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REVIEW 3 major objections 5 minor 51 references

Collaborative Prediction: To Join or To Disjoin Datasets

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper proves that merging two linear-regression datasets beats fitting them separately exactly when a scaled noise-variance term exceeds a Mahalanobis distance between the coefficient vectors, and packages this condition into a…

desk verdict Theorem 1 is a clean, citable decomposition of the merge-vs-separate OSE comparison, but Proposition 1 overclaims a two-sided guarantee the lemmas do not support. read the letter →

arxiv 2506.11271 v1 pith:N6ZOVFZQ submitted 2025-06-12 stat.ML cs.LG

Kyung Rok Kim , Yansong Wang , Xiaocheng Li , Guanting Chen This is my paper · ORCID
classification stat.MLcs.LG MSC 62J0568T05
keywords datasetmerginglinearregressionout-of-sampleerrororacleinequalityhigh-probabilityguaranteecollaborativepredictionmulti-tasklearningselection
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

This paper asks when it is better to fit one model to two merged datasets rather than separate models to each dataset, and gives an exact answer for linear regression. The merge is beneficial exactly when a scaled version of the common noise variance exceeds a Mahalanobis distance between the two true coefficient vectors: $h(\sigma^2)>g(\beta^{(1)},\beta^{(2)})$, a quadratic distance weighted by the covariate second-moment structure. The authors turn this oracle condition into a data-driven decision rule with a high-probability guarantee, and then into a practical approximation that tunes a confidence parameter and validates decisions on held-out data. The practical version is presented as an approximation whose success rate is estimated rather than guaranteed with high probability. Experiments on real regression data and on neural-network representations show large out-of-sample-error reductions from clustering datasets with the rule.

What carries the argument

The load-bearing object is the exact out-of-sample-error decomposition of Lemma 2. For the merged least-squares estimator $\hat{\beta}^{(c)}$, the error on population $k$ equals $\sigma^2+\sigma^2\operatorname{tr}(W_k E[(X^{(c)T}X^{(c)})^{-1}])+(\beta^{(1)}-\beta^{(2)})^T E[Z_{3-k}^T W_k Z_{3-k}](\beta^{(1)}-\beta^{(2)})$, where $W_k$ is the second-moment matrix of an out-of-sample covariate from population $k$ and $Z_k=(X^{(c)T}X^{(c)})^{-1}X^{(k)T}X^{(k)}$. This decomposition converts the merge decision into a direct comparison of a variance effect and a parameter-distance effect. The rest of the machinery packages that comparison for data: $\phi_\delta$ and $\psi_\delta$ are high-probability surrogates for the two sides of the oracle inequality, built from concentration bounds and anti-concentration bounds, and Algorithm 2 searches over the confidence parameter to maximize an estimated success rate.

What would settle it

Simulate two Gaussian linear populations with known $\sigma^2$, $\beta^{(1)}$, and $\beta^{(2)}$; compute $h(\sigma^2)-g(\beta^{(1)},\beta^{(2)})$ exactly from the population moments, then draw many datasets and compare Algorithm 2's merge decision with the sign of the true out-of-sample-error difference. If the agreement rate fails to match the claimed success rate, or if a case appears where the sample plug-in of $A_0$ and $B_0$ reverses the inequality, the practical guarantee is falsified.

Watch

Extended reading notes

Core claim

Under the paper's standing assumption that each dataset is generated by a linear model with Gaussian noise of the same variance $\sigma^2$, the authors derive an explicit formula for the out-of-sample error of the least-squares estimator trained on the merged data. The formula splits that error into a noise term proportional to $\sigma^2$ and a term quadratic in the coefficient difference $\beta^{(1)}-\beta^{(2)}$. Subtracting the two separate-fit errors gives Theorem 1: the merged model wins exactly when $h(\sigma^2)>g(\beta^{(1)},\beta^{(2)})$, where $h(x)=A_0x$, $g(y,z)=\|y-z\|_{B_0}^2$, and $A_0$, $B_0$ are constants determined by the covariate distributions. The paper then replaces the unknown $\sigma^2$, $\beta^{(1)}$, and $\beta^{(2)}$ by estimators and, using concentration and anti-concentration bounds, proves Lemma 1: with probability at least $1-5\delta$, the computable condition $\phi_\delta(\hat{\beta}^{(1)},\hat{\beta}^{(2)},\hat{\sigma}^{(c)2}) \ge \psi_\delta(\hat{\beta}^{(1)},\hat{\beta}^{(2)},\hat{\sigma}^{(c)2})$ certifies that merging reduces population loss. Algorithm 1 turns this into a decision rule whose output matches the better of the two out-of-sample losses with probability at least $1-5\delta$.

Load-bearing premise

The practical algorithm assumes that a few distribution-dependent constants appearing in the threshold inequality can be estimated from data without changing the decision, but the paper never defines those estimators or bounds their error, so the high-probability guarantee is proved for the distribution-known version only.

Editorial extensions

If this is right

  • For two linear-regression datasets, the optimal choice is known exactly from population quantities: merge if $h(\sigma^2)>g(\beta^{(1)},\beta^{(2)})$, and keep separate fits otherwise.
  • Algorithm 1 makes this choice with probability at least $1-5\delta$ from samples, so the merge decision does not require knowing the true coefficients or noise level.
  • Algorithm 2 makes the procedure operational by tuning a confidence parameter on a grid and validating decisions on held-out data, and Algorithm 3 extends it to many datasets with a greedy clustering loop.
  • On real regression datasets and on neural-network penultimate-layer representations, the algorithm reduces reported out-of-sample error by roughly 17.5% to 99.7% relative to fitting each data partition separately.
  • For classification with linear models, the parallel result says the combined model's error bound beats separate fits when the distance between the true task parameters is small enough, making the merge criterion one of parameter closeness rather than mere data size.

Reading between the lines

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

  • A direct extension the paper leaves untested is whether the same criterion shape holds for ridge regression, where the variance term depends on the regularizer; the Lemma 2 decomposition suggests the merge rule would become a comparison between a regularized variance term and the same Mahalanobis parameter distance.
  • Because the practical algorithm never defines or bounds plug-in estimators for $A_0$ and $B_0$, a finite-sample guarantee would need explicit $\hat{A}_0-A_0$ and $\hat{B}_0-B_0$ error bounds; until then, Algorithm 2's success-rate estimate is the only validation.
  • The greedy clustering in Algorithm 3 assumes pairwise signals are enough; a testable extension is whether a three-way merge can be beneficial when no two-way merge is, which would require a different clustering rule.
  • The representation-space experiments suggest the oracle inequality might serve as a general task-similarity score for transfer learning, where the 'coefficient' is a linear probe on shared features; this connection is not developed in the paper.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper studies when two (or more) datasets should be merged for training a linear regression model, with an extension to classification and to neural network representations. For two datasets generated from linear models with Gaussian noise, Theorem 1 gives an exact equivalence: merging reduces the sum of out-of-sample errors if and only if h(σ²)>g(β(1),β(2)), where h is an affine function of the noise variance and g is a Mahalanobis distance between the two coefficient vectors. The paper then proposes Algorithm 1, which replaces the unknown population quantities by estimators and decides to merge when a computable lower bound on h exceeds a computable upper bound on g; Proposition 1 claims a 1−5δ high-probability guarantee for this decision. Because Algorithm 1 requires distribution-dependent constants, the paper introduces Algorithm 2, which tunes a confidence surrogate α by estimated success rate, and Algorithm 3 for greedily clustering multiple datasets. Experiments on synthetic data, real regression datasets, and representations from simple MLPs are reported.

Significance. The exact out-of-sample-error decomposition in Appendix B.1.1 (Lemma 2, Lemma 3, and Theorem 1) is a clean and useful contribution: it makes explicit the bias-variance trade-off in merging two linear-regression datasets and gives an interpretable condition in terms of the coefficient distance and noise variance. If the advertised high-probability decision guarantee were established, the paper would provide a principled alternative to direct empirical-loss comparison, and the code and experimental comparisons are valuable. However, the central probability guarantee is not currently established: Proposition 1 does not follow from the one-sided bounds in Lemma 1, and the practical Algorithm 2 relies on plug-in estimators for distribution-dependent constants that are never defined or controlled. The classification extension compares upper bounds rather than actual population losses, so the broad applicability claimed in the abstract is stronger than what the theorems support.

major comments (3)
  1. [Section 2.2.2, Proposition 1 and Lemma 1] Proposition 1 asserts that with probability at least 1−5δ, Algorithm 1 outputs the decision rule with minimum out-of-sample error. The supporting Lemma 1 only proves the one-sided implication: if φδ(βhat(1),βhat(2),σhat(c)²) ≥ ψδ(βhat(1),βhat(2),σhat(c)²), then h(σ²) ≥ g(β(1),β(2)) with probability at least 1−5δ. Formally, Lemma 1 controls the false-merge event {φδ ≥ ψδ} ∩ {h < g} but gives no control over the false-no-merge event {φδ < ψδ} ∩ {h > g}. Since Algorithm 1 outputs 'no merge' whenever φδ < ψδ, the probability that the algorithm selects the suboptimal decision on the no-merge side is not bounded by 5δ. Therefore Proposition 1 does not follow from the stated lemmas. A correct proof would require a high-probability converse (for example, an upper bound on h and a lower bound on g), or the stated guarantee must be weakened to 'whenever Algorithm 1 merges, merging is correct with probability at least 1−5δ.' This issue is load-bearing because Proposition 1 is the theoretical basis for the paper's central claim of high-probability population-loss reduction.
  2. [Section 2.2.3 and Appendix B.1.2] Algorithm 2 is presented as the computationally feasible version of Algorithm 1, but it invokes Algorithm 1 as a subroutine. The functions φδ and ψδ used by Algorithm 1 depend on population-level constants: A0 appears in the definitions of Ã1(δ) and Ã2(δ) in Lemma 5, and B0 enters ψδ through the definition of g and the term Tδ. These constants are defined in Theorem 1 using population expectations such as Wk, E[(X(k)⊤X(k))^{-1}], and E[(X(c)⊤X(c))^{-1}]. No estimator for these constants is defined in Appendix B.1.2, and no error bound is provided for replacing them with sample quantities. The remark before Section 2.2.3 acknowledges that Algorithm 1 requires knowledge of the marginal distribution of x, but Algorithm 2 does not resolve this issue unless explicit plug-in estimators are supplied. Theorem 4 only proves consistency of the bootstrap estimator of the out-of-sample error; it does not control the error in the decision boundary φδ or ψδ. Thus the practical algorithm's theoretical support is incomplete.
  3. [Section 2.2.3 and Theorem 4 (Appendix B.1.4)] Even setting aside the missing estimators for A0 and B0, the claimed consistency of Algorithm 2 is not established. The text states that Theorem 4 justifies the consistency of the approximation, but Theorem 4 is a pointwise consistency statement for dOSEM(βhat(k),Dout_k) as an estimator of OSE(βhat(k), P(k)). It does not imply that the success-rate maximization over α in Part 1 of Algorithm 2 converges, nor that the final decision Merge=1{proxy_acc>λ} converges to the oracle decision. In addition, the same out-of-sample bootstrap is used both to tune α and to compute the final proxy_acc, so the reported proxy accuracy is a training-selected quantity; no uniform consistency or selection-bias control is provided. This gap affects the practical algorithm that is featured in the numerical experiments and in the abstract's claim of a practical method with theoretical guarantees.
minor comments (5)
  1. [Appendix B.1.2, Lemma 6] The statement of Lemma 6 contains a typographical error: D⊤D is written as {(X(1)⊤X(1))^{-1} + (X(2)⊤X(2))^{-2}}^{-1}, but the second term should be (X(2)⊤X(2))^{-1}.
  2. [Appendix B, Lemma 1 and Lemma 5] The restated Lemma 1 and Lemma 5 use the symbol f(σ²) in some places where the main text and Theorem 1 use h(σ²). The notation should be unified throughout.
  3. [Algorithm 2, line 8] The pseudocode for the update is missing the indicator notation: 'correct_α ← correct_α +1 (ϕα−ψα)×OSE_dif>0' should be written as 'correct_α ← correct_α + 1{(ϕα−ψα)×OSE_dif>0}'.
  4. [Section 2.3 and Appendix B.2] The classification criterion in Theorem 9 compares upper bounds Φ and Ψ on a surrogate loss, not the actual cross-entropy population losses. The main text should state clearly that the classification result is an error-bound comparison rather than an exact population-loss reduction.
  5. [Abstract and Section 2.2.3] The abstract claims the algorithm 'reduces population loss with high probability' by leveraging 'data-driven estimators,' but the only stated high-probability result is Proposition 1 for Algorithm 1, which requires unknown distributional constants. The presentation should distinguish the guaranteed regime from the heuristic/plug-in regime.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; central derivation self-contained, minor proxy-accuracy self-reference only.

full rationale

The central regression derivation chain is self-contained. Theorem 1 is an exact algebraic consequence of Lemma 2's expression for the out-of-sample error, with A0 and B0 defined from population expectations rather than assumed; Lemma 5 and Lemma 6 use external concentration and anti-concentration bounds to sandwich h(σ^2) from below and g(β(1),β(2)) from above, and Lemma 1 combines them by a union bound (2δ + 3δ = 5δ). Proposition 1 inherits this implication; the one-sidedness noted by the skeptic (no control of false negatives when φδ < ψδ) is a correctness gap, not circularity, because the claimed minimum-OSE property is not assumed as an input to Lemma 1. Algorithm 2 explicitly disclaims a high-probability guarantee and instead tunes α by maximizing an estimated success rate; the fact that the reported proxy_acc is the same objective used for selection, and that real-data reductions are computed with the same bootstrap dOSE the algorithm optimizes, is a mild evaluation self-reference, but it is labeled as 'proxy' and 'estimated ground truth' and does not feed back into Theorem 1 or Proposition 1. No load-bearing self-citation, imported uniqueness claim, or ansatz-smuggled-via-citation appears; the Arlot and Bach citation is only a grid-search heuristic. Overall, the paper's claimed derivation is not equivalent to its inputs, so circularity is minor and non-central.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central derivation rests on standard linear-model assumptions and concentration inequalities; no invented entities are introduced. The main unaccounted input is the practical estimation of the population constants A0 and B0, which the paper leaves implicit. The tuning parameters alpha and lambda are the only free parameters fitted or hand-set to data.

free parameters (2)
  • alpha (confidence-level surrogate) = selected from [2,10] step 0.01 by maximizing cSR
    Algorithm 2 Part1 tunes alpha by grid search on estimated success rate; no guarantee is provided for the selected value.
  • accuracy threshold lambda = 0.9
    Fixed across experiments (Appendix C.2); the merge decision hinges on proxy_acc > lambda.
assumptions (4)
  • domain assumption Assumption 1: each dataset follows y = x^T beta_k + epsilon with epsilon ~ N(0, sigma^2), same sigma^2 across datasets; x and epsilon independent.
    Used to derive exact OSE formulas and the normal distributions behind Lemma 1; if noise variances differ across datasets, Theorem 1 no longer applies.
  • domain assumption Assumption 2: Omega_k mu_k != 0 and sigma^2 Omega_c mu_k + Lambda_k mu_k != 0.
    Required for the bootstrap CLT argument (Theorem 4) proving consistency of dOSE; it is unverifiable in practice.
  • domain assumption Assumption 3 (margin gamma0) and Assumption 4 (bounded features ||x|| <= B).
    Used in the classification error-bound analysis in Appendix B.2; the experiments do not verify these for real datasets.
  • standard math Concentration inequalities of Hsu et al., Lovett, Hanson-Wright, and Gill's bootstrap CLT.
    Background results cited and used without proof; they are standard but their constants propagate into the bounds.

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Cite this review

Pith. "Pith review of Collaborative Prediction: To Join or To Disjoin Datasets." pith.science (2026). https://pith.science/paper/N6ZOVFZQ

@misc{pith2026250611271,
  author       = {Pith},
  title        = {Pith review of: Collaborative Prediction: To Join or To Disjoin Datasets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N6ZOVFZQ}},
  note         = {Machine review of arXiv:2506.11271}
}
read the original abstract

With the recent rise of generative Artificial Intelligence (AI), the need of selecting high-quality dataset to improve machine learning models has garnered increasing attention. However, some part of this topic remains underexplored, even for simple prediction models. In this work, we study the problem of developing practical algorithms that select appropriate dataset to minimize population loss of our prediction model with high probability. Broadly speaking, we investigate when datasets from different sources can be effectively merged to enhance the predictive model's performance, and propose a practical algorithm with theoretical guarantees. By leveraging an oracle inequality and data-driven estimators, the algorithm reduces population loss with high probability. Numerical experiments demonstrate its effectiveness in both standard linear regression and broader machine learning applications. Code is available at https://github.com/kkrokii/collaborative_prediction.

Figures

Figures reproduced from arXiv: 2506.11271 by the authors.

Figure 1
Figure 1. Representation of MLP2 on CFGSF The effectiveness of clustering the datasets can also be con￾firmed by visualizing the representation [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 47 canonical work pages

  1. [1]

    Demand F orecast for O ptimized I nventory P lanning, 2023

    Oscar Aguilar. Demand F orecast for O ptimized I nventory P lanning, 2023. URL www.kaggle.com/datasets/oscarm524/demand-forecast-for-optimized-inventory-planning

    work page 2023

  2. [2]

    Understanding I ntermediate L ayers U sing L inear C lassifier P robes

    Guillaume Alain and Yoshua Bengio. Understanding I ntermediate L ayers U sing L inear C lassifier P robes. arXiv:1610.01644, 2016

    arXiv 2016

  3. [3]

    Uncovering S hared S tructures in M ulticlass C lassification

    Yonatan Amit, Michael Fink, Nathan Srebro, and Shimon Ullman. Uncovering S hared S tructures in M ulticlass C lassification. In Proceedings of the 24th international conference on Machine learning, 2007

    work page 2007

  4. [4]

    A F ramework for L earning P redictive S tructures from M ultiple T asks and U nlabeled D ata

    Rie Kubota Ando and Tong Zhang. A F ramework for L earning P redictive S tructures from M ultiple T asks and U nlabeled D ata. Journal of Machine Learning Research, 6: 0 1817--1853, 2005

    work page 2005

  5. [5]

    Data-driven C alibration of L inear E stimators with M inimal P enalties

    Sylvain Arlot and Francis Bach. Data-driven C alibration of L inear E stimators with M inimal P enalties. Proceedings of the 23rd International Conference on Neural Information Processing Systems, page 46–54, 2009

    work page 2009

  6. [6]

    Feature Representation in Convolutional Neural Networks

    Ben Athiwaratkun and Keegan Kang. F eature R epresentation in C onvolutional N eural N etworks. arxiv:1507.02313, 2015

    work page Pith review arXiv 2015

  7. [7]

    Task C lustering and G ating for B ayesian M ultitask L earning

    Bart Bakker and Tom Heskes. Task C lustering and G ating for B ayesian M ultitask L earning. The Journal of Machine Learning Research, 4: 0 83--99, 2003

    work page 2003

  8. [8]

    Rademacher and G aussian C omplexities: R isk B ounds and S tructural R esults

    Peter Bartlett and Shahar Mendelson. Rademacher and G aussian C omplexities: R isk B ounds and S tructural R esults. Journal of Machine Learning Research, 3: 0 463--482, 2002

    work page 2002

Show all 51 references
  1. [9]

    C onvex M ulti- T ask L earning by C lustering

    Aviad Barzilai and Koby Crammer. C onvex M ulti- T ask L earning by C lustering. Proceedings of the 18th International Conference on Artificial Intelligence and Statistics, 38, 2015

    2015

  2. [10]

    Procaccia, and Mingda Qiao

    Avrim Blum, Nika Haghtalab, Ariel D. Procaccia, and Mingda Qiao. Collaborative PAC L earning. Proceedings of the 31st International Conference on Neural Information Processing Systems, 30: 0 2389–2398, 2017

    2017

  3. [11]

    Concentration I nequalities: A N onasymptotic T heory of I ndependence

    Stephane Boucheron, Gabor Lugosi, and Pascal Massart. Concentration I nequalities: A N onasymptotic T heory of I ndependence . Oxford Academic, 2013

    2013

  4. [12]

    Random F orests

    Leo Breiman. Random F orests. Machine Learning, 45 0 (1): 0 5–32, 2001

    2001

  5. [13]

    Xgboost: A S calable T ree B oosting S ystem

    Tianqi Chen and Carlos Guestrin. Xgboost: A S calable T ree B oosting S ystem. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, page 785–794, 2016

    2016

  6. [14]

    Walmart R ecruiting - S tore S ales F orecasting, 2014

    Will Cukierski. Walmart R ecruiting - S tore S ales F orecasting, 2014. URL https://www.kaggle.com/c/walmart-recruiting-store-sales-forecasting

    2014

  7. [15]

    An E lementary P roof of a T heorem of J ohnson and L indenstrauss

    Sanjoy Dasgupta and Anupam Gupta. An E lementary P roof of a T heorem of J ohnson and L indenstrauss. Random Structures & Algorithms, 22: 0 60--65, 2002

    2002

  8. [16]

    Regularized M ulti– T ask L earning

    Theodoros Evgeniou and Massimiliano Pontil. Regularized M ulti– T ask L earning. Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 109--117, 2004

    2004

  9. [17]

    Collaborative L earning via P rediction C onsensus

    Dongyang Fan, Celestine Mendler-D\" u nner, and Martin Jaggi. Collaborative L earning via P rediction C onsensus. In Proceedings of the 37th International Conference on Neural Information Processing Systems, 2023

    2023

  10. [18]

    Corporación F avorita G rocery S ales F orecasting, 2017

    Corporación Favorita, inversion, Julia Elliott, and Mark McDonald. Corporación F avorita G rocery S ales F orecasting, 2017. URL https://kaggle.com/competitions/favorita-grocery-sales-forecasting

    2017

  11. [19]

    Rossmann S tore S ales, 2015

    FlorianKnauer and Will Cukierski. Rossmann S tore S ales, 2015. URL https://kaggle.com/competitions/rossmann-store-sales

    2015

  12. [20]

    Non- and S emi- P arametric M aximum L ikelihood E stimators and the von M ises M ethod

    Richard Gill. Non- and S emi- P arametric M aximum L ikelihood E stimators and the von M ises M ethod. Scandinavian Journal of Statistics, 16: 0 97--128, 1989

    1989

  13. [21]

    D. L. Hanson and F. T. Wright. A B ound on T ail P robabilities for Q uadratic F orms in I ndependent R andom V ariables. The Annals of Mathematical Statistics, 42 0 (3): 0 1079--1083, 1971

    1971

  14. [22]

    M etro I nterstate T raffic V olume

    John Hogue. M etro I nterstate T raffic V olume. UCI Machine Learning Repository, 2019. DOI : https://doi.org/10.24432/C5X60B

    2019 doi

  15. [23]

    A T ail I nequality for Q uadratic F orms of S ubgaussian R andom V ectors

    Daniel Hsu, Sham Kakade, and Tong Zhang. A T ail I nequality for Q uadratic F orms of S ubgaussian R andom V ectors. Electronic Communications in Probability, 17, 2011

    2011

  16. [24]

    Brendan McMahan, Brendan Avent, Aur\' e lien Bellet, Mehdi Bennis, Arjun Nitin Bhagoji, Kallista Bonawitz, Zachary Charles, Graham Cormode, Rachel Cummings, Rafael G

    Peter Kairouz, H. Brendan McMahan, Brendan Avent, Aur\' e lien Bellet, Mehdi Bennis, Arjun Nitin Bhagoji, Kallista Bonawitz, Zachary Charles, Graham Cormode, Rachel Cummings, Rafael G. L. D’Oliveira, Hubert Eichner, Salim El Rouayheb, David Evans, Josh Gardner, Zachary Garrett...

    2021

  17. [25]

    Kolmogorov

    A. Kolmogorov. Sur les P ropriétés des F onctions de C oncentrations de M . P . L évy. Annales de l'institut Henri Poincaré, 1958

    1958

  18. [26]

    Learning T ask G rouping and O verlap in M ulti-task L earning

    Abhishek Kumar and Hal Daume III. Learning T ask G rouping and O verlap in M ulti-task L earning. Proceedings of the 29th International Coference on Machine Learning, 2012

    2012

  19. [27]

    Small B all P robability E stimatesin T erms of W idth

    Rafal Latala and Krzysztof Oleszkiewicz. Small B all P robability E stimatesin T erms of W idth. Studia Mathematica, 169: 0 305--314, 2005

    2005

  20. [28]

    Probability in B anach S paces

    Michel Ledoux and Michel Talagrand. Probability in B anach S paces. C lassics in M athematics. Springer-Verlag, Berlin, 2011

    2011

  21. [29]

    Convergent L earning: D o D ifferent N eural N etworks L earn the S ame R epresentations? International Conference on Learning Representation, 2016

    Yixuan Li, Yosinski Jason, Jeff Clune, Hod Lipson, and John Hopcroft. Convergent L earning: D o D ifferent N eural N etworks L earn the S ame R epresentations? International Conference on Learning Representation, 2016

    2016

  22. [30]

    Percy Liang, Francis Bach, Guillaume Bouchard, and Michael I. Jordan. Asymptotically O ptimal R egularizationin S mooth P arametric M odels. Advances in Neural Information Processing Systems, 22, 2009

    2009

  23. [31]

    A C ollaborative L earning F ramework for E stimating M any I ndividualized R egression M odels in a H eterogeneous P opulation

    Ying Lin, Kaibo Liu, Eunshin Byon, Xiaoning Qian, Shan Liu, and Shuai Huang. A C ollaborative L earning F ramework for E stimating M any I ndividualized R egression M odels in a H eterogeneous P opulation. IEEE Transactions on Reliability, 67 0 (1): 0 328--341, 2018

    2018

  24. [32]

    Tsybakov, and Sara van de Geer

    Karim Lounici, Massimiliano Pontil, Alexandre B. Tsybakov, and Sara van de Geer. Taking A dvantage of S parsity in M ulti- T ask L earning. Annual Conference Computational Learning Theory, 2009

    2009

  25. [33]

    An E lementary P roof of A nti- C oncentration of P olynomials in G aussian V ariables

    Shachar Lovett. An E lementary P roof of A nti- C oncentration of P olynomials in G aussian V ariables. Electronic Colloquium on Computational Complexity, 17: 0 182, 2010

    2010

  26. [34]

    On the M ethod of B ounded D ifferences

    Colin McDiarmid. On the M ethod of B ounded D ifferences. Invited Papers at the Twelfth British Combinatorial Conference, pages 148--188, 1989

    1989

  27. [35]

    Combining I nformation from M ultiple S urveys by U sing R egression for E fficient S mall D omain E stimation

    Takis Merkouris. Combining I nformation from M ultiple S urveys by U sing R egression for E fficient S mall D omain E stimation. Journal of the Royal Statistical Society, 2010

    2010

  28. [36]

    Boom B ikes - L inear R egression, 2021

    Aditya Mishra. Boom B ikes - L inear R egression, 2021. URL https://www.kaggle.com/datasets/kratos2597/boom-bikes-linear-regression

    2021

  29. [37]

    Co- C lustering for M ultitask L earning

    Keerthiram Murugesan, Jaime Carbonell, and Yiming Yang. Co- C lustering for M ultitask L earning. arxiv:1703.00994, 2017

    2017 arXiv

  30. [38]

    Long Ouyang, Jeff Wu, Xu Jiang, Diogo Almeida, Carroll L. Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, John Schulman, Jacob Hilton, Fraser Kelton, Luke Miller, Maddie Simens, Amanda Askell, Peter Welinder, Paul Christiano, Jan Leike, and...

    2022

  31. [39]

    Hanson- W right I nequality and S ub-gaussian C oncentration

    Mark Rudelson and Roman Vershynin. Hanson- W right I nequality and S ub-gaussian C oncentration. arXiv:1306.2872, 2013

    2013 arXiv

  32. [40]

    Walmart D ata A nalysis and F orcasting, 2023

    Amit Kumar Sahu. Walmart D ata A nalysis and F orcasting, 2023. URL https://www.kaggle.com/datasets/asahu40/walmart-data-analysis-and-forcasting

    2023

  33. [41]

    Minimization M ethods for N on-differentiable F unctions

    Naum Zuselevich Shor. Minimization M ethods for N on-differentiable F unctions . Springer, 1985

    1985

  34. [42]

    Productivity P rediction of G arment E mployees, 2021

    Sirisha Siri. Productivity P rediction of G arment E mployees, 2021. URL https://www.kaggle.com/datasets/ishadss/productivity-prediction-of-garment-employees

    2021

  35. [43]

    Multi-task R egression using M inimal P enalties

    Matthieu Solnon, Sylvain Arlot, and Francis Bach. Multi-task R egression using M inimal P enalties. Journal of Machine Learning Research, 13: 0 2773--2812, 2012

    2012

  36. [44]

    Jaakkola

    Nathan Srebro, Noga Alon, and Tommi S. Jaakkola. Generalization E rror B ounds for C ollaborative P rediction with L ow- R ank M atrices. In Proceedings of the 18th International Conference on Neural Information Processing Systems, 2004

    2004

  37. [45]

    Using D ata M ining T echniques for B ike S haring D emand P rediction in M etropolitan C ity

    Sathishkumar Veerappampalayam, Jangwoo Park, and Yongyun Cho. Using D ata M ining T echniques for B ike S haring D emand P rediction in M etropolitan C ity. Computer Communications, pages 353--366, 2020

    2020

  38. [46]

    High- D imensional P robability: A n I ntroduction with A pplications in D ata S cience

    Roman Vershynin. High- D imensional P robability: A n I ntroduction with A pplications in D ata S cience . Cambridge University Press, 2018

    2018

  39. [47]

    Robust T ask G rouping with R epresentative T asks for C lustered M ulti- T ask L earning

    Yaqiang Yao, Jie Cao, and Huanhuan Chen. Robust T ask G rouping with R epresentative T asks for C lustered M ulti- T ask L earning. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, page 1408–1417, 2019

    2019

  40. [48]

    Large- S cale C ollaborative P rediction U sing a N onparametric R andom E ffects M odel

    Kai Yu, John Lafferty, Shenghuo Zhu, and Yihong Gong. Large- S cale C ollaborative P rediction U sing a N onparametric R andom E ffects M odel. In Proceedings of the 26th Annual International Conference on Machine Learning, 2009

    2009

  41. [49]

    Probing gpt-3’s L inguistic K nowledge on S emantic T asks

    Lining Zhang, Mengchen Wang, Liben Chen, and Wenxin Zhang. Probing gpt-3’s L inguistic K nowledge on S emantic T asks. In Proceedings of the Fifth BlackboxNLP Workshop on Analyzing and Interpreting Neural Networks for NLP, pages 297--304, 2022

    2022

  42. [50]

    Collaborative P erformance P rediction for L arge L anguage M odels, 2024

    Qiyuan Zhang, Fuyuan Lyu, Xue Liu, and Chen Ma. Collaborative P erformance P rediction for L arge L anguage M odels, 2024

    2024

  43. [51]

    Flexible C lustered M ulti- T ask L earning by L earning R epresentative T asks

    Qiang Zhou and Qi Zhao. Flexible C lustered M ulti- T ask L earning by L earning R epresentative T asks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 38 0 (2): 0 266--278, 2016

    2016

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.