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/als.py

@@ -0,0 +1,111 @@
+"""ALS для неявной обратной связи (Hu, Koren, Volinsky, 2008) на numpy.
+
+На масштабе проекта (~100 пользователей × десятки тысяч треков) решение каждой строки — система 64×64:
+весь проход — секунды, без компилируемых зависимостей. Положительная оценка — предпочтение 1 с уверенностью
+c = 1 + α·score; отрицательная — предпочтение 0 с повышенной уверенностью (модель учит «не это»).
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+from numpy.typing import NDArray
+
+F32 = NDArray[np.float32]
+
+
+@dataclass
+class ALSModel:
+    users: list[str]
+    items: list[str]
+    user_factors: F32  # (n_users, k)
+    item_factors: F32  # (n_items, k)
+
+    def user_vec(self, user: str) -> F32 | None:
+        try:
+            i = self.users.index(user)
+        except ValueError:
+            return None
+        vec: F32 = self.user_factors[i]
+        return vec
+
+    def scores(self, user: str) -> NDArray[np.float64]:
+        u = self.user_vec(user)
+        if u is None:
+            return np.zeros(len(self.items))
+        return (self.item_factors @ u).astype(np.float64)
+
+
+def _solve_side(
+    fixed: F32,
+    rows: list[tuple[NDArray[np.intp], NDArray[np.float64], NDArray[np.float64]]],
+    reg: float,
+) -> F32:
+    """Пересчёт одной стороны: для каждой строки (индексы, уверенность, предпочтение) — закрытое решение
+    (YᵀY + Yᵀ(C−I)Y + λI) x = YᵀCp, где YᵀY общий для всех строк."""
+    k = fixed.shape[1]
+    yty = fixed.T @ fixed
+    out = np.zeros((len(rows), k), dtype=np.float32)
+    eye = reg * np.eye(k)
+    for r, (idx, conf, pref) in enumerate(rows):
+        if len(idx) == 0:
+            continue
+        y = fixed[idx].astype(np.float64)
+        a = yty + (y.T * (conf - 1.0)) @ y + eye
+        b = (y.T * conf) @ pref
+        out[r] = np.linalg.solve(a, b)
+    return out
+
+
+def train_als(
+    scores: dict[str, dict[str, float]],
+    factors: int = 64,
+    reg: float = 0.1,
+    alpha: float = 20.0,
+    iterations: int = 12,
+    seed: int = 0,
+) -> ALSModel | None:
+    """Обучает ALS по implicit_score. None — данных нет."""
+    users = sorted(u for u, row in scores.items() if row)
+    items = sorted({t for row in scores.values() for t in row})
+    if not users or not items:
+        return None
+    upos = {u: i for i, u in enumerate(users)}
+    ipos = {t: i for i, t in enumerate(items)}
+    by_user: list[list[tuple[int, float]]] = [[] for _ in users]
+    by_item: list[list[tuple[int, float]]] = [[] for _ in items]
+    for u, row in scores.items():
+        if u not in upos:
+            continue
+        for t, s in row.items():
+            by_user[upos[u]].append((ipos[t], s))
+            by_item[ipos[t]].append((upos[u], s))
+
+    def prep(
+        lists: list[list[tuple[int, float]]],
+    ) -> list[tuple[NDArray[np.intp], NDArray[np.float64], NDArray[np.float64]]]:
+        out = []
+        for lst in lists:
+            idx = np.array([i for i, _ in lst], dtype=np.intp)
+            s = np.array([v for _, v in lst], dtype=np.float64)
+            conf = 1.0 + alpha * np.abs(s) * np.where(s > 0, 1.0, 0.5)
+            pref = (s > 0).astype(np.float64)
+            out.append((idx, conf, pref))
+        return out
+
+    u_rows, i_rows = prep(by_user), prep(by_item)
+    k = min(factors, max(2, len(items) - 1))
+    rng = np.random.default_rng(seed)
+    x = (rng.standard_normal((len(users), k)) * 0.01).astype(np.float32)
+    y = (rng.standard_normal((len(items), k)) * 0.01).astype(np.float32)
+    for _ in range(iterations):
+        x = _solve_side(y, u_rows, reg)
+        y = _solve_side(x, i_rows, reg)
+    return ALSModel(users=users, items=items, user_factors=x, item_factors=y)
+
+
+def normalize(v: F32) -> F32:
+    """L2-нормировка строк (косинусное сходство в волне)."""
+    n = np.linalg.norm(v, axis=-1, keepdims=True)
+    return (v / np.where(n > 0, n, 1.0)).astype(np.float32)