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A Novel Approach to Temporal QoS Estimation via Extended Kalman Filter-Incorporated Latent Feature Analysis

Ye Yuan, Song Wang, Hongxun Zhou, Ling Wang, Xin Luo

arXiv:2606.23010v2cs.LG

TL;DR

Temporal QoS prediction is challenged by incomplete data and fluctuations that expose limits in purely data-driven methods. EKL combines EKF-based temporal modeling, ALS-based time-invariant features, and density-oriented parallelization, with experiments reporting strong accuracy and efficiency across real-world datasets.

  • Problem

    Purely data-driven temporal QoS predictors have limited ability to capture non-stationary fluctuations, while missing QoS data must be estimated efficiently.

  • Method

    EKL combines an EKF-based model-driven producer for temporal features, an ALS-based producer for time-invariant features, and density-oriented parallel computation.

  • Results

    EKL obtains the optimal estimation results in 13 of 16 cases and outperforms baselines on fluctuation samples.

  • Takeaways & Limitations

    EKL provides an efficient bidirectional model–data-driven approach for accurate missing temporal QoS prediction and can be integrated into an online autoscaler.

Abstract

from arXiv · show

Predicting temporal Quality of Service (QoS) data is critical for optimizing network services and rationalizing resource allocation in cloud computing and service-oriented systems. Existing mainstream methods have achieved promising predictive performance. However, their purely data-driven manner limits their ability to capture non-stationary temporal patterns, thereby leading to accuracy degradation when temporal QoS data exhibits fluctuations. To tackle this limitation, we propose a novel Extended Kalman Filter-Enhanced Latent Feature Analysis (EKL) model to perform efficient and accurate temporal QoS prediction from the perspective of bidirectional model-data-driven learning. Its main idea is three-fold: a) designing a model-driven feature producer to obtain the temporal latent features to capture the intricate temporal pattern following the principle of an Extended Kalman Filter; b) building a data-driven feature producer based on the alternating least squares algorithm to identify time-invariant latent features describing intrinsic user-service characteristics; c) exploiting a density-oriented parallel strategy that achieves workload balancing by sorting users in accordance with their service invocation density, which effectively elevates computational efficiency. In addition, we provide a rigorous theoretical analysis to formally prove the convergence of the proposed EKL. Experimental evaluations conducted on real-world temporal QoS datasets reveal that our proposed EKL surpasses existing state-of-the-art models with respect to both computational efficiency and prediction accuracy for missing temporal QoS data.

I. Introduction

Temporal QoS prediction matters because service evaluation is costly and user-service matrices are incomplete, while fluctuations bias purely data-driven predictors. EKL addresses this with bidirectional model–data-driven learning, convergence analysis, and density-oriented parallelization.

  • QoS prediction supports service selection because evaluating all candidate services is time-consuming and financially costly.
  • User-service QoS matrices are commonly incomplete, motivating latent feature analysis for missing-value prediction.
  • Purely data-driven predictors can be biased toward steady components and become insensitive to fluctuation components.
  • A density-oriented parallel strategy improves computational efficiency by balancing workload according to service invocation density.
  • EKL combines an EKF-based model-driven producer for temporal latent features with an ALS-based data-driven producer for time-invariant latent features.
  • EKL includes a convergence analysis and achieves gains in accuracy and efficiency on real-world missing-QoS estimation.

II. Related Work

Related work models temporal QoS using tensor factorization, dynamic graph neural networks, and dynamic matrix factorization. EKL differs by combining model- and data-driven learning, separating temporal and time-invariant features, and proving convergence.

  • A. Tensor Factorization: Tensor factorization maps temporal QoS tensors into low-dimensional spaces to construct low-rank approximations.
  • B. Dynamic Graph Neural Network: Dynamic graph neural networks combine graph and sequence networks to model spatial-temporal patterns in dynamic QoS data.
  • C. Dynamic Matrix Factorization: Dynamic matrix factorization incorporates temporal patterns into matrix factorization through state-space, autoregressive, or polynomial latent-factor models.
  • Differences from Existing Models: EKL uses a bidirectional model–data-driven framework, unlike existing purely data-driven approaches.
  • Differences from Existing Models: EKL distinguishes temporal user latent features from time-invariant service latent features, whereas existing models treat all latent features as time-varying.
  • Differences from Existing Models: EKL provides a theoretical convergence guarantee for its bidirectional learning process, which existing studies do not implement.

III. Preliminaries

Temporal QoS is represented as a sequence of incomplete user-service matrices. EKL learns time-dependent user features and time-invariant service features to reconstruct and predict missing QoS entries.

  • A. Symbol and Definition: A temporal user-service matrix sequence contains one user-service QoS matrix for each time slot.
  • A. Symbol and Definition: Each matrix element records a QoS invocation value for a user-service pair, while Λ denotes the known entries because users cannot invoke every service.
  • A. Symbol and Definition: Temporal latent features represent users’ time-dependent preferences, whereas time-invariant latent features capture stable service characteristics across time slots.
  • A. Symbol and Definition: EKL learns temporal and time-invariant latent features to approximate the temporal user-service matrix from its known entries.
  • A. Symbol and Definition: The predicted QoS value is computed as the inner product of a user’s time-specific latent vector and a service’s latent vector.

B. Extended Kalman Filter

The EKL model uses the Extended Kalman Filter principle to learn temporal latent features from evolving QoS states and observations, forming its model-driven feature producer. These features are combined with data-driven time-invariant features within a bidirectional representation-learning design.

  • B. Extended Kalman Filter: An Extended Kalman Filter recursively predicts evolving states in non-stationary temporal systems through state-transition and observation functions.The EKF uses nonlinear transitions and observations to capture complex temporal patterns.
  • B. Extended Kalman Filter: EKL’s model-driven feature producer applies the EKF principle to learn temporal latent features from temporal QoS data.The method uses independent EKFs for users and obtains temporal feature matrices across time slots.
  • B. Extended Kalman Filter: The state-transition function models dependencies between adjacent user states, while Gaussian transition noise represents uncertainty in state evolution.For each user, the state at time t depends nonlinearly on the preceding state.
  • B. Extended Kalman Filter: The observation function maps temporal latent features and invoked service features to observed QoS records, with Gaussian observation noise.The service feature subset for each user is denoted by M^(t)_u, and LeakyReLU is used for the nonlinear activation functions.
  • B. Extended Kalman Filter: Each EKF alternates prediction and update steps: it first produces a prior state estimate, then refines it using observation data and a gain matrix.The resulting temporal latent feature sequence P is constructed across all users and time slots.

B. Data-Driven Feature Producer

The data-driven feature producer learns time-invariant service features after EKL obtains temporal user features through EKF. It uses alternating least squares with regularization to fit the observed QoS records for each service.

  • B. Data-Driven Feature Producer: After obtaining temporal latent features P, EKL solves the time-invariant latent feature matrix Q using an alternating least squares algorithm.The optimization is performed service by service.
  • B. Data-Driven Feature Producer: The service-specific loss combines reconstruction error between invoked QoS records and latent-feature predictions with L2 regularization.The regularization coefficient is denoted by λ.
  • B. Data-Driven Feature Producer: The service-specific optimization is decomposed into linear equations over users invoking that service at different time slots.Different user sets may invoke the same service at different times, motivating the construction shown in Fig. 4.
  • B. Data-Driven Feature Producer: For each service, invoked QoS records are assembled into a vector, while corresponding temporal latent features form a matrix for optimization.The vector length |Λ_s| counts the service’s invoked records across time slots.

C. Density-Oriented Parallel Strategy

The density-oriented parallel strategy improves EKL’s computational efficiency by balancing independent user-level EKF workloads. It allocates users according to their invoked QoS record volumes rather than using an arbitrary distribution.

  • C. Density-Oriented Parallel Strategy: User-specific EKFs are independent, making the temporal feature producer suitable for multi-threaded parallel computation.The large number of matrix operations in temporal feature generation motivates this parallelization.
  • C. Density-Oriented Parallel Strategy: Different users invoke different numbers of QoS records, so naive multi-threading creates uneven workloads and thread waiting.The invoked record count for user u is |Λ_u|, summed across time slots.
  • C. Density-Oriented Parallel Strategy: DPS first limits each thread to a roughly equal number of users, with the maximum determined by the number of users and threads.The ceiling operation rounds the users-per-thread value upward.
  • C. Density-Oriented Parallel Strategy: DPS sorts users by invoked QoS record volume and assigns them round-robin across threads to balance computational density.Users are ranked descending and the middle segment is reversed, producing a descending-then-ascending order before assignment.

A. General Settings

The evaluation uses three real-world temporal QoS datasets, four testing cases per dataset, and twelve state-of-the-art temporal latent feature analysis baselines. Missing-QoS prediction is assessed primarily with RMSE and MAE under varied data-sparsity conditions.

  • A. General Settings: Three real-world datasets comprise two WS-DREAM datasets—Response Time and Throughput—and Alibaba microservice invocation data.Dataset details are summarized in Table I.
  • A. General Settings: Each dataset is evaluated using four testing cases with different training-validation-testing ratios to vary data sparsity.The testing cases are summarized in Table II.
  • A. General Settings: Twelve state-of-the-art temporal LFA models are used as baselines, including graph, tensor, dynamic factorization, and recurrent approaches.The listed baselines include CGTF, TeDCaN, HRST-LR, HMLET, GTN, SGP, MGDN, PGCN, WD-GCN, SGL-ED, hetGNN-LSTM, TM-GCN, and SDNMF.
  • A. General Settings: RMSE and MAE measure missing QoS estimation accuracy, with smaller values indicating higher accuracy.The experiments are repeated ten times per testing case and averaged; EKL uses latent dimension 10 and 16 threads.

B. Comparison Performance

EKL generally outperforms the compared temporal latent feature analysis models in missing QoS estimation accuracy and computational efficiency. Additional tests indicate that its gains are associated with EKF-based modeling, robustness to fluctuations, and competitive performance under temporal splitting.

  • EKL obtains the optimal estimation results on 13 of 16 cases, including the lowest RMSE on D13 at 0.1667.On D13, EKL’s RMSE is lower than every listed baseline, although individual baselines outperform EKL in some other cases.
  • EKL achieves the lowest total time cost in 12 of 16 test cases.On D11, EKL reaches the lowest MAE in 51 seconds, substantially less than the listed baselines.
  • Statistical tests report that EKL outperforms the comparative models, with p-values much lower than the 0.05 significance level.Friedman and Wilcoxon tests evaluate performance across datasets and pairwise against each baseline.
  • Exponential moving average does not improve CGTF or TeDCaN, indicating that EKL’s gain stems specifically from the EKF rather than generic smoothing.Additional fluctuation experiments show EKL outperforming all baselines, while temporal splitting preserves competitive performance.

C. Speedup

EKL’s parallel strategy substantially improves computational efficiency as thread count increases, with speedup measured against the corresponding serial implementation. Experiments also report stable convergence across datasets.

  • Speedup: Speedup measures the total time cost of the serial version against its corresponding parallel implementation.The experiment uses this formula to evaluate EKL’s parallel strategy.
  • Speedup: 11.70 speedup on D23 with M = 16 indicates that EKL’s parallel implementation improves computational efficiency by 11.7 times.The tested thread counts are M = {1, 2, 4, 8, 16}.
  • Speedup: On D23, speedup increases with thread count, reaching reported values of 1.85, 3.59, 6.74, and 11.70.The passage explicitly describes increasing speedup as the number of threads grows.
  • Convergence: EKL shows consistent and stable convergence across datasets, with RMSE declining sharply early in training before reaching a plateau.The reported behavior is attributed to alternating optimization of temporal and time-invariant latent features.

E. Hyperparameter Sensitivity

EKL’s performance is sensitive to key hyperparameters, whose effects motivate systematic tuning and robust default settings. The study also identifies manual tuning and simplified noise assumptions as limitations for broader adaptive use.

  • Hyperparameter sensitivity: EKL’s performance depends on λ, C[w(t)u], and C[r(t)u], with covariance matrices simplified as σwI and σrI.Grid search tunes λ, σw, and σr over predefined scales.
  • Hyperparameter sensitivity: 9.26% lower RMSE is achieved with λ=10−1 than with λ=10−4, corresponding to RMSE values of 0.1773 and 0.1954, respectively.The lower RMSE is reported for the setting λ=10−1.
  • Hyperparameter sensitivity: RMSE and MAE first decrease as σw and σr increase, then rise after those parameters exceed a certain threshold.The reported non-monotonic behavior indicates that both noise-scale parameters affect estimation accuracy.
  • Hyperparameter sensitivity: A robust default setting is provided, and EKL maintains competitive performance across datasets.The default settings and corresponding estimation errors are summarized in Table V.
  • Limitations: EKL’s performance heavily depends on manual hyperparameter tuning, limiting its adaptive capability across different scenarios.The authors propose Bayesian optimization or reinforcement learning for adaptive tuning.
  • Limitations: EKL simplifies state-transition and observation noises as Gaussian distributions, although real QoS data often exhibits spatial-temporal noise correlations.The authors propose adding a spatial-temporal correlation module to capture correlations across users, services, or time slots.
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