )\n", "# Mean absolute error \n", "print('Mean absolute error: %.2f' % mean_absolute_error(y, yt))" ] }, { "cell_type": "markdown", "id": "01a28cfd", "metadata": {}, "source": [ "The function **meansquarederror** gives us the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as\n", "$$\n", "MSE(\\boldsymbol{y},\\boldsymbol{\\tilde{y}}) = \\frac{1}{n}\n", "\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2,\n", "$$\n", "This function is equivalent to the $\\chi^2$ function defined above.\n", "\n", "Another quantity is the mean absolute error (MAE), a risk metric corresponding to the expected value of the absolute error loss using $l1$-norm. \n", "The MAE is defined as follows\n", "$$\n", "\\text{MAE}(\\boldsymbol{y}, \\boldsymbol{\\tilde{y}}) = \\frac{1}{n} \\sum_{i=0}^{n-1} \\left| y_i - \\tilde{y}_i \\right|.\n", "$$\n", "We present the \n", "squared logarithmic (quadratic) error\n", "$$\n", "\\text{MSLE}(\\boldsymbol{y}, \\boldsymbol{\\tilde{y}}) = \\frac{1}{n} \\sum_{i=0}^{n - 1} (\\log_e (1 + y_i) - \\log_e (1 + \\tilde{y}_i) )^2,\n", "$$\n", "where $\\log_e (x)$ stands for the natural logarithm of $x$. This error\n", "estimate is best to use when targets having exponential growth, such\n", "as population counts, average sales of a commodity over a span of\n", "years etc. \n", "\n", "Finally, another cost function is the Huber cost function used in robust regression.\n", "\n", "The rationale behind this possible cost function is its reduced\n", "sensitivity to outliers in the data set. In our discussions on\n", "dimensionality reduction and normalization of data we will meet other\n", "ways of dealing with outliers." ] }, { "cell_type": "markdown", "id": "a30c6b20", "metadata": {}, "source": [ "### Libraries\n", "\n", "A useful Python package for data analysics is\n", "[pandas](https://pandas.pydata.org/), which is an open source library\n", "providing high-performance data structures and data\n", "analysis tools for Python. **pandas** stands for panel data, a term borrowed from econometrics.\n", "\n", "**pandas** has two major classes, the **DataFrame** class with two-dimensional data objects and the class **Series** with a focus on one-dimensional data objects. Both classes allow you to index data easily as we will see in the examples below. \n", "\n", "**pandas** allows you also to perform mathematical operations on the data, spanning from simple reshapings of vectors and matrices to statistical operations. \n", "\n", "The following simple example shows how we can make tables of our data. Here we define a data set which includes names, place of birth and date of birth, and displays the data in an easy to read way. " ] }, { "cell_type": "code", "execution_count": 10, "id": "f3cd97da", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " First Name Last Name Place of birth Date of Birth T.A.\n", "0 Frodo Baggins Shire 2968\n", "1 Bilbo Baggins Shire 2890\n", "2 Aragorn II Elessar Eriador 2931\n", "3 Samwise Gamgee Shire 2980" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Standard Python print: {'First Name': ['Frodo', 'Bilbo', 'Aragorn II', 'Samwise'], 'Last Name': ['Baggins', 'Baggins', 'Elessar', 'Gamgee'], 'Place of birth': ['Shire', 'Shire', 'Eriador', 'Shire'], 'Date of Birth T.A.': [2968, 2890, 2931, 2980]}\n" ] } ], "source": [ "import pandas as pd\n", "from IPython.display import display\n", "data = {'First Name': [\"Frodo\", \"Bilbo\", \"Aragorn II\", \"Samwise\"],\n", " 'Last Name': [\"Baggins\", \"Baggins\",\"Elessar\",\"Gamgee\"],\n", " 'Place of birth': [\"Shire\", \"Shire\", \"Eriador\", \"Shire\"],\n", " 'Date of Birth T.A.': [2968, 2890, 2931, 2980]\n", " }\n", "data_pandas = pd.DataFrame(data)\n", "display(data_pandas)\n", "\n", "print('Standard Python print:', data)" ] }, { "cell_type": "markdown", "id": "27e035e2", "metadata": {}, "source": [ "In the above we have imported **pandas** with the shorthand **pd**, the latter has become the standard way we import **pandas**. We make then a list of various variables\n", "and reorganize the aboves lists into a **DataFrame** and then print out a neat table with specific column labels as *Name*, *place of birth* and *date of birth*.\n", "Displaying these results, we see that the indices are given by the default numbers from zero to three.\n", "**pandas** is extremely flexible and we can easily change the above indices by defining a new type of indexing as" ] }, { "cell_type": "code", "execution_count": 11, "id": "a8d70b1f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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First NameLast NamePlace of birthDate of Birth T.A.
FrodoFrodoBagginsShire2968
BilboBilboBagginsShire2890
AragornAragorn IIElessarEriador2931
SamSamwiseGamgeeShire2980
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" ], "text/plain": [ " First Name Last Name Place of birth Date of Birth T.A.\n", "Frodo Frodo Baggins Shire 2968\n", "Bilbo Bilbo Baggins Shire 2890\n", "Aragorn Aragorn II Elessar Eriador 2931\n", "Sam Samwise Gamgee Shire 2980" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data_pandas = pd.DataFrame(data,index=['Frodo','Bilbo','Aragorn','Sam'])\n", "display(data_pandas)" ] }, { "cell_type": "markdown", "id": "f7cdb130", "metadata": {}, "source": [ "Thereafter we display the content of the row which begins with the index **Aragorn**" ] }, { "cell_type": "code", "execution_count": 12, "id": "cbaffca2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "First Name Aragorn II\n", "Last Name Elessar\n", "Place of birth Eriador\n", "Date of Birth T.A. 2931\n", "Name: Aragorn, dtype: object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(data_pandas.loc['Aragorn'])" ] }, { "cell_type": "markdown", "id": "fcb03cf4", "metadata": {}, "source": [ "We can easily append data to this, for example" ] }, { "cell_type": "code", "execution_count": 13, "id": "1c562ef3", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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First NameLast NamePlace of birthDate of Birth T.A.
FrodoFrodoBagginsShire2968
BilboBilboBagginsShire2890
AragornAragorn IIElessarEriador2931
SamSamwiseGamgeeShire2980
PippinPeregrinTookShire2990
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" ], "text/plain": [ " First Name Last Name Place of birth Date of Birth T.A.\n", "Frodo Frodo Baggins Shire 2968\n", "Bilbo Bilbo Baggins Shire 2890\n", "Aragorn Aragorn II Elessar Eriador 2931\n", "Sam Samwise Gamgee Shire 2980\n", "Pippin Peregrin Took Shire 2990" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "new_hobbit = {'First Name': [\"Peregrin\"],\n", " 'Last Name': [\"Took\"],\n", " 'Place of birth': [\"Shire\"],\n", " 'Date of Birth T.A.': [2990]\n", " }\n", "#data_pandas=data_pandas.append(pd.DataFrame(new_hobbit, index=['Pippin']))\n", "\n", "data_pandas=pd.concat([data_pandas,pd.DataFrame(new_hobbit, index=['Pippin'])])\n", "display(data_pandas)" ] }, { "cell_type": "markdown", "id": "9b213af1", "metadata": {}, "source": [ "Here are other examples where we use the **DataFrame** functionality to handle arrays, now with more interesting features for us, namely numbers. We set up a matrix \n", "of dimensionality $10\\times 5$ and compute the mean value and standard deviation of each column. Similarly, we can perform mathematical operations like squaring the matrix elements and many other operations." ] }, { "cell_type": "code", "execution_count": 14, "id": "5f3c1a2a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " 0 1 2 3 4\n", "0 -1.749765 0.342680 1.153036 -0.252436 0.981321\n", "1 0.514219 0.221180 -1.070043 -0.189496 0.255001\n", "2 -0.458027 0.435163 -0.583595 0.816847 0.672721\n", "3 -0.104411 -0.531280 1.029733 -0.438136 -1.118318\n", "4 1.618982 1.541605 -0.251879 -0.842436 0.184519\n", "5 0.937082 0.731000 1.361556 -0.326238 0.055676\n", "6 0.222400 -1.443217 -0.756352 0.816454 0.750445\n", "7 -0.455947 1.189622 -1.690617 -1.356399 -1.232435\n", "8 -0.544439 -0.668172 0.007315 -0.612939 1.299748\n", "9 -1.733096 -0.983310 0.357508 -1.613579 1.470714" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "0 -0.175300\n", "1 0.083527\n", "2 -0.044334\n", "3 -0.399836\n", "4 0.331939\n", "dtype: float64\n", "our mean= [-0.1753003003007798, 0.08352721390288316, -0.044333972284362075, -0.39983564919591685, 0.33193916850842475]\n", "0 1.069584\n", "1 0.965548\n", "2 1.018232\n", "3 0.793167\n", "4 0.918992\n", "dtype: float64\n", "our sigma= [1.069584393754908, 0.9655479229776867, 1.0182315502230195, 0.7931668855918225, 0.918992356527374]\n" ] } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "from IPython.display import display\n", "np.random.seed(100) # some arbitrary random seed to always start the same\n", "# setting up a 10 x 5 matrix\n", "rows = 10\n", "cols = 5\n", "a = np.random.randn(rows,cols) # normal distributed random numbers (10x5)\n", "df = pd.DataFrame(a) # df is now panda DataFrame\n", "display(df)\n", "print(df.mean()) # easy to get mean of each column\n", "\n", "our_mean = [sum(a[:,i])/rows for i in range(cols)]\n", "print('our mean=', our_mean)\n", "\n", "print(df.std()) # easy to get standard deviation\n", "# Note that we have to use 1/(rows-1), which is more precise than 1/rows!\n", "our_s = [ np.sqrt(sum((a[:,i]-our_mean[i])**2)/(rows-1)) for i in range(cols)]\n", "print('our sigma=', our_s)\n" ] }, { "cell_type": "markdown", "id": "79ad31db", "metadata": {}, "source": [ "Thereafter we can select specific columns only and plot final results" ] }, { "cell_type": "code", "execution_count": 15, "id": "6017207f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " First Second Third Fourth Fifth\n", "1 -1.749765 0.342680 1.153036 -0.252436 0.981321\n", "2 0.514219 0.221180 -1.070043 -0.189496 0.255001\n", "3 -0.458027 0.435163 -0.583595 0.816847 0.672721\n", "4 -0.104411 -0.531280 1.029733 -0.438136 -1.118318\n", "5 1.618982 1.541605 -0.251879 -0.842436 0.184519\n", "6 0.937082 0.731000 1.361556 -0.326238 0.055676\n", "7 0.222400 -1.443217 -0.756352 0.816454 0.750445\n", "8 -0.455947 1.189622 -1.690617 -1.356399 -1.232435\n", "9 -0.544439 -0.668172 0.007315 -0.612939 1.299748\n", "10 -1.733096 -0.983310 0.357508 -1.613579 1.470714" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "= 0.08352721390288316\n", "\n", "Int64Index: 10 entries, 1 to 10\n", "Data columns (total 5 columns):\n", " # Column Non-Null Count Dtype \n", "--- ------ -------------- ----- \n", " 0 First 10 non-null float64\n", " 1 Second 10 non-null float64\n", " 2 Third 10 non-null float64\n", " 3 Fourth 10 non-null float64\n", " 4 Fifth 10 non-null float64\n", "dtypes: float64(5)\n", "memory usage: 480.0 bytes\n", "Info of DataFrame= None\n", " First Second Third Fourth Fifth\n", "count 10.000000 10.000000 10.000000 10.000000 10.000000\n", "mean -0.175300 0.083527 -0.044334 -0.399836 0.331939\n", "std 1.069584 0.965548 1.018232 0.793167 0.918992\n", "min -1.749765 -1.443217 -1.690617 -1.613579 -1.232435\n", "25% -0.522836 -0.633949 -0.713163 -0.785061 0.087887\n", "50% -0.280179 0.281930 -0.122282 -0.382187 0.463861\n", "75% 0.441264 0.657041 0.861676 -0.205231 0.923602\n", "max 1.618982 1.541605 1.361556 0.816847 1.470714\n" ] } ], "source": [ "df.columns = ['First', 'Second', 'Third', 'Fourth', 'Fifth']\n", "df.index = np.arange(1,11)\n", "\n", "display(df)\n", "print('=', df['Second'].mean() )\n", "print('Info of DataFrame=', df.info())\n", "print(df.describe())" ] }, { "cell_type": "code", "execution_count": 16, "id": "f7613111", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pylab import plt, mpl\n", "mpl.rcParams['font.family'] = 'serif'\n", "\n", "#usual type plotting \n", "plt.plot(df.cumsum(), lw=2.0)\n", "\n", "#using pandas makes it easier\n", "df.cumsum().plot(lw=2.0, figsize=(10,6))\n", "plt.show()\n", "\n", "#using bars\n", "df.plot.bar(figsize=(10,6), rot=15)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "74aa2423", "metadata": {}, "source": [ "Example of a nice print of $4\\times 4$ matrix" ] }, { "cell_type": "code", "execution_count": 17, "id": "d4eebb54", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0 1 2 3]\n", " [ 4 5 6 7]\n", " [ 8 9 10 11]\n", " [12 13 14 15]]\n", " 0 1 2 3\n", "0 0 1 2 3\n", "1 4 5 6 7\n", "2 8 9 10 11\n", "3 12 13 14 15\n" ] } ], "source": [ "b = np.arange(16).reshape((4,4))\n", "print(b)\n", "df1 = pd.DataFrame(b)\n", "print(df1)" ] }, { "cell_type": "markdown", "id": "4373d4e0", "metadata": {}, "source": [ "and many other operations. \n", "\n", "The **Series** class is another important class included in\n", "**pandas**. You can view it as a specialization of **DataFrame** but where\n", "we have just a single column of data. It shares many of the same features as _DataFrame. As with **DataFrame**,\n", "most operations are vectorized, achieving thereby a high performance when dealing with computations of arrays, in particular labeled arrays.\n", "As we will see below it leads also to a very concice code close to the mathematical operations we may be interested in.\n", "For multidimensional arrays, we recommend strongly [xarray](http://xarray.pydata.org/en/stable/). **xarray** has much of the same flexibility as **pandas**, but allows for the extension to higher dimensions than two. " ] }, { "cell_type": "code", "execution_count": null, "id": "least-remedy", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 5 }