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arxiv: 2605.19122 · v1 · pith:J3XD7Z4Knew · submitted 2026-05-18 · 📊 stat.ML · cs.LG

Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection

Elynn Chen , Jiayu Li , Zheshi Zheng , Jian Pei This is my paper

Pith reviewed 2026-05-20 07:16 UTC · model grok-4.3

classification 📊 stat.ML cs.LG
keywords tensor neural networksconformal inferencelow-rank tensor decompositionsparse refinementstructure selectionfinite-sample boundsROC curvesdistribution-free methods
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The pith

A dual-channel neural network decomposes each tensor into low-rank core plus sparse refinement for finite-sample valid structure selection.

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

The paper proposes a Dual-Channel Tensor Neural Network that splits every tensor input into a low-rank core and a sparse refinement, then routes the two pieces through coupled neural channels. The same architecture works with CP, Tucker, or tensor-train cores. Non-asymptotic risk bounds are derived that split into approximation error, core estimation error, and refinement selection error, with the controlling dimension set by the sum of core rank and refinement sparsity. A structure-aware conformal ROC procedure is introduced that calibrates inside the core-refinement space to deliver distribution-free finite-sample bands for ROC curves and AUC, and this is turned into a selector that picks among candidate decompositions while preserving the finite-sample coverage guarantee.

Core claim

We propose the Dual-Channel Tensor Neural Network (DC-TNN) that decomposes each tensor input into a low-rank core and a sparse refinement and processes the two components through coupled neural channels. The framework accommodates CP, Tucker, and tensor-train cores. Non-asymptotic risk bounds are established that decompose into network approximation, core estimation, and refinement-selection terms, with effective dimension determined jointly by core rank and refinement sparsity. A structure-aware conformal ROC procedure calibrates within the core-refinement latent space to produce ROC and AUC confidence bands with finite-sample, distribution-free coverage, and a conformal structure selector,

What carries the argument

The dual-channel decomposition into low-rank core and sparse refinement, which separates global structure from local detail and permits conformal calibration directly in the reduced latent space.

If this is right

  • Risk bounds depend on the joint dimension of core rank and refinement sparsity instead of the full ambient tensor size.
  • The conformal ROC procedure supplies finite-sample distribution-free bands around ROC curves and AUC values.
  • The conformal structure selector returns a decomposition (CP, Tucker, or tensor-train) with guaranteed finite-sample validity.
  • Simulations and a protein-structure dataset exhibit competitive prediction accuracy together with reliable recovery of the underlying tensor structure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The latent-space calibration may allow reliable model choice with smaller sample sizes than cross-validation when tensors exhibit approximate low-rank plus sparse structure.
  • The same core-refinement split could be applied to other multiway data such as video volumes or spatiotemporal graphs to obtain valid uncertainty bands.
  • The approach points toward a general template for marrying low-rank tensor models with neural networks while retaining distribution-free inference guarantees.

Load-bearing premise

Tensor inputs admit an effective low-rank core plus sparse refinement decomposition whose joint dimension governs risk, and conformal calibration performed inside that decomposed space automatically inherits distribution-free finite-sample coverage.

What would settle it

If repeated trials on fresh tensor data show that the empirical coverage of the conformal AUC bands falls below the nominal 1-alpha level for a decomposition whose core-refinement split is misspecified, the finite-sample guarantee is refuted.

Figures

Figures reproduced from arXiv: 2605.19122 by Elynn Chen, Jian Pei, Jiayu Li, Zheshi Zheng.

Figure 1
Figure 1. Figure 1: ROC bands with 90% conformal confidence intervals for Tucker-generated data [PITH_FULL_IMAGE:figures/full_fig_p040_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: ROC bands with 90% conformal confidence intervals for CP-generated data [PITH_FULL_IMAGE:figures/full_fig_p040_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Difference ROC bands with 90% conformal confidence intervals for CP-generated data. 40 [PITH_FULL_IMAGE:figures/full_fig_p040_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: Difference ROC bands with 90% conformal confidence intervals for Tucker-generated data. 8 Real Data Analysis We apply the proposed framework to the DD benchmark from TUDataset, a collection of graphs representing protein structures, where each observation is a graph G with a binary label y ∈ {0, 1} indicating enzyme or non-enzyme status. Our analysis pursues two objectives: (i) benchmarking the core-refine… view at source ↗
Figure 5
Figure 5. Figure 5: ROC bands with 90% conformal confidence intervals for DC-TNN methods on [PITH_FULL_IMAGE:figures/full_fig_p043_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Test 1 (H (1) 0 ): Difference ROC bands with 90% conformal confidence intervals for d (1)(X ) = πbTucker(X ) − πbCP(X ) on the DD dataset (α = 0.1). by reversing the difference score to d (2)(X ) = πbCP(X ) − πbTucker(X ), and changing to the CP latent space for local neighborhoods [PITH_FULL_IMAGE:figures/full_fig_p044_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Test 2 (H (2) 0 ): Difference ROC bands with 90% conformal confidence intervals for d (2)(X ) = πbCP(X ) − πbTucker(X ) on the DD dataset (α = 0.1). 9 Conclusion We developed a unified framework for tensor regression in which a single core–refinement representation supports estimation, distribution-free inference, and structure selection. The Dual-Channel Tensor Neural Network decomposes each tensor input … view at source ↗
read the original abstract

Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either impose a single low-rank structure, which can miss localized signal, or treat the tensor as a long vector, which discards its multiway geometry. We propose a *Dual-Channel Tensor Neural Network* (DC-TNN) that decomposes each tensor input into a low-rank core and a sparse refinement, and processes the two components through coupled neural channels. The framework is structure-agnostic and accommodates CP, Tucker, and tensor-train cores within a single architecture. For estimation, we establish non-asymptotic risk bounds for the DC-TNN estimator that decompose into network approximation, core estimation, and refinement-selection terms, and show that the effective dimension is determined jointly by the core rank and refinement sparsity rather than by the ambient tensor size. For inference, we develop a *structure-aware conformal ROC* procedure that calibrates within the core-refinement latent space and produces ROC and AUC confidence bands with finite-sample, distribution-free coverage. Building on this, we propose a *conformal structure selector* that, to our knowledge, is the *first distribution-free procedure* for choosing among candidate tensor decompositions with finite-sample validity. Simulations and an analysis of a protein dataset demonstrate competitive predictive accuracy, reliable uncertainty quantification, and consistent recovery of the tensor structure.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a Dual-Channel Tensor Neural Network (DC-TNN) that decomposes each tensor input into a low-rank core and a sparse refinement processed through coupled neural channels. It establishes non-asymptotic risk bounds in which the effective dimension is jointly controlled by core rank and refinement sparsity rather than ambient size, and introduces a structure-aware conformal ROC procedure that calibrates in the core-refinement latent space to produce finite-sample distribution-free coverage for ROC/AUC bands together with a conformal structure selector claimed to be the first distribution-free method for choosing among tensor decompositions.

Significance. If the distribution-free coverage guarantees survive the data-dependent decomposition step, the work would provide a useful advance for tensor-valued prediction and structure selection in domains such as neuroimaging and genomics. The explicit non-asymptotic decomposition of risk into approximation, core, and refinement terms, together with the attempt to obtain valid conformal bands without asymptotic approximations, are strengths worth preserving.

major comments (2)
  1. [Abstract and conformal procedure] Abstract and § on structure-aware conformal ROC: the claim of finite-sample distribution-free coverage for ROC/AUC bands and the structure selector rests on calibrating conformity scores inside a latent space whose core ranks and sparsity pattern are estimated from the same data. Standard conformal arguments require exchangeability of the scores; the manuscript must supply either an explicit sample-splitting argument that isolates decomposition estimation from calibration or a separate proof that the data-dependent map preserves the necessary exchangeability. Without this, the distribution-free property does not follow from the usual conformal reasoning and is load-bearing for the central inference contribution.
  2. [Risk bounds] Risk-bound derivation (presumably §3 or §4): the non-asymptotic bounds are stated to decompose into network-approximation, core-estimation, and refinement-selection terms whose effective dimension depends only on core rank and sparsity. The manuscript should exhibit the precise form of these bounds and verify that the effective-dimension term does not implicitly re-introduce dependence on the chosen ranks or sparsity levels selected on the same sample, which would render the bound circular.
minor comments (2)
  1. [Model definition] Clarify the precise definition of the dual-channel architecture and how the coupled neural channels interact with the core-refinement split; a diagram or explicit equations would improve readability.
  2. [Experiments] In the simulation section, report the empirical coverage rates for the conformal bands across different core ranks and sparsity levels to allow direct assessment of the finite-sample claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below, indicating the revisions we will make to strengthen the presentation and proofs.

read point-by-point responses

  1. Referee: [Abstract and conformal procedure] Abstract and § on structure-aware conformal ROC: the claim of finite-sample distribution-free coverage for ROC/AUC bands and the structure selector rests on calibrating conformity scores inside a latent space whose core ranks and sparsity pattern are estimated from the same data. Standard conformal arguments require exchangeability of the scores; the manuscript must supply either an explicit sample-splitting argument that isolates decomposition estimation from calibration or a separate proof that the data-dependent map preserves the necessary exchangeability. Without this, the distribution-free property does not follow from the usual conformal reasoning and is load-bearing for the central inference contribution.

    Authors: We appreciate this observation regarding the data-dependent nature of the decomposition. The current manuscript calibrates conformity scores in the core-refinement latent space after estimating the structure, but does not explicitly detail a mechanism to preserve exchangeability. To address this rigorously, we will revise the paper to incorporate an explicit sample-splitting argument: the dataset is partitioned into disjoint subsets for structure estimation (core ranks and sparsity patterns), conformity score calibration, and final testing. This isolates the estimation step, restores exchangeability for the calibration scores, and thereby establishes the finite-sample distribution-free coverage guarantees. We will also add a brief remark clarifying why the structure-aware conformal ROC and selector retain their validity under this splitting scheme. revision: yes

  2. Referee: [Risk bounds] Risk-bound derivation (presumably §3 or §4): the non-asymptotic bounds are stated to decompose into network-approximation, core-estimation, and refinement-selection terms whose effective dimension depends only on core rank and refinement sparsity. The manuscript should exhibit the precise form of these bounds and verify that the effective-dimension term does not implicitly re-introduce dependence on the chosen ranks or sparsity levels selected on the same sample, which would render the bound circular.

    Authors: We thank the referee for pointing out the need for greater precision here. The risk bounds in the manuscript are derived conditionally on a fixed tensor structure, with the effective dimension controlled explicitly by the core rank and refinement sparsity (rather than ambient dimensions). However, to eliminate any potential ambiguity about data-dependent selection, we will expand the relevant section to display the exact mathematical statements of the bounds (including the decomposition into approximation, core-estimation, and refinement terms). We will also add a clarifying paragraph stating that the bounds hold for any fixed structure and that the conformal structure selector provides separate finite-sample guarantees for choosing among candidate decompositions, thereby avoiding circularity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper presents non-asymptotic risk bounds that explicitly decompose into separate network approximation, core estimation, and refinement-selection terms, with effective dimension stated as jointly controlled by chosen core rank and sparsity level rather than ambient size. The structure-aware conformal ROC procedure is introduced as an adaptation that calibrates conformity scores inside the estimated core-refinement latent space and asserts finite-sample distribution-free coverage. No quoted step reduces a claimed prediction or coverage guarantee to a quantity defined by the same fitted parameters on identical data, nor does any central claim rest on a self-citation chain or imported uniqueness theorem. The derivation therefore does not collapse to its inputs by construction and qualifies as an independent theoretical contribution under the circularity criteria.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

Abstract-only review yields limited visibility into explicit free parameters or axioms; the architecture implicitly treats core rank and refinement sparsity as tunable quantities whose joint dimension governs risk, while relying on standard concentration tools for non-asymptotic bounds and on the usual conformal exchangeability assumption for coverage.

free parameters (1)
  • core rank and refinement sparsity level
    Determines effective dimension in the risk bound; chosen per tensor decomposition candidate.
axioms (2)
  • standard math Standard sub-Gaussian or bounded-moment concentration inequalities hold for the tensor entries and network outputs.
    Invoked to obtain non-asymptotic risk bounds that decompose into approximation, estimation, and selection terms.
  • domain assumption Exchangeability of calibration and test points in the core-refinement latent space.
    Required for the structure-aware conformal ROC to deliver finite-sample, distribution-free coverage.
invented entities (1)
  • Dual-channel tensor neural network with core-refinement split no independent evidence
    purpose: Separately process low-rank and sparse components while preserving multiway geometry.
    New architectural entity introduced to handle tensor inputs without vectorization or single low-rank assumption.

pith-pipeline@v0.9.0 · 5796 in / 1634 out tokens · 36939 ms · 2026-05-20T07:16:50.104402+00:00 · methodology

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Reference graph

Works this paper leans on

98 extracted references · 98 canonical work pages · 2 internal anchors

  1. [1]

    Journal of the American Statistical Association , volume=

    Statistical inference for high-dimensional matrix-variate factor models , author=. Journal of the American Statistical Association , volume=. 2023 , publisher=

    work page 2023

  2. [2]

    Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS) , series=

    On projection robust optimal transport: Sample complexity and model misspecification , author=. Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS) , series=. 2021 , publisher=

    work page 2021

  3. [3]

    Helping Effects Against Curse of Dimensionality in Threshold Factor Models for Matrix Time Series

    Helping effects against curse of dimensionality in threshold factor models for matrix time series , author=. arXiv preprint arXiv:1904.07383 , year=

    work page internal anchor Pith review Pith/arXiv arXiv 1904

  4. [4]

    Journal of Econometrics , volume=

    Community network auto-regression for high-dimensional time series , author=. Journal of Econometrics , volume=. 2023 , publisher=

    work page 2023

  5. [5]

    Journal of the American Statistical Association , volume=

    Constrained factor models for high-dimensional matrix-variate time series , author=. Journal of the American Statistical Association , volume=. 2020 , publisher=

    work page 2020

  6. [6]

    Journal of Data Science , volume=

    Modeling dynamic transport network with matrix factor models: with an application to international trade flow , author=. Journal of Data Science , volume=. 2022 , doi=

    work page 2022

  7. [7]

    arXiv preprint arXiv:2002.01305 , year=

    Modeling multivariate spatial-temporal data with latent low-dimensional dynamics , author=. arXiv preprint arXiv:2002.01305 , year=

    work page arXiv 2002

  8. [8]

    Journal of the American Statistical Association , volume=

    Reinforcement learning in latent heterogeneous environments , author=. Journal of the American Statistical Association , volume=. 2024 , publisher=

    work page 2024

  9. [9]

    Proceedings of the 27th International Conference on Artificial Intelligence and Statistics (AISTATS) , series=

    Tensor-view topological graph neural network , author=. Proceedings of the 27th International Conference on Artificial Intelligence and Statistics (AISTATS) , series=. 2024 , publisher=

    work page 2024

  10. [10]

    2023 , publisher=

    Li, Yuhao and Zhang, Mengqian and Li, Jichen and Chen, Elynn and Chen, Xi and Deng, Xiaotie , booktitle=. 2023 , publisher=

    work page 2023

  11. [11]

    Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=

    Semi-parametric tensor factor analysis by iteratively projected singular value decomposition , author=. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=. 2024 , publisher=

    work page 2024

  12. [12]

    arXiv preprint arXiv:2404.01546 , year=

    Time-varying matrix factor models , author=. arXiv preprint arXiv:2404.01546 , year=

    work page arXiv

  13. [13]

    Proceedings of the 26th ACM Conference on Economics and Computation (EC '25) , pages=

    Maximal extractable value in batch auctions , author=. Proceedings of the 26th ACM Conference on Economics and Computation (EC '25) , pages=. 2025 , publisher=

    work page 2025

  14. [14]

    Journal of the American Statistical Association , year=

    Data-driven knowledge transfer in batch Q^* learning , author=. Journal of the American Statistical Association , year=

    work page

  15. [15]

    arXiv preprint arXiv:2405.06866 , year=

    Dynamic contextual pricing with doubly non-parametric random utility models , author=. arXiv preprint arXiv:2405.06866 , year=

    work page arXiv

  16. [16]

    Journal of the American Statistical Association , pages=

    Factor augmented matrix regression , author=. Journal of the American Statistical Association , pages=. 2026 , publisher=

    work page 2026

  17. [17]

    High-dimensional tensor classification with

    Chen, Elynn and Han, Yuefeng and Li, Jiayu , journal=. High-dimensional tensor classification with

    work page

  18. [18]

    arXiv preprint arXiv:2407.00561 , note=

    Advancing information integration through empirical likelihood: Selective reviews and a new idea , author=. arXiv preprint arXiv:2407.00561 , note=

    work page arXiv

  19. [19]

    arXiv preprint arXiv:2410.14783 , year=

    High-dimensional tensor discriminant analysis with incomplete tensors , author=. arXiv preprint arXiv:2410.14783 , year=

    work page arXiv

  20. [20]

    arXiv preprint arXiv:2410.15241 , year=

    Conditional uncertainty quantification for tensorized topological neural networks , author=. arXiv preprint arXiv:2410.15241 , year=

    work page arXiv

  21. [21]

    2025 , note=

    Kong, Linghang and Chen, Elynn and Chen, Yuzhou and Han, Yuefeng , booktitle=. 2025 , note=

    work page 2025

  22. [22]

    Statistics in Medicine , year=

    Exploring causal effects of hormone- and radio-treatments in an observational study of breast cancer using copula-based semi-competing risks models , author=. Statistics in Medicine , year=

    work page

  23. [23]

    Deep transferq-learning for offline non-stationary reinforcement learning.arXiv preprint arXiv:2501.04870,

    Deep transfer Q -learning for offline non-stationary reinforcement learning , author=. arXiv preprint arXiv:2501.04870 , year=

    work page arXiv

  24. [24]

    arXiv preprint arXiv:2501.16223 , year=

    Statistical inference for low-rank tensor models , author=. arXiv preprint arXiv:2501.16223 , year=

    work page arXiv

  25. [25]

    Conference on Parsimony and Learning (CPAL) , year=

    Bridging domain adaptation and graph neural networks: A tensor-based framework for effective label propagation , author=. Conference on Parsimony and Learning (CPAL) , year=

    work page

  26. [26]

    Journal of the American Statistical Association , volume=

    Distributed tensor principal component analysis with data heterogeneity , author=. Journal of the American Statistical Association , volume=. 2025 , publisher=

    work page 2025

  27. [27]

    Advances in Neural Information Processing Systems (NeurIPS) , note=

    Transfer faster, price smarter: Minimax dynamic pricing under cross-market preference shift , author=. Advances in Neural Information Processing Systems (NeurIPS) , note=

    work page

  28. [28]

    Transfer

    Chai, Jinhang and Chen, Elynn and Yang, Lin , booktitle=. Transfer. 2025 , publisher=

    work page 2025

  29. [29]

    NSF Award Number 1803241, Directorate for Mathematical and Physical Sciences , year=

    Postdoctoral research fellowship , author=. NSF Award Number 1803241, Directorate for Mathematical and Physical Sciences , year=

    work page

  30. [30]

    2020 , note=

    High-dimensional structured bandits: Minimax regret, estimation and inference , author=. 2020 , note=

    work page 2020

  31. [31]

    Collaborative research: High-dimensional tensor learning under labeled-data scarcity , author=

    work page

  32. [32]

    Proceedings of the 6th ACM International Conference on AI in Finance (ICAIF) , year=

    Time-varying factor-augmented models for volatility forecasting , author=. Proceedings of the 6th ACM International Conference on AI in Finance (ICAIF) , year=

    work page

  33. [33]

    2025 , publisher=

    Mo, Junyi and Li, Jiayu and Zhang, Duo and Chen, Elynn , booktitle=. 2025 , publisher=

    work page 2025

  34. [34]

    Prior-aligned meta-

    Zhou, Runlin and Chen, Chixiang and Chen, Elynn , journal=. Prior-aligned meta-

    work page

  35. [35]

    Advances in Knowledge Discovery and Data Mining (PAKDD) , series=

    Tensor-fused multi-view graph contrastive learning , author=. Advances in Knowledge Discovery and Data Mining (PAKDD) , series=. 2025 , publisher=

    work page 2025

  36. [36]

    Seeing through the brain: New insights from decoding visual stimuli with

    Huang, Zheng and Zhang, Enpei and Cai, Yinghao and Qiu, Weikang and Yang, Carl and Chen, Elynn and Zhang, Xiang and Ying, Rex and Zhou, Dawei and Yan, Yujun , booktitle=. Seeing through the brain: New insights from decoding visual stimuli with

    work page

  37. [37]

    , journal=

    Chen, Elynn and Li, Sai and Jordan, Michael I. , journal=. Transfer. 2025 , publisher=

    work page 2025

  38. [38]

    Conditional prediction

    Wu, Yujia and Yang, Bo and Chen, Elynn and Chen, Yuzhou and Zheng, Zheshi , booktitle=. Conditional prediction. 2025 , publisher=

    work page 2025

  39. [39]

    Liu, Lingchong and Chen, Elynn and Han, Yuefeng and Xia, Lucy , journal=. Tensor

    work page

  40. [40]

    arXiv preprint arXiv:2512.12122 , year=

    High-dimensional tensor discriminant analysis: Low-rank discriminant structure, representation synergy, and theoretical guarantees , author=. arXiv preprint arXiv:2512.12122 , year=

    work page arXiv

  41. [41]

    arXiv preprint arXiv:2512.25025 , year=

    Modewise additive factor model for matrix time series , author=. arXiv preprint arXiv:2512.25025 , year=

    work page arXiv

  42. [42]

    Scandinavian Journal of Statistics , volume=

    Identification and estimation of threshold matrix-variate factor models , author=. Scandinavian Journal of Statistics , volume=. 2022 , publisher=

    work page 2022

  43. [43]

    arXiv preprint arXiv:2601.21873 , year=

    Low-rank plus sparse matrix transfer learning under growing representations and ambient dimensions , author=. arXiv preprint arXiv:2601.21873 , year=

    work page arXiv

  44. [44]

    Optimistic transfer under task shift via

    Chai, Jinhang and Zhang, Enpei and Chen, Elynn and Yan, Yujun , journal=. Optimistic transfer under task shift via

    work page

  45. [45]

    Proceedings of the 29th International Conference on Artificial Intelligence and Statistics (AISTATS) , year=

    Quantifying epistemic uncertainty in diffusion models , author=. Proceedings of the 29th International Conference on Artificial Intelligence and Statistics (AISTATS) , year=

    work page

  46. [46]

    High-dimensional linear bandits under stochastic latent heterogeneity.arXiv preprint arXiv:2502.00423, 2025

    High-dimensional linear bandits under stochastic latent heterogeneity , author=. arXiv preprint arXiv:2502.00423 , year=

    work page arXiv

  47. [47]

    Transfer learning for contextual joint assortment-pricing under cross-market heterogeneity.arXiv preprint arXiv:2603.18114, 2026

    Transfer learning for contextual joint assortment-pricing under cross-market heterogeneity , author=. arXiv preprint arXiv:2603.18114 , year=

    work page arXiv

  48. [48]

    Low-Rank Principal Eigenmatrix Analysis

    Low-rank principal eigenmatrix analysis , author=. arXiv preprint arXiv:1904.12369 , year=

    work page internal anchor Pith review Pith/arXiv arXiv 1904

  49. [49]

    SIAM Review , volume=

    Tensor decompositions and applications , author=. SIAM Review , volume=. 2009 , publisher=

    work page 2009

  50. [50]

    Oseledets, I. V. , title=. SIAM Journal on Scientific Computing , volume=. 2011 , doi=

    work page 2011

  51. [51]

    Journal of the American Statistical Association , volume=

    Tensor regression with applications in neuroimaging data analysis , author=. Journal of the American Statistical Association , volume=. 2013 , publisher=

    work page 2013

  52. [52]

    Statistics in Biosciences , volume=

    Tucker tensor regression and neuroimaging analysis , author=. Statistics in Biosciences , volume=. 2018 , publisher=

    work page 2018

  53. [53]

    arXiv preprint arXiv:2205.13734 , year=

    An efficient tensor regression for high-dimensional data , author=. arXiv preprint arXiv:2205.13734 , year=

    work page arXiv

  54. [54]

    Journal of the American Statistical Association , volume=

    Parsimonious tensor response regression , author=. Journal of the American Statistical Association , volume=. 2017 , publisher=

    work page 2017

  55. [55]

    Journal of Computational and Graphical Statistics , volume=

    Tensor-on-tensor regression , author=. Journal of Computational and Graphical Statistics , volume=. 2018 , publisher=

    work page 2018

  56. [56]

    Annals of Statistics , volume=

    Convex regularization for high-dimensional multiresponse tensor regression , author=. Annals of Statistics , volume=. 2019 , publisher=

    work page 2019

  57. [57]

    Journal of Machine Learning Research , volume=

    Bayesian tensor regression , author=. Journal of Machine Learning Research , volume=. 2017 , note=

    work page 2017

  58. [58]

    Advances in Neural Information Processing Systems 31 (NeurIPS) , year=

    Boosted sparse and low-rank tensor regression , author=. Advances in Neural Information Processing Systems 31 (NeurIPS) , year=

    work page

  59. [59]

    IEEE Transactions on Information Theory , volume=

    Sparse and low-rank tensor estimation via cubic sketchings , author=. IEEE Transactions on Information Theory , volume=. 2020 , publisher=

    work page 2020

  60. [60]

    Journal of the Royal Statistical Society, Series B , volume=

    Provable sparse tensor decomposition , author=. Journal of the Royal Statistical Society, Series B , volume=. 2017 , publisher=

    work page 2017

  61. [61]

    Sun, Will Wei and Li, Lexin , journal=

    work page

  62. [62]

    , journal=

    Ahmed, Talal and Raja, Haroon and Bajwa, Waheed U. , journal=. Tensor regression using low-rank and sparse. 2020 , publisher=

    work page 2020

  63. [63]

    Generalized low-rank plus sparse tensor estimation by fast

    Cai, Jian-Feng and Li, Jingyang and Xia, Dong , journal=. Generalized low-rank plus sparse tensor estimation by fast. 2023 , publisher=

    work page 2023

  64. [64]

    Annals of Statistics , volume=

    An optimal statistical and computational framework for generalized tensor estimation , author=. Annals of Statistics , volume=. 2022 , publisher=

    work page 2022

  65. [65]

    Zhang, Anru and Xia, Dong , journal=. Tensor. 2018 , publisher=

    work page 2018

  66. [66]

    Journal of the American Statistical Association , volume=

    Fan, Jianqing and Gu, Yihong , title=. Journal of the American Statistical Association , volume=. 2023 , publisher=

    work page 2023

  67. [67]

    Nonparametric regression using deep neural networks with

    Schmidt-Hieber, Johannes , journal=. Nonparametric regression using deep neural networks with. 2020 , publisher=

    work page 2020

  68. [68]

    Annals of Statistics , volume=

    On deep learning as a remedy for the curse of dimensionality in nonparametric regression , author=. Annals of Statistics , volume=. 2019 , publisher=

    work page 2019

  69. [69]

    The Annals of Statistics , volume=

    On the rate of convergence of fully connected deep neural network regression estimates , author=. The Annals of Statistics , volume=. 2021 , publisher=

    work page 2021

  70. [70]

    Neural Computation , volume=

    Ohn, Ilsang and Kim, Yongdai , title=. Neural Computation , volume=. 2022 , issn=

    work page 2022

  71. [71]

    Advances in Neural Information Processing Systems 28 (NeurIPS) , pages=

    Tensorizing neural networks , author=. Advances in Neural Information Processing Systems 28 (NeurIPS) , pages=

    work page

  72. [72]

    Journal of Machine Learning Research , volume=

    Tensor regression networks , author=. Journal of Machine Learning Research , volume=

    work page

  73. [73]

    Algorithmic Learning in a Random World , author=

    work page

  74. [74]

    Journal of Machine Learning Research , volume=

    A tutorial on conformal prediction , author=. Journal of Machine Learning Research , volume=

    work page

  75. [75]

    Journal of the American Statistical Association , volume=

    Distribution-free predictive inference for regression , author=. Journal of the American Statistical Association , volume=. 2018 , publisher=

    work page 2018

  76. [76]

    Advances in Neural Information Processing Systems 32 (NeurIPS) , year=

    Conformalized quantile regression , author=. Advances in Neural Information Processing Systems 32 (NeurIPS) , year=

    work page

  77. [77]

    Biometrika , volume=

    Localized conformal prediction: A generalized inference framework for conformal prediction , author=. Biometrika , volume=. 2023 , publisher=

    work page 2023

  78. [78]

    2008 , publisher=

    Inductive conformal prediction: Theory and application to neural networks , author=. 2008 , publisher=

    work page 2008

  79. [79]

    Quantifying uncertainty in classification performance:

    Zheng, Zheshi and Yang, Bo and Song, Peter , journal=. Quantifying uncertainty in classification performance:

    work page

  80. [80]

    Classification uncertainty quantification: A comparison between bootstrap and conformal

    Zheng, Zheshi and Yang, Bo and Song, Peter , journal=. Classification uncertainty quantification: A comparison between bootstrap and conformal. 2025 , note=

    work page 2025

Showing first 80 references.