feat(recommender): nightly ALS with offline metrics and CF candidates in the wave (M6)

- Implicit scores from play events and reactions per the signals table
  (90-day half-life, weaker skips outside the wave, dislikes override).
- numpy ALS for implicit feedback; time-split evaluation on the last
  7 days (NDCG@10, Recall@50) against a popularity baseline; a new model
  is activated only if NDCG@10 does not regress by more than 2%.
- Vectors are written to track_embeddings.cf and user_profiles_rec.taste_cf,
  versions to model_versions; NightlyTrainer runs at TRAIN_HOUR and on
  first start, `pipu-rec train` runs it manually.
- Wave: cf and item_cf candidate sources and a 0.10 cf term in the v1
  score; impressions are tagged heuristic-v1+cf.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

services/recommender/pipu_rec/train/metrics.py

@@ -0,0 +1,39 @@
+"""Офлайн-метрики на отложенной по времени выборке: NDCG@10, Recall@50 (docs/recommendations.md#1)."""
+
+from __future__ import annotations
+
+import math
+from collections.abc import Callable, Iterable
+
+
+def ndcg_at_k(ranked: list[str], relevant: set[str], k: int = 10) -> float:
+    dcg = sum(1.0 / math.log2(i + 2) for i, t in enumerate(ranked[:k]) if t in relevant)
+    ideal = sum(1.0 / math.log2(i + 2) for i in range(min(k, len(relevant))))
+    return dcg / ideal if ideal > 0 else 0.0
+
+
+def recall_at_k(ranked: list[str], relevant: set[str], k: int = 50) -> float:
+    if not relevant:
+        return 0.0
+    return len(set(ranked[:k]) & relevant) / len(relevant)
+
+
+def evaluate(
+    users: Iterable[str],
+    relevant: dict[str, set[str]],
+    rank: Callable[[str], list[str]],
+) -> dict[str, float]:
+    """Средние метрики по пользователям, у которых в тесте есть хотя бы один релевантный трек."""
+    n = 0
+    ndcg = rec = 0.0
+    for u in users:
+        rel = relevant.get(u)
+        if not rel:
+            continue
+        ranked = rank(u)
+        ndcg += ndcg_at_k(ranked, rel, 10)
+        rec += recall_at_k(ranked, rel, 50)
+        n += 1
+    if n == 0:
+        return {"users": 0, "ndcg@10": 0.0, "recall@50": 0.0}
+    return {"users": n, "ndcg@10": round(ndcg / n, 4), "recall@50": round(rec / n, 4)}