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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 | """Evaluation utilities for decomposition benchmarks."""
from __future__ import annotations
from typing import Any, Dict, List, Optional, Tuple
import numpy as np
import pandas as pd
from .decomp_methods import (
DecompConfig,
DecompMethodName,
decompose_series,
)
from .scenarios import generate_dataset
def _safe_pearson(x: np.ndarray, y: np.ndarray) -> float:
"""
Compute Pearson correlation between x and y with basic safety checks.
"""
x = np.asarray(x, dtype=float)
y = np.asarray(y, dtype=float)
if x.shape != y.shape or x.size == 0:
return float("nan")
x_c = x - x.mean()
y_c = y - y.mean()
vx = np.mean(x_c**2)
vy = np.mean(y_c**2)
if vx <= 1e-12 or vy <= 1e-12:
return float("nan")
cov = np.mean(x_c * y_c)
return float(cov / np.sqrt(vx * vy))
def _safe_spearman(x: np.ndarray, y: np.ndarray) -> float:
"""
Spearman rank correlation implemented via ranking + Pearson.
"""
x = np.asarray(x, dtype=float)
y = np.asarray(y, dtype=float)
if x.shape != y.shape or x.size == 0:
return float("nan")
def _rankdata(arr: np.ndarray) -> np.ndarray:
n = arr.size
order = np.argsort(arr, kind="mergesort")
ranks = np.empty(n, dtype=float)
ranks[order] = np.arange(1, n + 1)
sorted_vals = arr[order]
i = 0
while i < n:
j = i + 1
while j < n and sorted_vals[j] == sorted_vals[i]:
j += 1
if j - i > 1:
avg_rank = np.mean(ranks[order[i:j]])
ranks[order[i:j]] = avg_rank
i = j
return ranks
rx = _rankdata(x)
ry = _rankdata(y)
return _safe_pearson(rx, ry)
def _max_lag_corr(x: np.ndarray, y: np.ndarray, max_lag: int = 10) -> float:
"""
Maximum Pearson correlation over lags in [-max_lag, max_lag].
"""
x = np.asarray(x, dtype=float)
y = np.asarray(y, dtype=float)
if x.size == 0 or y.size == 0:
return float("nan")
n = min(x.size, y.size)
x = x[:n]
y = y[:n]
if n <= 2:
return float("nan")
best = -np.inf
for lag in range(-max_lag, max_lag + 1):
if lag == 0:
xc, yc = x, y
elif lag > 0:
xc = x[lag:]
yc = y[:-lag]
else:
k = -lag
xc = x[:-k]
yc = y[k:]
if xc.size < 3:
continue
r = _safe_pearson(xc, yc)
if not np.isnan(r) and r > best:
best = r
return float(best if best != -np.inf else np.nan)
def _dtw_distance(x: np.ndarray, y: np.ndarray) -> float:
"""
Simple DTW distance (Euclidean cost) with O(T^2) DP.
"""
x = np.asarray(x, dtype=float)
y = np.asarray(y, dtype=float)
n, m = x.size, y.size
if n == 0 or m == 0:
return float("nan")
D = np.full((n + 1, m + 1), np.inf)
D[0, 0] = 0.0
for i in range(1, n + 1):
for j in range(1, m + 1):
cost = (x[i - 1] - y[j - 1]) ** 2
D[i, j] = cost + min(D[i - 1, j], D[i, j - 1], D[i - 1, j - 1])
return float(np.sqrt(D[n, m]))
def compute_time_domain_metrics(
true: np.ndarray,
est: np.ndarray,
prefix: str = "T",
max_lag: int = 10,
) -> Dict[str, float]:
"""
Compute error, bias, correlation, and DTW-style metrics for a component.
"""
true_arr = np.asarray(true, dtype=float).reshape(-1)
est_arr = np.asarray(est, dtype=float).reshape(-1)
metrics: Dict[str, float] = {}
keys = [
f"{prefix}_rmse",
f"{prefix}_mae",
f"{prefix}_bias",
f"{prefix}_r2",
f"{prefix}_pearson",
f"{prefix}_spearman",
f"{prefix}_maxlag_corr",
f"{prefix}_dtw",
]
if true_arr.shape != est_arr.shape or true_arr.size == 0:
for key in keys:
metrics[key] = float("nan")
return metrics
diff = est_arr - true_arr
rmse = float(np.sqrt(np.mean(diff**2)))
mae = float(np.mean(np.abs(diff)))
bias = float(np.mean(diff))
centered_true = true_arr - np.mean(true_arr)
sse = float(np.sum(diff**2))
sst = float(np.sum(centered_true**2))
r2 = float(1.0 - sse / sst) if sst > 1e-12 else float("nan")
pearson = _safe_pearson(true_arr, est_arr)
spearman = _safe_spearman(true_arr, est_arr)
maxlag_corr = _max_lag_corr(true_arr, est_arr, max_lag=max_lag)
dtw = _dtw_distance(true_arr, est_arr)
metrics[f"{prefix}_rmse"] = rmse
metrics[f"{prefix}_mae"] = mae
metrics[f"{prefix}_bias"] = bias
metrics[f"{prefix}_r2"] = r2
metrics[f"{prefix}_pearson"] = pearson
metrics[f"{prefix}_spearman"] = spearman
metrics[f"{prefix}_maxlag_corr"] = maxlag_corr
metrics[f"{prefix}_dtw"] = dtw
return metrics
def compute_freq_metrics(
true: np.ndarray,
est: np.ndarray,
fs: float = 1.0,
prefix: str = "S",
n_peaks: int = 3,
) -> Dict[str, float]:
"""
Compare dominant frequencies in the power spectra of true and estimated components.
"""
true_arr = np.asarray(true, dtype=float).reshape(-1)
est_arr = np.asarray(est, dtype=float).reshape(-1)
metrics = {
f"{prefix}_dom_freq_true": float("nan"),
f"{prefix}_dom_freq_est": float("nan"),
f"{prefix}_dom_freq_abs_err": float("nan"),
f"{prefix}_spectral_corr": float("nan"),
f"{prefix}_topk_freq_hit_rate": float("nan"),
}
if true_arr.shape != est_arr.shape or true_arr.size < 2:
return metrics
sample_spacing = 1.0 / fs if fs > 0 else 1.0
n = true_arr.size
freqs = np.fft.rfftfreq(n, d=sample_spacing)
fft_true = np.fft.rfft(true_arr - true_arr.mean())
fft_est = np.fft.rfft(est_arr - est_arr.mean())
mag_true = np.abs(fft_true)
mag_est = np.abs(fft_est)
if mag_true.size <= 1 or mag_est.size <= 1:
return metrics
mag_true_no_dc = mag_true.copy()
mag_est_no_dc = mag_est.copy()
mag_true_no_dc[0] = 0.0
mag_est_no_dc[0] = 0.0
idx_true = int(np.argmax(mag_true_no_dc))
idx_est = int(np.argmax(mag_est_no_dc))
dom_true = float(freqs[idx_true])
dom_est = float(freqs[idx_est])
dom_err = float(abs(dom_true - dom_est))
spectral_corr = _safe_pearson(mag_true_no_dc[1:], mag_est_no_dc[1:])
peak_count = max(1, min(int(n_peaks), mag_true_no_dc.size - 1))
top_true = set(np.argsort(mag_true_no_dc)[-peak_count:].tolist())
top_est = set(np.argsort(mag_est_no_dc)[-peak_count:].tolist())
topk_hit_rate = float(len(top_true.intersection(top_est)) / float(peak_count))
metrics[f"{prefix}_dom_freq_true"] = dom_true
metrics[f"{prefix}_dom_freq_est"] = dom_est
metrics[f"{prefix}_dom_freq_abs_err"] = dom_err
metrics[f"{prefix}_spectral_corr"] = spectral_corr
metrics[f"{prefix}_topk_freq_hit_rate"] = topk_hit_rate
return metrics
def compute_event_metrics(
true_events: np.ndarray,
est_residual: np.ndarray,
threshold: float = 2.0,
) -> Dict[str, float]:
"""
Approximate event detection metrics using residual thresholding.
"""
true_events = np.asarray(true_events, dtype=float).reshape(-1)
est_residual = np.asarray(est_residual, dtype=float).reshape(-1)
if true_events.shape != est_residual.shape:
raise ValueError("Event and residual arrays must align.")
eps = 1e-8
true_mask = np.abs(true_events) > eps
resid_std = np.std(est_residual)
if resid_std <= 1e-12:
pred_mask = np.zeros_like(true_mask, dtype=bool)
else:
thresh = threshold * resid_std
pred_mask = np.abs(est_residual) > thresh
tp = int(np.logical_and(true_mask, pred_mask).sum())
fp = int(np.logical_and(~true_mask, pred_mask).sum())
fn = int(np.logical_and(true_mask, ~pred_mask).sum())
precision = tp / (tp + fp) if (tp + fp) > 0 else 0.0
recall = tp / (tp + fn) if (tp + fn) > 0 else 0.0
if precision + recall == 0:
f1 = 0.0
else:
f1 = 2 * precision * recall / (precision + recall)
return {
"event_precision": float(precision),
"event_recall": float(recall),
"event_f1": float(f1),
}
def evaluate_decomposition_on_series(
true_series: Dict[str, Any],
method: DecompMethodName,
method_config: Optional[DecompConfig] = None,
fs: float = 1.0,
) -> Dict[str, Any]:
"""
Evaluate one decomposition method on one synthetic series with known ground truth.
"""
y = np.asarray(true_series["y"], dtype=float).reshape(-1)
result = decompose_series(
y,
method=method,
config=method_config,
fs=fs,
meta=true_series.get("meta", {}),
)
metrics: Dict[str, Any] = {
"method": method,
"length": len(y),
"fs": fs,
"method_config": dict(method_config or {}),
"residual_std": float(np.std(result.residual)),
}
meta = true_series.get("meta", {})
metrics["scenario_name"] = meta.get("scenario_name", "")
metrics["global_seed"] = meta.get("global_seed")
metrics["index_within_scenario"] = meta.get("index_within_scenario")
if "trend" in true_series:
metrics.update(
compute_time_domain_metrics(true_series["trend"], result.trend, prefix="T")
)
if "season" in true_series:
season_true = true_series["season"]
metrics.update(
compute_time_domain_metrics(season_true, result.season, prefix="S")
)
metrics.update(
compute_freq_metrics(season_true, result.season, fs=fs, prefix="S")
)
if "events" in true_series and np.any(np.abs(true_series["events"]) > 1e-8):
metrics.update(
compute_event_metrics(true_series["events"], result.residual)
)
return metrics
def evaluate_methods_on_scenarios(
scenario_names: List[str],
methods: List[Tuple[DecompMethodName, Optional[DecompConfig]]],
n_per_scenario: int = 50,
length: int = 512,
base_seed: int = 0,
fs: float = 1.0,
) -> pd.DataFrame:
"""
Generate synthetic data for scenarios, run methods, and aggregate metrics.
"""
dataset = generate_dataset(
scenario_names=scenario_names,
n_per_scenario=n_per_scenario,
length=length,
base_seed=base_seed,
save_dir=None,
)
records: List[Dict[str, Any]] = []
for series_idx, series in enumerate(dataset):
scenario_name = series.get("meta", {}).get("scenario_name", "")
sample_idx = series.get("meta", {}).get("index_within_scenario", series_idx)
for method_name, method_cfg in methods:
metrics = evaluate_decomposition_on_series(
true_series=series,
method=method_name,
method_config=method_cfg,
fs=fs,
)
metrics["method"] = method_name
metrics["sample_index"] = sample_idx
metrics.setdefault("scenario_name", scenario_name)
metrics.setdefault("global_seed", series.get("meta", {}).get("global_seed"))
metrics["series_idx"] = series_idx
records.append(metrics)
if not records:
return pd.DataFrame()
return pd.DataFrame.from_records(records)
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