Pith. sign in

REVIEW 4 major objections 4 minor 43 references

Compressed Bayesian Tensor Regression

T0 review · 4 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Compressed Bayesian tensor regression projects high-dimensional tensor covariates into a small subspace and predicts out-of-sample at least as well as—often better than—the full tensor regression, with far lower cost.

desk verdict GTRP is a sensible extension and the real-data gains are real, but the JL-type theory is mis-normalized and needs major repair before the paper's central claims can be trusted. read the letter →

arxiv 2510.01861 v2 pith:4KCFV6SJ submitted 2025-10-02 stat.ME stat.CO

Roberto Casarin , Radu Craiu , Qing Wang This is my paper · ORCID
classification stat.MEstat.CO
keywords BayesiantensorregressionrandomprojectioncompressedposteriorconsistencyGibbssamplermodelaveragingdecompositionpriorhigh-dimensionalcovariates
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper takes on a practical bottleneck: tensor-valued covariates can be so large that a Bayesian tensor regression becomes computationally prohibitive. The authors propose to compress the covariates first, by multiplying the tensor along its modes with sparse random projection matrices (and optionally with a random projection tensor across several modes), and then to run the regression on the compressed tensor. Their main claim is that this compression loses little of the information that drives the response: they prove concentration inequalities showing that pairwise distances among covariate tensors are nearly preserved, and posterior consistency results showing the compressed-model predictive density converges to the truth. The simulations and a financial application then show the compressed model can achieve better out-of-sample prediction while cutting computation considerably, especially when the projection preserves the tensor modes rather than flattening them. A Gibbs sampler and Bayesian model averaging over several random projections make the method ready to use.

What carries the argument

The key identity is the distance-preservation bound for GTRP: for all U,V, (1−ε)||U−V||² ≤ ||√(p(N)/q(M))GTRP(U−V)||² ≤ (1+ε)||U−V||² with probability at least 1−n^{−β}, provided q(M) is large enough. This is what connects the compressed covariates to the original signal. The second piece is the hierarchical low-rank prior B = Σ_d γ_1^{(d)}∘...∘γ_M^{(d)} with shrinkage scales, which makes the Gibbs updates closed-form; and Bayesian model averaging over L random projections addresses the variability introduced by any single projection.

What would settle it

Generate a fixed tensor A with a single 1 and zeros elsewhere, sample many projection matrices/tensors from Eq. (5), and compute ||√(p(N)/q(M))GTRP(A)||². Its average is p(N), not 1; for p(N)>1 this contradicts the claimed (1±ε) bound around ||A||². A reader can see this directly from the second moment calculation in the proof of Theorem 1.

Watch

Extended reading notes

Core claim

The central object is the Generalized Tensor Random Projection (GTRP), which maps an order-N covariate tensor to a smaller order-M tensor by mode-wise products with sparse random matrices along some modes and a tensor-wise product with a random projection tensor along the rest. The paper proves that, with scaling √(p(N)/q(M)), squared distances between any two projected tensors are preserved within 1±ε with high probability once the compressed dimension is large enough, and it proves posterior consistency for the tensor coefficient under both a tensor-normal prior and a low-rank parallel-factor prior. A closed-form Gibbs sampler approximates the posterior of the low-rank compressed model. Th

Load-bearing premise

The load-bearing premise is that the scaling √(p(N)/q(M)) makes GTRP norm-preserving in expectation; with the paper's unit-variance projection entries, the expected squared distance is multiplied by p(N), so the concentration inequalities as stated hold only after an additional 1/√p(N) rescaling.

Editorial extensions

If this is right

  • Tensor regressions that were previously infeasible because of the size of the covariate array become tractable: project first, then run the Gibbs sampler on the small compressed tensor.
  • Mode-preserving projections should be preferred in practice; the simulations and the financial application show they predict better than projections that flatten the tensor.
  • Averaging over several random projections brings the method close to the stability of the uncompressed fit, removing dependence on a single projection draw.
  • The posterior consistency theorems say that as n grows, the compressed-model predictive distribution converges to the truth, so the compression does not silently destroy inferential validity.
  • In the reported 60×60 simulation with 2,000 observations, the compressed model runs roughly two orders of magnitude faster than the uncompressed Bayesian tensor regression while achieving lower out-of-sample RMSE.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A corrected normalization (e.g., scaling by 1/√q(M) or drawing projection entries with variance 1/p(N)) would restore the literal distance-preservation inequalities; because a global rescaling of covariates can be absorbed by the regression coefficients, the paper's predictive conclusions would likely survive the fix.
  • The GTRP framework could be pushed beyond prediction: if the projection is designed to be nearly invertible on low-rank tensors, the posterior for the compressed coefficient could be used to recover the support or structure of the original coefficient tensor; the paper does not explore this.
  • A natural next experiment is to let Bayesian model averaging mix over projection types (tensor-wise vs mode-wise) rather than only over matrices of the same type; the paper's simulations show type choice is the largest performance lever.
  • The consistency rate ε_n = n^{δ}, δ<0, with compressed dimension growing sublinearly in n, suggests a direct empirical check: tracking predictive error as n and q grow should show the predicted contraction; that would test whether the theoretical rate is tight.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper proposes a Compressed Bayesian Tensor Regression (CBTR) framework in which tensor-valued covariates are mapped by a Generalized Tensor Random Projection (GTRP) into a lower-dimensional tensor, combined with a hierarchical PARAFAC prior, a closed-form Gibbs sampler, and Bayesian model averaging over random projections. The main theoretical claims are JL-type concentration inequalities for GTRP (Prop. 1, Thm. 1, Thm. 2) and posterior consistency of the predictive density (Thm. 3, Thm. 4). The method is evaluated through extensive simulations and a financial application.

Significance. If the theoretical claims were valid, this would be a useful contribution to high-dimensional tensor regression: the GTRP framework is flexible, the Gibbs sampler is explicit, and the simulation study and real-data application are substantial. However, the central concentration inequalities are mis-scaled, and the posterior consistency theorems inherit the same normalization problem. The advertised 'strong theoretical support' does not hold as stated, so the paper's main formal contribution is currently unsupported.

major comments (4)
  1. [Sec. 2.2, Eq. (2), Eq. (5), Prop. 1, Thm. 1] The map f is not norm-preserving. The entries in (5) have variance 1. For any fixed A, E[GTRP(A)_i^2] = ||A||^2; summing over q(M) output entries gives E||GTRP(A)||^2 = q(M)||A||^2. Since f(X) = sqrt(c) GTRP(X) with c = p(N)/q(M), E||f(A)||^2 = p(N)||A||^2, not ||A||^2. Thus the claimed (1±epsilon) preservation cannot hold for p(N) > 1. The correct normalization would be f = GTRP/sqrt(q(M)) (or equivalent), which changes the theorem statements and subsequent proofs.
  2. [Appendix A.2, Lemma 1] The Gaussian comparison is reversed. For Q in (A.1), Q_{i1...iN} = (1/sqrt(p(N))) sum_{j1...jN} prod H_{m,j_m,i_m}; the sum contains p(N) independent zero-mean unit-variance terms, so E(Q^2) = 1. For T, E(T^2) = prod(1/p_m) = 1/p(N). Hence E(Q^2) <= E(T^2) fails for k=1. Lemma 3 and the upper-tail bound inherit this error. The lower-tail inequality (A.43) also uses E(Q^2) = 1/p(N), contradicting Lemma 1. The proof of Theorem 1 is therefore invalid.
  3. [Sec. 4, Assumption A.3, Thms. 3 and 4] Assumption A.3 asserts that the norm condition is satisfied with high probability 'as described in Proposition 1 and Theorem 1'. Since those results are false without renormalization, the justification for A.3 collapses. In the proof of Theorem 3 (Appendix A.4, condition (c)), the lower bound on prior mass uses Var(<GTRP(X),B>) proportional to ||GTRP(X)||^2; without a valid normalized projection, this bound is not established. Theorem 4 relies on the same assumptions through A.4. Thus the posterior consistency results are unsupported as stated.
  4. [Appendix A.3, proof of Thm. 2] The proof redefines f(X) as (1/sqrt(q(N))) <H_{1,:,i1} o ... o H_{N,:,iN}, X>, whereas Section 2.2 defines f(X) = sqrt(p(N)/q(N)) GTRP(X). Since a GTRP entry equals that inner product, the factor is inconsistent; this changes the variance computation and the resulting bound. The normalization problem is systemic rather than a local typo.
minor comments (4)
  1. [Eq. (20)] The efficiency score formula should read 1/(RMSE x Cost); as printed, '1 RMSE x Cost' is ambiguous.
  2. [Sec. 5.1] The statement 'This required 2560 simulations for a given psi' is not justified from the described designs; please clarify the counting.
  3. [Thm. 1] The phrase 'Assume a sequence ... satisfy q(N) >= q0 with probability at least 1 - n^{-beta}' is unclear: q is a chosen dimension, not a random quantity. Rephrase to separate the choice of q from the probability over projections.
  4. [Sec. 2.3] The prior in (9) is written for B in R^{p1 x ... x pM}, but after compression B should be in R^{q1 x ... x qM}; align notation.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central theoretical claims are derived from external benchmarks (Achlioptas 2003, Jiang 2007, Guhaniyogi & Dunson 2015); self-citations are contextual, not load-bearing. A mathematical normalization issue in the JL bounds is a correctness risk, not a circularity.

full rationale

The derivation chain is not circular in the sense defined by this pass. Proposition 1 is explicitly reduced to an external result: 'The proof of Prop. 1 follows immediately from the proof of (Achlioptas, 2003, Thm.1.1), as the GTRT-TW is equivalent to the random projection in Achlioptas (2003).' Theorem 1 is proved from Lemmas 1-3 that build on Achlioptas (2003) and Mathai et al. (2010), again external sources. The posterior consistency results (Theorems 3 and 4) verify the sufficient conditions of Jiang (2007)'s Proposition 2, with Proposition 3 following from Guhaniyogi and Dunson (2015); the assumptions A.1-A.5 are stated independently and are not fitted to the claimed conclusions. The BMA weights are estimated by reverse logistic regression (Geyer 1994) from MCMC output, so they are not a fitted parameter renamed as a prediction. The self-citations to Casarin et al. (2025) provide the uncompressed tensor regression benchmark, the mixed-frequency dataset, and a statement that Gibbs sampling is computationally efficient in the uncompressed case; none of these is the load-bearing identity that makes the central claim true. The reader should note a separate mathematical-correctness concern in Section 2.2: with the projection entries used in (5), E||GTRP(A)||^2 = q(M)||A||^2, so the scaling f(X) = sqrt(c(N,M)) GTRP(X) gives E||f(A)||^2 = p(N)||A||^2, not ||A||^2. This appears to invalidate Proposition 1 and Theorem 1 as stated and also affects Assumption A.3's claim that those results justify the norm condition. That is a substantial technical error, but it is not a circularity: the paper does not define the projection or the fitted parameters in terms of the target distance-preservation claim, nor does it rely on a self-citation to establish the normalization. The appropriate classification for this paper is 'no significant circularity,' with the mathematical issue flagged as a correctness risk.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central theoretical claims rest on: (i) the specific discrete random projection distribution (Eq. 5) whose unnormalized entries (variance 1) create the scaling error; (ii) external results from Achlioptas (2003), Jiang (2007), and Guhaniyogi & Dunson (2015); (iii) paper-specific Assumptions A.1-A.5 that constrain the growth of the compressed dimension and projection norms. The projection normalization is the load-bearing premise that fails.

free parameters (5)
  • PARAFAC rank D = 5 (simulations)
    Controls coefficient tensor complexity; chosen by the user without guidance.
  • Number of projections L = 10
    Used for BMA in all experiments; no sensitivity analysis.
  • Sparsity ψ = 3 (main), 2-4 sensitivity
    Controls projection sparsity; the paper finds a V-shape for mode-wise projections, showing sensitivity.
  • Compression rate r = 0.09-0.36
    Equivalently q_m; chosen by user; RMSE improves as r increases (less compression) in Fig. 6.
  • Prior hyperparameters = aτ=3, bτ=100, aλ=20, bλ=2, aσ=3, bσ=1
    Fixed in Appendix C; no sensitivity analysis reported.
assumptions (6)
  • domain assumption Entries of projection matrices/tensors are iid from the discrete distribution r=√ψ{+1 w.p. 1/(2ψ); 0 w.p. 1-1/ψ; -1 w.p. 1/(2ψ)}, with variance 1 (Eq. 5).
    Used in all concentration results; the unnormalized variance creates the scaling error in Prop. 1/Thm. 1.
  • standard math Achlioptas (2003) JL lemma for sparse random projections holds and can be applied to vectorized tensors.
    Basis of Prop. 1; requires the 1/√k scaling absent in the paper's f.
  • standard math Jiang (2007) posterior consistency conditions a,b,c are sufficient for Hellinger consistency of the predictive density.
    Used to prove Theorems 3 and 4.
  • ad hoc to paper Assumptions A.1-A.5: compressed dimension grows sublinearly, prior eigenvalues are bounded, projection norms grow slowly, and contraction rate ε_n²=n^δ with -1<δ<0.
    These assumptions are imposed specifically to make the consistency proofs go through; no empirical verification that they hold in applications.
  • standard math Meijer G-function identities and power-log expansions (Mathai et al. 2010; Stojanac et al. 2018) provide the MGF bounds used in Thm. 1's proof.
    Used in the upper-tail bound; the resulting bound is mis-scaled due to the projection normalization.
  • domain assumption Different entries of the mode-wise projection are independent, enabling the factorization of the MGF of S(A).
    Valid because disjoint projection columns are used; stated in Appendix A.2.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Compressed Bayesian Tensor Regression." pith.science (2026). https://pith.science/paper/4KCFV6SJ

@misc{pith2026251001861,
  author       = {Pith},
  title        = {Pith review of: Compressed Bayesian Tensor Regression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4KCFV6SJ}},
  note         = {Machine review of arXiv:2510.01861}
}
read the original abstract

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of information about the responses. The method is flexible, allowing for tensor-wise, mode-wise, or combined random projections as special cases. A Bayesian inference framework is provided featuring the use of a hierarchical prior distribution and a low-rank representation of the parameter. Strong theoretical support is provided for the concentration properties of the random projection and posterior consistency of the Bayesian inference. An efficient Gibbs sampler is developed to perform inference on the compressed data. To mitigate the sensitivity introduced by random projections, Bayesian model averaging is employed, with normalising constants estimated using reverse logistic regression. An extensive simulation study is conducted to examine the effects of different tuning parameters. Simulations indicate, and the real data application confirms, that compressed Bayesian tensor regression can achieve better out-of-sample prediction while significantly reducing computational cost compared to standard Bayesian tensor regression.

Figures

Figures reproduced from arXiv: 2510.01861 by the authors.

Figure 1
Figure 1. The plot shows the two bounds obtained by tensor-wise random projection accord [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. RMSE comparison across types of random projections (TW: tensor-wise, MW: [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 4
Figure 4. Prediction errors. Panel (a) shows RMSE vs actual distance [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: Effects of using random projection matrices of different sparsity levels on prediction [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: Prediction performances of different compression rates [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: Total computational cost in a log scale (blue bars, left vertical axis) and efficiency [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

43 extracted references · 6 linked inside Pith

  1. [1]

    Achlioptas, D. (2003). Database-friendly random projections: Johnson - Lindenstrauss with binary coins. Journal of Computer and System Sciences , 66(4):671--687

    2003

  2. [2]

    and Chazelle, B

    Ailon, N. and Chazelle, B. (2009). The fast J ohnson-- L indenstrauss transform and approximate nearest neighbors. SIAM Journal on Computing , 39(1):302--322

    2009

  3. [3]

    Anagnostopoulos, A., Angeletti, F., Arcangeli, F., Schwiegelshohn, C., Vitaletti, A., et al. (2018). Random projection to preserve patient privacy. In ACM 1st International Workshop on Knowledge Management for Healthcare (KMH2018)

    2018

  4. [4]

    and Wong, N

    Batselier, K. and Wong, N. (2017). A constructive arbitrary-degree K ronecker product decomposition of tensors. Numerical Linear Algebra with Applications , 24(5):e2097

    2017

  5. [5]

    Billio, M., Casarin, R., and Iacopini, M. (2024). Bayesian M arkov-switching tensor regression for time-varying networks. Journal of the American Statistical Association , 119(545):109--121

    2024

  6. [6]

    Billio, M., Casarin, R., Iacopini, M., and Kaufmann, S. (2023). Bayesian dynamic tensor regression. Journal of Business & Economic Statistics , 41(2):429--439

    2023

  7. [7]

    Cannings, T. I. and Samworth, R. J. (2017). Random-projection ensemble classification. Journal of the Royal Statistical Society Series B: Statistical Methodology , 79(4):959--1035

    2017

  8. [8]

    V., and Wang, Q

    Casarin, R., Craiu, R. V., and Wang, Q. (2025). Markov switching multiple-equation tensor regressions. Journal of Multivariate Analysis , 208:105427

    2025

Show all 43 references
  1. [9]

    Chakraborty, A. (2023). Efficient Bayesian High - Dimensional Classification via Random Projection with Application to Gene Expression Data . Journal of Data Science , pages 1--21

    2023

  2. [10]

    Charikar, M., Chen, K., and Farach-Colton, M. (2004). Finding frequent items in data streams. Theoretical Computer Science , 312(1):3--15

    2004

  3. [11]

    Dasgupta, S. (1999). Learning mixtures of G aussians. In 40th Annual Symposium on Foundations of Computer Science (Cat. No. 99CB37039) , pages 634--644. IEEE

    1999

  4. [12]

    Dasgupta, S. (2013). Experiments with random projection. arXiv preprint arXiv:1301.3849

    2013 arXiv

  5. [13]

    and Gupta, A

    Dasgupta, S. and Gupta, A. (2003). An elementary proof of a theorem of Johnson and Lindenstrauss . Random Structures & Algorithms , 22(1):60--65

    2003

  6. [14]

    Datar, M., Immorlica, N., Indyk, P., and Mirrokni, V. S. (2004). Locality-sensitive hashing scheme based on p-stable distributions. In Proceedings of the twentieth annual symposium on Computational geometry , pages 253--262

    2004

  7. [15]

    Farahmand, A.-m., Pourazarm, S., and Nikovski, D. (2017). Random projection filter bank for time series data. Advances in Neural Information Processing Systems , 30

    2017

  8. [16]

    and Yang, G

    Feng, L. and Yang, G. (2024). Deep K ronecker network. Biometrika , 111(2):707--714

    2024

  9. [17]

    N., Ickstadt, K., Munteanu, A., Quedenfeld, J., and Sohler, C

    Geppert, L. N., Ickstadt, K., Munteanu, A., Quedenfeld, J., and Sohler, C. (2017). Random projections for Bayesian regression. Statistics and Computing , 27(1):79--101

    2017

  10. [18]

    Geyer, C. J. (1994). Estimating normalizing constants and reweighting mixtures in markov chain monte carlo. Technical Report 568

    1994

  11. [19]

    and Wang, K

    Gondara, L. and Wang, K. (2020). Differentially private small dataset release using random projections. In Conference on Uncertainty in Artificial Intelligence , pages 639--648. PMLR

    2020

  12. [20]

    Guhaniyogi, R. (2020). Bayesian Methods for Tensor Regression . In Balakrishnan, N., Colton, T., Everitt, B., Piegorsch, W., Ruggeri, F., and Teugels, J. L., editors, Wiley StatsRef : Statistics Reference Online , pages 1--18. Wiley, 1 edition

    2020

  13. [21]

    and Dunson, D

    Guhaniyogi, R. and Dunson, D. B. (2015). Bayesian Compressed Regression . Journal of the American Statistical Association , 110(512):1500--1514

    2015

  14. [22]

    Guhaniyogi, R., Qamar, S., and Dunson, D. B. (2017). Bayesian tensor regression. Journal of Machine Learning Research , 18(79):1--31

    2017

  15. [23]

    Hackbusch, W. (2019). Tensor Spaces and Numerical Tensor Calculus , volume 56 of Springer Series in Computational Mathematics . Springer International Publishing, Cham

    2019

  16. [24]

    Hanson, D. L. and Wright, F. T. (1971). A bound on tail probabilities for quadratic forms in independent random variables. The Annals of Mathematical Statistics , 42(3):1079--1083

    1971

  17. [25]

    and Motwani, R

    Indyk, P. and Motwani, R. (1998). Approximate nearest neighbors: towards removing the curse of dimensionality. In Proceedings of the thirtieth annual ACM Symposium on Theory of Computing , pages 604--613

    1998

  18. [26]

    Jiang, W. (2007). Bayesian variable selection for high dimensional generalized linear models: Convergence rates of the fitted densities. The Annals of Statistics , 35(4):1487--1511

    2007

  19. [27]

    Johnson, W. B. and Lindenstrauss, J. (1984). Extensions of Lipschitz mappings into a Hilbert space. In Beals, R., Beck, A., Bellow, A., and Hajian, A., editors, Contemporary Mathematics , volume 26, pages 189--206. American Mathematical Society, Providence, Rhode Island

    1984

  20. [28]

    and Bissu, S

    Joshi, C. and Bissu, S. (1991). Some inequalities of B essel and modified B essel functions. Journal of the Australian Mathematical Society , 50(2):333--342

    1991

  21. [29]

    Kolda, T. G. and Bader, B. W. (2009). Tensor Decompositions and Applications . SIAM Review , 51(3):455--500

    2009

  22. [30]

    Koop, G., Korobilis, D., and Pettenuzzo, D. (2019). Bayesian compressed vector autoregressions. Journal of Econometrics , 210(1):135--154

    2019

  23. [31]

    J., and Church, K

    Li, P., Hastie, T. J., and Church, K. W. (2006). Very sparse random projections. In Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , pages 287--296, Philadelphia PA USA. ACM

    2006

  24. [32]

    Li, P., Karim, R., and Maiti, T. (2021). Tec: Tensor ensemble classifier for big data. arXiv preprint arXiv:2103.00025

    2021 arXiv

  25. [33]

    and Li, X

    Li, P. and Li, X. (2023). Differential privacy with random projections and sign random projections. arXiv preprint arXiv:2306.01751

    2023 arXiv

  26. [34]

    and Griffin, J

    Luo, Y. and Griffin, J. E. (2025). Bayesian inference of vector autoregressions with tensor decompositions. Journal of Business & Economic Statistics , pages 1--29

    2025

  27. [35]

    M., Saxena, R

    Mathai, A. M., Saxena, R. K., and Haubold, H. J. (2010). The H -function: theory and applications . Springer, New York

    2010

  28. [36]

    Matou s ek, J. (2008). On variants of the J ohnson-- L indenstrauss lemma. Random Structures & Algorithms , 33(2):142--156

    2008

  29. [37]

    and Dunson, D

    Mukhopadhyay, M. and Dunson, D. B. (2020). Targeted Random Projection for Prediction From High - Dimensional Features . Journal of the American Statistical Association , 115(532):1998--2010

    2020

  30. [38]

    Oseledets, I. V. (2011). Tensor-train decomposition. SIAM Journal on Scientific Computing , 33(5):2295--2317

    2011

  31. [39]

    and Rabusseau, G

    Rakhshan, B. and Rabusseau, G. (2020). Tensorized random projections. In International Conference on Artificial Intelligence and Statistics , pages 3306--3316

    2020

  32. [40]

    Rakhshan, B. T. and Rabusseau, G. (2021). Rademacher random projections with tensor networks. arXiv preprint arXiv:2110.13970

    2021 arXiv

  33. [41]

    and Sviridenko, M

    Schudy, W. and Sviridenko, M. (2012). Concentration and moment inequalities for polynomials of independent random variables. In Proceedings of the Twenty-third Annual ACM-SIAM Symposium on Discrete Algorithms , pages 437--446. SIAM

    2012

  34. [42]

    and Anandkumar, A

    Shi, Y. and Anandkumar, A. (2019). Higher-order Count Sketch : Dimensionality Reduction That Retains Efficient Tensor Operations . arXiv:1901.11261 [cs, stat]

    2019 arXiv

  35. [43]

    Stojanac, Z., Suess, D., and Kliesch, M. (2018). On products of Gaussian random variables. arXiv:1711.10516 [math]

    2018 arXiv

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.