REVIEW 4 major objections 3 minor 49 references
Byzantine-resilient federated online learning for Gaussian process regression
T0 review · 4 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash
Pith's one-line read Federated Gaussian process regression can tolerate up to a quarter of malicious agents, and fusing the cloud's trimmed product-of-experts model with each agent's local model strictly improves that agent's predictions.
desk verdict The agent-level fusion idea is sensible, but Theorem 2 Part II's strict MSE improvement claim is not established because inequality (30) is false as written. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the Byzantine-resilient product-of-experts aggregation rule (7). The cloud first removes the $\beta$-largest and $\beta$-smallest local predictive means and the same for local predictive variances, forming the common survivor set $I(t) = I^{\mu}(t) \cap I^{\sigma}(t)$; it then computes $\hat{\mu}_{z_*|D(t)} = \frac{\hat{\sigma}^2_{z_*|D(t)}}{|I(t)|} \sum_{i \in I(t)} \check{\mu}'_{z_*|D^{[i]}(t)} \check{\sigma}'^{-2}_{z_*|D^{[i]}(t)}$ and $\hat{\sigma}^2_{z_*|D(t)} = |I(t)| / \sum_{i \in I(t)} \check{\sigma}'^{-2}_{z_*|D^{[i]}(t)}$. Lemma 2 is the step that makes the trimming work: because $\alpha \leq \beta$, every value surviving in $I(t)$ lies between the minimum and maximum of the benign agents' values, so the weighted average cannot be pulled outside the benign envelope. The second object is the fusion test (9): a per-test-point comparison of $\hat{\theta}\hat{\sigma}^2$ against $\check{\theta}^{[i]}\check{\sigma}^2$ with threshold $\Gamma$, which links the cloud's mean-squared-error bound (Lemma 9) to the local predictor's error floor (Lemma 8) so that the chosen model is the one with the strictly smaller guaranteed error. The whole engine runs on the local GPR variance bounds $\frac{\sigma_f^2 (\sigma_e^{[i]})^2}{\sigma_f^2 + (\sigma_e^{[i]})^2} \leq \check{\sigma}^2_{z_*|D^{[i]}(t)} \leq \sigma_f^2 - \frac{\kappa(d^{[i]}(t))^2}{\sigma_f^2 + (\sigma_e^{[i]})^2}$, which connect the geometric dispersion of each agent's data to the achievable uncertainty.
What would settle it
Choose a regime at the boundary of the claimed tolerance: $\alpha = 0.2$ Byzantine agents and $\beta = 0.1$, a choice the attack model permits since the cloud only knows $\alpha < 1/4$. Let the Byzantine agents report predictive means equal to the largest benign mean plus a small $\varepsilon$, with variances drawn from the benign range so they pass the variance trimming; because $\beta < \alpha$, the mean trimming removes at most $\beta n$ of the extremes, leaving roughly $(\alpha - \beta)n$ Byzantine reports in $I(t)$, and Lemma 2's conclusion fails. Measure the cloud's mean squared error at such points: if it exceeds the $\Theta(d_{\max}(t)) + \Delta(d_{\max}(t))$ bound of Theorem 1 while the benign agents alone would satisfy it, the guarantee is refuted; if it still holds, the tolerance is stronger than the proof suggests.
Extended reading notes
Core claim
The central claim is stated as Theorem 2, Part II. Suppose Assumptions 1–3 hold (the kernel decomposes as a radially decreasing function, the latent function is a Lipschitz Gaussian process, and $0 < \alpha \leq \beta < 1/4$), and build the fusion set by the rule $Z_{\mathrm{fused}}(t) = \{z_* \in Z_* \mid \hat{\theta} \hat{\sigma}^2_{z_*|D(t)} - \check{\theta}^{[i]}(t) \check{\sigma}^2_{z_*|D^{[i]}(t)} < -\Gamma\}$, with the threshold $\Gamma$ and the coefficients $\hat{\theta}$, $\check{\theta}^{[i]}$ defined in the paper. Then for every benign agent $i$ and every test point $z_*$ in the fusion set, $E[(\tilde{\mu}^{[i]}_{z_*|D(t)} - \eta(z_*))^2] < E[(\check{\mu}_{z_*|D^{[i]}(t)} - \eta(z_*))^2]$, and outside the fusion set the two errors are equal. The engine of the proof is the cloud error bound of Theorem 1: with probability at least $1-\delta$, $|\hat{\mu}_{z_*|D(t)} - \eta(z_*)| \leq \Theta(d_{\max}(t)) + \Delta(d_{\max}(t))$, where $\Theta$ captures the attack-free prediction error, which decays as the agents' data become spatially dense, and $\Delta = \frac{\sigma_f^4 + \sigma_f^2 (\sigma_e^{\max})^2 - \kappa(d_{\max})^2}{\sigma_f^2 (\sigma_e^{\min})^2} \cdot \frac{2\alpha}{1-4\beta} \cdot \Theta$ captures the cost inflicted by Byzantine agents. The fusion threshold compares the local predictor's error floor (its variance scaled by $\check{\theta}^{[i]}$) against the cloud's error bound (scaled by $\hat{\theta}$ and the cloud variance) and selects the better model per test point, which yields the strict improvement.
Load-bearing premise
The whole error analysis assumes the trimming fraction $\beta$ is at least the unknown Byzantine fraction $\alpha$ (Assumption 1: $0 < \alpha \leq \beta < 1/4$), but the attack model only tells the cloud that $\alpha$ is below $1/4$; when $\alpha$ approaches $1/4$ the cloud cannot choose a $\beta$ that is both smaller than $1/4$ and at least as large as $\alpha$, so the claimed tolerance is not guaranteed by the stated knowledge.
Editorial extensions
If this is right
- As agents accumulate data and $d_{\max}(t) \to 0$, the cloud's prediction error bound converges to a noise- and kernel-dependent constant, and the Byzantine term $\Delta$ vanishes when $\alpha$ and $\beta$ are small, so robustness costs less as learning progresses.
- On the fusion set, each benign agent is guaranteed a strictly smaller mean squared error than running alone, so the protocol turns communication into a provable per-agent accuracy gain rather than a heuristic.
- The global predictive variance is sandwiched between $(1-2\beta) \frac{\sigma_f^2 (\sigma_e^{\min})^2}{\sigma_f^2 + (\sigma_e^{\max})^2}$ and, in the limit, $\frac{1}{1-4\beta} \left[\sigma_f^2 - \frac{\kappa(d_{\max}(t))^2}{\sigma_f^2 + (\sigma_e^{\max})^2}\right]$: heavier trimming buys robustness at the price of wider confidence intervals.
- With $\beta = \alpha = 0$ the aggregation rule coincides with standard product-of-experts aggregation, so the Byzantine-resilient rule is a strict generalization of that classical baseline.
- Agents exchange only predictive means and variances of shared test points, never raw data, so the privacy posture of federated learning is preserved.
Reading between the lines
- The strict-improvement guarantee is proven for the fusion rule (9), which needs the latent function's Lipschitz constant and the dispersion bound $\gamma_d$; the variance-comparison rule (8) used in the toy experiments needs no such knowledge, and proving the improvement directly for (8) would close the gap between theory and implementation.
- All guarantees are stated for scalar outputs, with vector outputs handled coordinate-wise (Remark 2); a joint multivariate statement would need a matrix-valued kernel argument, and per-coordinate fusion may not be what a vector-valued prediction application wants.
- Because the error bounds depend on the maximum local dispersion $d_{\max}(t)$, the most data-starved benign agent sets the pace; weighting the aggregation by each agent's dispersion could transfer the benefit of dense data to sparse agents more evenly.
- The cloud is assumed to know only that $\alpha < 1/4$, yet the theory requires $\beta \geq \alpha$; an online estimator of the Byzantine fraction, or an adaptive trimming fraction chosen to satisfy the variance bounds, would turn the claimed 'less than one quarter' tolerance into an implementable parameter choice.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper studies Byzantine-resilient federated online learning for Gaussian process regression. A cloud aggregates local GPR predictions from agents using a trimmed product-of-experts rule, and each agent fuses the cloud prediction with its local prediction according to a variance-based criterion. The authors prove upper bounds on the prediction error of the cloud-based aggregated GPR, bounds on predictive variance, and claim that the agent-based fused GPR strictly improves mean squared error over the local GPR when a certain condition holds. Experiments on a synthetic function and two real-world datasets (SARCOS, Kin40k) illustrate robustness of the aggregation rule and apparent gains from fusion.
Significance. The problem is timely and important: Byzantine-robust federated learning for nonparametric online regression has not been thoroughly explored, and the proposed trimmed PoE aggregation is a natural extension of existing robust aggregation ideas. If the theoretical claims were established, the paper would provide a useful contribution, especially the explicit variance-based fusion criterion and the associated performance bounds. The manuscript also includes extensive experiments and a reproducible algorithm description. However, the central theoretical result on fusion improvement is not proven as written, and several proof steps in the cloud-bound chain have rigor gaps, so the significance of the contribution is currently conditional on substantial corrections.
major comments (4)
- [Section 5.3, Lemma 4 and Lemma 5] Lemma 4 is stated as holding for every agent with probability at least 1−δ, but its proof fixes an arbitrary agent and applies a sub-Gaussian concentration bound for that agent only. Lemma 5 then asserts that all agents in I(t) satisfy the same bound with probability 1−δ, again without a union bound. In Theorem 1 Part I these statements are used to bound a weighted sum over all i∈I(t) simultaneously. A union bound over the n agents would require replacing δ by δ/n (or an equivalent probabilistic budget), changing the constants in Θ and Δ. This gap propagates to Lemma 9 and to the cloud MSE bound used in Theorem 2 Part II, so it is load-bearing and must be fixed.
- [Section 5.4, Lemma 9] Lemma 9 concludes E[(μ̂_{z*|D(t)} − η(z*))²] ≤ (Θ(d_max(t)))² from the pointwise high-probability bound |μ̂_{z*|D(t)} − η(z*)| ≤ Θ(d_max(t)) that holds with probability at least 1−δ. A high-probability bound on a random variable does not, by itself, imply an unconditional second-moment bound; the contribution of the complementary event can be arbitrarily large unless the variable is almost surely bounded or a tail bound is provided. This step is used in inequality (31) to upper-bound the cloud MSE, which is essential for the strict improvement claim in Part II, so it cannot be left as is.
- [Section 5.4, inequality (30)] Inequality (30) is algebraically false under the paper's own definitions. From Theorem IV.3 of Yuan & Zhu (2024) one has σ̌²_{z*|D[i]} ≤ A/(σ_f²+(σ_e^[i])²) with A = σ_f²(σ_f²+(σ_e^[i])²) − κ(d^[i])², and θ̌^[i] = σ_e^[i]κ(d^[i])/A. These give σ̌²_{z*|D[i]}/θ̌^[i] ≤ A²/[σ_e^[i]κ(d^[i])(σ_f²+(σ_e^[i])²)]. The claimed lower bound (σ̌²/θ̌)² ≤ (σ_e^[i]κ(d^[i])/(σ_f²+(σ_e^[i])²))² would require A² ≤ (σ_e^[i]κ(d^[i]))², which is not implied by Assumption 2. For a squared-exponential kernel with σ_f²=1, σ_e=0.1, and κ(d)=0.9, A=0.20 so A²=0.04 while (σ_eκ)²=0.0081, contradicting the inequality. Since (30) provides the lower bound on the local MSE that makes the fused prediction look better by comparison, Theorem 2 Part II is not established.
- [Section 3.2 and Assumption 1] The attack model states that the cloud knows only that 1/4 is an upper bound of α, but Assumption 1 requires α ≤ β < 1/4. If α is unknown, the cloud cannot in general choose β to guarantee β ≥ α; for example, if α=0.24, every admissible β<0.25 is smaller than α. Thus the claimed tolerance of 'less than one quarter' Byzantine agents is not achievable from the stated knowledge. Lemma 2 and the subsequent error bounds depend on this choice, so the assumption needs either a revised knowledge model (e.g., a known lower bound on α) or an adaptive choice of β.
minor comments (3)
- [Section 5.2, proof of Lemma 2] The proof of Lemma 2 concludes bounds for all i∈I^µ(t) using a contradiction argument with αn ≥ βn+1; the argument is sound only when n is large enough that the sets T_max^µ and T_min^µ are disjoint, which is not stated. The final claim also writes 'i∈I^σ(t)' in the variance part where 'i∈I(t)' is intended, though this is a notational slip.
- [Section 4.2, text before Theorem 2] The construction of Z_fused^[i](t) in (9) uses constants θ-hat, Γ, and θ-check that depend on γ_d, ℓ_η, and δ, but the text does not discuss how these constants would be obtained in practice (e.g., how γ_d is computed from the compact domain). This makes the fusion criterion difficult to implement without additional assumptions.
- [Section 6, Figure/Table references] Several figure captions are uninformative: Fig. 3(a)-(c) are captioned only 'Attack-free standard PoE' etc., without explaining what is plotted on the axes, and Fig. 6 similarly lacks a description of the metric. Please add axis labels and a legend to each panel.
Circularity Check
No significant circularity: the fused-GPR improvement theorem is a bound-based sufficient-condition proof, and the only load-bearing external result is a parameter-free prior theorem that does not assume the paper's target claim.
full rationale
The derivation chain of Theorem 2 Part II is not circular. The fused set Z_fused(t) in (9) is defined through analytic constants (theta_hat, theta_check, Gamma) obtained from variance bounds, and the proof then shows that membership in this set implies that the cloud error upper bound is below the local error lower bound. That is a substantive implication about the variance-based selection rule, not a restatement of the rule: the actual mean squared errors E[(mu_hat - eta)^2] and E[(mu_check - eta)^2] are not used to define Z_fused(t). No parameter is fitted to the data that is later announced as a prediction. The cited Theorem IV.3 of Yuan & Zhu (2024) supplies local NNGPR variance bounds; it is parameter-free, is not the target improvement statement, and is used as an independently stated lemma, so under the review rules this self-citation does not constitute circularity. The main threat to Theorem 2 Part II is the algebraic correctness of inequality (30) and the absence of a tail argument in Lemma 9, but those are proof gaps, not circular reductions. The 'otherwise equality' branch is definitional in Algorithm 4 but is not used as evidence of improvement. The assumption alpha <= beta is an explicit hypothesis, not a fitted prediction, so the resilience claim is conditional rather than circular.
Assumptions & free parameters
free parameters (3)
- β (trimming fraction) =
β = α in most experiments; up to 0.225
- Kernel hyperparameters σ_f² and ℓ =
not reported
- Constants for condition (9): ℓη, ∥η∥∞, γd, δ =
not reported
assumptions (6)
- domain assumption Assumption 1: 0 < α ≤ β < 1/4 and the cloud knows 1/4 is an upper bound on α.
- domain assumption Assumption 2: ker(z,z') = κ(D(z,z')) with κ continuous, decreasing, κ(0)=σ_f².
- domain assumption Assumption 3: η ~ GP(0, ker) and η is Lipschitz continuous with constant ℓη.
- domain assumption Theorem IV.3 of Yuan & Zhu (2024) bounding the predictive variance of one-neighbor NNGPR.
- standard math Sub-Gaussian concentration inequality (Rigollet & Hütter 2015, Lemma 1.3).
- standard math Joint Gaussian identities for GPR prediction (Williams & Rasmussen 2006).
Cite this review
Pith. "Pith review of Byzantine-resilient federated online learning for Gaussian process regression." pith.science (2026). https://pith.science/paper/BICF3FF3
@misc{pith2026250714021,
author = {Pith},
title = {Pith review of: Byzantine-resilient federated online learning for Gaussian process regression},
year = {2026},
howpublished = {\url{https://pith.science/paper/BICF3FF3}},
note = {Machine review of arXiv:2507.14021}
}
read the original abstract
In this paper, we study Byzantine-resilient federated online learning for Gaussian process regression (GPR). We develop a Byzantine-resilient federated GPR algorithm that allows a cloud and a group of agents to collaboratively learn a latent function and improve the learning performances where some agents exhibit Byzantine failures, i.e., arbitrary and potentially adversarial behavior. Each agent-based local GPR sends potentially compromised local predictions to the cloud, and the cloud-based aggregated GPR computes a global model by a Byzantine-resilient product of experts aggregation rule. Then the cloud broadcasts the current global model to all the agents. Agent-based fused GPR refines local predictions by fusing the received global model with that of the agent-based local GPR. Moreover, we quantify the learning accuracy improvements of the agent-based fused GPR over the agent-based local GPR. Experiments on a toy example and two medium-scale real-world datasets are conducted to demonstrate the performances of the proposed algorithm.
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Works this paper leans on
-
[1]
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work page 1991
-
[5]
Abbasifard, M.R., Ghahremani, B., & Naderi, H. (2014). A survey on nearest neighbor search methods. International Journal of Computer Applications, 95(25), 39--52
work page 2014
-
[6]
Allouah, Y., Farhadkhani, S., Guerraoui, R., Gupta, N., Pinot, R., & Stephan, J. (2023). Fixing by mixing: A recipe for optimal B yzantine M L under heterogeneity. In International Conference on Artificial Intelligence and Statistics, 1232--1300. PMLR
work page 2023
-
[7]
Blanchard, P., Mhamdi, E.M.E., Guerraoui, R., & Stainer, J. (2017). Machine learning with adversaries: Byzantine tolerant gradient descent. In Proceedings of International Conference on Neural Information Processing Systems, 118--128
work page 2017
-
[8]
Chen, J., Low, K.H., Yao, Y., & Jaillet, P. (2015). G aussian process decentralized data fusion and active sensing for spatiotemporal traffic modeling and prediction in mobility-on-demand systems. IEEE Transactions on Automation Science and Engineering, 12(3), 901--921
work page 2015
Show all 49 references
-
[9]
Chen, Y., Su, L., & Xu, J. (2017). Distributed statistical machine learning in adversarial settings: B yzantine gradient descent. Proceedings of the ACM on Measurement and Analysis of Computing Systems, 1(2), 1--25
2017
-
[10]
& Srivastava, A.N
Das, K. & Srivastava, A.N. (2013). Sparse inverse kernel G aussian process regression. Statistical Analysis and Data Mining, 6(3), 205--220
2013
-
[11]
& Diggavi, S
Data, D. & Diggavi, S. (2021). Byzantine-resilient high-dimensional S G D with local iterations on heterogeneous data. In Proceedings of the International Conference on Machine Learning, 2478--2488
2021
-
[12]
Duy, N.T., Seeger, M., & Peters, J. (2009). Model learning with local G aussian process regression. Advanced Robotics, 23(15), 2015--2034
2009
-
[13]
Farhadkhani, S., Guerraoui, R., Gupta, N., Pinot, R., & Stephan, J. (2022). Byzantine machine learning made easy by resilient averaging of momentums. In International Conference on Machine Learning
2022
-
[14]
Gorbunov, E., Horv\' a th, S., Richt\' a rik, P., & Gidel, G. (2022). Variance reduction is an antidote to B yzantines: B etter rates, weaker assumptions and communication compression as a cherry on the top. arXiv:2206.00529
2022 arXiv
-
[15]
He, S., Guo, L., Ghanem, M., & Guo, Y. (2012). Improving resource utilisation in the cloud environment using multivariate probabilistic models. In International Conference on Cloud Computing, 574--581. IEEE
2012
-
[16]
Hinton, G.E. (2002). Training products of experts by minimizing contrastive divergence. Neural Computation, 14(8), 1771--1800
2002
-
[17]
Huber, M.F. (2004). Recursive G aussian process: O n-line regression and learning. Pattern Recognition Letters, 45, 85 -- 91
2004
-
[18]
Jang, D., Yoo, J., Son, C.Y., Kim, D., & Kim, H. (2020). Multi-robot active sensing and environmental model learning with distributed gaussian process. IEEE Robotics and Automation Letters, 5(4), 5905--5912
2020
-
[19]
Karimireddy, S.P., He, L., & Jaggi, M. (2021). Learning from history for B yzantine robust optimization. In International Conference on Machine Learning
2021
-
[20]
Karimireddy, S.P., He, L., & Jaggi, M. (2022). Byzantine-robust learning on heterogeneous datasets via bucketing. In International Conference on Learning Representations
2022
-
[21]
Kehoe, B., Patil, S., Abbeel, P., & Goldberg, K. (2015). A survey of research on cloud robotics and automation. IEEE Transactions on Automation Science and Engineering, 12(2), 398--409
2015
-
[22]
Khazbak, Y., Tan, T., & Cao, G. (2020). Mlguard: M itigating poisoning attacks in privacy preserving distributed collaborative learning. In International Conference on Computer Communications and Networks, 1--9
2020
-
[23]
Kone c n \`y , J., McMahan, H.B., Yu, F.X., Richt \'a rik, P., Suresh, A.T., & Bacon, D. (2016). Federated learning: S trategies for improving communication efficiency. In Proceedings of International Conference on Neural Information Processing Systems, 1--5
2016
-
[24]
Li, L., Xu, W., Chen, T., Giannakis, G.B., & Ling, Q. (2019). RSA : Byzantine-robust stochastic aggregation methods for distributed learning from heterogeneous datasets. In Proceedings of the AAAI Conference on Artificial Intelligence, 1544--1551
2019
-
[25]
Liu, H., Cai, J., Wang, Y., & Ong, Y.S. (2018). Generalized robust B ayesian committee machine for large-scale G aussian process regression. In Proceedings of the International Conference on Machine Learning, 3131--3140
2018
-
[26]
Liu, H., Ong, Y.S., Shen, X., & Cai, J. (2020). When G ausian process meets big data: A review of scalable G P s. IEEE Transactions on Neural Networks and Learning Systems, 31(11), 4405--4423
2020
-
[27]
McMahan, B., Moore, E., Ramage, D., Hampson, S., & y Arcas, B.A. (2017). Communication-efficient learning of deep networks from decentralized data. In Proceedings of International Conference on Artificial Intelligence and Statistics, 1273--1282
2017
-
[28]
& Grance, T
Mell, P. & Grance, T. (2011). The N I S T definition of cloud computing. National Institute of Standards and Technology
2011
-
[29]
Mothukuri, V., Parizi, R.M., Pouriyeh, S., Huang, Y., Dehghantanha, A., & Srivastava, G. (2021). A survey on security and privacy of federated learning. Future Generation Computer Systems, 115, 619--640
2021
-
[30]
Mukadam, M., Yan, X., & Boots, B. (2016). Gaussian process motion planning. In International Conference on Robotics and Automation, 9--15. IEEE
2016
-
[31]
Patra, M., Thakur, R., & Murthy, C.S.R. (2016). Improving delay and energy efficiency of vehicular networks using mobile femto access points. IEEE Transactions on Vehicular Technology, 66(2), 1496--1505
2016
-
[32]
& H \"u tter, J.C
Rigollet, P. & H \"u tter, J.C. (2015). High dimensional statistics. Lecture notes for course
2015
-
[33]
Seeger, M.W., Williams, C.K., & Lawrence, N.D. (2003). Fast forward selection to speed up sparse G aussian process regression. In International Workshop on Artificial Intelligence and Statistics, 254--261
2003
-
[34]
So, J., G \"u ler, B., & Avestimehr, A.S. (2020). Byzantine-resilient secure federated learning. IEEE Journal on Selected Areas in Communications, 39(7), 2168--2181
2020
-
[35]
Srinivas, N., Krause, A., Kakade, S.M., & Seeger, M.W. (2012). Information-theoretic regret bounds for G aussian process optimization in the bandit setting. IEEE Transactions on Information Theory, 58(5), 3250--3265
2012
-
[36]
Sui, Y., Gotovos, A., Burdick, J., & Krause, A. (2015). Safe exploration for optimization with G aussian processes. In International Conference on Machine Learning, 997--1005. PMLR
2015
-
[37]
Tao, T. (2012). Topics in random matrix theory. American Mathematical Society
2012
-
[38]
Tiwari, K., Honor \'e , V., Jeong, S., Chong, N.Y., & Deisenroth, M.P. (2016). Resource-constrained decentralized active sensing for multi-robot systems using distributed G aussian processes. In International Conference on Control, Automation and Systems, 13--18. IEEE
2016
-
[39]
Tolpegin, V., Truex, S., Gursoy, M.M., & Liu, L. (2020). Data poisoning attacks against federated learning systems. In European Symposium on Research in Computer Security, 480--501. Springer
2020
-
[40]
Vacca, J.R. (2012). Computer and Information Security Handbook. Newnes
2012
-
[41]
Wainwright, M.J. (2019). High-dimensional statistics: A non-asymptotic viewpoint. NY Cambridge University Press
2019
-
[42]
& Rasmussen, C.E
Williams, C.K. & Rasmussen, C.E. (2006). Gaussian processes for machine learning. MIT press Cambridge, MA
2006
-
[43]
& Eckert, C
Xiao, H. & Eckert, C. (2013). Lazy G aussian process committee for real-time online regression. In Proceedings of the AAAI Conference on Artificial Intelligence, 969--976
2013
-
[44]
Yang, Q., Liu, Y., Chen, T., & Tong, Y. (2019). Federated machine learning: C oncept and applications. ACM Transactions on Intelligent Systems and Technology, 10(2), 1--19
2019
-
[45]
Yin, D., Chen, Y., Kannan, R., & Bartlett, P. (2018). Byzantine-robust distributed learning: T owards optimal statistical rates. In Proceedings of the International Conference on Machine Learning, 5650--5659
2018
-
[46]
Yuan, Z., Xu, S., & Zhu, M. (2024). Federated reinforcement learning for robot motion planning with zero-shot generalization. Automatica, 166, 111709
2024
-
[47]
& Zhu, M
Yuan, Z. & Zhu, M. (2024). Lightweight distributed gaussian process regression for online machine learning. IEEE Transactions on Automatic Control, 69(6), 3928--3943
2024
-
[48]
Zhang, X., Yuan, Z., & Zhu, M. (2022). Byzantine-tolerant federated G aussian process regression for streaming data. In Proceedings of International Conference on Neural Information Processing Systems, 13499--13511
2022
-
[49]
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Reviewed August 6, 2026 · model on record in the stance chip above.
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