Pith. sign in

REVIEW 2 major objections 4 minor 34 references

Adaptive Grid Designs for Classifying Monotonic Binary Deterministic Computer Simulations

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read Nested adaptive grids that skip logically forced runs trace a monotone simulator's success–failure boundary at the best possible adaptive rate — about $v^{-(p-1)}$ runs in $p \ge 2$ dimensions, an order of magnitude better than any static…

desk verdict Useful worst-case lower bounds for static and adaptive designs, but the paper's advertised upper bound for the adaptive grid design does not match its own algorithm; the central rate claim is unsupported as printed. read the letter →

arxiv 2506.03815 v1 pith:PBWYBKQB submitted 2025-06-04 stat.ME

Tian Bai , Dianpeng Wang , Kuangqi Chen , Xu He This is my paper
classification stat.ME MSC 62K0562L05
keywords adaptivedesigncomputerexperimentsmonotonicbinarysimulationdeterministicuncertaintyquantificationspace-fillingminimaxlowerboundice-breaking
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 asks how many runs of an expensive deterministic simulator are needed to find the boundary between "success" and "failure" outputs when the response is binary and monotone in the inputs. It proves that the answer depends on whether runs can be chosen adaptively: any static design needs on the order of $v^{-p}$ runs in $p \ge 2$ dimensions to bring the uncertain volume below $v$, any adaptive design needs at least on the order of $v^{-(p-1)}$ runs, and the proposed adaptive grid designs attain the $v^{-(p-1)}$ rate. The net claim is that adaptivity buys a full power of $1/v$ — an order of magnitude in the worst-case exponent — and that no adaptive procedure of any kind can do better. The benefit matters because the motivating applications cost hours per run: the paper's adaptive scheme reproduces the information of a 125-run grid with 29 runs in the ice-breaking simulator, and it outperforms standard static and active-learning designs on test functions, a road-crash simulation, and the ice-breaking problem.

What carries the argument

The engine of the method is logical run-skipping under total monotonicity. After a point $x$ is evaluated, the outcome is forced at every point in the lower orthant $[0, x]$ if $f(x) = -1$ and in the upper orthant $[x, 1]$ if $f(x) = 1$, so the uncertain region $U(D, f)$ is the complement of these covered orthants and its volume $V(U)$ is the paper's measure of classification error. The adaptive grid design is a named class of designs: sequences of nested full grids with $(2^l + 1)^p$ points per grid ($3^p, 5^p, 9^p, 17^p, \ldots$), run from coarse to fine, in which only points that fall inside the current uncertain region get evaluated. The grouped variant (GG, Algorithm 1) processes one whole resolution before updating $U$ and carries the proved rate; the fully adaptive variant (AG, Algorithm 2) updates $U$ after every run and chooses next the point that maximizes the number of remaining candidates it will render skippable, $\min\{\mathrm{card}(A_x), \mathrm{card}(B_x)\}$ — numerically stronger, without a matching theorem. The lower bounds are proved by an adversarial monotone threshold function on $\sum_k x_k$ that forces any design with few points to leave thin uncovered slices of the input box, which makes the static and adaptive exponents $n^{-1/p}$ and $n^{-1/(p-1)}$ unavoidable.

What would settle it

Run the ice-breaking finite-element model at pairs of inputs ordered by the paper's reparameterization (higher velocity, lower thickness, lower modulus all push the output up); the first pair with a 'break' at the lower input and a 'no break' at the higher input refutes the monotonicity premise on which the skipping logic and the $V(U)$ guarantee rest. Separately, run the fully adaptive grid method on a known monotone test function with boundary $\sum_k x_k = p/2$ for $p = 2$ and $p = 3$, record the evaluations needed to reach $V(U) \le v$ for $v = 10^{-1}, 10^{-2}, 10^{-3}$, and check that the count grows as $v^{-(p-1)}$ rather than $v^{-p}$.

Watch

Extended reading notes

Core claim

The central claim is that the worst-case cost of classifying a monotone binary deterministic simulator is governed by the dimension of the boundary, not of the input space, provided runs may be chosen adaptively. For $p \ge 2$, the volume of the uncertain region $V(U)$ after $n$ runs is at most a constant times $n^{-1/(p-1)}$ for the proposed adaptive grid design (Theorem 3), while no adaptive design can force it below a constant times $n^{-1/(p-1)}$ (Theorem 4) and no static design can beat a constant times $n^{-1/p}$ (Theorems 1 and 2). In terms of runs needed to guarantee $V(U) \le v$, that is order $v^{-(p-1)}$ for the adaptive grid, order $v^{-(p-1)}$ for the best possible adaptive design, and order $v^{-p}$ for the best possible static design — so the adaptive grid is worst-case optimal up to constants among all adaptive procedures and better than any static design by a full power of $1/v$; for $p = 1$ the comparison is $\log(1/v)$ versus $1/v$. The paper's grouped-adaptive grid design carries this rate guarantee; its fully adaptive variant is shown numerically to be even better, and the authors state that they could not prove a matching theorem for it. Applications to a road-crash simulator and an ice-breaking finite-element model, where one run costs about ten hours on 120 cores, confirm the practical gain.

Load-bearing premise

The load-bearing premise is that the simulator's output is exactly monotone — non-decreasing in every input coordinate after reparameterization — so that an unevaluated point's outcome is logically forced by comparisons with evaluated points; in the ice-breaking application this is assumed from domain knowledge, and any small numerical non-monotonicity would let a skipped run be misclassified and would void the $V(U)$ guarantee.

Editorial extensions

If this is right

  • In $p \ge 2$ dimensions no static design — grid, Latin hypercube, Monte Carlo, or space-filling — can achieve better than order $v^{-p}$ runs, so the $n^{-1/p}$ static rate is a genuine floor (Theorems 1 and 2).
  • No adaptive design of any kind can beat order $v^{-(p-1)}$ runs, and the adaptive grid attains it, so the proposed method is minimax-rate optimal up to constants among all adaptive strategies (Theorems 3 and 4).
  • On the ice-breaking simulator, 29 adaptive grid runs reproduce the uncertainty level of the 125-run static grid — about 12 days of simulation instead of close to two months — and the road-crash results show the same pattern across all 40 reconstructed crash occasions.
  • For $p = 1$ the adaptive advantage is exponential: roughly $\log(1/v)$ runs versus order $1/v$ runs for any static design.
  • Because all runs in one grid resolution can be evaluated in parallel, the grouped variants (GG, GI) offer a parallel-friendly route, whereas the fully adaptive variants (AG, AI) are sequential but empirically stronger.

Reading between the lines

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

  • Editorial inference: the $v^{-(p-1)}$ rate reads as the cost of locating a $(p-1)$-dimensional boundary to accuracy $v$, whereas static designs pay to resolve the whole $p$-dimensional box; if that geometric reading is right, skipping schemes built on monotone covering should be near-optimal wherever the target is a low-codimension manifold, not only for monotone binary simulators.
  • Editorial inference: the same orthant-skipping logic transfers, via the paper's own reparameterizations, to simulators that are monotone decreasing in some coordinates or defined on rectangular domains, and to shape-constrained classification problems beyond deterministic simulation.
  • Editorial inference: the paper's numerical comparisons show the grid's edge fading by $p = 6$, where the entropy-based active learning baseline overtakes it, so a hybrid that applies adaptive grids in a few coordinates and entropy acquisition in the rest is a natural, testable next step that the paper does not propose.
  • Editorial inference: the lower bounds are driven by adversarial step-shaped boundaries, so on smooth monotone simulators the realized saving over static designs could be larger than the worst-case comparison; a direct measurement on smooth simulators would quantify how much the minimax guarantee understates the practical gain.
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

2 major / 4 minor

Summary. The paper studies experimental design for deterministic, binary, monotone computer simulations. It measures design quality by the worst-case volume V(U) of the region whose outcome is not logically forced by the evaluated runs, and it derives lower bounds on the number of runs required by any static design (Theorem 2) and any adaptive design (Theorem 4). It then proposes grouped-adaptive grid (GG) and fully adaptive grid (AG) designs, and proves an upper bound for GG (Theorem 3) that is intended to show that O(v^{-(p-1)}) runs suffice to guarantee V(U)≤v, matching the adaptive lower bound and improving on the static O(v^{-p}) rate. Numerical comparisons on synthetic test functions, road-crash simulation data, and an ice-breaking finite-element simulation demonstrate practical gains for the proposed adaptive grid methods.

Significance. The worst-case rate results are the main contribution. If the intended geometric-grid reading of Theorem 3 is confirmed, the paper provides the first matching-order lower and upper bounds for this class of problems, with a constructive design that is simple to implement and substantially cheaper than static grids. The paper also includes detailed proofs, comparisons with many existing design methods, and two real simulation applications, which strengthen its practical relevance. The main reservation is that the theoretical optimality statement applies to the grouped variant GG, while the fully adaptive variant AG, which is the method recommended for applications, has no supporting theorem; in addition, the grid-level notation in the central upper-bound theorem needs to be made unambiguous.

major comments (2)
  1. [Section 2.3, Theorem 3, Algorithm 1, Appendix C.3] The grid-level notation must be disambiguated. In the manuscript as reproduced, Algorithm 1 and Theorem 3 state levels with (2l+1) points per dimension, while the proof in Appendix C.3 sets m=2^l and analyzes refinement from m+1 to 2m+1 points per dimension, and the asymptotic sentence after Theorem 3 claims m_GG(g)=O(2^{g(p-1)}). If read arithmetically, the displayed bound sum_{l=1}^g p(2l+1)^{p-1} is O(g^p), so with grid spacing O(1/g) the resulting number of runs is O(v^{-p}), not the claimed O(v^{-(p-1)}); the theorem would then not support the paper's central claim. The surrounding text and proof indicate that the intended construction is geometric, with 2^l+1 points per dimension, in which case the advertised rate follows. Because this is the load-bearing upper bound, the published version must use unambiguous notation throughout and align Algorithm 1, the group definitions, Theorem 3, and the proof; I recommend explicitly writing 2^l+1 rather than 2l+1 and stating the initial level l=0 corresponds to the 2^p corner grid.
  2. [Abstract, Section 2.3, Section 6] The theoretical optimality result is proved only for the grouped-adaptive grid design GG, not for the fully adaptive grid design AG. Section 2.3 explicitly says that no rigorous theory is established for AG, yet the abstract and conclusions use the phrase 'adaptive grid designs' without qualification when claiming a v^{-(p-1)} evaluation rate that matches the best possible adaptive design. Since AG is the method recommended in the numerical sections and the applications, the paper should either scope the optimality claim to GG or clearly state that the optimality statement is conjectural for AG, so that readers do not attribute a proven rate to the algorithm actually used in practice.
minor comments (4)
  1. [Appendix C.5, Theorem 5] The displayed limit in Theorem 5 is garbled; it should be lim_{n→∞} E[V{U(D_MC,p,n, f_tilde)}]/n^{-1/p}, not the expression with an extra factor of n in the numerator.
  2. [Algorithm 1] When l=0, the candidate set is D_SG,p,2^p, the 2^p corner grid. This should be stated explicitly, because a literal reading of '(2l+1)^p' with l=0 would give a degenerate one-point grid that is not covered by the definition of D_SG,p,n.
  3. [Sections 3-5] The support vector classifier with a Gaussian kernel is not guaranteed to produce monotone predictions. Since the theoretical bounds concern V(U), not classifier accuracy, the paper should clarify that V(U) is the design-efficiency criterion and that the downstream classifier is not assumed to respect monotonicity.
  4. [Section 5] The ice-breaking application assumes exact monotonicity of the finite-element simulator from domain knowledge. A brief caveat that small numerical non-monotonicities could invalidate the skipping step and hence the V(U) interpretation would be useful, since the paper later says it plans to study violations of the monotonicity assumption.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: all rate claims are supported by in-paper lower and upper bound proofs from the monotonicity assumption, with no fitted parameter renamed as a prediction and no load-bearing self-citation chain.

full rationale

The central claims do not reduce to their inputs. The worst-case volume of uncertainty is defined directly from the monotonicity assumption, and the upper bound on the grouped-adaptive grid design (Theorem 3) is proved by counting grid points whose outcomes are not forced by monotonic comparisons; no fitted constant enters that count. The lower bounds for static and adaptive designs (Theorems 2 and 4) are proved by explicit adversary constructions, such as threshold functions f_alpha, and are not imported from the authors' prior work or from any citation. The claim that the grouped-adaptive grid design matches the best possible adaptive design is an external comparison of a proved upper bound with a proved lower bound, not a restatement of the algorithm's definition. Numerical sections use independent test functions, the Volvo road-crash dataset, and the ice-breaking simulation as benchmarks; no estimated parameter is subsequently reported as a prediction. The paper contains no self-citation chain that carries a load-bearing premise: references to [24] merely describe the existing adaptive Monte Carlo method, and the road-crash data citation in [4] is external empirical material. There is a genuine internal consistency concern that the proof of Theorem 3 sets m=2l and refines from m+1 to 2m+1 points per dimension, corresponding to geometric grid levels, whereas Algorithm 1 and the theorem statement use arithmetic grid levels with 2l+1 points per dimension; this is a potential proof gap about the advertised v^{-(p-1)} rate, but it is a correctness issue, not a circularity issue, because the derivation is not equivalent to its own conclusion by construction. Under the review rule that most papers are not circular, no circular step is exhibited, so the circularity score is 0.

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

No numerical constants are fitted in the theorems; the run-count bounds are parameter-free in the design sense. The central claim depends on exact monotonicity, deterministic binary outputs, and a worst-case volume-of-uncertainty criterion. The only identifiable free tuning in the numerical pipeline is the SVC kernel parameter gamma, selected by cross-validation, but it does not enter the theoretical analysis.

assumptions (4)
  • domain assumption The simulation is deterministic and the outcome is exactly binary at every input point.
    Section 2.1 defines f(x) in {-1,1}; the certainty arguments for A and B require that repeated runs at the same input give the same answer. Section 6 lists this as an assumption to relax in future work.
  • domain assumption The response is monotone non-decreasing in every coordinate after linear rescaling.
    Section 2.1 places f in Omega with f(x)<=f(y) whenever x<=y coordinatewise, and Sections 4-5 build monotone reparameterizations for road crash and ice-breaking. If the real simulator is only approximately monotone, skipped runs can be misclassified.
  • ad hoc to paper Worst-case performance, sup over Omega of V(U(D,f)), is the correct efficiency measure.
    All theorems quantify this quantity rather than average-case behavior or the accuracy of a particular classifier. The abstract's phrase 'classification accuracy' is, in the theory, this worst-case uncertainty volume, so the guarantees are conservative rather than direct classifier-accuracy bounds.
  • ad hoc to paper The candidate grids in Algorithm 1 are nested in the sense needed for the counting proof.
    The claimed exponential 2^{g(p-1)} bound requires doubling-resolution nested grids of sizes 3^p, 5^p, 9^p, and so on. The printed Theorem 3 writes (2l+1), which does not yield that asymptotic, so the proof silently relies on the intended nesting that the text does not state unambiguously.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Adaptive Grid Designs for Classifying Monotonic Binary Deterministic Computer Simulations." pith.science (2026). https://pith.science/paper/PBWYBKQB

@misc{pith2026250603815,
  author       = {Pith},
  title        = {Pith review of: Adaptive Grid Designs for Classifying Monotonic Binary Deterministic Computer Simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PBWYBKQB}},
  note         = {Machine review of arXiv:2506.03815}
}
read the original abstract

This research is motivated by the need for effective classification in ice-breaking dynamic simulations, aimed at determining the conditions under which an underwater vehicle will break through the ice. This simulation is extremely time-consuming and yields deterministic, binary, and monotonic outcomes. Detecting the critical edge between the negative-outcome and positive-outcome regions with minimal simulation runs necessitates an efficient experimental design for selecting input values. In this paper, we derive lower bounds on the number of functional evaluations needed to ensure a certain level of classification accuracy for arbitrary static and adaptive designs. We also propose a new class of adaptive designs called adaptive grid designs, which are sequences of grids with increasing resolution such that lower resolution grids are proper subsets of higher resolution grids. By prioritizing simulation runs at lower resolution points and skipping redundant runs, adaptive grid designs require the same order of magnitude of runs as the best possible adaptive design, which is an order of magnitude fewer than the best possible static design. Numerical results across test functions, the road crash simulation and the ice-breaking simulation validate the superiority of adaptive grid designs.

Figures

Figures reproduced from arXiv: 2506.03815 by the authors.

Figure 1
Figure 1. Simulation on the local damage of the ice sheet at different times. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. SG and AG designs, showing the curve separating the two regions [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Averaged volume of uncertain area V (U) (left) and classification accuracy (right) for the test function in (2) with p = 2 (top), p = 4 (middle), and p = 6 (bottom). 8 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Averaged volume of uncertain area V (U) (left) and classification accuracy (right) for the test function in (2) with p = 2, 3, 4. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Averaged volume of uncertain area V (U) (left) and classification accuracy (right) for the test function in (2) with p = 5, 6 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: Proportions of negative responses for p = 2 (left) and p = 4 (right). 10 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Four designs in p = 2, showing the design points with negative response (red dots, or dots to the bottom-left of the dotted line) and positive response (blue dots, or dots to the top-right of the dotted line), the curve separating the two regions A and B (purple dotted…
Figure 8
Figure 8. Figure 8: The DAG,2,10, DAG,2,20, and DAG,2,30 for the 17th crash occasion, showing the design points with crash avoidance (red dots) and crash (blue dots), the certainly crash avoidance area (red shaded area, or the bottom-left shaded area), the certainly crash area (blue shade…
Figure 9
Figure 9. Figure 9: Averaged volume of uncertain area V (U) (left) and classification accuracy (right) for the 17th crash occasion. 13 [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: Averaged volume of uncertain area V (U) (left) and classification accuracy (right) across all 40 crash occasions. impacts a cuboid ice sheet with 0.15 meters long and wide and xt millimeters thick. The ice sheet is assumed to has a Poisson ratio of 0.33 and an elastic…
Figure 11
Figure 11. Figure 11: The DAG,3,29 for all five xe values, showing the design points with negative response (red dots, or dots to the bottom-left of the dotted line) and positive response (blue dots, or dots to the top-right of the dotted line), the skipped design points (crosses), and the…
Figure 12
Figure 12. Figure 12: Volume of uncertain area V (U) for the ice-breaking dynamics. 15 [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]
Figure 13
Figure 13. Figure 13: Four static designs, showing the design points with negative response (red dots, or dots to the bottom-left of [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]
Figure 14
Figure 14. Figure 14: Four adaptive designs, showing the design points with negative response (red dots, or dots to the bottom-left [PITH_FULL_IMAGE:figures/full_fig_p021_14.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

34 extracted references · 32 canonical work pages

  1. [1]

    Santner, Brian J

    Thomas J. Santner, Brian J. Williams, and William I. Notz.The design and analysis of computer experiments. Springer New York, New York, 2003

    work page 2003

  2. [2]

    A numerical simulation method for ice-breaking and cavitation effects on the water-exiting vehicle.Ocean Engineering, 314:119659, 2024

    Qingchen Dong, Wenxin Xue, Taotao Liu, Xin Zhao, and Biao Huang. A numerical simulation method for ice-breaking and cavitation effects on the water-exiting vehicle.Ocean Engineering, 314:119659, 2024

    work page 2024

  3. [3]

    Les investigation on cavitating flow structures and loads of water-exiting submerged vehicles using a uniform filter of octree-based grids.Ocean Engineering, 225:108811, 2021

    Ying Chen, Jie Li, Zhaoxin Gong, Xin Chen, and Chuanjing Lu. Les investigation on cavitating flow structures and loads of water-exiting submerged vehicles using a uniform filter of octree-based grids.Ocean Engineering, 225:108811, 2021

    work page 2021

  4. [4]

    Active sampling: A machine-learning-assisted framework for finite population inference with optimal subsamples.Technometrics, 0(0):1–12, 2024

    Henrik Imberg, Xiaomi Yang, Carol Flannagan, and Jonas Bärgman. Active sampling: A machine-learning-assisted framework for finite population inference with optimal subsamples.Technometrics, 0(0):1–12, 2024

    work page 2024

  5. [5]

    Numerical investigation on the formation of the re-entrant flow and the transformation of varying shedding modes in cloud cavitation.Ocean Engineering, 279:114557, 2023

    Jiakun Zhang, Liang Hao, Qin Wu, and Biao Huang. Numerical investigation on the formation of the re-entrant flow and the transformation of varying shedding modes in cloud cavitation.Ocean Engineering, 279:114557, 2023

    work page 2023

  6. [6]

    Zhuan-Tao He, Chun-Mei Wu, Jia jia Yu, and You-Rong Li. Dynamic analysis of adsorbate behavior in nanopores: Liquid bridge formation, cavitation, and contact angle evaluation via molecular dynamics simulations.Journal of Molecular Liquids, 414:126146, 2024

    work page 2024

  7. [7]

    John Wiley & Sons, Ltd, 2012

    John Stufken and Min Yang.Optimal designs for generalized linear models, chapter 4, pages 137–164. John Wiley & Sons, Ltd, 2012

    work page 2012

  8. [8]

    Silvapulle

    Mervyn J. Silvapulle. On the existence of maximum likelihood estimators for the binomial response models. Journal of the Royal Statistical Society: Series B (Methodological), 43(3):310–313, 1981

    work page 1981

Show all 34 references
  1. [9]

    Golchi, D

    S. Golchi, D. R. Bingham, H. Chipman, and D. A. Campbell. Monotone emulation of computer experiments. SIAM/ASA Journal on Uncertainty Quantification, 3(1):370–392, 2015

    2015

  2. [10]

    Xiaojing Wang and James O. Berger. Estimating shape constrained functions using gaussian processes.SIAM/ASA Journal on Uncertainty Quantification, 4(1):1–25, 2016

    2016

  3. [11]

    Shape-constrained statistical inference.Annual Review of Statistics and Its Application, 11(V olume 11, 2024):373–391, 2024

    Lutz Dümbgen. Shape-constrained statistical inference.Annual Review of Statistics and Its Application, 11(V olume 11, 2024):373–391, 2024

    2024

  4. [12]

    Chih-Li Sung, Ying Hung, William Rittase, Cheng Zhu, and C. F. Jeff Wu. A generalized gaussian process model for computer experiments with binary time series.Journal of the American Statistical Association, 115(530):945–956, 2020

    2020

  5. [13]

    Monotonic random forest with an ensemble pruning mechanism based on the degree of monotonicity.New Generation Computing, 33(4):367–388, 2015

    Sergio González, Francisco Herrera, and Salvador García. Monotonic random forest with an ensemble pruning mechanism based on the degree of monotonicity.New Generation Computing, 33(4):367–388, 2015

    2015

  6. [14]

    Xgboost: A scalable tree boosting system

    Tianqi Chen and Carlos Guestrin. Xgboost: A scalable tree boosting system. InProceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, page 785–794. Association for Computing Machinery, 2016

    2016

  7. [15]

    Monotonic classification: An overview on algorithms, performance measures and data sets.Neurocomputing, 341:168–182, 2019

    José-Ramón Cano, Pedro Antonio Gutiérrez, Bartosz Krawczyk, Michał Wo´ zniak, and Salvador García. Monotonic classification: An overview on algorithms, performance measures and data sets.Neurocomputing, 341:168–182, 2019

    2019

  8. [16]

    Support-vector networks.Machine Learning, 20(3):273–297, 1995

    Corinna Cortes and Vladimir Vapnik. Support-vector networks.Machine Learning, 20(3):273–297, 1995

    1995

  9. [17]

    A comprehensive survey on support vector machine classification: Applications, challenges and trends.Neurocomputing, 408:189–215, 2020

    Jair Cervantes, Farid Garcia-Lamont, Lisbeth Rodríguez-Mazahua, and Asdrubal Lopez. A comprehensive survey on support vector machine classification: Applications, challenges and trends.Neurocomputing, 408:189–215, 2020

    2020

  10. [18]

    M. D. McKay, R. J. Beckman, and W. J. Conover. Comparison of three methods for selecting values of input variables in the analysis of output from a computer code.Technometrics, 21(2):239–245, 1979. 35 APREPRINT- SEPTEMBER22, 2025

    1979

  11. [19]

    Myers, and William A

    Shan Ba, William R. Myers, and William A. Brenneman. Optimal sliced latin hypercube designs.Technometrics, 57(4):479–487, 2015

    2015

  12. [20]

    Probal Chaudhuri and Per A. Mykland. Nonlinear experiments: optimal design and inference based on likelihood. Journal of the American Statistical Association, 88(422):538–546, 1993

    1993

  13. [21]

    Optimal designs for two-level factorial experiments with binary response.Statistica Sinica, 22(2):885–907, 2012

    Jie Yang, Abhyuday Mandal, and Dibyen Majumdar. Optimal designs for two-level factorial experiments with binary response.Statistica Sinica, 22(2):885–907, 2012

    2012

  14. [22]

    Jones, Matthias Schonlau, and William J

    Donald R. Jones, Matthias Schonlau, and William J. Welch. Efficient global optimization of expensive black-box functions.Journal of Global Optimization, 13(4):455–492, Dec 1998

    1998

  15. [23]

    Partitioned active learning for heterogeneous systems.Journal of Computing and Information Science in Engineering, 23(4):041009, 01 2023

    Cheolhei Lee, Kaiwen Wang, Jianguo Wu, Wenjun Cai, and Xiaowei Yue. Partitioned active learning for heterogeneous systems.Journal of Computing and Information Science in Engineering, 23(4):041009, 01 2023

    2023

  16. [24]

    de Rocquigny

    E. de Rocquigny. Structural reliability under monotony: Properties of form, simulation or response surface methods and a new class of monotonous reliability methods (mrm).Structural Safety, 31(5):363–374, 2009

    2009

  17. [25]

    Roshan Joseph, Tirthankar Dasgupta, Rui Tuo, and C

    V . Roshan Joseph, Tirthankar Dasgupta, Rui Tuo, and C. F. Jeff Wu. Sequential exploration of complex surfaces using minimum energy designs.Technometrics, 57(1):64–74, 2015

    2015

  18. [26]

    Lewis and William A

    David D. Lewis and William A. Gale. A sequential algorithm for training text classifiers. InProceedings of the 17th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 3–12, London, 1994. Springer London

    1994

  19. [27]

    Active learning by acquiring contrastive examples

    Katerina Margatina, Giorgos Vernikos, Loïc Barrault, and Nikolaos Aletras. Active learning by acquiring contrastive examples. InProceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 650–663, Online and Punta Cana, Dominican Republic, Nov...

    2021

  20. [28]

    Active learning query strategies for classification, rgression, and clustering: A survey.Journal of Computer Science and Technology, 35(4):913–945, Jul 2020

    Punit Kumar and Atul Gupta. Active learning query strategies for classification, rgression, and clustering: A survey.Journal of Computer Science and Technology, 35(4):913–945, Jul 2020

    2020

  21. [29]

    Support vector machine active learning with applications to text classification

    Simon Tong and Daphne Koller. Support vector machine active learning with applications to text classification. Journal of Machine Learning Research, 2:45–66, March 2001

    2001

  22. [30]

    Safety assessment and a parametric study of forward collision-avoidance assist based on real-world crash simulations.Journal of Advanced Transportation, 2021:1–24, 2021

    MohammadReza Seyedi, MohammadReza Koloushani, Sungmoon Jung, and Arda Vanli. Safety assessment and a parametric study of forward collision-avoidance assist based on real-world crash simulations.Journal of Advanced Transportation, 2021:1–24, 2021

    2021

  23. [31]

    Collision warning with auto brake: A real-life safety perspective

    Erik Coelingh, Lotta Jakobsson, Henrik Lind, and Magdalena Lindman. Collision warning with auto brake: A real-life safety perspective. Inthe 20th International Technical Conference on the Enhanced Safety of Vehicles. National Highway Traffic Safety Administration, 2007

    2007

  24. [32]

    John C. Platt. Probabilities for sv machines. InAdvances in Large-Margin Classifiers. The MIT Press, 09 2000

    2000

  25. [33]

    Computational aspects of three-term recurrence relations.SIAM Review, 9(1):24–82, 1967

    Walter Gautschi. Computational aspects of three-term recurrence relations.SIAM Review, 9(1):24–82, 1967

    1967

  26. [34]

    Princeton University Press, New Jersey, 2003

    Julian Havil.Gamma: exploring Euler’s constant. Princeton University Press, New Jersey, 2003. 36

    2003

Pith tools

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