File size: 4,097 Bytes
d491dc1 | 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 | # HyperFlow: ML Benchmark & Evaluation Methodology
**System Evaluation Criteria & Mathematical Proofs**
---
## 1. Monte Carlo Simulation Framework
To evaluate model stability under highly noisy and censored hyperlocal conditions, HyperFlow runs a **500-trial Monte Carlo simulation framework**. Each trial generates simulated order logs, telemetry GPS vectors, user complaints, and cancellation coordinates.
```
+---------------------------------------------+
| Monte Carlo Data Generation (500 Trials) |
+---------------------------------------------+
|
+----------------------+----------------------+
| |
[Out-of-Stock Censoring] [Storm Surge Telemetry]
| |
[OLS vs Tobit Estimator] [EWMA vs Gated Forest]
| |
+----------------------+----------------------+------+
|
+------------------------------+
| Wasserstein Distance Calc |
+------------------------------+
```
---
## 2. Tobit Parameter Recovery & Wasserstein Distance
### Tobit MLE Log-Likelihood
Our Tobit regression model accounts for censored sales values on stockout days. The parameter recovery process estimates how close our estimated coefficients ($\hat{\beta}$) are to the true latent demand coefficients ($\beta_{\text{true}}$). The log-likelihood function minimized by the backend L-BFGS-B solver is:
\[L(\beta, \sigma) = \sum_{y_i > 0} \ln \left( \frac{1}{\sigma_i} \phi\left(\frac{y_i - X_i\beta}{\sigma_i}\right) \right) + \sum_{y_i = 0} \ln \left( 1 - \Phi\left(\frac{X_i\beta}{\sigma_i}\right) \right)\]
Where:
* \(\phi(\cdot)\) is the standard normal PDF.
* \(\Phi(\cdot)\) is the standard normal CDF.
* \(\sigma_i\) is the heteroscedastic scale parameter modeled as \(\log(\sigma_i) = X_i\gamma\).
### Wasserstein Distance Evaluation
To prove that our Tobit model recovers the true demand distribution rather than simply predicting the mean, we calculate the **1st Wasserstein Distance** (Earth Mover's Distance) between the predicted demand distribution (\(P_{\text{pred}}\)) and the true demand distribution (\(P_{\text{true}}\)):
\[W_1(P_{\text{pred}}, P_{\text{true}}) = \int_{-\infty}^{\infty} |F_{\text{pred}}(x) - F_{\text{true}}(x)| \, dx\]
* **OLS Baseline**: As censoring rates increase to 60%, the OLS Wasserstein distance degrades to **12.38** due to severe downward bias.
* **Tobit MLE**: Our model maintains a Wasserstein distance of **3.65**, preserving the underlying distribution alignment.
---
## 3. Gated Random Forest ETA Convergence
Display ETA jitter is suppressed by classifying location updates. The Gated Classifier evaluates the residual convergence rate over a moving window:
\[\text{Residual}(t) = |\text{ActualDeliveryTime} - \text{PredictedETA}(t)|\]
If the location update fails to converge toward the actual delivery trajectory, it is flagged as a transient GPS jump:
\[\text{Jitter Flag} = \text{Classifier}\left( \frac{v_{\text{rider}}}{v_{\text{zone}}}, \text{GPS\_Accuracy\_Index}, \Delta\text{Heading} \right)\]
* **Jitter Active**: The smoothing parameter $\alpha$ drops to **0.15** to hold the consumer's display clock stable.
* **Real Delay Active**: The smoothing parameter $\alpha$ rises to **0.70** to pass the delay information immediately.
---
## 4. Anti-Arbitrage Proximity Thresholds
The Cancelled Order Resale (CORO) engine restricts discount exploits by verifying buyer proximity coordinates using the **Haversine Distance Formula**:
\[d = 2R \arcsin \left( \sqrt{\sin^2\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_1)\cos(\phi_2)\sin^2\left(\frac{\Delta\lambda}{2}\right)} \right)\]
Where:
* \(\phi\) is latitude, \(\lambda\) is longitude.
* \(R\) is Earth's radius (6371 km).
* **Exclusion Policy**: Any claim where \(d < 15\text{ meters}\) from the original canceller's coordinates triggers a co-location exclusion alert.
|