[危機感知AI #2] 14天縱向時序融合與86.7%極值偏置攻克

**【生命支持與緊急心理援助提示】 本文探討高危自殺危機文本檢測系統中的機率論除錯與時間序列狀態推斷工程。如果您或身邊的人正在經歷嚴重心理危機或需要緊急幫助，請聯繫專業援助機構：

• 台灣地區：安心專線 1925 / 生命線 1995 / 張老師專線 1980
• 香港特區：撒瑪利亞防止自殺會 2389 2222 / 協青社 9088 1023
• 國際援助：請查閱 findahelpline.com 獲取各國即時援助管道。 ※文中所用所有日誌與文本均經過100%合成生成與嚴格假名化脫敏，杜絕臨床隱私洩露。**

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引言：從單句危機感知(Level 2)邁向多模態縱向狀態融合(Level 4)

在第1篇中，我們攻克了高達524倍的貝氏先驗賠率壁壘，透過兩階段級聯分流架構將高危自殺言論的漏報率(FNR)從98.3%壓縮至7.6%。

但在真實心理危機干預平台中，僅憑單句判定就調動緊急干預專員是不現實的。自殺風險與心理危機是動態演化的時間序列，交織著連續數日的情感下墜軌跡、日常步數衰減與晝夜作息崩塌。

為此，系統設計了基於14天（336小時）滑動窗口整合文本日記、行為日誌的多模態縱向狀態融合引擎（Level 4）。

然而，剛接入測試環境便遭遇了災難性事故：「即便單句分類器擁有高達98%的特異度（誤報率僅2.0%），在連續監測1,000名健康對照人群14天後，竟有867人（86.7%）錯誤觸發了高危緊急預警！」

危機干預中心的工單隊列在72小時內被衝垮，第一線諮商師因警報疲勞（Alert Fatigue）強烈要求下線系統。其元兇並非模型擬合欠佳，而是極值理論中的「極值偏置（Extreme Value Bias）」。

1. Architectural Blueprint: From Level 2 to Level 4

flowchart TD
    subgraph Level2 ["Level 2: Real-time Sentence NLP Inference (Sub-30ms)"]
        A["User Diary Entry / Chat Message"] --> B["Frozen RoBERTa + Logistic Head"]
        B --> C["2-Stage Triage: Cumulative Gate P(y>=2)>=0.12"]
        C --> D["Continuous Expected Risk Output S_expected<br/>(sum k * p_k / 4)"]
    end

    subgraph RingBuffer ["14-Day Circular Rolling Buffer (336 Hours)"]
        D --> E["14-Day Circular State Buffer<br/>(~100 sentences per user)"]
        F["Circadian Activity / Sleep Disruption Logs"] --> E
    end

    subgraph Level4 ["Level 4: Robust Longitudinal Fusion Engine"]
        E --> G{"Emergency Tripwire Check<br/>P(y=4) >= 0.85 ?"}
        G -- "YES (Acute Crisis)" --> H["Tier-1 Immediate Dispatch (0-sec lag)"]
        G -- "NO (Longitudinal)" --> I["Exponential Recency Decay Kernel<br/>w_i = exp(-0.15 * delta_t_days)"]
        I --> J["Top-3 Robust Weighted Trimmed Mean"]
        J --> K{"Fused Score S_fused >= 0.35 ?"}
        K -- "YES" --> L["Tier-2 Clinical Review Ticket"]
        K -- "NO" --> M["Normal Monitoring / Supportive Care"]
    end

    style G fill:#7f1d1d,stroke:#ef4444,stroke-width:2px,color:#fee2e2
    style H fill:#991b1b,stroke:#f87171,stroke-width:2px,color:#ffffff
    style J fill:#065f46,stroke:#34d399,stroke-width:2px,color:#ecfdf5

---

2. [ERR-005] The 86.7% Alert Fatigue Cascade in 14-Day Sliding Windows

1. Raw Error Log & Incident Report

Below is the verified test harness output from simulating 1,000 non-crisis, psychologically healthy users writing daily text journals (average 100 sentences per user across 14 days):

[SIM-ALERT-RUN: 2026-10-28 17:05:41 KST]
INFO:longitudinal_eval: Evaluating 14-Day Sliding Window Aggregator
INFO:longitudinal_eval: Configuration: Window=14 days (336 hrs), Daily sentences=7~8, Total N=100 sentences/user
INFO:longitudinal_eval: Sentence detector per-sentence FPR = 0.020 (2.0% false alarm rate on Class 0 Normal)
--------------------------------------------------------------------------------
Longitudinal Max Fusion Test Results (N=1,000 Normal Non-Crisis Users):
  - Ground Truth Crisis Users: 0 / 1,000 (100% healthy control cohort)
  - Threshold: Window Max Score >= Level 2 (Severe Distress)
  - Simulated Users with at least ONE False Alert in 14 days: 867 / 1,000
  - Empirical 14-Day User-Level False Positive Rate: 86.70% (Theoretical: 86.74%)
  - Total Emergency Alert Tickets Dispatched: 1,248 tickets
CRITICAL: Alert fatigue crash! 86.7% of healthy users triggered active emergency intervention.
Caseworker incident: Automated dispatch queue saturated; center requested pipeline shutdown.

• Error Classification: Statistical Compounding & False Positive Cascade (Extreme Value Explosion)
• Symptom: Out of 1,000 completely healthy individuals, 867 users (86.7%) triggered at least one emergency caseworker intervention ticket over two weeks, rendering the automated alarm system unusable.

2. Environment & Context

• Compute: NVIDIA RTX 4090 GPU Node (VESSL AI) + AMD EPYC 64-Core CPU, Python 3.11.9, NumPy 1.26.4
• Observation Window: 14 days (336 hours), sliding daily with a 24-hour step size.
• Initial Aggregation Logic: Following the clinical safety mandate of "Never miss a single high-risk crisis indicator", the engineering team took the window maximum (np.max) across all sentence risk scores:

  # Initial Flawed Implementation
  window_risk = np.max([sent.risk_level for sent in user_sentences_14d])
  if window_risk >= 2:
      dispatch_emergency_caseworker(user_id)

3. Failed Hypotheses & Attempts

• Hypothesis 1: "Stiffen the single-sentence threshold (tau) to suppress sentence FPR below 0.1%."

  • Attempt: Raised Stage 1 cumulative gate threshold $\tau$ from 0.12 to 0.45.
  • Outcome: Sentence FPR dropped to 0.12%. However, Active Suicidality (Level 4) recall collapsed from 95.0% down to 31.2%. The model failed to detect 68.8% of genuine suicidal patients who used metaphorical or understated despair, violating fundamental clinical safety constraints.

• Hypothesis 2: "Apply a Simple Moving Average (SMA) across all 100 sentences in the window."

  • Attempt: Calculated the unweighted arithmetic mean of expected risk scores across all 14-day sentences.
  • Outcome: The 14-day user-level FPR dropped dramatically to 0.8%. However, for a user who wrote calm, everyday messages for 13 days and suddenly composed an acute suicidal crisis note on Day 14, the 1 acute score was diluted by 90+ preceding normal sentences.
  • The alert was delayed by an average of 72.4 hours, completely missing the acute intervention window.

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3. Deep Root Cause: Mathematical Proof of Extreme Value Bias

Why did an exceptionally accurate sentence classifier (98% specificity, 2% error) compound into an 86.7% disaster over 14 days?

Let $N$ denote the total number of sentences a user writes during the 14-day window. Let $\alpha$ represent the per-sentence False Positive Rate (FPR on Class 0 Normal text).

Assuming independent Bernoulli trials across sentences, the probability that a single normal sentence is correctly classified as Normal is $(1 - \alpha)$.

The probability that all $N$ sentences across the 14-day window are correctly classified without a single false alarm is:

P(All N sentences are correctly classified as Normal) = (1 - alpha)^N

Consequently, the probability that at least one false alarm occurs, driving the window maximum into Level 2+, is derived by the complement rule:

P(At least one False Alarm in Window) = 1 - (1 - alpha)^N

Analytical Table: Cumulative False Alarm Rates Across Window Lengths

Sentence FPR ($\alpha$)	N = 10 sentences	N = 30 sentences	N = 50 sentences	N = 100 sentences (14-Day Avg)	N = 200 sentences
0.5% (0.005)	4.89%	13.96%	22.17%	39.42%	63.30%
1.0% (0.010)	9.56%	26.03%	39.50%	63.40%	86.60%
2.0% (0.020)	18.29%	45.45%	63.58%	86.74% (Empirical Bug)	98.24%
5.0% (0.050)	40.13%	78.54%	92.31%	99.41%	99.99%

• Our sentence-level specificity was an outstanding 98.0% ($\alpha = 0.02$).
• But evaluated across 100 sentences:

P = 1 - (1 - 0.02)^100 = 1 - (0.98)^100 = 1 - 0.1326 = 86.74%

• Taking the naive maximum over a sliding time-series window mathematically guarantees false alarm explosion. The system was doomed to fail regardless of model optimization.

---

4. Clean Code Solution: The Three-Pillar Robust Longitudinal Fuser

To eliminate the 86.7% false alarm cascade while guaranteeing immediate response for acute crises, we developed the RobustTopKTrimmedDecayFuser built on three statistical pillars:

1. Continuous Expected Severity (S_expected):
   • Rather than collapsing predictions into discrete argmax integers (0 to 4), we pass a continuous risk score S = sum(k * p_k / 4).
2. Exponential Recency Decay Kernel:
   • Recent sentences carry more evidentiary weight than older text. Using a half-life of t_half = 4.62 days (λ = 0.15), older isolated spikes decay gracefully:

   w_i = exp(-lambda * delta_t_days)

3. Top-$k$ Weighted Trimmed Mean ($k=3$) & Emergency Tripwire:
   • We extract the top-$k=3$ most severe sentence scores within the window and calculate their weighted mean. An isolated single false positive is absorbed by the other 2 normal samples. However, recurring distress reinforces the score above the threshold.
   • For undeniable acute suicide threats where $P(y=4) \ge 0.85$, an Emergency Tripwire bypasses window smoothing entirely, triggering instant Tier-1 dispatch with zero lag.

Production Implementation Diff

--- a/tests/synth/model/longitudinal_fuser.py
+++ b/tests/synth/model/longitudinal_fuser.py
@@ -35,16 +35,46 @@ class LongitudinalFuser:
-    def aggregate_window_risk(self, sentence_scores):
-        # CRITICAL BUG: Naive max causes 86.7% extreme value bias
-        # return np.max(sentence_scores)
+    def aggregate_window_risk(
+        self,
+        sentence_records,
+        tripwire_thresh: float = 0.85,
+        top_k: int = 3,
+        decay_lambda: float = 0.15
+    ):
+        '''
+        Defeats Extreme Value Bias while guaranteeing zero delay for acute crises.
+        sentence_records: list of dicts: {'expected_score', 'prob_y4', 'timestamp_hours_ago'}
+        '''
+        if not sentence_records:
+            return 0.0, False
+            
+        # 1. Immediate Emergency Tripwire (Zero-delay bypass for acute active crisis)
+        for rec in sentence_records:
+            if rec.get('prob_y4', 0.0) >= tripwire_thresh:
+                return 1.0, True  # Immediate Tier-1 Emergency Alert
+                
+        # 2. Compute Exponential Recency Weights (Half-life = 4.62 days)
+        scores = []
+        weights = []
+        for rec in sentence_records:
+            dt_days = max(0.0, rec['timestamp_hours_ago']) / 24.0
+            w = np.exp(-decay_lambda * dt_days)
+            scores.append(rec['expected_score'])
+            weights.append(w)
+            
+        scores = np.array(scores, dtype=np.float64)
+        weights = np.array(weights, dtype=np.float64)
+        
+        # 3. Top-k Robust Weighted Trimmed Mean
+        if len(scores) <= top_k:
+            fused_score = np.sum(scores * weights) / (np.sum(weights) + 1e-8)
+        else:
+            top_idx = np.argsort(scores)[-top_k:]
+            fused_score = np.sum(scores[top_idx] * weights[top_idx]) / (np.sum(weights[top_idx]) + 1e-8)
+            
+        is_alert = bool(fused_score >= 0.35)
+        return float(fused_score), is_alert

---

5. Empirical Benchmarks: 1,000 Normal Controls vs 60 Crisis Cohorts

We re-evaluated the three aggregation strategies across 1,000 normal controls and 60 verified crisis cohorts:

Evaluation Metric	Naive Max (Baseline)	Simple Moving Average (SMA)	Robust Top-3 Trimmed Decay (Proposed)	Delta vs Naive Max
14-Day Normal Cohort FPR	86.7% (867/1,000)	0.8% (8/1,000)	3.2% (32/1,000)	-83.5%p False Alarms Crushed
Active ($y=4$) Recall	95.0% (57/60)	58.3% (35/60)	95.0% (57/60)	100% Sensitivity Retained
Severe+ ($y \ge 2$) Recall	92.4%	61.2%	94.8%	+2.4%p (Trajectory Boost)
Acute Crisis Detection Lag	0 min (Instant)	72.4 hours (Deadly Lag)	0 min (Tripwire Bypass)	Zero Golden-Time Delay
Caseworker Tickets Issued	1,248 (Queue Crash)	43 (Severe Under-alert)	89 (Clinical Sweet Spot)	92.9% Alert Fatigue Reduction

xychart-beta
    title "14-Day User-Level False Positive Rate Comparison (%)"
    x-axis ["Naive Max (Initial)", "Simple Average (SMA)", "Robust Top-3 Decay (Proposed)"]
    y-axis "User FPR (%)" 0 --> 100
    bar [86.7, 0.8, 3.2]

• False Alarms Slashed by -83.5%p: The 14-day user-level false positive rate dropped from 86.7% down to 3.2%, comfortably beating clinical operational standards (< 5.0%).
• Zero Lag on Acute Emergencies: Unlike simple averages which introduced a lethal 72-hour delay, the Emergency Tripwire guarantees instant dispatch the second an acute suicide signal emerges.

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6. Architectural Summary & Episode #3 Preview

1. Never use naive max() in longitudinal time-series monitoring: Even with 98% specificity, compounding Bernoulli trials over $N=100$ sentences cause an 86.7% false alarm catastrophe.
2. Never rely on naive moving averages (mean) in high-stakes safety AI: Historical calm text dilutes acute distress, leading to fatal 72-hour intervention delays.
3. The 3-Pillar Solution: Continuous Severity + Exponential Decay + Top-k Trimmed Mean + Emergency Tripwire is the only statistically sound framework that achieves 3.2% false alarms and 95.0% acute recall simultaneously.

flowchart LR
    EP1["Episode #1: Sentence NLP & Bayes Barrier<br/>(FNR 98% -> 7%)"] --> EP2["Episode #2: 14-Day Longitudinal Fusion<br/>(86.7% Extreme Value Bias Defeated)"]
    EP2 --> EP3["Episode #3: LightGBM Ordinal Trees<br/>(-log(0)=inf Collapse & Quantile Calibration)"]

In Episode #3, we examine the multimodal gradient boosting stage: How enforcing monotonic probabilities in Frank & Hall ordinal LightGBM models via minimum.accumulate caused Zero-Probability Collapse ($-\log(0) = \infty$) and cross-entropy divergence (ERR-003), and how we stabilized it with epsilon smoothing and quantile calibration.