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<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Bias-Variance Tradeoff Visualization</title>
<style>
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background: linear-gradient(135deg, #667eea 0%, #764ba2 100%);
margin: 0;
padding: 20px;
min-height: 100vh;
}
.container {
max-width: 1200px;
margin: 0 auto;
background: rgba(255, 255, 255, 0.95);
border-radius: 20px;
padding: 30px;
box-shadow: 0 20px 40px rgba(0, 0, 0, 0.1);
}
h1 {
text-align: center;
color: #2c3e50;
margin-bottom: 10px;
font-size: 2.5em;
}
.subtitle {
text-align: center;
color: #7f8c8d;
margin-bottom: 40px;
font-size: 1.1em;
}
.scenarios-grid {
display: grid;
grid-template-columns: repeat(auto-fit, minmax(280px, 1fr));
gap: 30px;
margin-bottom: 40px;
}
.scenario {
background: white;
border-radius: 15px;
padding: 20px;
box-shadow: 0 10px 20px rgba(0, 0, 0, 0.1);
transition: transform 0.3s ease, box-shadow 0.3s ease;
border: 3px solid transparent;
}
.scenario:hover {
transform: translateY(-5px);
box-shadow: 0 15px 30px rgba(0, 0, 0, 0.15);
}
.scenario.high-bias-high-variance {
border-color: #e74c3c;
}
.scenario.high-bias-low-variance {
border-color: #f39c12;
}
.scenario.low-bias-high-variance {
border-color: #3498db;
}
.scenario.low-bias-low-variance {
border-color: #27ae60;
}
.scenario h3 {
text-align: center;
margin-bottom: 20px;
font-size: 1.2em;
}
.dartboard {
width: 200px;
height: 200px;
margin: 0 auto 20px;
position: relative;
background: #f8f9fa;
border-radius: 50%;
border: 3px solid #34495e;
}
.target {
width: 20px;
height: 20px;
background: #e74c3c;
border-radius: 50%;
position: absolute;
top: 50%;
left: 50%;
transform: translate(-50%, -50%);
z-index: 10;
}
.target::after {
content: '×';
color: white;
font-size: 14px;
font-weight: bold;
position: absolute;
top: 50%;
left: 50%;
transform: translate(-50%, -50%);
}
.shot {
width: 8px;
height: 8px;
background: #2c3e50;
border-radius: 50%;
position: absolute;
transform: translate(-50%, -50%);
box-shadow: 0 2px 4px rgba(0, 0, 0, 0.3);
}
.rings {
position: absolute;
top: 0;
left: 0;
width: 100%;
height: 100%;
}
.ring {
border: 1px solid rgba(52, 73, 94, 0.2);
border-radius: 50%;
position: absolute;
top: 50%;
left: 50%;
transform: translate(-50%, -50%);
}
.description {
text-align: center;
color: #2c3e50;
line-height: 1.6;
}
.controls {
text-align: center;
margin-bottom: 30px;
}
.btn {
background: linear-gradient(45deg, #3498db, #2980b9);
color: white;
border: none;
padding: 12px 24px;
border-radius: 25px;
cursor: pointer;
font-size: 16px;
margin: 0 10px;
transition: all 0.3s ease;
box-shadow: 0 4px 15px rgba(52, 152, 219, 0.3);
}
.btn:hover {
transform: translateY(-2px);
box-shadow: 0 6px 20px rgba(52, 152, 219, 0.4);
}
.legend {
background: #f8f9fa;
border-radius: 15px;
padding: 20px;
margin-top: 20px;
}
.legend h3 {
color: #2c3e50;
margin-bottom: 15px;
}
.legend-item {
display: flex;
align-items: center;
margin-bottom: 10px;
}
.legend-color {
width: 20px;
height: 20px;
border-radius: 50%;
margin-right: 10px;
}
</style>
</head>
<body>
<div class="container">
<h1>Bias-Variance Tradeoff</h1>
<p class="subtitle">Understanding the four fundamental scenarios in machine learning</p>
<div class="controls">
<button class="btn" onclick="generateAllShots()">🎯 Generate New Shots</button>
<button class="btn" onclick="animateShots()">🎬 Animate Shots</button>
</div>
<div class="scenarios-grid">
<div class="scenario high-bias-high-variance">
<h3>High Bias, High Variance</h3>
<div class="dartboard" id="dartboard1">
<div class="rings">
<div class="ring" style="width: 60px; height: 60px;"></div>
<div class="ring" style="width: 120px; height: 120px;"></div>
<div class="ring" style="width: 180px; height: 180px;"></div>
</div>
<div class="target"></div>
</div>
<div class="description">
<strong>Worst Case:</strong> Shots are both far from target (biased) and scattered everywhere (high variance). The model is both systematically wrong and inconsistent.
</div>
</div>
<div class="scenario high-bias-low-variance">
<h3>High Bias, Low Variance</h3>
<div class="dartboard" id="dartboard2">
<div class="rings">
<div class="ring" style="width: 60px; height: 60px;"></div>
<div class="ring" style="width: 120px; height: 120px;"></div>
<div class="ring" style="width: 180px; height: 180px;"></div>
</div>
<div class="target"></div>
</div>
<div class="description">
<strong>Underfitting:</strong> Shots are consistently off-target but grouped together. The model is predictable but systematically wrong.
</div>
</div>
<div class="scenario low-bias-high-variance">
<h3>Low Bias, High Variance</h3>
<div class="dartboard" id="dartboard3">
<div class="rings">
<div class="ring" style="width: 60px; height: 60px;"></div>
<div class="ring" style="width: 120px; height: 120px;"></div>
<div class="ring" style="width: 180px; height: 180px;"></div>
</div>
<div class="target"></div>
</div>
<div class="description">
<strong>Overfitting:</strong> Shots are centered around the target but widely scattered. The model can be accurate on average but inconsistent.
</div>
</div>
<div class="scenario low-bias-low-variance">
<h3>Low Bias, Low Variance</h3>
<div class="dartboard" id="dartboard4">
<div class="rings">
<div class="ring" style="width: 60px; height: 60px;"></div>
<div class="ring" style="width: 120px; height: 120px;"></div>
<div class="ring" style="width: 180px; height: 180px;"></div>
</div>
<div class="target"></div>
</div>
<div class="description">
<strong>Ideal Case:</strong> Shots are tightly grouped around the target. The model is both accurate and consistent - perfect generalization!
</div>
</div>
</div>
<div class="legend">
<h3>Key Concepts:</h3>
<div class="legend-item">
<div class="legend-color" style="background: #e74c3c;"></div>
<span><strong>Target (×):</strong> True value we want to predict</span>
</div>
<div class="legend-item">
<div class="legend-color" style="background: #2c3e50;"></div>
<span><strong>Shots (●):</strong> Model predictions from different training sets</span>
</div>
<div style="margin-top: 15px;">
<p><strong>Bias:</strong> How far the average prediction is from the target</p>
<p><strong>Variance:</strong> How much predictions vary between different training sets</p>
<p><strong>Goal:</strong> Minimize total error = Bias² + Variance + Noise</p>
</div>
</div>
</div>
<script>
function generateShots(dartboardId, biasOffset, varianceLevel) {
const dartboard = document.getElementById(dartboardId);
const centerX = 100;
const centerY = 100;
// Clear existing shots
const existingShots = dartboard.querySelectorAll('.shot');
existingShots.forEach(shot => shot.remove());
// Generate 8 shots
for (let i = 0; i < 8; i++) {
const shot = document.createElement('div');
shot.className = 'shot';
let x, y;
if (varianceLevel === 'high') {
// High variance: shots spread widely
const angle = Math.random() * 2 * Math.PI;
const distance = Math.random() * 70 + 10;
x = centerX + biasOffset.x + Math.cos(angle) * distance;
y = centerY + biasOffset.y + Math.sin(angle) * distance;
} else {
// Low variance: shots grouped tightly
const angle = Math.random() * 2 * Math.PI;
const distance = Math.random() * 15 + 5;
x = centerX + biasOffset.x + Math.cos(angle) * distance;
y = centerY + biasOffset.y + Math.sin(angle) * distance;
}
// Keep shots within dartboard bounds
x = Math.max(10, Math.min(190, x));
y = Math.max(10, Math.min(190, y));
shot.style.left = x + 'px';
shot.style.top = y + 'px';
dartboard.appendChild(shot);
}
}
function generateAllShots() {
// High bias, high variance - shots far from center and scattered
generateShots('dartboard1', {x: 40, y: -30}, 'high');
// High bias, low variance - shots far from center but grouped
generateShots('dartboard2', {x: -45, y: 35}, 'low');
// Low bias, high variance - shots around center but scattered
generateShots('dartboard3', {x: 0, y: 0}, 'high');
// Low bias, low variance - shots around center and grouped (ideal)
generateShots('dartboard4', {x: 0, y: 0}, 'low');
}
function animateShots() {
const shots = document.querySelectorAll('.shot');
shots.forEach((shot, index) => {
shot.style.opacity = '0';
shot.style.transform = 'translate(-50%, -50%) scale(0)';
setTimeout(() => {
shot.style.transition = 'all 0.5s ease';
shot.style.opacity = '1';
shot.style.transform = 'translate(-50%, -50%) scale(1)';
}, index * 100);
});
}
// Initialize with shots
generateAllShots();
// Add some interactive hover effects
document.querySelectorAll('.scenario').forEach(scenario => {
scenario.addEventListener('mouseenter', function() {
const shots = this.querySelectorAll('.shot');
shots.forEach(shot => {
shot.style.transform = 'translate(-50%, -50%) scale(1.2)';
shot.style.transition = 'transform 0.2s ease';
});
});
scenario.addEventListener('mouseleave', function() {
const shots = this.querySelectorAll('.shot');
shots.forEach(shot => {
shot.style.transform = 'translate(-50%, -50%) scale(1)';
});
});
});
</script>
</body>
</html> |