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proof-of-concept / timeseries-compressibility
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timeseries-compressibility / src / App.tsx
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36e8ceaInteractive explorer for compressibility of quantized filtered Gaussian time seriesJeremy Magland 1import { useEffect, useMemo, useRef, useState } from 'react'
95929e6Monte-Carlo ground-truth script for R, with the command printed in the UIJeremy Magland 2import CopyableCommand from './components/CopyableCommand'
36e8ceaInteractive explorer for compressibility of quantized filtered Gaussian time seriesJeremy Magland 3import Controls from './components/Controls'
4import FilterViz from './components/FilterViz'
5import ScrollingView from './components/ScrollingView'
6import CompressionChart from './components/CompressionChart'
43704d2Clear the analytic rate: R now comes from the timeseries-entropy estimatorJeremy Magland 7import MethodNote from './components/MethodNote'
6b485dfCall R the entropy rate, and put the estimate button under its readoutJeremy Magland 8import { useEntropyRate } from './components/useEntropyRate'
fb1a12fSnap every parameter slider to a ladder of round valuesJeremy Magland 9import { DEFAULT_SPEC, clampSpec, designKernel, kernelNorm } from './model/filters'
e411dffMake LPC order and compression block size controlsJeremy Magland 10import { LATENT_SEED } from './model/latent'
11import { DEFAULT_LPC_ORDER, LPC_ORDERS } from './compress/codecs'
355ddbbAdd per-group entropy limit bars to the compression chartJeremy Magland 12import type { BoundResult, CodecResult } from './compress/codecs'
36e8ceaInteractive explorer for compressibility of quantized filtered Gaussian time seriesJeremy Magland 13import type { CompressRequest, CompressResponse } from './worker/compressWorker'
e411dffMake LPC order and compression block size controlsJeremy Magland 15const BLOCK_SIZES = [10000, 20000, 50000, 100000, 200000, 500000, 1000000]
16const DEFAULT_BLOCK_SIZE = 100000
18interface CompressionState {
19 results: CodecResult[]
355ddbbAdd per-group entropy limit bars to the compression chartJeremy Magland 20 bounds: BoundResult[]
22 computing: boolean
23 error: string | null
26/** The nine codec sizes, measured in a worker on a debounced parameter set. */
e411dffMake LPC order and compression block size controlsJeremy Magland 27function useCompression(
28 kernel: Float64Array,
29 sigma: number,
30 lpcOrder: number,
31 blockSize: number,
32): CompressionState {
36e8ceaInteractive explorer for compressibility of quantized filtered Gaussian time seriesJeremy Magland 33 const [state, setState] = useState<CompressionState>({
34 results: [],
37 computing: true,
38 error: null,
39 })
40 const workerRef = useRef<Worker | null>(null)
41 const idRef = useRef(0)
43 useEffect(() => {
44 const worker = new Worker(new URL('./worker/compressWorker.ts', import.meta.url), {
45 type: 'module',
46 })
47 worker.onmessage = (e: MessageEvent<CompressResponse>) => {
48 if (e.data.id !== idRef.current) return
49 setState({
50 results: e.data.error ? [] : e.data.results,
355ddbbAdd per-group entropy limit bars to the compression chartJeremy Magland 51 bounds: e.data.error ? [] : e.data.bounds,
36e8ceaInteractive explorer for compressibility of quantized filtered Gaussian time seriesJeremy Magland 52 empiricalStd: e.data.empiricalStd,
53 computing: false,
54 error: e.data.error ?? null,
55 })
56 }
57 workerRef.current = worker
58 return () => {
59 worker.terminate()
60 workerRef.current = null
61 }
62 }, [])
64 useEffect(() => {
65 setState(s => ({ ...s, computing: true }))
66 const id = ++idRef.current
67 const timer = setTimeout(() => {
68 const request: CompressRequest = {
69 id,
70 kernel,
71 sigma,
73 lpcOrder,
74 // The same seed the signal view draws from, so the block really is
75 // the data on screen.
76 seed: LATENT_SEED,
78 workerRef.current?.postMessage(request)
79 }, 250)
80 return () => clearTimeout(timer)
43704d2Clear the analytic rate: R now comes from the timeseries-entropy estimatorJeremy Magland 81 }, [kernel, sigma, lpcOrder, blockSize])
83 return state
6b485dfCall R the entropy rate, and put the estimate button under its readoutJeremy Magland 87 * The terminal command that estimates the entropy rate R at the current
43704d2Clear the analytic rate: R now comes from the timeseries-entropy estimatorJeremy Magland 88 * settings, using the unbiased Monte-Carlo estimator from the companion
89 * timeseries-entropy package.
90 */
91function mcCommand(sigma: number, spec: ReturnType<typeof clampSpec>, rate: number): string {
92 const parts = [
93 'uvx --from git+https://github.com/concept-collection/timeseries-entropy',
94 'timeseries-entropy',
95 `--sigma ${sigma}`,
96 ]
98 case 'none':
99 parts.push('--filter none')
100 break
101 case 'movingAverage':
102 parts.push('--filter moving-average', `--width ${spec.width}`)
103 break
104 case 'lowpass':
105 parts.push('--filter lowpass', `--high ${spec.highHz}`, `--taps ${spec.taps}`, `--rate ${rate}`)
106 break
107 case 'bandpass':
108 parts.push(
109 '--filter bandpass',
110 `--low ${spec.lowHz}`,
111 `--high ${spec.highHz}`,
112 `--taps ${spec.taps}`,
113 `--rate ${rate}`,
114 )
115 break
116 case 'firstDifference':
117 parts.push('--filter first-difference')
118 break
119 }
120 return parts.join(' ')
124 const [sigma, setSigma] = useState(5)
125 const [sampleRateHz, setSampleRateHz] = useState(30000)
126 const [spec, setSpec] = useState(DEFAULT_SPEC)
e411dffMake LPC order and compression block size controlsJeremy Magland 127 const [lpcOrder, setLpcOrder] = useState(DEFAULT_LPC_ORDER)
128 const [blockSize, setBlockSize] = useState(DEFAULT_BLOCK_SIZE)
130 const kernel = useMemo(() => designKernel(spec, sampleRateHz), [spec, sampleRateHz])
43704d2Clear the analytic rate: R now comes from the timeseries-entropy estimatorJeremy Magland 131 const sigmaY = useMemo(() => sigma * kernelNorm(kernel), [kernel, sigma])
132 const compression = useCompression(kernel, sigma, lpcOrder, blockSize)
6b485dfCall R the entropy rate, and put the estimate button under its readoutJeremy Magland 133 const entropyRate = useEntropyRate(kernel, sigma)
135 return (
136 <div className="app">
137 <header className="app-header">
138 <h1>Time-series compressibility</h1>
139 <p>
43704d2Clear the analytic rate: R now comes from the timeseries-entropy estimatorJeremy Magland 140 Gaussian noise → FIR filter → round to integers. How well can the integer stream be
141 losslessly compressed, and how close do practical codecs get to the entropy rate of
142 the process?
144 </header>
8a09dfcPin the parameter bar, put compression first, shrink signal and filter panelsJeremy Magland 146 {/* The controls stay pinned so the parameters and the ratios they move
147 are always on screen together, whatever is scrolled to. */}
148 <section className="card control-bar">
150 sigma={sigma}
151 setSigma={setSigma}
152 sampleRateHz={sampleRateHz}
fb1a12fSnap every parameter slider to a ladder of round valuesJeremy Magland 153 setSampleRateHz={rate => {
154 // Band edges are absolute, so a new rate can push them past
155 // Nyquist; re-snap the spec so sliders and kernel stay in step.
156 setSampleRateHz(rate)
157 setSpec(s => clampSpec(s, rate))
158 }}
160 setSpec={setSpec}
161 />
162 </section>
164 <section className="card">
165 <h2>Compression</h2>
166 <div className="stat-row">
167 <div className="stat">
168 <span className="label">predicted std of z</span>
169 <span className="value">
170 {sigmaY.toFixed(2)} <small>steps</small>
171 </span>
172 </div>
173 <div className="stat">
174 <span className="label">measured std of z</span>
175 <span className="value">
176 {compression.results.length > 0 ? compression.empiricalStd.toFixed(2) : '…'}{' '}
177 <small>steps</small>
178 </span>
179 </div>
180 <div className="stat">
6b485dfCall R the entropy rate, and put the estimate button under its readoutJeremy Magland 181 <span className="label">entropy rate R</span>
6b485dfCall R the entropy rate, and put the estimate button under its readoutJeremy Magland 183 {entropyRate.mean !== null ? entropyRate.mean.toFixed(2) : '—'}
184 {entropyRate.se !== null && <small> ± {entropyRate.se.toFixed(2)}</small>}{' '}
3f857e3Estimate the reference rate R in the browserJeremy Magland 185 <small>bits/sample</small>
186 </span>
6b485dfCall R the entropy rate, and put the estimate button under its readoutJeremy Magland 187 {/* The estimate lives with its readout: start, watch it refine,
188 stop; a model change resets it. */}
189 <span className="stat-action">
190 <button onClick={entropyRate.running ? entropyRate.stop : entropyRate.start}>
191 {entropyRate.running ? 'stop' : entropyRate.perPast.length > 0 ? 'refine' : 'estimate'}
192 </button>
193 {/* Each independent past contributes one unbiased estimate;
194 the readout is their average, so that is the word used. */}
195 <span className="estimate-status">
196 {entropyRate.running
197 ? `${entropyRate.perPast.length} estimates · ${entropyRate.progress ?? 'starting…'}`
198 : entropyRate.perPast.length > 0
199 ? `${entropyRate.perPast.length} estimates · M = ${entropyRate.past}`
200 : `M = ${entropyRate.past}`}
201 </span>
202 </span>
204 <div className="stat">
205 <span className="label">implied best ratio</span>
206 <span className="value">
6b485dfCall R the entropy rate, and put the estimate button under its readoutJeremy Magland 207 {entropyRate.mean !== null && entropyRate.mean > 0
208 ? `${(16 / entropyRate.mean).toFixed(2)}×`
209 : '—'}
211 </div>
212 </div>
e411dffMake LPC order and compression block size controlsJeremy Magland 213 {/* Settings of the measurement, not of the model — so they live with
214 the chart they change rather than in the model bar. */}
215 <div className="measure-row">
216 <label>
217 LPC order
218 <select value={lpcOrder} onChange={e => setLpcOrder(Number(e.target.value))}>
219 {LPC_ORDERS.map(o => (
220 <option key={o} value={o}>
221 {o}
222 </option>
223 ))}
224 </select>
225 </label>
226 <label>
227 block size
228 <select value={blockSize} onChange={e => setBlockSize(Number(e.target.value))}>
229 {BLOCK_SIZES.map(n => (
230 <option key={n} value={n}>
231 {n.toLocaleString()} samples
232 </option>
233 ))}
234 </select>
235 </label>
236 </div>
238 <p className="card-note">Compression failed: {compression.error}</p>
239 ) : (
240 <CompressionChart
241 results={compression.results}
355ddbbAdd per-group entropy limit bars to the compression chartJeremy Magland 242 bounds={compression.bounds}
6b485dfCall R the entropy rate, and put the estimate button under its readoutJeremy Magland 243 rateBits={entropyRate.mean}
245 />
246 )}
247 <p className="card-note">
e411dffMake LPC order and compression block size controlsJeremy Magland 248 Measured on a {blockSize.toLocaleString()}-sample block of the same latent data the
5bab85aRatio-first chart, quantization-floor theory formula, line-segment view, fixed latent dataJeremy Magland 249 signal view shows; sizes include everything a decoder needs (ANS symbol table, LPC
355ddbbAdd per-group entropy limit bars to the compression chartJeremy Magland 250 coefficients). Baseline is raw int16 (16 bits/sample). The hollow bar in each group is
251 that group's entropy limit — the order-0 entropy of the stream being coded, which no
252 per-sample entropy coder can beat and ANS falls short of by its symbol table plus its
6b485dfCall R the entropy rate, and put the estimate button under its readoutJeremy Magland 253 own arithmetic loss. The dashed line is the entropy rate R of the process itself,
254 estimated by the button in the stat row above — the limit no lossless method
255 whatsoever can beat (see the method section at the bottom).
6b485dfCall R the entropy rate, and put the estimate button under its readoutJeremy Magland 258 label="cross-check R from the command line:"
43704d2Clear the analytic rate: R now comes from the timeseries-entropy estimatorJeremy Magland 259 command={mcCommand(sigma, spec, sampleRateHz)}
264 <h2>Quantized signal z</h2>
43704d2Clear the analytic rate: R now comes from the timeseries-entropy estimatorJeremy Magland 265 <ScrollingView kernel={kernel} sigma={sigma} sigmaY={sigmaY} />
267 A window of samples from the model, drawn from a fixed latent noise sequence — changing
43704d2Clear the analytic rate: R now comes from the timeseries-entropy estimatorJeremy Magland 268 σ or the filter transforms the same underlying data, so the trace morphs rather than
269 resampling. Press play to advance through the sequence.
271 </section>
273 <section className="card">
274 <h2>Filter</h2>
43704d2Clear the analytic rate: R now comes from the timeseries-entropy estimatorJeremy Magland 275 <FilterViz kernel={kernel} sampleRateHz={sampleRateHz} />
282 </div>
283 )
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