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time-series
time-series-decomposition
benchmark
component-recovery
symbolic-regression
icml-2026
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17b7ba4 | 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 | from __future__ import annotations
from time import perf_counter
from typing import Any, Dict, Optional
import numpy as np
from .._native import invoke_native
from ..backends import finalize_result, resolve_backend, result_from_native_payload, split_runtime_params
from ..core import DecompResult
from ..registry import MethodRegistry
def _infer_period(y: np.ndarray, max_period_search: int = 128) -> int:
y_arr = np.asarray(y, dtype=float).ravel()
n = y_arr.size
if n < 4:
return max(1, n)
centered = y_arr - float(np.mean(y_arr))
spectrum = np.abs(np.fft.rfft(centered))
freqs = np.fft.rfftfreq(n)
if spectrum.size <= 1:
return max(2, min(max_period_search, max(2, n // 4)))
spectrum[0] = 0.0
peak_idx = int(np.argmax(spectrum))
if peak_idx <= 0 or freqs[peak_idx] <= 1e-12:
return max(2, min(max_period_search, max(2, n // 4)))
period = int(round(1.0 / freqs[peak_idx]))
return max(2, min(period, max_period_search, n))
def compute_std_components(
y: np.ndarray,
period: Optional[int] = None,
*,
variant: str = "STD",
max_period_search: int = 128,
eps: float = 1e-12,
) -> Dict[str, Any]:
y_arr = np.asarray(y, dtype=float).ravel()
n = y_arr.size
if n == 0:
zeros = np.zeros(0, dtype=float)
return {
"trend": zeros,
"season": zeros,
"residual": zeros,
"dispersion": zeros,
"seasonal_shape": zeros,
"period": 0,
"variant": variant.upper(),
"n_cycles": 0,
"incomplete_cycle": False,
}
variant_norm = str(variant).upper()
resolved_period = int(period) if period not in (None, 0) else _infer_period(y_arr, max_period_search=max_period_search)
resolved_period = max(1, min(resolved_period, n))
trend = np.zeros(n, dtype=float)
dispersion = np.zeros(n, dtype=float)
seasonal_shape = np.zeros(n, dtype=float)
season = np.zeros(n, dtype=float)
block_shapes = []
block_slices = []
for start in range(0, n, resolved_period):
stop = min(start + resolved_period, n)
sl = slice(start, stop)
block = y_arr[sl]
block_mean = float(np.mean(block))
centered = block - block_mean
block_diversity = float(np.linalg.norm(centered))
if block_diversity <= eps:
shape = np.zeros_like(block)
block_diversity = 0.0
else:
shape = centered / block_diversity
trend[sl] = block_mean
dispersion[sl] = block_diversity
seasonal_shape[sl] = shape
season[sl] = block_diversity * shape
block_shapes.append(shape)
block_slices.append(sl)
average_seasonal_shape = None
if variant_norm == "STDR":
average_seasonal_shape = np.zeros(resolved_period, dtype=float)
counts = np.zeros(resolved_period, dtype=float)
for shape in block_shapes:
average_seasonal_shape[: shape.size] += shape
counts[: shape.size] += 1.0
valid = counts > 0
average_seasonal_shape[valid] /= counts[valid]
season = np.zeros_like(y_arr)
seasonal_shape = np.zeros_like(y_arr)
for sl in block_slices:
avg_shape = average_seasonal_shape[: sl.stop - sl.start]
seasonal_shape[sl] = avg_shape
season[sl] = dispersion[sl] * avg_shape
residual = y_arr - trend - season
return {
"trend": trend,
"season": season,
"residual": residual,
"dispersion": dispersion,
"seasonal_shape": seasonal_shape,
"average_seasonal_shape": average_seasonal_shape,
"period": resolved_period,
"variant": variant_norm,
"n_cycles": len(block_slices),
"incomplete_cycle": bool(n % resolved_period),
}
def _wrap_std_result(result: Dict[str, Any]) -> DecompResult:
components = {
"dispersion": np.asarray(result["dispersion"], dtype=float),
"seasonal_shape": np.asarray(result["seasonal_shape"], dtype=float),
}
if result.get("average_seasonal_shape") is not None:
components["average_seasonal_shape"] = np.asarray(result["average_seasonal_shape"], dtype=float)
return DecompResult(
trend=np.asarray(result["trend"], dtype=float),
season=np.asarray(result["season"], dtype=float),
residual=np.asarray(result["residual"], dtype=float),
components=components,
meta={
"method": result["variant"],
"period": int(result["period"]),
"n_cycles": int(result["n_cycles"]),
"incomplete_cycle": bool(result["incomplete_cycle"]),
},
)
def _single_channel_std(
y: np.ndarray,
*,
cfg: Dict[str, Any],
variant: str,
backend: str,
) -> DecompResult:
period = cfg.get("period", cfg.get("primary_period"))
max_period_search = int(cfg.get("max_period_search", 128))
eps = float(cfg.get("eps", 1e-12))
if backend == "native":
payload = invoke_native(
"std_decompose",
np.asarray(y, dtype=float),
period=period,
variant=variant,
max_period_search=max_period_search,
eps=eps,
)
return result_from_native_payload(payload, method=variant)
result = compute_std_components(
y,
period=period,
variant=variant,
max_period_search=max_period_search,
eps=eps,
)
return _wrap_std_result(result)
def _stack_channelwise_results(results: list[DecompResult], variant: str) -> DecompResult:
trend = np.column_stack([np.asarray(result.trend, dtype=float) for result in results])
season = np.column_stack([np.asarray(result.season, dtype=float) for result in results])
residual = np.column_stack([np.asarray(result.residual, dtype=float) for result in results])
components: Dict[str, np.ndarray] = {}
for key in ("dispersion", "seasonal_shape"):
components[key] = np.column_stack(
[np.asarray(result.components[key], dtype=float) for result in results]
)
avg_shapes = [
np.asarray(result.components["average_seasonal_shape"], dtype=float)
for result in results
if "average_seasonal_shape" in result.components
]
if avg_shapes:
max_len = max(shape.size for shape in avg_shapes)
avg_matrix = np.full((max_len, len(results)), np.nan, dtype=float)
for idx, result in enumerate(results):
if "average_seasonal_shape" not in result.components:
continue
shape = np.asarray(result.components["average_seasonal_shape"], dtype=float)
avg_matrix[: shape.size, idx] = shape
components["average_seasonal_shape"] = avg_matrix
periods = [int(result.meta.get("period", 0)) for result in results]
meta: Dict[str, Any] = {
"method": variant,
"periods": periods,
"n_channels": len(results),
"decomposition_mode": "channelwise",
}
if periods and all(period == periods[0] for period in periods):
meta["period"] = periods[0]
return DecompResult(
trend=trend,
season=season,
residual=residual,
components=components,
meta=meta,
)
def _std_dispatch(y: np.ndarray, params: Dict[str, Any], *, variant: str) -> DecompResult:
started_at = perf_counter()
cfg, runtime = split_runtime_params(params)
backend = resolve_backend(variant, runtime, native_methods=("std_decompose",))
y_arr = np.asarray(y, dtype=float)
if y_arr.ndim == 1:
result = _single_channel_std(y_arr, cfg=cfg, variant=variant, backend=backend)
elif y_arr.ndim == 2:
results = [
_single_channel_std(y_arr[:, idx], cfg=cfg, variant=variant, backend=backend)
for idx in range(y_arr.shape[1])
]
result = _stack_channelwise_results(results, variant)
else:
raise ValueError(f"{variant} expects a 1D series or a 2D (T, C) array.")
return finalize_result(
result,
method=variant,
runtime=runtime,
backend_used=backend,
started_at=started_at,
)
@MethodRegistry.register("STD", input_mode="channelwise")
def std_decompose(
y: np.ndarray,
params: Dict[str, Any],
) -> DecompResult:
return _std_dispatch(y, params, variant="STD")
@MethodRegistry.register("STDR", input_mode="channelwise")
def stdr_decompose(
y: np.ndarray,
params: Dict[str, Any],
) -> DecompResult:
return _std_dispatch(y, params, variant="STDR")
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