stoch/examples/linear_regression.html at main · statsim/stoch · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>stoch — Bayesian Linear Regression</title>
<style>
  * { margin: 0; padding: 0; box-sizing: border-box; }
  body {
    font-family: 'Segoe UI', system-ui, -apple-system, sans-serif;
    background: #0f1117;
    color: #e1e4e8;
    min-height: 100vh;
    padding: 24px;
  }
  h1 {
    font-size: 28px;
    font-weight: 600;
    margin-bottom: 4px;
    color: #f0f6fc;
  }
  .subtitle {
    color: #8b949e;
    font-size: 14px;
    margin-bottom: 24px;
  }
  .panels {
    display: grid;
    grid-template-columns: 1fr 1fr;
    gap: 20px;
    margin-bottom: 20px;
  }
  .panel {
    background: #161b22;
    border: 1px solid #30363d;
    border-radius: 8px;
    padding: 16px;
  }
  .panel h2 {
    font-size: 14px;
    font-weight: 600;
    color: #8b949e;
    text-transform: uppercase;
    letter-spacing: 0.5px;
    margin-bottom: 12px;
  }
  canvas {
    width: 100%;
    border-radius: 4px;
    background: #0d1117;
  }
  #status {
    background: #161b22;
    border: 1px solid #30363d;
    border-radius: 8px;
    padding: 16px;
    margin-bottom: 20px;
    font-family: 'SF Mono', 'Fira Code', monospace;
    font-size: 13px;
    color: #58a6ff;
    min-height: 44px;
    display: flex;
    align-items: center;
  }
  #status .spinner {
    display: inline-block;
    width: 14px;
    height: 14px;
    border: 2px solid #30363d;
    border-top-color: #58a6ff;
    border-radius: 50%;
    animation: spin 0.8s linear infinite;
    margin-right: 10px;
    flex-shrink: 0;
  }
  @keyframes spin { to { transform: rotate(360deg); } }
  table {
    width: 100%;
    border-collapse: collapse;
    font-family: 'SF Mono', 'Fira Code', monospace;
    font-size: 13px;
  }
  th {
    text-align: left;
    padding: 8px 12px;
    border-bottom: 1px solid #30363d;
    color: #8b949e;
    font-weight: 500;
  }
  td {
    padding: 8px 12px;
    border-bottom: 1px solid #21262d;
  }
  td.value { color: #79c0ff; }
  td.true-val { color: #3fb950; }
  .histograms {
    display: grid;
    grid-template-columns: 1fr 1fr 1fr;
    gap: 20px;
  }
  @media (max-width: 900px) {
    .panels { grid-template-columns: 1fr; }
    .histograms { grid-template-columns: 1fr; }
  }
</style>
</head>
<body>

<h1>Bayesian Linear Regression</h1>
<p class="subtitle">
  Inferring parameters of y = 4x + 2 using Hamiltonian Monte Carlo (stoch)
</p>

<div id="status"><span class="spinner"></span> Loading TensorFlow.js...</div>

<div class="panels">
  <div class="panel">
    <h2>Data &amp; Posterior Fit</h2>
    <canvas id="scatter" width="600" height="400"></canvas>
  </div>
  <div class="panel">
    <h2>Summary</h2>
    <table id="summary">
      <thead>
        <tr><th>Parameter</th><th>True</th><th>Mean</th><th>Std</th><th>95% CI</th></tr>
      </thead>
      <tbody id="summary-body">
        <tr><td colspan="5" style="color:#8b949e">Waiting for inference...</td></tr>
      </tbody>
    </table>
  </div>
</div>

<div class="histograms">
  <div class="panel">
    <h2>Slope Posterior</h2>
    <canvas id="hist-slope" width="400" height="250"></canvas>
  </div>
  <div class="panel">
    <h2>Intercept Posterior</h2>
    <canvas id="hist-intercept" width="400" height="250"></canvas>
  </div>
  <div class="panel">
    <h2>Sigma Posterior</h2>
    <canvas id="hist-sigma" width="400" height="250"></canvas>
  </div>
</div>

<script src="https://cdn.jsdelivr.net/npm/@tensorflow/tfjs@4/dist/tf.min.js"></script>
<script src="../dist/stoch.min.js"></script>
<script>
'use strict'

// ── Helpers ────────────────────────────────────────────────────

function setStatus(msg, done) {
  const el = document.getElementById('status')
  if (done) {
    el.innerHTML = '<span style="color:#3fb950">&#10003;</span>&nbsp; ' + msg
  } else {
    el.innerHTML = '<span class="spinner"></span> ' + msg
  }
}

function percentile(arr, p) {
  const sorted = [...arr].sort((a, b) => a - b)
  const idx = Math.floor(sorted.length * p)
  return sorted[Math.min(idx, sorted.length - 1)]
}

function mean(arr) {
  return arr.reduce((a, b) => a + b, 0) / arr.length
}

function std(arr) {
  const m = mean(arr)
  return Math.sqrt(arr.reduce((s, x) => s + (x - m) ** 2, 0) / (arr.length - 1))
}

// ── Canvas drawing ─────────────────────────────────────────────

function setupCanvas(canvas) {
  const dpr = window.devicePixelRatio || 1
  const rect = canvas.getBoundingClientRect()
  canvas.width = rect.width * dpr
  canvas.height = rect.height * dpr
  const ctx = canvas.getContext('2d')
  ctx.scale(dpr, dpr)
  return { ctx, w: rect.width, h: rect.height }
}

function drawScatter(canvasId, xs, ys, lines, trueSlope, trueIntercept) {
  const canvas = document.getElementById(canvasId)
  const { ctx, w, h } = setupCanvas(canvas)
  const pad = { top: 20, right: 20, bottom: 40, left: 50 }
  const pw = w - pad.left - pad.right
  const ph = h - pad.top - pad.bottom

  const xMin = Math.min(...xs) - 0.2
  const xMax = Math.max(...xs) + 0.2
  const yMin = Math.min(...ys) - 1
  const yMax = Math.max(...ys) + 1

  function toX(v) { return pad.left + (v - xMin) / (xMax - xMin) * pw }
  function toY(v) { return pad.top + ph - (v - yMin) / (yMax - yMin) * ph }

  // Background
  ctx.fillStyle = '#0d1117'
  ctx.fillRect(0, 0, w, h)

  // Grid
  ctx.strokeStyle = '#21262d'
  ctx.lineWidth = 1
  for (let i = 0; i <= 4; i++) {
    const y = pad.top + (ph / 4) * i
    ctx.beginPath(); ctx.moveTo(pad.left, y); ctx.lineTo(w - pad.right, y); ctx.stroke()
    const x = pad.left + (pw / 4) * i
    ctx.beginPath(); ctx.moveTo(x, pad.top); ctx.lineTo(x, pad.top + ph); ctx.stroke()
  }

  // Axis labels
  ctx.fillStyle = '#8b949e'
  ctx.font = '11px system-ui'
  ctx.textAlign = 'center'
  for (let i = 0; i <= 4; i++) {
    const v = xMin + (xMax - xMin) * i / 4
    ctx.fillText(v.toFixed(1), pad.left + (pw / 4) * i, h - pad.bottom + 16)
  }
  ctx.textAlign = 'right'
  for (let i = 0; i <= 4; i++) {
    const v = yMin + (yMax - yMin) * i / 4
    ctx.fillText(v.toFixed(1), pad.left - 8, pad.top + ph - (ph / 4) * i + 4)
  }

  // Posterior regression lines (thin, semi-transparent)
  if (lines && lines.length > 0) {
    ctx.globalAlpha = 0.08
    ctx.strokeStyle = '#f97583'
    ctx.lineWidth = 1
    for (const { slope, intercept } of lines) {
      ctx.beginPath()
      ctx.moveTo(toX(xMin), toY(slope * xMin + intercept))
      ctx.lineTo(toX(xMax), toY(slope * xMax + intercept))
      ctx.stroke()
    }
    ctx.globalAlpha = 1
  }

  // True line
  ctx.strokeStyle = '#3fb950'
  ctx.lineWidth = 2
  ctx.setLineDash([6, 4])
  ctx.beginPath()
  ctx.moveTo(toX(xMin), toY(trueSlope * xMin + trueIntercept))
  ctx.lineTo(toX(xMax), toY(trueSlope * xMax + trueIntercept))
  ctx.stroke()
  ctx.setLineDash([])

  // Mean posterior line
  if (lines && lines.length > 0) {
    const avgSlope = mean(lines.map(l => l.slope))
    const avgIntercept = mean(lines.map(l => l.intercept))
    ctx.strokeStyle = '#f97583'
    ctx.lineWidth = 2.5
    ctx.beginPath()
    ctx.moveTo(toX(xMin), toY(avgSlope * xMin + avgIntercept))
    ctx.lineTo(toX(xMax), toY(avgSlope * xMax + avgIntercept))
    ctx.stroke()
  }

  // Data points
  ctx.fillStyle = '#58a6ff'
  for (let i = 0; i < xs.length; i++) {
    ctx.beginPath()
    ctx.arc(toX(xs[i]), toY(ys[i]), 4, 0, Math.PI * 2)
    ctx.fill()
  }

  // Legend
  const lx = pad.left + 10, ly = pad.top + 14
  ctx.font = '11px system-ui'
  ctx.fillStyle = '#58a6ff'
  ctx.beginPath(); ctx.arc(lx, ly, 3, 0, Math.PI * 2); ctx.fill()
  ctx.fillStyle = '#8b949e'
  ctx.textAlign = 'left'
  ctx.fillText('Data', lx + 8, ly + 4)

  ctx.strokeStyle = '#3fb950'; ctx.lineWidth = 2; ctx.setLineDash([4, 3])
  ctx.beginPath(); ctx.moveTo(lx - 6, ly + 18); ctx.lineTo(lx + 6, ly + 18); ctx.stroke()
  ctx.setLineDash([])
  ctx.fillText('True (y=4x+2)', lx + 8, ly + 22)

  if (lines && lines.length > 0) {
    ctx.strokeStyle = '#f97583'; ctx.lineWidth = 2.5
    ctx.beginPath(); ctx.moveTo(lx - 6, ly + 36); ctx.lineTo(lx + 6, ly + 36); ctx.stroke()
    ctx.fillText('Posterior mean', lx + 8, ly + 40)
  }
}

function drawHistogram(canvasId, values, trueValue, label) {
  const canvas = document.getElementById(canvasId)
  const { ctx, w, h } = setupCanvas(canvas)
  const pad = { top: 10, right: 20, bottom: 40, left: 50 }
  const pw = w - pad.left - pad.right
  const ph = h - pad.top - pad.bottom

  const nBins = 30
  const vMin = Math.min(...values)
  const vMax = Math.max(...values)
  const range = vMax - vMin || 1
  const binWidth = range / nBins
  const bins = new Array(nBins).fill(0)

  for (const v of values) {
    const idx = Math.min(Math.floor((v - vMin) / binWidth), nBins - 1)
    bins[idx]++
  }

  const maxCount = Math.max(...bins)

  // Background
  ctx.fillStyle = '#0d1117'
  ctx.fillRect(0, 0, w, h)

  // Bars
  ctx.fillStyle = '#1f6feb'
  for (let i = 0; i < nBins; i++) {
    const x = pad.left + (i / nBins) * pw
    const barH = (bins[i] / maxCount) * ph
    ctx.fillRect(x, pad.top + ph - barH, pw / nBins - 1, barH)
  }

  // True value line
  const trueX = pad.left + ((trueValue - vMin) / range) * pw
  ctx.strokeStyle = '#3fb950'
  ctx.lineWidth = 2
  ctx.setLineDash([4, 3])
  ctx.beginPath()
  ctx.moveTo(trueX, pad.top)
  ctx.lineTo(trueX, pad.top + ph)
  ctx.stroke()
  ctx.setLineDash([])

  // Posterior mean line
  const m = mean(values)
  const meanX = pad.left + ((m - vMin) / range) * pw
  ctx.strokeStyle = '#f97583'
  ctx.lineWidth = 2
  ctx.beginPath()
  ctx.moveTo(meanX, pad.top)
  ctx.lineTo(meanX, pad.top + ph)
  ctx.stroke()

  // X-axis labels
  ctx.fillStyle = '#8b949e'
  ctx.font = '11px system-ui'
  ctx.textAlign = 'center'
  for (let i = 0; i <= 4; i++) {
    const v = vMin + range * i / 4
    ctx.fillText(v.toFixed(2), pad.left + (pw / 4) * i, h - pad.bottom + 16)
  }

  // Legend
  ctx.font = '11px system-ui'
  ctx.textAlign = 'right'
  ctx.fillStyle = '#3fb950'
  ctx.fillText('true = ' + trueValue.toFixed(2), w - pad.right, pad.top + 14)
  ctx.fillStyle = '#f97583'
  ctx.fillText('mean = ' + m.toFixed(3), w - pad.right, pad.top + 28)
}

// ── Main ───────────────────────────────────────────────────────

async function main() {
  await tf.ready()
  setStatus('Generating synthetic data...')
  await new Promise(r => setTimeout(r, 50))

  const { distributions, mcmc, bijectors } = stoch

  // ── Generate data: y = 4x + 2 + noise ──

  const TRUE_SLOPE = 4
  const TRUE_INTERCEPT = 2
  const TRUE_SIGMA = 0.5
  const N = 50

  const xArr = []
  const yArr = []
  for (let i = 0; i < N; i++) {
    const x = (Math.random() * 4) - 1  // x in [-1, 3]
    const y = TRUE_SLOPE * x + TRUE_INTERCEPT + (Math.random() + Math.random() + Math.random() - 1.5) * TRUE_SIGMA * 1.63
    xArr.push(x)
    yArr.push(y)
  }

  const xData = tf.tensor1d(xArr)
  const yData = tf.tensor1d(yArr)

  // Draw initial scatter
  drawScatter('scatter', xArr, yArr, null, TRUE_SLOPE, TRUE_INTERCEPT)

  setStatus('Setting up HMC kernel...')
  await new Promise(r => setTimeout(r, 50))

  // ── Target log probability ──

  const targetLogProb = ({ slope, intercept, sigma }) => {
    return tf.tidy(() => {
      const yPred = tf.add(tf.mul(slope, xData), intercept)
      const residuals = tf.sub(yData, yPred)
      // Manual Normal log prob to avoid creating/disposing distribution objects in hot loop
      const logLik = tf.sum(
        tf.sub(
          tf.mul(-0.5, tf.square(tf.div(residuals, sigma))),
          tf.add(tf.log(sigma), 0.5 * Math.log(2 * Math.PI))
        )
      )
      // Priors: N(0, 10) for slope/intercept
      const priorSlope = tf.mul(-0.5, tf.square(tf.div(slope, 10)))
      const priorIntercept = tf.mul(-0.5, tf.square(tf.div(intercept, 10)))
      // LogNormal(0, 1) prior for sigma: logP(sigma) = -log(sigma) - 0.5*log(sigma)^2 - 0.5*log(2pi)
      const logSigma = tf.log(sigma)
      const priorSigma = tf.sub(tf.mul(-0.5, tf.square(logSigma)), logSigma)
      return tf.addN([logLik, priorSlope, priorIntercept, priorSigma])
    })
  }

  // ── HMC with step size adaptation + bijector for sigma > 0 ──

  const NUM_RESULTS = 500
  const NUM_BURNIN = 300

  const kernel = new mcmc.DualAveragingStepSizeAdaptation({
    innerKernel: new mcmc.TransformedTransitionKernel({
      innerKernel: new mcmc.HamiltonianMonteCarlo({
        targetLogProbFn: targetLogProb,
        stepSize: 0.05,
        numLeapfrogSteps: 10
      }),
      bijectors: { sigma: new bijectors.Exp() }
    }),
    numAdaptationSteps: NUM_BURNIN
  })

  setStatus(`Running HMC: ${NUM_BURNIN} burn-in + ${NUM_RESULTS} samples...`)
  await new Promise(r => setTimeout(r, 50))

  const startTime = performance.now()

  const { samples } = mcmc.sampleChain({
    numResults: NUM_RESULTS,
    numBurninSteps: NUM_BURNIN,
    currentState: {
      slope: tf.scalar(0),
      intercept: tf.scalar(0),
      sigma: tf.scalar(1)
    },
    kernel
  })

  const elapsed = ((performance.now() - startTime) / 1000).toFixed(1)

  // ── Extract results ──

  const slopeArr = Array.from(samples.slope.dataSync())
  const interceptArr = Array.from(samples.intercept.dataSync())
  const sigmaArr = Array.from(samples.sigma.dataSync())

  // Dispose sample tensors
  samples.slope.dispose()
  samples.intercept.dispose()
  samples.sigma.dispose()
  xData.dispose()
  yData.dispose()

  setStatus(`Done in ${elapsed}s. ${NUM_RESULTS} posterior samples collected.`, true)

  // ── Draw results ──

  // Posterior regression lines (subsample 100 for plotting)
  const lines = []
  const step = Math.max(1, Math.floor(slopeArr.length / 100))
  for (let i = 0; i < slopeArr.length; i += step) {
    lines.push({ slope: slopeArr[i], intercept: interceptArr[i] })
  }
  drawScatter('scatter', xArr, yArr, lines, TRUE_SLOPE, TRUE_INTERCEPT)

  // Histograms
  drawHistogram('hist-slope', slopeArr, TRUE_SLOPE, 'Slope')
  drawHistogram('hist-intercept', interceptArr, TRUE_INTERCEPT, 'Intercept')
  drawHistogram('hist-sigma', sigmaArr, TRUE_SIGMA, 'Sigma')

  // Summary table
  const params = [
    { name: 'Slope', true: TRUE_SLOPE, samples: slopeArr },
    { name: 'Intercept', true: TRUE_INTERCEPT, samples: interceptArr },
    { name: 'Sigma (&sigma;)', true: TRUE_SIGMA, samples: sigmaArr }
  ]

  let html = ''
  for (const p of params) {
    const m = mean(p.samples)
    const s = std(p.samples)
    const lo = percentile(p.samples, 0.025)
    const hi = percentile(p.samples, 0.975)
    html += `<tr>
      <td>${p.name}</td>
      <td class="true-val">${p.true.toFixed(2)}</td>
      <td class="value">${m.toFixed(3)}</td>
      <td class="value">${s.toFixed(3)}</td>
      <td class="value">[${lo.toFixed(3)}, ${hi.toFixed(3)}]</td>
    </tr>`
  }
  document.getElementById('summary-body').innerHTML = html
}

main().catch(err => {
  setStatus('Error: ' + err.message, true)
  console.error(err)
})
</script>

</body>
</html>