{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "K9rgN5_aJGc_" }, "source": [ "# Simple Linear Model\n", "\n", "ถ้าลองนึกภาพตามง่ายๆในมุมมองของผู้สร้างโมเดล เราอาจจะสร้างโมเดลที่มีความซับซ้อนมากๆและทำนายชุดข้อมูลที่เรามีได้ดีมาก หรืออาจจะสร้างโมเดลที่ซับซ้อนน้อยลงมาหน่อยแต่ก็ยังทำนายชุดข้อมูลที่เรามีได้ดีรองลงมาก็ได้ ตัวเลือกในการสร้างโมเดลมีหลากหลายรูปแบบ แต่ว่าเราจะเลือกโมเดลที่เหมาะสมได้อย่างไร?\n", "\n", "ในบทเรียนนี้เราจะลองสร้างโมเดลทำนายชุดข้อมูลในรูปแบบต่าง ๆ และดูกันว่าโมเดลแบบใดจะเหมาะสมกับชุดข้อมูลตัวอย่างของเรา" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "UwSov8-9Tivi" }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.linear_model import LinearRegression\n", "\n", "import ipywidgets as widgets # ใช้สำหรับการทำ interactive display\n", "\n", "np.random.seed(42) # ตั้งค่า random seed เอาไว้ เพื่อให้การรันโค้ดนี้ได้ผลเหมือนเดิม" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "_iwAc339cbU9" }, "source": [ "\n", "\n", "[Slides: Simple Linear Models 1](https://github.com/ichatnun/brainCodeCamp2023_lectures/blob/main/IntroToModeling/modeling_part1a_linear1.pdf)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "X-v93fa3Tj74" }, "source": [ "## โมเดลเชิงเส้น (Linear Model)\n", "\n", "กำหนดให้สมการความสัมพันธ์ระหว่าง $x$ และ $y$ ที่แท้จริง เป็นสมการเชิงเส้น\n", "\n", "$$y = w_0 + w_1x$$\n", "\n", "โดยที่ $w_0$ คือค่าจุดตัดแกน $y$ และ $w_1$ คือค่าความชันของเส้นตรง\n", "\n", "ในการเก็บข้อมูลจริงมักมีสัญญาณรบกวน (noise) ที่มาจากหลายปัจจัย เช่น ความไม่เสถียรของเครื่องมือเก็บข้อมูล คลื่นไฟฟ้ากระแสสลับที่ใช้ในประเทศ ในกรณีที่เก็บข้อมูลผ่านอุปกรณ์อิเล็กทรอนิคส์ หรืออาจจะมี noise ที่เราไม่รู้ว่ามาจากกระบวนการไหนก็ตาม ปัจจัยเหล่านี้ส่งผลให้ข้อมูลที่เก็บมานั้นมีค่าที่แตกต่างไปจากความสัมพันธ์ที่แท้จริง ซึ่งสามารถเขียนอธิบายได้ด้วยสมการ\n", "\n", "$$y = w_0 + w_1x + noise$$\n", "\n", "แทน\n", "\n", "

\n", "ในส่วนนี้เราจะลองทดลองเลียนแบบกระบวนการเก็บข้อมูลผ่านการเรียกใช้ `generate_sample_linear`\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 449 }, "id": "7jKtIz8d-tDH", "outputId": "b21ae785-55b0-4317-ddf2-f03754eb3b7a" }, "outputs": [], "source": [ "def generate_sample_linear(x, w0=1, w1=2, include_noise=True):\n", "\n", " # สร้างสมการเส้นตรงโดยที่จำลองการใส่สัญญาณรบกวนเข้าไป\n", " # เลือก include_noise เป็น True เพื่อกำหนดให้มีค่า noise เพิ่มเข้าไปในสมการ\n", " if include_noise:\n", " # สร้าง Gaussian noise\n", " noise = 0.20 * np.max(x) * np.random.standard_normal(x.shape)\n", " else:\n", " noise = 0\n", " y = w0 + (w1 * x) + noise\n", " return y\n", "\n", "# ทดลองสร้างข้อมูลโดยการเรียกใช้ generate_sample_linear\n", "num_samples = 100\n", "w0_true, w1_true = 1, 2 # กำหนดค่า w0 และ w1 ที่แท้จริง สำหรับสร้างข้อมูล\n", "x = 5 * np.random.rand(num_samples, 1) - 2.5 # สุ่มค่า x จากพิสัย -2.5 ถึง 2.5\n", "y = generate_sample_linear(x, w0_true, w1_true, include_noise=True)\n", "\n", "# สร้างข้อมูลที่ไม่มีสัญญาณรบกวนมาเปรียบเทียบ ซึ่งเป็นข้อมูลที่เรามักไม่มีโอกาสเข้าถึงในชีวิตจริง (จะใช้ในภายหลัง)\n", "y_true = generate_sample_linear(x, w0_true, w1_true, include_noise=False)\n", "\n", "# สร้างข้อมูลที่ไม่มีสัญญาณรบกวนมาแบบละเอียดสำหรับค่า x จำนวนมาก เพื่อใช้ในการวาดกราฟ (เส้นประสีดำ)\n", "x_whole_line = np.linspace(-2.5, 2.5, 100)\n", "y_true_whole_line = generate_sample_linear(x_whole_line, w0_true, w1_true, include_noise=False)\n", "\n", "# Plot ข้อมูล x, y ที่มีอยู่\n", "fig, ax = plt.subplots()\n", "ax.scatter(x, y, c='b', label='Observed')\n", "ax.plot(x_whole_line, y_true_whole_line, 'k--', label='True')\n", "ax.set(xlabel='x', ylabel='y')\n", "ax.legend()\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "DZua7f9ME1_r" }, "source": [ "\n", "กำหนดให้เรามีจำนวนจุดข้อมูลในรูปด้านบนทั้งหมด $n$ จุด $(x_1,y_1), (x_2,y_2), ..., (x_i,y_i),.., (x_n,y_n)$ แสดงด้วยสีน้ำเงิน หากเราพิจารณาภาพความสัมพันธ์ระหว่าง $x$ กับ $y$ จากการรันโค้ดด้านบน จะพบว่ามีลักษณะคล้ายกับเส้นตรง\n", "\n", "**หมายเหตุ** ถึงแม้ว่าในรูปด้านบน เราจะ plot เส้นประสีดำ ซึ่งแสดงความสัมพันธ์ระหว่าง $x$ และ $y$ ที่แท้จริง (ปราศจากสัญญาณรบกวน) ได้ แต่ในชีวิตจริง เรามักจะไม่มีโอกาสเข้าถึงข้อมูลตรงนี้ได้เลย\n", "\n", "

\n", "\n", "\n", "\n", "สมมติว่ามีคนเดินมาถามเราว่า ถ้า $x$ มีค่าเป็น $0.8$ แล้ว $y$ ควรจะมีค่าเป็นเท่าไหร่ เราจะตอบเค้าว่าอย่างไรดี\n", "\n", "\n", "ในการให้คำตอบตรงนี้ เราสามารถทำได้หลายวิธีมาก ๆ เช่น\n", "\n", "\n", "* ถ้าเกิดว่าเราไปไล่ดูจุดข้อมูลทั้ง $n$ จุดในชุดข้อมูลของเรา พบว่ามีจุด $(0.8, 2.6)$ อยู่ เราก็อาจจะตอบได้ว่า $y$ น่าจะมีค่าเป็น $2.6$\n", "\n", "* ถ้าเกิดว่าเราไปไล่ดูจุดข้อมูลทั้ง $n$ จุดในชุดข้อมูลของเรา แต่ไม่พบจุดที่มีค่า $x$ เป็น $0.8$ เลย แต่ดันมีจุด $(0.7, 2.4)$ และ $(0.9, 2.8)$ เราก็อาจจะตอบว่าค่า $y$ ที่สอดคล้องกับค่า $x=0.8$ ซึ่งเป็นจุดกึ่งกลางระหว่าง $x=0.7$ และ $x=0.9$ น่าจะมีค่า $y$ เป็นจุดตรงกลางระหว่าง $2.4$ และ $2.8$ หรือว่ามีค่าเท่ากับ $\\frac{2.4+2.8}{2}=2.6$ นั่นเอง\n", "\n", "หากสังเกตตัวอย่างด้านบนทั้ง 2 ตัวอย่าง เราจะเห็นว่าทุกครั้งที่เราจะตอบค่า $y$ เราจะต้องไปไล่ดูจุดข้อมูลในชุดข้อมูลของเรา สมมติว่า $n=1,000,000$ ล่ะ เราจะทำอย่างไรกันดี เราพอจะมีวิธีอะไรบางอย่างที่ช่วยให้เราสามารถตอบค่า $y$ ที่เหมาะสมจากค่า $x$ ใด ๆ ก็ตามได้อย่างรวดเร็วหรือไม่\n", "\n", "---\n", "\n", "เนื่องจากข้อมูลใน plot ด้านบน ดูมีลักษณะเป็นเส้นตรง เรามาทดลองใช้โมเดลที่เป็นสมการเชิงเส้น $\\hat{y}=\\hat{w_0} + \\hat{w_1} x$ กันดีกว่า ซึ่งสมการนี้มี\n", "\n", "* $\\hat{w_0}$ เป็นค่าจุดตัดแกน $y$\n", "\n", "* $\\hat{w_1}$ เป็นค่าความชันของเส้นตรง\n", "\n", "* $\\hat{y}$ เป็นค่า $y$ ที่ทำนายมาจากสมการเส้นตรงของเรา สำหรับค่า $x$ ใด ๆ\n", "\n", "ถ้าเกิดว่าเราสามารถหาค่า $\\hat{w_0}$ และ $\\hat{w_1}$ ที่เหมาะสมออกมาได้ (ซึ่งเราก็หวังว่ามันจะเป็นค่าเดียวกับ $w_0$ และ $w_1$ ของความสัมพันธ์จริง) เราจะสามารถทำนายค่า $y$ เป็น $\\hat{w_0} + \\hat{w_1} x$ จากค่า $x$ ใด ๆ ได้ทันที โดยที่ไม่ต้องไปนั่งไล่ดูจุดข้อมูลทั้ง $n$ จุดในชุดข้อมูลเลย\n", "\n", "**หมายเหตุ** ในบทเรียนนี้เราใส่สัญลักษณ์ hat เข้าไปบนตัวแปร (เช่น $\\hat{w_0}$ และ $\\hat{w_1}$) เพื่อทำให้เห็นชัดว่าเรากำลังพูดถึงตัวแปรที่เราประมาณค่าออกมา ไม่ได้กำลังพูดถึงค่าจริงของตัวแปรเหล่านั้น (เช่น $w_0$ และ $w_1$) \n", "\n", "

\n", "\n", "ใน code ด้านล่าง เรามาลองปรับค่า $\\hat{w_0}$ และ $\\hat{w_1}$ กัน เพื่อหาดูว่าค่าที่เหมาะสมมีค่าเป็นเท่าไหร่\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 484, "referenced_widgets": [ "70d9d87296b74b1f82432d9a0ac5bd86", "ef19ab4cd2c64ae0a49ef0d074a072ba", "f2c5782eb9bc4bc1868c436f1c2a7292", "9e79cf5733344557bf851d5680cf8919", "7a237c16e3344aa9b9f0e3f06d1bd663", "9c0f8126b4364da48d29f586ff49b80b", "54e7b013419f4e258138dc4ce9cf3e77", "421375ea3c37432b845568a2a0f76e25", "f8289003774f4bc6943b0cab66c10ded", "8fd7de507935409ba03adef534bd7343", "648245e8cc5f45e5ad10ab16f4c17a5a", "b280f0b4240e4aa383b35e3e41850e8e", "4fa2fedf8cdd4f77b73f2b16809b247b" ] }, "id": "sIFdIr5m01fT", "outputId": "d886c82d-ea96-468c-a66c-31601367b53d" }, "outputs": [], "source": [ "# ใส่แถบสำหรับปรับค่า w1_hat และ w2_hat รวมถึงช่องสำหรับให้เลือกว่าจะโขว์เส้นความสัมพันธ์ระหว่าง x และ y ที่แท้จริงหรือไม่\n", "@widgets.interact(w0_hat=widgets.FloatSlider(0.0, min=-4, max=4),\n", " w1_hat=widgets.FloatSlider(0.0, min=-4, max=4),\n", " show_true_line=widgets.Checkbox(False, description='Show true data'))\n", "def plot_linear_results(w0_hat, w1_hat, show_true_line):\n", "\n", " # คำนวณค่า y จากค่า w0_hat และ w1_hat ที่เราเดามา โดยจะคำนวณมาเฉพาะอันที่มีค่า x ตรงกับที่มีในชุดข้อมูล\n", " y_predicted_partial = w0_hat + w1_hat * x\n", "\n", " # คำนวณค่า y จากค่า w0_hat และ w1_hat ที่เราเดามา สำหรับค่า x จำนวนมาก\n", " y_predicted = w0_hat + w1_hat * x_whole_line\n", "\n", " # สร้าง figure\n", " fig, ax = plt.subplots(figsize=(4,4))\n", "\n", " # Plot ข้อมูล x, y ที่มีอยู่ด้วยสีน้ำเงิน\n", " ax.scatter(x, y, c='b', label='Observed')\n", "\n", " # Plot ข้อมูลค่า y ที่เราทำนายมาที่ตำแหน่งค่า x ต่าง ๆ กัน ด้วยสีแดง\n", " ax.plot(x_whole_line, y_predicted, c='r', label='Predicted')\n", "\n", " # Plot ข้อมูลที่ไม่มี noise ด้วยสีดำ ซึ่งในความเป็นจริง เรามักไม่มีโอกาสเข้าถึงข้อมูลตรงนี้\n", " if show_true_line:\n", " ax.plot(x_whole_line, y_true_whole_line, 'k--', label='True')\n", "\n", " ax.set(xlabel='x', ylabel='y')\n", " ax.legend()\n", " plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "cSeTb-gj6aji" }, "source": [ "จะเห็นได้ว่าเราสามารถลองปรับค่าความชันและจุดตัดแกน $y$ ของเส้นตรงไปเรื่อย ๆ จนมีความสอดคล้องกับชุดข้อมูลที่เราเก็บมา (สีน้ำเงิน)\n", "\n", "หากเรากำหนดให้ค่า $\\hat{w_0}=1$ และ $\\hat{w_1}=2$ จะพบว่าเส้นตรงสีแดงมีความสอดคล้องกับจุดสีน้ำเงินค่อนข้างดี โดยเส้นตรงนั้นมีสมการคือ $y = 2x + 1$ ซึ่งเป็นเส้นตรงที่มีความชันเป็น $2$ และมีจุดตัดแกน $y$ คือ $(0,1)$\n", "\n", "\n", "\n", "อีกวิธีหนึ่งที่อาจจะช่วยให้เราเลือกค่า $\\hat{w_0}$ และ $\\hat{w_0}$ ด้วยตาได้ง่ายขึ้น คือการ plot โชว์ความแตกต่างระหว่างจุดที่ observed มา (สีน้ำเงิน) และสิ่งที่โมเดลทำนายออกมา (สีแดง) ดังตัวอย่างโค้ดด้านล่าง โดยเราจะพยายามเลือกเอาค่า $\\hat{w_0}$ และ $\\hat{w_0}$ ที่ทำให้เส้นสีส้ม ๆ ในรูปมีขนาดรวมกันสั้นที่สุด\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 516, "referenced_widgets": [ "ab153cfa1dbc4b0cb9a33fd56fc24ef4", "fe78bfb4e3c34a899a5602721dba5c4b", "0517d36ab7314630bd3917d9b2871e0c", "50f7739fe3684ebd911adc049dd90450", "4cc312350983441a95eb4cf26cb2a39c", "939a3b04c88a438dbafa05bb6dde1a5a", "3eac7da081f84de2afd902523ac92e4c", "a6b4f6fac9f245bdb54b391047389ef6", "a498630bf91b471488a3fd2178b3c804", "b2fdbd93fe3e4ac99a512eaf3c74708f", "cf681e43569e4674aa211b7c7ac9d4b9", "3a66c7520d744580b05de68a2d67a98f", "d45c625ab04640a6bb621a3862f177dc", "d29104f91fb64b6da62b2ab6a534c603", "ac8d37aec8c84c4aa1280cdb96813ee2", "61e318eb28174bd5931a712e31ba2b7f" ] }, "id": "TlaTlUU_OBT4", "outputId": "c50f0d2a-30a5-46bb-cca5-57ad66e74d1e" }, "outputs": [], "source": [ "# เหมือน cell ก่อนหน้า แต่เพิ่มช่องสำหรับเลือกว่าจะโชว์ error หรือไม่\n", "@widgets.interact(w0_hat=widgets.FloatSlider(0.0, min=-4, max=4),\n", " w1_hat=widgets.FloatSlider(0.0, min=-4, max=4),\n", " show_true_line=widgets.Checkbox(False, description='Show true data'),\n", " show_error=widgets.Checkbox(True, description='Show error'))\n", "def plot_linear_results(w0_hat, w1_hat, show_true_line, show_error):\n", "\n", " # คำนวณค่า y จากค่า w0_hat และ w1_hat ที่เราเดามา สำหรับค่า x จำนวนมาก\n", " y_predicted = w0_hat + w1_hat * x_whole_line\n", "\n", " # สร้าง figure\n", " fig, ax = plt.subplots(figsize=(4,4))\n", "\n", " # Plot ข้อมูล x, y ที่มีอยู่ด้วยสีน้ำเงิน\n", " ax.scatter(x, y, c='b', label='Observed')\n", "\n", " # Plot ข้อมูลค่า y ที่เราทำนายมาที่ตำแหน่งค่า x ต่าง ๆ กัน ด้วยสีแดง\n", " ax.plot(x_whole_line, y_predicted, c='r', label='Predicted')\n", "\n", " # Plot ข้อมูลที่ไม่มี noise ด้วยสีดำ ซึ่งในความเป็นจริง เรามักไม่มีโอกาสเข้าถึงข้อมูลตรงนี้\n", " if show_true_line:\n", " ax.plot(x_whole_line, y_true_whole_line, 'k--', label='True')\n", "\n", " # Plot ความแตกต่างระหว่างค่า y ที่ observed มา และค่า y ที่ทำนายมาด้วยสีส้ม\n", " if show_error:\n", "\n", " # คำนวณค่า y จากค่า w0_hat และ w1_hat ที่เราเดามา โดยจะคำนวณมาเฉพาะอันที่มีค่า x ตรงกับที่มีในชุดข้อมูล\n", " y_predicted_partial = w0_hat + w1_hat * x\n", "\n", " ymin = np.minimum(y, y_predicted_partial)\n", " ymax = np.maximum(y, y_predicted_partial)\n", " ax.vlines(x, ymin, ymax, 'darkorange', alpha=0.3, label='errors')\n", "\n", " ax.set(xlabel='x', ylabel='y')\n", " ax.legend()\n", " plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "[Slides: Simple Linear Models 2](https://github.com/ichatnun/brainCodeCamp2023_lectures/blob/main/IntroToModeling/modeling_part1b_linear2.pdf)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "5Dwl8LDmNWyU" }, "source": [ "ที่ผ่านมาเราเลือกค่า $\\hat{w_0}$ และ $\\hat{w_1}$ โดยการดูด้วยตาว่าเส้นตรงสีแดงที่เกิดขึ้นมานั้น ดูสอดคล้องกับจุดข้อมูลสีน้ำเงินมากน้อยแค่ไหน ซึ่งนับว่าเป็นจากวัดความเหมือนหรือความแตกต่างเชิงคุณภาพ (qualitative)\n", "\n", "ในลำดับถัดไป เราจะมาลองดูวิธีการวัดความเหมือนหรือความแตกต่างเชิงปริมาณกันบ้าง (quantitative)\n", "\n", "เรามาลองใช้ฟังก์ชัน $L(y_{i},\\hat{y_i})$ สำหรับวัดความต่างระหว่าง $y_{i}$ และ $\\hat{y_i}$ ออกมาเป็นตัวเลข 1 ตัว โดยการนำเอาค่าทั้งสองมาลบกันแล้วยกกำลังสอง\n", "\n", "$$L(y_{i},\\hat{y_i}) = (y_{i} - \\hat{y_i})^2$$\n", "\n", "* ถ้าหากเราพยายามนำเอาสมการนี้ไปตีความทางเรขาคณิต เราจะเห็นว่าค่า $y_{i} - \\hat{y_i}$ แสดงถึง\"ความยาว\"ของเส้นสีส้มแต่ละเส้นในโค้ดของ cell ก่อนหน้า (อาจะมีค่าเป็นลบหรือบวกก็ได้) ซึ่งแปลว่าค่า $L(y_{i},\\hat{y_i})$ นี้ ก็คือค่าความยาวของเส้นสีส้มยกกำลังสองนั่นเอง\n", "* ถ้า $L(y_{i},\\hat{y_i})$ มีค่าน้อย แสดงว่า $y_{i}$ กับ $\\hat{y_i}$ มีความแตกต่างกันน้อย (เส้นสีส้มจะสั้น)\n", "* ถ้า $L(y_{i},\\hat{y_i})$ มีค่ามาก แสดงว่า $y_{i}$ และ $\\hat{y_i}$ มีความแตกต่างกันมาก (เส้นสีส้มจะยาว)\n", "\n", "\n", "ชุดข้อมูลของเรามีทั้งหมด $n$ จุด ซึ่งหากเราต้องการวัดความแตกต่างในระดับชุดข้อมูล เราก็สามารถเอาค่า $L(y_{i},\\hat{y_i})$ จากแต่ละจุดข้อมูลมาเฉลี่ยกันได้ เกิดเป็นสมการ\n", "\n", "$$L(Y,\\hat{Y}) =\\frac{1}{n}\\sum_{i=1}^{n}\\left(y_{i}-\\hat{y_i}\\right)^{2}$$\n", "\n", "ที่มีชื่อเรียกอีกว่า mean squared error (MSE) โดยในที่นี้เราใช้สัญลักษณ์\n", "\n", "* $Y$ เพื่ออ้างอิงถึง $y_1, y_2, ..., y_i, ..., y_n$\n", "\n", "* $\\hat{Y}$ เพื่ออ้างอิงถึง $\\hat{y_1}, \\hat{y_2}, ..., \\hat{y_i}, ..., \\hat{y_n}$\n", "\n", "หากเราย้อนกลับไปที่ตัวอย่างด้านบนที่เราพยายามปรับค่า $\\hat{w_0} และ \\hat{w_1}$ (จุดตัดแกน $y$ และค่าความชัน ตามลำดับ) แทนที่เราจะวัดผลด้วยตา เราสามารถลองใช้ $L$ สำหรับช่วยในการวัดผล โดยสุดท้ายแล้ว เราจะเลือกค่า $\\hat{w_0} และ \\hat{w_1}$ ที่ทำให้ $L$ มีค่าน้อยที่สุด\n", "\n", "อย่างไรก็ตาม การทดลองสุ่มค่าไปเรื่อย ๆ ในลักษณะนี้ เป็นวิธีการที่ใช้เวลานานมาก และไม่ค่อยมีประสิทธิภาพ\n", "\n", "

\n", "\n", "หากเรามองออกว่าโจทย์ที่เราพยายามแก้อยู่ เป็นโจทย์การหาค่าต่ำสุดของฟังก์ชัน $L$ ซึ่งสามารถเขียนในทางคณิตศาสตร์ได้ว่า\n", "\n", "$$\n", "\\min_{\\hat{w_{0}},\\hat{w_{1}}}L(Y,\\hat{Y})\n", "=\\min_{\\hat{w_{0}},\\hat{w_{1}}}\\frac{1}{n}\\sum_{i=1}^{n}\\left(y_{i}-\\hat{y_i}\\right)^{2}\n", "= \\min_{\\hat{w_{0}},\\hat{w_{1}}}\\frac{1}{n}\\sum_{i=1}^{n}\\left(y_{i}-(\\hat{w_{0}}+\\hat{w_{1}}x_{i})\\right)^{2}\n", "$$\n", "\n", "เราก็สามารถเอาเครื่องมือทางคณิตศาสตร์ (เช่น calculus, สถิติ และ linear algebra) มาแก้โจทย์ข้อนี้ได้ ซึ่งคำตอบที่ $\\hat{w_{0}}$ และ $\\hat{w_{1}}$ ที่ได้รับจากการแก้โจทย์ข้อนี้ ก็คือคำตอบที่ทำให้เส้นตรงของเรามีความแตกต่างจากข้อมูลที่เราเก็บมาน้อยที่สุดภายใต้มาตรวัดประเภทนี้ หรือพูดอีกอย่างว่ามีความเหมือนที่สุดนั่นเอง\n", "\n", "\n", "**หมายเหตุ** เนื่องจาก $L$ ในที่นี้แสดงถึงความแตกต่าง ซึ่งเราต้องการหาคำตอบที่ทำให้มันมีค่าน้อย (ความสูญเสียน้อย) เรามักจะเรียก $L$ ในบริบทนี้ว่า loss function\n", "\n", "\n", "---\n", "\n", "เนื่องจากมีผู้เรียนจำนวนหนึ่งยังไม่มีโอกาสได้เรียนเนื้อหาทางคณิตศาสตร์ที่จำเป็นต่อการแก้โจทย์ข้อนี้ (เช่น การใช้ calculus และ linear algebra) เราจะแก้โจทย์ข้อนี้ผ่านการเรียกใช้ `LinearRegression` จากไลบรารี่ `scikit-learn` เลย" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "qSuDsZG0CzjV", "outputId": "6026a9f3-042f-4ac2-cc18-2cbd51e0115d" }, "outputs": [], "source": [ "model_linear = LinearRegression()\n", "\n", "# ให้โมเดลหาค่า w_0 and w_1 จากข้อมูล (x,y) ทั้งหมดที่มี\n", "model_linear.fit(x, y)\n", "w0_hat = model_linear.intercept_[0]\n", "w1_hat = model_linear.coef_[0][0]\n", "\n", "print(f\"True slope {w1_true:0.2f}\")\n", "print(f\"Estimated slope {w1_hat:0.2f}\\n\")\n", "print(f\"True intercept {w0_true:0.2f}\")\n", "print(f\"Estimated intercept {w0_hat:0.2f}\")" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "PZl_HD6IK_Wj" }, "source": [ "จะเห็นว่าความชันและจุดตัดแกน $y$ ที่ประมาณจากโมเดล linear regression มีค่าใกล้กับค่าที่เรากำหนดมาตอนสร้างชุดข้อมูล\n", "\n", "หลังจากที่เรา fit โมเดลแล้ว (โมเดลได้ทำการประมาณค่า $\\hat{w_0}$ และ $\\hat{w_1}$ เรียบร้อยแล้ว) เราสามารถทำนายค่า $y$ จาก $x$ ใดๆ ได้จากสมการ $ \\hat{y} = \\hat{w_0} + \\hat{w_1}x$ ได้โดยตรง หรือผ่านการเรียกใช้ฟังก์ชัน `predict` ได้เช่นกัน" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 472 }, "id": "s72s_4NWK_oo", "outputId": "5ec12bac-6fbf-4fa8-95d3-1c94120f0463" }, "outputs": [], "source": [ "# ใช้โมเดลทำนายค่า y จากค่า x วิธีที่ 1\n", "y_hat = w0_hat + w1_hat*x\n", "\n", "# ใช้โมเดลทำนายค่า y จากค่า x วิธีที่ 2\n", "# y_hat = model_linear.predict(x)\n", "\n", "# วัด mean squared error จากการทำนาย\n", "def mse(y,y_hat):\n", " return np.mean((y-y_hat)**2)/y.shape[0]\n", "\n", "mse_val = mse(y_true, y_hat)\n", "mse_val_noisy = mse(y_true, y)\n", "\n", "# แสดงผลการทำนาย\n", "fig, ax = plt.subplots()\n", "ax.scatter(x, y, c='b', label='Observed')\n", "ax.set(xlabel='x', ylabel='y')\n", "ax.scatter(x, y_hat, c='r', label='Predicted')\n", "ax.plot(x_whole_line, y_true_whole_line, 'k--', label='True')\n", "ax.legend()\n", "ax.set_title(f\"The error as measured by MSE = {mse_val:0.4f} (red) and {mse_val_noisy:0.4f} (blue) with respect to the black dash line\")\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "ed2kL65NZcOP" }, "source": [ "จากการสังเกตด้วยตา จะเห็นว่าค่า $y$ ที่โมเดลได้ทำนายออกมา (จุดสีแดง) มีความสอดคล้องกับความสัมพันธ์ระหว่าง $x$ และ $y$ ที่แท้จริง (เส้นประสีดำ) มากกว่าข้อมูลที่เราเก็บมาเสียอีก (จุดสีน้ำเงิน)\n", "\n", "นอกจากนั้น เราก็ได้ใช้ loss function ตัวเดิม\n", "\n", "$$MSE(Y,\\hat{Y}) = L(Y,\\hat{Y}) =\\frac{1}{n}\\sum_{i=1}^{n}\\left(y_{i}-\\hat{y_i}\\right)^{2}$$\n", "\n", "มาเป็นมาตรวัดความเหมือน/ความคล้ายระหว่างชุดข้อมูลเชิงปริมาณ และพบว่า MSE ระหว่างค่า $y$ ของจุดสีแดงกับค่า $y$ ที่มาจากความสัมพันธ์ที่แท้จริง (สีดำ) มีค่าต่ำกว่า MSE ระหว่างค่า $y$ ที่เราเก็บมาซึ่งมีสัญญาณรบกวน​ (สีน้ำเงิน) กับ ค่า $y$ ที่มาจากความสัมพันธ์ที่แท้จริง (สีดำ)\n", "\n", "จะเห็นได้ว่าการเปรียบเทียบทั้งแบบเชิงคุณภาพและเชิงปริมาณมีความสอดคล้องกันในระดับหนึ่ง\n", "\n", "\n", "

\n", "MSE เป็นแค่หนึ่งในวิธีสำหรับวัดผล (evaluation metric) เท่านั้น ยังมีอีกหลายวิธีที่ใช้วัดผลออกมาเป็นตัวเลข เช่น mean absolution error (MAE), root mean squared error (RMSE), correlation coeficient, หรือแม้กระทั่งความเป็นไปได้(likelihood) ของแบบจำลองเทียบกับชุดข้อมูลที่เก็บรวบรวมได้

แต่ละวิธีในการวัดผลต่างมีสมมติฐานของข้อมูลที่แตกต่างกันจึงเหมาะสมกับข้อมูลที่ต่างกัน การเลือกใช้ evaluation metric ที่เหมาะสมจะส่งผลให้แบบจำลองที่เราสร้างขึ้นสามารถอธิบายข้อมูลได้ดีมากขึ้น

\n", "อย่างไรก็ตามวิธีการวัดผลข้างต้นนั้นหมาะสำหรับการสร้างแบบจำลองประเภท regression ส่วนปัญหาอื่นๆ เช่น classification ก็จำเป็นต้องมีการวัดความสามารถของแบบจำลองที่แตกต่างออกไป เช่น ความแม่นยำ (accuracy), F-score ฯลฯ
\n", "\n", "ใน module นี้ เราจะใช้ MSE เป็น evaluation metric ไปก่อน แต่ใน module ถัด ๆ ไป หรือการทำงานจริง เราจะได้เห็น evaluation metric ที่หลากหลายมากยิ่งขึ้น" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "QUAPcvutPUn8" }, "source": [ "\n", "---\n", "เราลองกลับมาดูตัวอย่างที่คล้าย ๆ กับตัวอย่างที่พูดไว้ในช่วง Introduction ของ module นี้ ที่เราให้แมวดูภาพที่มีลักษณะต่าง ๆ กัน ในขณะที่เราใช้ electrode บันทึกการส่งสัญญาณของ neuron ใน visual cortex ของแมวตัวนั้น\n", "\n", "หากเราลองเปลี่ยนแปลง contrast ของภาพที่ให้แมวดู (โดยใช้ orientation ที่ neuron ตัวนั้น sensitive ที่สุดเท่านั้น ไม่มีการเปลี่ยน orientation เลย) แล้วเก็บค่า average firing rate เอาไว้ เราสามารถลองศึกษาดูว่าการเปลี่ยน contrast ของภาพมันมีผลอย่างไรต่อ average firing rate ของ neuron ตัวนั้น\n", "\n", "สมมติว่าเราลองเอาข้อมูลมา plot ดู แล้วพบข้อมูลที่หน้าตาเหมือน code ใน cell ถัดไป" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 449 }, "id": "FrqWw1h1Lr1X", "outputId": "8d0b3159-778c-467b-f00a-c3ad8450aeb7" }, "outputs": [], "source": [ "# ทดลองสร้างข้อมูลโดยการเรียกใช้ generate_sample_linear\n", "num_samples = 25\n", "w0_true, w1_true = 1, 2 # กำหนดค่า w0 และ w1 ที่แท้จริง สำหรับสร้างข้อมูล\n", "x_example = 3 * np.random.rand(num_samples, 1) + 3\n", "y_example = generate_sample_linear(x_example, w0_true, w1_true, include_noise=True)\n", "\n", "# Plot ข้อมูล x, y ที่มีอยู่\n", "fig, ax = plt.subplots()\n", "ax.scatter(x_example, y_example, c='b')\n", "ax.set(xlabel='contrast [a.u.]', ylabel='average firing rate [a.u]')\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "5ajoqeR3S0HS" }, "source": [ "จากการดูหน้าตาของกราฟนี้ เราพบว่ามีลักษณะเป็นคล้ายเส้นตรง (อย่างน้อยก็ในช่วงค่า $x$ ระหว่าง $3$ กับ $6$)\n", "\n", "ถ้าเราต้องการทำนายค่า average firing rate ของ neuron ตัวนี้จากค่า contrast ค่าใดค่าหนึ่งในช่วง $x$ ระหว่าง $3$ กับ $6$ วิธีหนึ่งที่เราได้เรียนจากเนื้อหาในบทเรียนนี้ก็คือการประมาณค่าความสัมพันธ์ระหว่าง average firing rate ของ neuron (แกน $y$) กับค่า contrast (แกน $x$) ด้วยสมการเส้นตรง\n", "\n", "$$ \\hat{y} = \\hat{w_0} + \\hat{w_1} x$$\n", "\n", "โดยสามารถหาค่า $\\hat{w_0}$ และ $\\hat{w_1}$ การเรียกใช้ `sklearn.linear_model.LinearRegression` ได้อย่างง่ายดาย\n", "\n", "**ข้อควรระวัง**\n", "\n", "ข้อมูลแสดงความสัมพันธ์ที่แท้จริงระหว่าง average firing rate กับ contrast มีความซับซ้อนกว่าตัวอย่างที่เราสร้างไว้ตรงนี้มาก เช่น หากเราดูค่า contrast ที่นอกเหนือจากช่วง $3 - 6$ เราอาจพบว่า\n", "\n", "* ความสัมพันธ์เริ่มมีความโค้งงอ ไม่เป็นเส้นตรงอีกต่อไป\n", "* เมื่อมีค่า contrast สูงถึงระดับหนึ่ง ค่า average firing rate ก็ไม่เพิ่มขึ้นแล้ว\n", "\n", "ถ้าเราต้องการใช้โมเดลตัวเดียว เพื่ออธิบายความสัมพันธ์ทั้งหมดได้ เรามีความจำเป็นต้องพัฒนาโมเดลที่มีความซับซ้อนมากยิ่งขึ้น\n", "\n", "หรืออีกวิธีหนึ่งก็คือการแบ่งแกน $x$ ออกเป็นช่วงต่าง ๆ แล้วเราใช้สมการต่างชนิดกัน อธิบายความสัมพันธ์ในแต่ละช่วง" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "nm6kOPEOW5nl" }, "source": [ "## Multiple Linear Regression\n", "\n", "\n", "\n", "[Slides: Simple Linear Models 3](https://github.com/ichatnun/brainCodeCamp2023_lectures/blob/main/IntroToModeling/modeling_part1c_linear3_multivariate1.pdf)\n", "\n", "ทีนี้เรามาลองดูการทดลองที่เปลี่ยนไปเล็กน้อย\n", "\n", "สมมติเราให้น้องแมวดูภาพที่มีการเปลี่ยนแปลง contrast แต่ไม่เปลี่ยน orientation เหมือนในตัวอย่างที่แล้ว **พร้อมกันกับ** การให้ฟังเสียงที่เรากำหนดความดังได้\n", "\n", "แล้วเราไปวัด ค่า average firing rate จาก neuron ประเภท multi-sensory neuron ในขณะที่เราเปลี่ยน contrast ของภาพ และ ความดังของเสียง ไปเรื่อย ๆ เราสามารถเอาข้อมูลนี้มาศึกษาดูว่าการเปลี่ยน contrast และความดัง มีผลต่อ average firing rate ของ neuron ตัวนั้นอย่างไร\n", "\n", "สมมติว่าเราลองเอาข้อมูล (contrast, loudness, average firing rate) มา plot ดู แล้วพบข้อมูลที่หน้าตาเหมือน code ใน cell ถัดไป" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 345 }, "id": "rQYob21hV1Md", "outputId": "5395c46e-ff7b-4d01-87f3-4c3775491ced" }, "outputs": [], "source": [ "def generate_sample_multi_linear(x1, x2, w0=1, w1=2, w2=1, include_noise=True):\n", "\n", " # สร้างสมการเส้นตรงโดยที่จำลองการใส่สัญญาณรบกวนเข้าไป\n", " # เลือก include_noise เป็น True เพื่อกำหนดให้มีค่า noise เพิ่มเข้าไปในสมการ\n", " if include_noise:\n", " # สร้าง Gaussian noise\n", " noise = 0.1*np.random.randn(*x1.shape)\n", " else:\n", " noise = 0\n", "\n", " y = w0 + (w1 * x1) + (w2* x2) + noise\n", "\n", " return y\n", "\n", "\n", "# ทดลองสร้างข้อมูลโดยการเรียกใช้ generate_sample_multi_linear\n", "num_samples = 200\n", "w0_true, w1_true, w2_true = 1, 2, 1\n", "x1 = 3 + 3*np.random.rand(num_samples, 1)\n", "x2 = 3 + 3*np.random.rand(num_samples, 1)\n", "y_multi = generate_sample_multi_linear(x1, x2, w0_true, w1_true, w2_true)\n", "\n", "# แสดงผลภาพ\n", "fig = plt.figure(figsize=(4, 4))\n", "ax = fig.add_subplot(projection='3d')\n", "ax.scatter(x1, x2, y_multi, c='b', marker='o')\n", "ax.set_xlabel('contrast [a.u.]')\n", "ax.set_ylabel('loudness [a.u.]')\n", "ax.set_zlabel('average firing rate [a.u.]')\n", "ax.view_init(elev=20, azim=-70)\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "lWlncYPDnJnX" }, "source": [ "หากเราสังเกตรูปด้านบน เราจะเห็นว่าข้อมูลมีลักษณะเป็นเหมือนแผ่นกระดาษสี่เหลี่ยมผืนผ้า\n", "\n", "ในทางคณิตศาสตร์เราสามารถเขียนสมการของแผ่นกระดาษสี่เหลี่ยมผืนผ้าได้\n", "\n", "$$ y = w_0 + w_1 x_1 + w_2 x_2 $$\n", "\n", "โดยที่ $w_0$, $w_1$ และ $w_2$ เป็นตัวแปรที่เราปรับค่าได้ ซึ่งการปรับค่าตัวแปรเหล่านี้ จะส่งผลให้แผ่นกระดาษนี้ (เราเรียกมันว่า **plane**) มันหมุนไปมา หรือเลื่อนขึ้นลงได้\n", "\n", "

\n", "เราสามารถลองใช้สมการนี้ มาเปรียบเทียบกับข้อมูลของเราดู โดยการลองปรับค่า $w_0$, $w_1$ และ $w_2$ ไปเรื่อย ๆ ตาม code ใน cell ถัดมา" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 441, "referenced_widgets": [ "6e9de88449404beabd223d3c5c8975c8", "b4895d9a84f54dc29d720be32ea3c61e", "2ffb54c36cdd4992870f069562c54dcc", "e9926ecb78784ad497b975e06fbc9235", "ca203f5162ca475dbc5995d11b470876", "7233b59147bd4251b2e3554ded4e5452", "015c5f95c9cb4fd1bbd2b2365f744a88", "50d1a2b2065f46ffa198151952f5072c", "b7f24b5a7d1543f6963c952aeb8e5274", "078c065820834fa682a63943f3a17482", "ba52f23fe8294ebbb3588bfafe7f310f", "ffc2e36d3e264ae6a0bf5358dbc58f06", "417dab5530c846e2be4de00f03a241c1" ] }, "id": "65XSgJDSol-s", "outputId": "84899925-f5d4-4a82-eebd-6b6bd9cf1d2f" }, "outputs": [], "source": [ "# ใส่แถบสำหรับปรับค่า w1_hat และ w2_hat รวมถึงช่องสำหรับให้เลือกว่าจะโขว์เส้นความสัมพันธ์ระหว่าง x และ y ที่แท้จริงหรือไม่\n", "@widgets.interact(w0_hat=widgets.FloatSlider(0.0, min=0.5, max=4),\n", " w1_hat=widgets.FloatSlider(0.0, min=-1, max=4),\n", " w2_hat=widgets.FloatSlider(0.0, min=-1, max=4))\n", "def plot_plane_results(w0_hat, w1_hat, w2_hat):\n", "\n", " # สร้างข้อมูลที่ไม่มีสัญญาณรบกวนมาแบบละเอียดสำหรับค่า x1 และ x2 จำนวนมาก เพื่อใช้ในการวาด plane\n", " num_sample_per_axis = 100\n", " X1_whole_plane, X2_whole_plane = np.meshgrid(3 + 3*np.random.rand(num_sample_per_axis),\n", " 3 + 3*np.random.rand(num_sample_per_axis))\n", "\n", " x1_whole_plane = np.reshape(X1_whole_plane, (-1, 1))\n", " x2_whole_plane = np.reshape(X2_whole_plane, (-1, 1))\n", "\n", " # คำนวณค่า y จากค่า w0_hat และ w1_hat ที่เราเดามา สำหรับค่า x จำนวนมาก\n", " y_predicted_whole_plane = w0_hat + w1_hat * x1_whole_plane + w2_hat * x2_whole_plane\n", "\n", " # Plot รูปออกมา\n", " fig = plt.figure(figsize=(4, 4))\n", " ax = fig.add_subplot(projection='3d')\n", " ax.scatter(x1_whole_plane, x2_whole_plane, y_predicted_whole_plane, c='k', marker='.', label='Predicted', alpha=0.03)\n", " ax.scatter(x1, x2, y_multi, c='b', marker='o')\n", " ax.set_xlabel('contrast [a.u.]')\n", " ax.set_ylabel('loudness [a.u.]')\n", " ax.set_zlabel('average firing rate [a.u.]')\n", " ax.view_init(elev=20, azim=-70)\n", " plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "fc90mQG7uU7q" }, "source": [ "การลองปรับค่า $w_0$, $w_1$ และ $w_2$ ไปเรื่อย ๆ เราน่าจะพอเห็นภาพแล้วว่าตัวแปรแต่ละตัวส่งผลอย่างไรต่อ plane ของเรา เช่น การปรับ $w_0$ เพียงอย่างเดียวจะยก plane ขึ้นหรือลงโดยไม่เปลี่ยนความชันของ plane เลย\n", "\n", "อย่างที่เราได้เคยคุยกันแล้วว่าการลองปรับค่าตัวแปรไปเรื่อย ๆ จนกว่าจะเจอค่าที่อธิบายจุดข้อมูลสีน้ำเงินได้ดีที่สุด เป็นอะไรที่ค่อนข้างใช้เวลานาน เรามาลองใช้เทคนิคที่เราเรียนรู้มาในช่วงแรกของบทเรียนนี้กันดีกว่า\n", "\n", "

\n", "เราจะใช้ mean squared error (MSE) เป็นมาตรวัดเหมือนเดิม แล้วก็หาค่า $w_0$, $w_1$ และ $w_2$ ที่ทำให้มีค่า MSE น้อยที่สุด\n", "\n", "$$ MSE(Y, \\hat{Y})\n", "= L(Y,\\hat{Y})\n", "=\\frac{1}{n}\\sum_{i=1}^{n}\\left(y_{i}-\\hat{y_i}\\right)^{2}\n", "=\\frac{1}{n}\\sum_{i=1}^{n}\\left(y_{i}-(\\hat{w_0} + \\hat{w_1} x_{i1} + \\hat{w_2} x_{i2})\\right)^{2} $$\n", "\n", "เราจะเห็นว่าสมการแทบจะมีหน้าตาเหมือนเดิมเลย ยกเว้นแค่เราเปลี่ยนจาก $\\hat{y} = \\hat{w_0} + \\hat{w_1} x_1$ ไปเป็น $\\hat{y} = \\hat{w_0} + \\hat{w_1} x_{i1} + \\hat{w_2} x_{i2}$\n", "\n", "โดยที่\n", "\n", "* $x_{i1}$ แสดงถึงค่า feature ที่ 1 ของจุดข้อมูลที่ $i$ (ค่า contrast ของจุดที่ $i$)\n", "* $x_{i2}$ แสดงถึงค่า feature ที่ 2 ของจุดข้อมูลที่ $i$ (ค่า loudness ของจุดที่ $i$)\n", "\n", "\n", "

\n", "การหาค่า $w_0$, $w_1$ และ $w_2$ ที่ทำให้มีค่า MSE น้อยที่สุด สามารถเขียนเป็นสมการทางคณิตศาสตร์ได้เป็น\n", "\n", "$$\n", "\\min_{\\hat{w_{0}},\\hat{w_{1}},\\hat{w_2}}L(Y,\\hat{Y})\n", "=\\min_{\\hat{w_{0}},\\hat{w_{1}},\\hat{w_2}}\\frac{1}{n}\\sum_{i=1}^{n}\\left(y_{i}-\\hat{y_i}\\right)^{2}\n", "= \\min_{\\hat{w_{0}},\\hat{w_{1}},\\hat{w_2}}\\frac{1}{n}\\sum_{i=1}^{n}\\left(y_{i}-(\\hat{w_0} + \\hat{w_1} x_{i1} + \\hat{w_2} x_{i2})\\right)^{2}\n", "$$\n", "\n", "ซึ่งเราสามารถแก้สมการนี้ผ่านการเรียกใช้ `LinearRegression` จากไลบรารี่ `scikit-learn` เลย ได้เช่นกัน แต่ต้องลองอ่าน documentation ดูว่าเราจะต้องจัดเรียง dimension ของข้อมูลของเราอย่างไร เพื่อให้เรียกใช้ `LinearRegression` ได้อย่างถูกต้อง\n", "\n", "**ความท้าทาย** สำหรับคนที่มีโอกาสได้ศึกษา linear algebra มาแล้ว อยากให้ลองเขียนสมการนี้ให้อยู่ในรูป vector และ matrix ดู รวมถึงลองแก้สมการดูด้วยเทคนิคที่ผู้เรียนถนัด เช่น การคำนวณ gradient แล้วจับมาเท่ากับศูนย์ (สามารถมองได้ว่า คล้าย ๆ กับการคำนวน derivative แล้วจับมาเท่ากับ $0$ ที่เราเคยเรียนกันมาใน calculus ม. ปลาย)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "VewjCxubhzOm", "outputId": "88633142-3888-4b84-9b14-967acc3ece34" }, "outputs": [], "source": [ "# จัดเรียงข้อมูลให้อยู่ในรูปแบบที่เหมาะสม\n", "X = np.concatenate((x1, x2), axis=1)\n", "\n", "# ให้โมเดลหาค่า w_0, w_1 และ w_2 จากข้อมูลทั้งหมดที่มี\n", "model_multi_linear = LinearRegression()\n", "model_multi_linear.fit(X, y_multi)\n", "w0_hat = model_multi_linear.intercept_[0]\n", "w1_hat = model_multi_linear.coef_[0][0]\n", "w2_hat = model_multi_linear.coef_[0][1]\n", "\n", "print(f\"True w0 {w0_true:0.2f}\")\n", "print(f\"Estimated w0 {w0_hat:0.2f}\\n\")\n", "print(f\"True w1 {w1_true:0.2f}\")\n", "print(f\"Estimated w1 {w1_hat:0.2f}\\n\")\n", "print(f\"True w2 {w2_true:0.2f}\")\n", "print(f\"Estimated w2 {w2_hat:0.2f}\")" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "2sIuSmdP1Wl9" }, "source": [ "จะเห็นว่าค่า $w_0$, $w_1$ และ $w_2$ ที่ประมาณจากโมเดล linear regression มีค่าใกล้กับค่าที่เรากำหนดมาตอนสร้างชุดข้อมูล\n", "\n", "หลังจากที่เรา fit โมเดลแล้ว (โมเดลได้ทำการประมาณค่า $w_0$, $w_1$ และ $w_2$ เรียบร้อยแล้ว) เราสามารถทำนายค่า $y$ จาก $x_1$ และ $x_2$ ใดๆ ได้จากสมการ $ \\hat{y} = \\hat{w_0} + \\hat{w_1} x_1 + \\hat{w_2} x_2$ ได้โดยตรง หรือผ่านการเรียกใช้ฟังก์ชัน `predict` ได้เช่นกัน" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 499 }, "id": "c1LMJh-Z0NSX", "outputId": "58c34613-0179-4ce9-8d26-6182a8f5052a" }, "outputs": [], "source": [ "# สร้างข้อมูลที่ไม่มีสัญญาณรบกวนมาแบบละเอียดสำหรับค่า x1 และ x2 จำนวนมาก เพื่อใช้ในการวาด plane\n", "num_sample_per_axis = 100\n", "X1_whole_plane, X2_whole_plane = np.meshgrid(3 + 3*np.random.rand(num_sample_per_axis),\n", " 3 + 3*np.random.rand(num_sample_per_axis))\n", "x1_whole_plane = np.reshape(X1_whole_plane, (-1, 1))\n", "x2_whole_plane = np.reshape(X2_whole_plane, (-1, 1))\n", "\n", "# ปรับให้อยู่ในรูปแบบที่เหมาะสมกับ LinearRegression\n", "X_whole_plane = np.concatenate((x1_whole_plane, x2_whole_plane), axis=1)\n", "\n", "# ทำนายค่า y ออกมา\n", "y_predicted_whole_plane = model_multi_linear.predict(X_whole_plane)\n", "\n", "# Plot รูปออกมา\n", "fig = plt.figure(figsize=(6, 6))\n", "ax = fig.add_subplot(projection='3d')\n", "ax.scatter(x1_whole_plane, x2_whole_plane, y_predicted_whole_plane, c='k', marker='.', label='Predicted', alpha=0.03)\n", "ax.scatter(x1, x2, y_multi, c='b', marker='o')\n", "ax.set_xlabel('contrast [a.u.]')\n", "ax.set_ylabel('loudness [a.u.]')\n", "ax.set_zlabel('average firing rate [a.u.]')\n", "ax.view_init(elev=20, azim=-70)\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "tK00miuo28ov" }, "source": [ "จะเห็นได้ว่าเรา plane ที่เราหามาจากการแก้โจทย์ สามารถอธิบายข้อมูลที่เรามีอยู่ได้ดีพอสมควร\n", "\n", "---\n", "\n", "การเปลี่ยนจาก\n", "\n", "$$y=w_0 + w_1 x_1$$\n", "\n", "ไปเป็น\n", "\n", "$$y=w_0 + w_1 x_1 + w_2 x_2$$\n", "\n", "ส่งผลให้เรา\n", "\n", "* เปลี่ยนจากเส้นตรงใน 2 มิติ ไปเป็น plane ใน 3 มิติ\n", "\n", "* เปลี่ยนจากการใช้แค่ค่า $x_1$ ในการทำนายค่า $y$ ไปเป็นการมีโอกาสใช้ทั้ง $x_1$ และ $x_2$ ในการทำนายค่า $y$\n", "\n", "**ข้อสังเกต** สมการ $y=w_0 + w_1 x_1$ เป็นกรณีพิเศษ (special case) ของสมการ $y=w_0 + w_1 x_1 + w_2 x_2$ ที่กำหนดให้ $w_2=0$\n", "\n", "\n", "

\n", "เราสามารถเพิ่มจำนวนตัวแปรเข้าไปอีกจนเกิดเป็นสมการ\n", "\n", "$$ y=w_0 + w_1 x_1 + w_2 x_2 + ... + w_p x_p $$\n", "\n", "ที่มีตัวแปรทั้งหมด\n", "$p+1$\n", "ตัว ซึ่งประกอบด้วย $w_0, w_1, ..., w_p$\n", "\n", "ซึ่งสมการนี้จะถือเป็นสมการเชิงเส้นเหมือนเดิม แต่เราจะอยู่ในมิติที่สูงขึ้นเรื่อย ๆ เช่น\n", "\n", "* $p=1$: $ y=w_0 + w_1 x_1$ เป็นเส้นตรง\n", "* $p=2$: $ y=w_0 + w_1 x_1 + w_2 x_2$ เป็นแผ่นกระดาษสี่เหลี่ยม (plane)\n", "* $p>2$: $ y=w_0 + w_1 x_1 + ... + w_p x_p$ เป็นแผ่นกระดาษใน $p+1$ มิติ หรือมีชื่อเรียกทางเทคนิคว่า hyperplane\n", "\n", "\n", "ไม่ว่าเราจะใช้ $p$ มีค่าเป็นเท่าไหร่ก็ตาม เราก็ยังสามารถหาค่า $w_0, w_1, ..., w_p$ ได้โดยการเรียกใช้ `LinearRegression` จากไลบรารี่ `scikit-learn` ได้เหมือนเดิม!\n", "\n", "**หมายเหตุ** ในกรณีที่เราทำงานกับสมการเชิงเส้น (linear) ที่มีจำนวนมิติสูง เรามักจะใช้ linear algebra มาใช้ในการเขียนสมการออกมาให้อยู่ในรูปแบบที่กระชับในรูปของ vector และ matrix และสามารถแก้สามารถที่มีได้โดยใช้เทคนิคทาง optmization ดังแสดงเอาไว้ใน video ที่เป็น optional สำหรับผู้ที่สนใจด้านล่าง\n", "\n", "\n", "\n", "[Slides: Simple Linear Models 4](https://github.com/ichatnun/brainCodeCamp2023_lectures/blob/main/IntroToModeling/modeling_part1d_linear4_multivariate2.pdf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**ผู้จัดเตรียม code ใน tutorial**: ดร. อิทธิ ฉัตรนันทเวช" ] } ], "metadata": { "colab": { "provenance": [] }, "kernelspec": { "display_name": "Python 3", "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": "3.11.3" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "015c5f95c9cb4fd1bbd2b2365f744a88": { "model_module": "@jupyter-widgets/base", "model_module_version": "1.2.0", "model_name": "LayoutModel", "state": { "_model_module": "@jupyter-widgets/base", "_model_module_version": "1.2.0", "_model_name": "LayoutModel", 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\n", 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\n", 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