Network Regression Analyses

• Network regression analyses are computational frameworks using regression techniques to predict and optimize network behaviors in distributed and B5G environments.
• They leverage hierarchical architectures that combine centralized training at the root with decentralized, latency-sensitive inference at leaf nodes using caching policies.
• Performance metrics such as MSE, MAE, and provision time validate the scalability and low latency benefits in complex network deployments.

Network regression analyses refer to computational and statistical frameworks that model, infer, and optimize the behavior or structure of complex networks using regression-based techniques, typically focusing on the prediction and explanation of network-dependent outcomes. In telecommunications and computer networking contexts—especially under high service modularity, distributed functions, and data-driven automation—network regression analyses underpin critical analytics such as traffic prediction, anomaly detection, resource placement, and latency/accuracy trade-off optimization. Emerging paradigms, notably in Beyond-5G (B5G) environments, require hierarchical, distributed, and latency-sensitive network analytics, often leveraging deep learning models with partitioned training and inference stages (Jeon et al., 2023).

1. Hierarchical Frameworks for Network Regression

Network regression analyses in B5G systems are characterized by hierarchical partitioning of analytics tasks. The root node (Root NWDAF) centrally aggregates data, trains global models (e.g., LSTM predictors), and manages model repositories. Leaf NWDAFs, each co-located with individual network function (NF) instances, handle inference locally to achieve low-latency response. Subscription-based model delivery (periodic push of trained models from root to leaf) dominates scheduled inference, while on-demand requests trigger ad hoc model fetch and caching at the leaf (Jeon et al., 2023).

Task assignment is based on compute and latency sensitivity. Offline, high-cost training is centralized; online, latency-sensitive inference is fully decentralized. The model placement at leafs is managed via a frequency-aware caching policy: models with higher request frequency are retained; evictions prioritize least-used models, subject to storage constraints.

2. Mathematical Formulations and Performance Metrics

Regression analyses in such frameworks utilize explicit performance metrics derived from queueing theory, control overhead, and ML model accuracy:

• Analytics Provision Time: $T_{prov} = T_q + T_{trans} + T_{inf} + T_{ctrl}$, where $T_q$ is the queuing delay, $T_{trans}$ is the round-trip time for model and data exchange, $T_{inf}$ is the inference execution time, and $T_{ctrl}$ is the control overhead for model-miss notification.
• Prediction Accuracy: Standard regression metrics are used:
  • Mean Squared Error (MSE): $MSE = \frac{1}{N} \sum_{i=1}^N (y_i - \hat{y}_i)^2$
  • Mean Absolute Error (MAE): $MAE = \frac{1}{N} \sum_{i=1}^N |y_i - \hat{y}_i|$
  • Root Mean Squared Error (RMSE): $RMSE = \sqrt{MSE}$
• Accuracy Loss: $\Delta A = A_{global} - A_{leaf}$
• Optimization Objective: Minimize $\max_n T_{prov}(n)$ subject to $\Delta A \leq \epsilon$ and leaf model store constraints $S_{leaf} \leq S_{max}$.

No closed-form global optimization is implemented; instead, the policy approximates a frequency-aware (LFU) caching solution that addresses the model reuse and storage constraints.

3. System Architecture, Workflow, and Protocols

The architectural design leverages 3GPP-defined Nnwdaf_SBI (REST over HTTP/2) for all analytics, subscription, and model fetch/delivery communications. Root NWDAF registers services with the NRF for discovery and delivers models to leaves. The leaves expose endpoints to the hosting NF, handling all local inference. The root and leaf NWDAFs interoperate via RESTful APIs to synchronize models and subscriptions.

The software stack (reference implementation: free5GC) combines Go (service abstraction, API endpoints) and Python (deep learning modules, PyTorch LSTM with MSE loss). Model storage is managed as flat files with indexed lookup; TorchScript is used for rapid inference deployment in leaf NWDAFs. The main workflow is outlined in the following pseudocode:

def handleAnalyticsRequest(request): if modelStore.contains(request.model_id): result = AnLF.infer(request.input_vector) return AnalyticsResponse(result) else: model = fetchModelFromRoot(request.model_id) modelStore.cache(model) result = AnLF.infer(request.input_vector) return AnalyticsResponse(result)

4. Empirical Evaluation and Comparative Results

Extensive evaluations were performed across three analytics frameworks: conventional centralized (CONV), multi-NWDAF disjoint deployment (MULTI), and hierarchical H-NDAF.

Testbed included Intel i7-10700, RTX2070 GPU, Ubuntu 20.04, with throughput prediction workloads from Lumos5G (input dimensions $D={3,5}$, LSTM 15MB models). Metric results:

• Accuracy: For $D=3$, $MSE=0.29$, $MAE=0.33$, $RMSE=0.53$; for $D=5$, $MSE=0.14$, $MAE=0.21$, $RMSE=0.34$. Global models consistently outperform local-data-only MULTI deployment.
• Provision Time Scaling: With $N_T$ increase ($\alpha=0.5$, $\beta=0.5$), CONV scales by $7.1\times$, MULTI by $6.7\times$, H-NDAF by $3.6\times$; H-NDAF demonstrates superior scalability.
• Cache Hit Effect: Provision time decreases in MULTI and H-NDAF as model reuse probability $\alpha$ increases; CONV lacks local cache, so time remains constant.
• Leaf Storage Impact: Increasing $S_{leaf}$ from 100 to 400MB drives $25$–$40\%$ reduction in $T_{prov}$.
• Request/Subscription Ratio: Higher $\beta$ (demand for on-demand requests) slightly increases $T_{prov}$, mainly when $S_{leaf}$ is constrained.

5. Strengths, Limitations, and Future Directions

Strengths:

• Local inference significantly minimizes latency for analytics.
• Centralized training at root maintains high-fidelity regression models.
• Scalable architecture by offloading online inference to distributed leaves.
• Near-centralized accuracy is maintained with substantial latency reduction.

Limitations and Open Challenges:

• Model store management is limited by simple frequency-based eviction; further development is needed to integrate cost-aware policies and prioritize models by latency sensitivity.
• Root NWDAF becomes a bottleneck for distributed training; federated learning introduces new resiliency and data heterogeneity challenges.
• Data confidentiality and model integrity require robust encryption (TLS 1.3) and signature validation; model poisoning and inversion attacks remain unsolved.

Future Enhancements:

• A learning-aware model caching algorithm optimizing both latency and accuracy under leaf storage constraints.
• Integration of federated or split learning methods to offload training from root NWDAF, facilitating privacy-aware collaborative regression model updates.
• Formalization of hierarchical task allocation under explicit SLA and resource budgets.

6. Generalization and Application Scope

The hierarchical regression analysis framework embodied by H-NDAF (Jeon et al., 2023) generalizes to any distributed, modular network paradigm where local inference is latency-critical and global training is resource-intensive. Network regression analyses enable high-throughput, low-latency service analytics with scalable architectures fit for B5G, SDN, and virtualized infrastructure environments. These frameworks set the foundation for future analytic automation, adaptive resource management, and multi-tiered collaborative intelligence in complex networked systems.