{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\"Open" ] }, { "cell_type": "markdown", "metadata": { "id": "2fNa3bQYIowo" }, "source": [ "# Machine learning\n", "\n", "$$\n", "\\newcommand{\\eg}{{\\it e.g.}}\n", "\\newcommand{\\ie}{{\\it i.e.}}\n", "\\newcommand{\\argmin}{\\operatornamewithlimits{argmin}}\n", "\\newcommand{\\mc}{\\mathcal}\n", "\\newcommand{\\mb}{\\mathbb}\n", "\\newcommand{\\mf}{\\mathbf}\n", "\\newcommand{\\minimize}{{\\text{minimize}}}\n", "\\newcommand{\\diag}{{\\text{diag}}}\n", "\\newcommand{\\cond}{{\\text{cond}}}\n", "\\newcommand{\\rank}{{\\text{rank }}}\n", "\\newcommand{\\range}{{\\mathcal{R}}}\n", "\\newcommand{\\null}{{\\mathcal{N}}}\n", "\\newcommand{\\tr}{{\\text{trace}}}\n", "\\newcommand{\\dom}{{\\text{dom}}}\n", "\\newcommand{\\dist}{{\\text{dist}}}\n", "\\newcommand{\\R}{\\mathbf{R}}\n", "\\newcommand{\\SM}{\\mathbf{S}}\n", "\\newcommand{\\ball}{\\mathcal{B}}\n", "\\newcommand{\\bmat}[1]{\\begin{bmatrix}#1\\end{bmatrix}}\n", "\\newcommand{\\loss}{\\ell}\n", "\\newcommand{\\eloss}{\\mc{L}}\n", "\\newcommand{\\abs}[1]{| #1 |}\n", "\\newcommand{\\norm}[1]{\\| #1 \\|}\n", "\\newcommand{\\tp}{T}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "id": "nvFGLD8OI15C" }, "source": [ "__
ASE3001: Computational Experiments for Aerospace Engineering, Inha University.
__\n", "_
Jong-Han Kim (jonghank@inha.ac.kr)
_" ] }, { "cell_type": "markdown", "metadata": { "id": "H8UEOJKKe8Es" }, "source": [ "\n", "
\n", "\n", "---\n", "\n", "\n", "## Supervised learning\n", "\n", "- 입력벡터 $x\\in\\R^d$와 출력값 $y\\in\\R$가 대략적으로 아래와 같은 관계를 갖는다고 하자.\n", "\n", "$$\n", "y \\approx f(x)\n", "$$\n", "\n", "- 입력벡터 $x$를 _independent variable_ 또는 _feature vector_ 라고 부른다.\n", "\n", "- 출력값 $y$는 _outcome_, _response_, _target_, _label_, 또는 _dependent variable_ 이라 부른다. 보통 $y$가 머신러닝 모델을 통해 예측하고자 하는 값이 된다.\n", "\n", "- 실제로는 $x$와 $y$ 사이의 정확한 관계는 알 수 없는 경우가 대부분이다.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "TJtJBVlrfSfa" }, "source": [ "
\n", "\n", "## Features\n", "\n", "머신러닝 모델의 입력 벡터 $x$는 입력 데이타의 특징들을 수치화한 벡터이다.:\n", "\n", "_문서 데이타:_\n", "\n", "- 문서의 경우, 정해진 사전에 포함된 단어들 각각에 대해 해당 문서에 나타나는 빈도를 수치화한 _word count histogram_ 을 feature vector로 사용할 수 있다.\n", "\n", "_환자 데이타:_\n", "\n", "- 환자의 개인정보 및 검사결과 등을 수치화하여 feature vector로 사용할 수 있다.\n", "\n", "_고객 데이타:_\n", "\n", "- 고객 각각의 물품 구매이력과 고객의 개인정보 등을 수치화하여 feature vector로 활용할 수 있다." ] }, { "cell_type": "markdown", "metadata": { "id": "PqArZnGUIowq" }, "source": [ "
\n", "\n", "### Where features come from\n", "\n", "- 이미지, 비디오, 오디오, 문서 등, 입력에 사용되는 실제 데이타(수치화되지 않았을 수도 있음)를 $u$라고 부르자.\n", "\n", "- 실제 데이타와 피처 벡터는 $x = \\phi(u)$와 같은 관계로 정의하며, 이 함수 $\\phi$를 _embedding_ 또는 _feature function_ 이라 한다.\n", "\n", "- 임베딩 함수 $\\phi$는 단순할 수도 있으며 매우 복잡할 수도 있다.\n", "\n", "- 마찬가지로 출력에 대해서도 수치화되지 않은 실제 데이타 $v$와 모델 출력값 $y$의 관계를 $y=\\psi(v)$와 같은 임베딩 함수로 표현한다.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "-iG1X19TgsrL" }, "source": [ "
\n", "\n", "### Data and prior knowledge\n", "\n", "- 짝지어진 $n$쌍의 데이타 세트를 $x^{(t)},\\dots,x^{(n)} \\in \\R^d$와 $y^{(1)},\\dots,y^{(n)} \\in \\R$로 표현하자.\n", "\n", "- $(x^{(i)},y^{(i)})$는 $i$번째 _data pair_ , _observation_ , _example_ 라고 할 수 있다.\n", "\n", "- 데이타 또는 데이타간의 관계에 대한 사전 정보(_prior knowledge_)가 활용될 수도 있다. 예를 들어 관계 함수 $f$가 연속적인 함수인지, 또는 출력 $y$가 항상 양수인지 등의 사전정보를 활용하면 머신러닝 예측 성능을 개선할 수도 있다.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "Lm-sDORNiDSH" }, "source": [ "
\n", "\n", "## Predictor\n", "\n", "- 예측기(_predictor_) 또는 모델(_model_)을 $g:\\R^d \\rightarrow \\R$와 같이 정의한다.\n", "\n", "- 예측기는 피처 벡터 $x$로부터 출력 $y$를 예측해내는 역할을 하며, 예측기의 출력값을 $\\hat{y}$로 표현한다. 즉, $\\hat{y} = g(x)$로 표현한다.\n", "\n", "- 주어진 데이타와 사전지식을 활용하여 예측기 $g$가 주어진 데이타를 잘 설명하도록 $g$를 정하는 일을 머신러닝 모델을 학습한다고 한다.\n", "\n", "- 수치화되지 않았던 날것의 데이타들로는 아래와 같은 관계로 설명할 수 있다.\n", "\n", "$$\n", "\\hat v = \\psi^{-1}\\left(g\\left(\\phi(u)\\right)\\right)\n", "$$\n", "\n", "- 예측치 $\\hat y^{(i)}$와 실제 출력값 $y^{(i)}$가 가깝다면, 즉 $\\hat y^{(i)} \\approx y^{(i)}$라면, 예측기가 $i$번째 데이타를 잘 설명한다고 할 수 있다.\n", "\n", "- 그러나 실제로 머신러닝 문제의 목표는 학습 과정에서 보지 못했던 데이타에 대해서도 $\\hat y \\approx y$를 잘 만족하도록 하는 모델을 설계하는 것이다.\n", "\n", "
\n", "\n", "\n", "
\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "fQq8nou8jkAr" }, "source": [ "
\n", "\n", "### Information flow\n", "\n", "
\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": { "id": "Rs3upnYRjvxs" }, "source": [ "\n", "
\n", "\n", "\n", "---\n", "\n", "## Linear predictor\n", "\n", "- 아래와 같이 피처 벡터 $x$에 대한 선형함수로 표현되는 선형 예측기가 널리 사용된다.\n", "\n", "$$\n", " g(x) = \\theta^T x\n", "$$\n", "여기서 벡터 $\\theta\\in \\R^d$는 예측기를 표현하는 파라미터로, _predictor parameter vector_ 라고 한다.\n", "\n", "- 이와 같은 모델을 _regression model_ 이라고도 부른다.\n", "\n", "- $x_j$는 $j$번째 피처 성분을 믜미하며, 예측기의 출력값은 피처들의 선형 조합으로 표현된다.\n", "\n", "$$\n", "\\hat y = g(x) = \\theta_1 x_1 + \\cdots + \\theta_d x_d\n", "$$\n", "\n", "- 이제, 예측기 설계 문제는 주어진 데이타를 가장 잘 설명하는 예측기 파라미터 벡터 $\\theta \\in \\R^d$를 고르는 문제가 된다.\n", "\n", "- 예측기가 $\\theta$로 설명되므로, $g_\\theta(x)$로 표현하기도 한다.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "hRA7EtGBL8qX" }, "source": [ "\n", "
\n", "\n", "### Interpreting a linear predictor\n", "\n", "$$\n", "\\hat y = g(x) = \\theta_1 x_1 + \\cdots + \\theta_d x_d\n", "$$\n", "\n", "- 예를 들어, $\\theta_3$는 세 번째 피처 $x_3$의 증가에 따라 예측값 $\\hat y = g(x)$가 증가하는 비율로 이해할 수 있다.\n", "\n", "- 예를 들어, $\\theta_7=0$은 일곱번째 피처가 예측값에 아무런 영향을 주지 못한다는 의미가 된다.\n", "\n", "- $\\theta$의 크기가 작다는 것은 예측기가 $x$의 변화에 민감하지 않다는 뜻이 된다:\n", "\n", "$$\n", "|g(x)-g(\\tilde x)| = \\left| \\theta^T x - \\theta^T \\tilde x \\right|\n", "= \\left| \\theta^T (x - \\tilde x) \\right| \\leq \\|\\theta \\|\\; \\|x-\\tilde x\\|\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "id": "kqYTPWBfNcJ7" }, "source": [ "\n", "
\n", "\n", "### Affine predictor\n", "\n", "- 만약 우리가 첫번째 피처 $x_1$을 상수 1로 지정했다고 하면, 선형 예측기는 나머지 피처 $x_{2:d}$에 대한 _affine function_ 이 된다.\n", "\n", "$$\n", "g(x) = \\theta ^T x = \\theta_1 + \\theta_2 x_2 + \\cdots+ \\theta_dx_d\n", "$$\n", "\n", "- 이 때, 첫번째 파라미터 $\\theta_1$를 예측기의 _offset_ 또는 _constant term_ 이라고 부른다. 이 파라미터는 나머지 모든 피처가 0일 때의 예측값을 의미하기도 한다.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "toZ9MrCjSmqF" }, "source": [ "
\n", "\n", "---\n", "\n", "## Empirical risk minimization\n" ] }, { "cell_type": "markdown", "metadata": { "id": "8ZtScBu5N8xO" }, "source": [ "
\n", "\n", "### Loss function\n", "\n", "- 예측 모델의 정확도를 표현하기 위해, 다음과 같이 _loss function_ 또는 _risk function_, $\\loss:\\R \\times \\R \\to \\R$ 정의하여 $\\hat y$와 $y$의 차이를 정량화한다.\n", "\n", "- 여기서 $\\loss(\\hat y, y)$는 예측값 $\\hat y$가 얼마나 실제 출력값 $y$와 가까운지를 표현한다.\n", "\n", "- 통상적으로 모든 $\\hat y$, $y$에 대해 $\\loss(y,y)=0$ 이며$\\loss(\\hat y,y)\\geq 0$이다.\n", "\n", "
\n", "\n", "**Examples**\n", "\n", "- _quadratic loss_:\n", "\n", "$$\\loss(\\hat y, y) = (\\hat y - y)^2$$\n", "\n", "- _absolute loss_:\n", "\n", "$$\\loss(\\hat y,y)=|\\hat y-y|$$\n", "\n", "- _fractional error_: for $\\hat y, y >0$,\n", "\n", "$$\n", " \\loss(\\hat y, y) = \\max\\left\\{\\frac{\\hat y}{y}-1, \\frac{y}{\\hat y}-1\\right\\}\n", " = \\exp \\left(\\abs{\\log \\hat y - \\log y} \\right) -1\n", "$$\n", "(100을 곱해 퍼센트 오차로 표현하기도 한다.)\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "q7qPjWinSthO" }, "source": [ "
\n", "\n", "### Empirical risk\n", "\n", "예측기 $g$가 모든 데이타 $(x^{(i)},y^{(i)})$, $i=1, \\ldots, n$에 대해 좋은 성능을 갖는 것이 바람직하므로, 아래와 같이 모든 데이타들에 대한 평균 loss 값으로 정의되는 _empirical risk_ 를 정의한다.\n", "\n", "$$\n", "\\eloss = \\frac{1}{n} \\sum_{i=1}^n \\loss \\left( \\hat y^{(i)} , y^{(i)} \\right)\n", "= \\frac{1}{n} \\sum_{i=1}^n \\loss \\left( g(x^{(i)}) , y^{(i)}\\right)\n", "$$\n", "\n", "- 만약 $\\eloss$가 작다면 주어진 데이타 세트에 대해 예측기의 성능이 좋다고 할 수 있다.\n", "\n", "- 예측기가 파라미터 $\\theta$로 표현되는 경우, 아래와 같이 구체적으로 표현할 수 있다.\n", "\n", "$$\n", "\\eloss(\\theta) = \\frac{1}{n} \\sum_{i=1}^n \\loss \\left( g_\\theta(x^{(i)}) , y^{(i)}\\right)\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "id": "5jRanTkfUMv0" }, "source": [ "
\n", "\n", "### Mean square error\n", "\n", "- 제곱 함수로 표현되는 손실함수 $\\loss (\\hat y, y) = (\\hat y-y)^2$가 적용되는 경우, empirical risk는 _mean-square error_ (MSE)가 된다.\n", "\n", "$$\n", " \\eloss = \\text{MSE} = \\frac{1}{n} \\sum_{i=1}^n \\left(g(x^{(i)})- y^{(i)}\\right)^2\n", "$$\n", "\n", "- 이 값에 제곱근을 취해 root-mean-square error,\n", "$\\text{RMSE} = \\sqrt{\\text{MSE}}$, 출력 $y^{(i)}$와 같은 단위를 갖는 값으로 예측기 평균 오차를 표현하기도 한다.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "wAA7hSSUU0T6" }, "source": [ "
\n", "\n", "### Mean absolute error\n", "\n", "- 절댓값으로 표현되는 손실함수 $\\loss (\\hat y, y) = |\\hat y-y|$가 적용되면, empirical risk는 _mean-absolute error_ 가 된다.\n", "\n", "$$\n", " \\eloss = \\frac{1}{n} \\sum_{i=1}^n |g(x^i)- y^i|\n", "$$\n", "\n", "- 이 경우는 이 자체가 출력 $y^i$와 동일한 단위를 갖는다.\n", "- 이는 위에서 정의한 mean-square error와 유사해 보이지만 많은 면에서 그렇지 않다.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "0u-eDVg_VHYN" }, "source": [ "
\n", "\n", "### Empirical risk minimization\n", "\n", "how do we pick our prediction rule $g$?\n", "\n", "- 예측기 $g_\\theta(x)$의 파라미터 $\\theta$를 결정하는 것을 예측기를 데이타에 _fitting_ 한다고 부른다.\n", "\n", "- 일반적으로 empirical risk $\\eloss(\\theta)$를 최소화하도록 예측기를 fiting하며, 이를 _empirical risk minimization (ERM)_ 이라 부른다. 즉, ERM은 $\\eloss(\\theta)$를 최소화하는 $\\theta$를 찾는 작업이다.\n", "\n", "- 즉, ERM을 통해 주어진 데이타를 가장 잘 설명할 수 있는 $\\theta$를 정할 수 있다.\n", "\n", "- 선형 예측기 $g_\\theta(x)=\\theta^T x$의 경우는 아래와 같은 함수를 최소화하는 $\\theta$를 고르는 문제로 표현할 수 있다.\n", "\n", "$$\n", "\\eloss(\\theta) = \\frac{1}{n} \\sum_{i=1}^n \\loss (\\theta^T x^{(i)} , y^{(i)})\n", "$$\n", "\n", "- 일반적으로 임의의 empirical risk를 최소화하는 파라미터 $\\theta$를 찾는 문제는 해석적으로 해결하기 어려우며 수치적인 최적화 _numerical optimization_ 기법을 적용하여 해결한다.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "CkZVHLFoYrCc" }, "source": [ "
\n", "\n", "---\n", "\n", "## Least squares linear regression" ] }, { "cell_type": "markdown", "metadata": { "id": "yQgxw15SYy_L" }, "source": [ "- 예측기 파라미터 $\\theta \\in \\R^d$를 갖는 선형 예측기 $\\hat y = g_\\theta(x) = \\theta^\\tp x$를 가정하자.\n", "\n", "- 손실함수는 제곱 함수로 $\\loss(\\hat y, y) = (\\hat y - y)^2$ 정의하자.\n", "\n", "- 그러면 empirical risk인 MSE는 아래와 같이 표현된다.\n", "\n", "$$\n", "\\eloss(\\theta) = \\frac{1}{n} \\sum_{i=1}^n \\left(\\theta^\\tp x^{(i)} - y^{(i)}\\right)^2\n", "$$\n", "\n", "- ERM 문제는 예측기의 MSE를 최소화하는 $\\theta$를 찾는 문제가 되며, 이와 같은 문제를 _linear least squares fitting_ 또는 _linear regression_ 이라 부른다.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "LzVscZ0DZdFV" }, "source": [ "
\n", "\n", "### Least squares formulation\n", "\n", "- MSE를 아래와 같이 행렬을 사용하여 표현해 보자.\n", "\n", "$$\n", "\\begin{align*}\n", " \\frac{1}{n} \\sum_{i=1}^n (\\theta^\\tp x^{(i)} -y^{(i)})^2\n", " &= \\frac{1}{n}\\left\\{ (\\theta^Tx^{(1)}-y^{(1)})^2 + \\cdots (\\theta^Tx^n-y^n)^2 \\right\\} \\\\\n", " &= \\frac{1}{n}\\left\\{ ((x^{(1)})^T\\theta-y^{(1)})^2 + \\cdots ((x^{(n)})^T\\theta-y^{(n)})^2 \\right\\} \\\\\n", " &=\\frac{1}{n} \\left\\|\\, \\bmat{(x^{(1)})^T\\theta-y^{(1)} \\\\ \\vdots \\\\ (x^{(n)})^T\\theta-y^{(n)} }\\, \\right\\|^2\\\\\n", " &=\\frac{1}{n} \\left\\|\\,\\bmat{(x^{(1)})^T \\\\ \\vdots \\\\ (x^{(n)})^T }\\theta - \\bmat{y^{(1)} \\\\ \\vdots \\\\ y^{(n)}}\\,\\right\\|^2\\\\\n", " &= \\frac{1}{n} \\norm{X \\theta - y}^2\n", "\\end{align*}\n", "$$\n", "\n", "여기서 행렬 $X\\in\\R^{n \\times d}$와 벡터 $y\\in\\R^n$는 주어진 데이타 세트를 이용해 아래와 같이 정의된다.\n", "\n", "$$\n", "X = \\bmat{(x^{(1)})^\\tp \\\\ \\vdots \\\\ (x^{(n)})^\\tp} \\qquad y = \\bmat{y^{(1)} \\\\ \\vdots \\\\ y^{(n)}}\n", "$$\n", "\n", "- ERM 문제는 _least squares problem_ 표현됨을 확인할 수 있다. 즉, $\\|X \\theta - y\\|^2$를 최소화하는 $\\theta$를 찾음으로써 ERM 문제는 해결된다. \n" ] }, { "cell_type": "markdown", "metadata": { "id": "itVRJI6ieZRg" }, "source": [ "
\n", "\n", "### Least squares solution\n", "\n", "- Least squares 문제는 주어진 $X$와 $y$에 대해 $\\norm{X\\theta-y}^2$를 최소화하는 $\\theta$를 찾는 문제이다.\n", "\n", "- 여기서 $X \\in\\R^{n \\times d}$는 정사각형이거나 위아래로 긴 행렬이다 ($d \\leq n$).\n", "\n", "- $\\norm{X\\theta-y}^2$는 최소화하기 위한 목적함수 _objective function_ 라고 부른다.\n", "\n", "- $X$의 컬럼들이 linearly independent columns하다면 목적함수를 최소화하는 최적해 $\\theta$는 아래와 같이 찾을 수 있다.\n", "\n", "$$\n", "\\theta^* = (X^\\tp X)^{-1}X^\\tp y= X^\\dagger y\n", "$$\n", "\n", "- 참고로, 실제로는 $X^\\dagger=(X^\\tp X)^{-1}X^\\tp$를 직접적으로 계산하지는 않고 QR 분해 등의 효율적인 방법을 통해 최적해를 계산할 수 있다.\n", "\n", "- 예를 들어, Python에서는 `numpy`의 `numpy.linalg.lstsq` 함수를 통해 위와 동일한 최적해를 매우 효율적인 방법으로 얻을 수 있다.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "IFXAebKNz-Lk" }, "source": [ "\n", "
\n", "\n", "\n", "\n", "---\n", "\n", "\n", "## Numerical examples\n", "\n", "
\n", "\n", "### Polynomial fit\n", "\n", "아래의 셀을 실행하면 실수 입력 데이타 $x$와 출력 데이타 $y$를 담고 있는 `csv` 파일을 로드한다. 이 데이타를 가지고 입력과 출력 사이의 관계를 찾아내 새로운 $x$가 들어오면 출력값을 예측할 수 있는 예측 모델을 만들려고 한다." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 564 }, "id": "jAAcu7gXgSlF", "outputId": "7e03cbeb-8eb9-440b-fb6e-5843595d5f54" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "data = np.loadtxt('https://jonghank.github.io/ase3001/files/fit_data.csv', \\\n", " delimiter=',')\n", "x, y = data[:,0], data[:,1]\n", "\n", "plt.figure(figsize=(6,6), dpi=100)\n", "plt.plot(x, y, 'o', alpha=0.5)\n", "plt.grid()\n", "plt.axis('square')\n", "plt.xlim(0, 1)\n", "plt.ylim(0, 1)\n", "plt.xlabel(r'$x$')\n", "plt.ylabel(r'$y$')\n", "plt.title('Raw data')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "jdGZBr234g4Q" }, "source": [ "주어진 데이타 $y$를 $x$에 대한 5차 다항식 모델로 fitting하기로 한다.\n", "\n", "$$\n", "\\begin{align*}\n", " \\hat{y} &= \\theta_0 + \\theta_1 x + \\theta_2 x^2 + \\theta_3 x^3 + \\theta_4 x^4 + \\theta_5 x^5 \\\\\n", " &= \\bmat{1 & x & x^2 & x^3 & x^4 & x^5 }\\bmat{\\theta_0 \\\\ \\theta_1 \\\\ \\theta_2 \\\\ \\theta_3 \\\\ \\theta_4 \\\\ \\theta_5}\n", "\\end{align*}\n", "$$\n", "\n", "모든 데이타에 대해 $\\hat{y}$를 ${y}$에 가깝도록 만드는 $\\theta = \\bmat{\\theta_0 & \\cdots & \\theta_5}^T$를 찾으려고 하며, 이는 아래에 정의된 empirical risk를 최소화하는 $\\theta$를 찾음으로써 해결된다.\n", "\n", "$$\n", "\\begin{align*}\n", "\\eloss\\left(\\theta\\right) &= \\sum_{i=1}^{n} \\left(\\hat{y}^{(i)}-y^{(i)}\\right)^2 \\\\\n", "&= \\sum_{i=1}^{n} \\left( \\bmat{1 & x^{(i)} & (x^{(i)})^2 & (x^{(i)})^3 & (x^{(i)})^4 & (x^{(i)})^5}\n", "\\bmat{\\theta_0 \\\\ \\theta_1 \\\\ \\theta_2 \\\\ \\theta_3 \\\\ \\theta_4 \\\\ \\theta_5} - y^{(i)} \\right)^2 \\\\\n", "&= \\left\\| \\bmat{1 & x^{(1)} & (x^{(1)})^2 & (x^{(1)})^3 & (x^{(1)})^4 & (x^{(1)})^5 \\\\\n", "1 & x^{(2)} & (x^{(2)})^2 & (x^{(2)})^3 & (x^{(2)})^4 & (x^{(2)})^5 \\\\\n", "\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots \\\\\n", "1 & x^{(n)} & (x^{(n)})^2 & (x^{(n)})^3 & (x^{(n)})^4 & (x^{(n)})^5 }\n", "\\bmat{\\theta_0 \\\\ \\theta_1 \\\\ \\theta_2 \\\\ \\theta_3 \\\\ \\theta_4 \\\\ \\theta_5} - \\bmat{y^{(1)} \\\\ y^{(2)} \\\\ \\vdots \\\\ y^{(n)}} \\right\\|_2^2 \\\\\n", "&= \\left\\| X \\theta - y \\right\\|_2^2 \\end{align*}\n", "$$\n", "\n", "여기서 행렬 $X$와 벡터 $y$는 아래와 같다.\n", "\n", "$$\n", " X = \\bmat{1 & x^{(1)} & (x^{(1)})^2 & (x^{(1)})^3 & (x^{(1)})^4 & (x^{(1)})^5 \\\\\n", "1 & x^{(2)} & (x^{(2)})^2 & (x^{(2)})^3 & (x^{(2)})^4 & (x^{(2)})^5 \\\\\n", "\\vdots & \\vdots & \\vdots & \\vdots & \\vdots & \\vdots \\\\\n", "1 & x^{(n)} & (x^{(n)})^2 & (x^{(n)})^3 & (x^{(n)})^4 & (x^{(n)})^5 }\n", ", \\qquad\n", "y = \\bmat{y^{(1)} \\\\ y^{(2)} \\\\ \\vdots \\\\ y^{(n)}}\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 598 }, "id": "Z3WkKS9Xg4ss", "outputId": "afa40a63-7311-483b-c3a5-73aae6650d8e" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimal theta: [-1.08775601e-01 1.51579304e+01 -9.49190641e+01 2.39806312e+02\n", " -2.64399727e+02 1.05545151e+02]\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = len(x)\n", "d = 6\n", "\n", "X = np.zeros((n,d))\n", "for i in range(d):\n", " X[:,i] = x**i\n", "\n", "theta_opt = np.linalg.lstsq(X, y, rcond=None)[0]\n", "\n", "print(f'Optimal theta: {theta_opt}')\n", "\n", "vp = np.linspace(0, 1, 100)\n", "\n", "X_vp = np.zeros((len(vp),d))\n", "for i in range(d):\n", " X_vp[:,i] = vp**i;\n", "\n", "plt.figure(figsize=(6,6), dpi=100)\n", "plt.plot(x, y, 'o', alpha=0.5, label='Raw data')\n", "plt.plot(vp, np.dot(X_vp, theta_opt), label='Predictor')\n", "plt.grid()\n", "plt.axis('square')\n", "plt.xlim(0, 1)\n", "plt.ylim(0, 1)\n", "plt.xlabel(r'$u$')\n", "plt.ylabel(r'$v$')\n", "plt.title(\"Polynomial predictor\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "HPfzVTmqFJGq" }, "source": [ "
\n", "\n", "### Diabete progression\n", "\n", "아래의 셀은 442명의 환자에 대한 의료 정보를 담고 있으며, 각각의 row가 환자 1명의 데이타를 의미한다. 왼쪽 열 개의 컬럼은 나티, 성별, BMI 등, 환자의 정보와 검사 기록 등을 포함하며, 가장 오른쪽 걸럼은 1년의 추적검사를 통해 확인된 해당 환자의 당뇨병 진행도를 의미한다.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 419 }, "id": "Ql_YwvK4Co1o", "outputId": "c1521a2b-060a-4197-a0ed-76da0d5bf53a" }, "outputs": [ { "data": { "text/html": [ "\n", "
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\n" ], "text/plain": [ " AGE SEX BMI BP S1 S2 S3 S4 S5 S6 Y\n", "0 59 2 32.1 101.00 157 93.2 38.0 4.00 4.8598 87 151\n", "1 48 1 21.6 87.00 183 103.2 70.0 3.00 3.8918 69 75\n", "2 72 2 30.5 93.00 156 93.6 41.0 4.00 4.6728 85 141\n", "3 24 1 25.3 84.00 198 131.4 40.0 5.00 4.8903 89 206\n", "4 50 1 23.0 101.00 192 125.4 52.0 4.00 4.2905 80 135\n", ".. ... ... ... ... ... ... ... ... ... ... ...\n", "437 60 2 28.2 112.00 185 113.8 42.0 4.00 4.9836 93 178\n", "438 47 2 24.9 75.00 225 166.0 42.0 5.00 4.4427 102 104\n", "439 60 2 24.9 99.67 162 106.6 43.0 3.77 4.1271 95 132\n", "440 36 1 30.0 95.00 201 125.2 42.0 4.79 5.1299 85 220\n", "441 36 1 19.6 71.00 250 133.2 97.0 3.00 4.5951 92 57\n", "\n", "[442 rows x 11 columns]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "df = pd.read_csv('https://jonghank.github.io/ase3001/files/diabetes_data.txt', delimiter='\\t')\n", "\n", "df" ] }, { "cell_type": "markdown", "metadata": { "id": "e3pgmMO3M62K" }, "source": [ "주어진 10개의 입력 feature(와 1개의 constant feature)를 입력받아 1년 후의 당뇨병 진행도를 예측하는 선형 모델을 아래와 같이 설계할 수 있다. \n", "\n", "* Diabete progression, $y$:\n", "\n", "$$\n", "\\begin{align*}\n", "&y\\approx \\theta_0 + \\theta_1\\text{Age} + \\theta_2\\text{Sex} + \\theta_3\\text{BMI} + \\theta_4\\text{BP} + \\theta_5\\text{S}_1\n", "+ \\theta_6\\text{S}_2 + \\theta_7\\text{S}_3 + \\theta_8\\text{S}_4 + \\theta_9\\text{S}_5 + \\theta_{10}\\text{S}_6\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "YuZwk_MeGfX8", "outputId": "6de0ecd6-49ff-40ff-9354-d0198b2fb5bf" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE: 2859.6963475867506\n", "RMSE: 53.476128764026576\n" ] } ], "source": [ "n, d = df.shape\n", "X = np.hstack((np.ones((n,1)), df.values[:,:-1]))\n", "y = df.values[:,-1]\n", "\n", "theta_opt = np.linalg.lstsq(X, y, rcond=None)[0]\n", "\n", "MSE = np.linalg.norm(X.dot(theta_opt)-y)**2/n\n", "\n", "print(f'MSE: {MSE}')\n", "print(f'RMSE: {np.sqrt(MSE)}')" ] }, { "cell_type": "markdown", "metadata": { "id": "racWaysArP86" }, "source": [ "아래의 플롯은 설계된 예측기가 출력한 진행도와 실제 진행도를 비교한 것으로, diagonal 방향의 검정 실선에 놓인 데이타는 ($\\hat{y}=y$) 예측 모델의 결과가 정확한 경우를 의미하고, 검정 실선과 먼 데이타는 예측 모델의 오차가 큰 경우를 의미한다." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 542 }, "id": "gug7TuMOGg5q", "outputId": "008e152c-94e2-43f5-b7c6-9030c6d09ccf" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,6), dpi=100)\n", "plt.plot(y, y, 'k')\n", "plt.plot(y, X.dot(theta_opt), 'o', alpha=0.5)\n", "plt.xlabel('y')\n", "plt.ylabel(r'$\\hat{y}$')\n", "plt.axis('square')\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": { "id": "n3jlbOC5rcdt" }, "source": [ "이제 이 모델을 활용하여 새로운 환자가 들어왔을 때 ($X_\\text{new}$) 그 환자의 미래 1년간 당뇨병 진행도를 예측해 보자.Now suppose we got a new medical record from a new patient. 새 환자의 당뇨병 진행도는 $\\hat{y}_\\text{new}=X_\\text{new}\\theta^*$를 통해 쉽게 예측할 수 있으며, 이를 통해 대략적으로 이 환자가 당뇨병에 대하 얼마나 취약한지 예상할 수 있다." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 542 }, "id": "ekP-x9D_PkvG", "outputId": "6da661ac-ac1f-4746-a762-f4beb7de9ff3" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# note that each feature represents\n", "# u1: age\n", "# u2: sex\n", "# u3: bmi body mass index\n", "# u4: map\t mean arterial pressure\n", "# u5: s1 (tc) : total cholesterol\n", "# u6: s2 (ldl): low density lipoprotein\n", "# u7: s3 (hdl): high density lipoprotein\n", "# u8: s4 (tch):\n", "# u9: s5 (ltg):\n", "# u10: s6 (glu):\n", "# features: age sex bmi map tc ldl hdl tch ltg glu\n", "X_JHK = np.array([41, 1, 18.3, 90, 171, 80.0, 74.9, 2, 4.75, 90.0])\n", "X_JHK = np.hstack((1, X_JHK))\n", "\n", "y_JHK = X_JHK.dot(theta_opt)\n", "\n", "plt.figure(figsize=(6,6), dpi=100)\n", "plt.plot(y, y, 'k')\n", "plt.plot(y, X.dot(theta_opt), 'o', alpha=0.5)\n", "plt.plot(y_JHK, y_JHK, 'ro', label='JHK')\n", "plt.xlabel('y')\n", "plt.ylabel(r'$\\hat{y}$')\n", "plt.legend()\n", "plt.axis('square')\n", "plt.grid()" ] } ], "metadata": { "colab": { "provenance": [] }, "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": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 1 }