REVIEW 4 major objections 6 minor 35 references
Accelerated Bayesian Optimal Experimental Design via Conditional Density Estimation and Informative Data
T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash
Pith's one-line read This paper claims that Bayesian optimal experimental designs can be computed by replacing repeated Gaussian-process refits with a conditional density estimator, giving a 6- to 13-fold speedup over standard BOED while selecting the same…
desk verdict A practical idea undermined by an undefined conditional distribution: p(y|d,z) depends on a virtual observation that is never specified, so the claimed acceleration is not measurable. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the Gaussian-ratio identity in Eq. (9): the ratio $N(y|m_1,\Sigma_1)/N(y|m_2,\Sigma_2)$ is an unnormalized Gaussian $N(y|m,\Sigma)$ with precision difference $\Sigma^{-1} = \Sigma_1^{-1} - \Sigma_2^{-1}$ (equivalently $\Sigma=(\Sigma_1^{-1}-\Sigma_2^{-1})^{-1}$) and mean $m=\Sigma(\Sigma_1^{-1}m_1-\Sigma_2^{-1}m_2)$, times a normalizer $Z$. The paper trains a kernel mixture network $q_{\mathrm{CDE}}(y|d,z)$ to approximate this ratio, so that $\hat{p}(y|d,z)=q_{\mathrm{CDE}}(y|d,z)p_{\mathrm{GP}}(y|d)$ costs almost nothing to evaluate. A second mechanism is the covariance screen: since the GP kernel decays with distance, samples $z$ with $\mathrm{COV}(y_d,y_z)$ below a tolerance $\epsilon_{\mathrm{cov}}$ are dropped from CDE training and from the Monte Carlo sum, on the grounds that such $z$ barely affect the prediction at $d$.
What would settle it
Run the erf parameter-estimation example from Section 6.2.1 with identical settings but assign two different values to the virtual observation $y_z$ in Algorithm 1; if the CDE training targets or the final optimal design change, the method depends on a quantity that the paper never defines, so Eq. (11) is not fully specified.
Extended reading notes
Core claim
The paper's central claim is that the ratio $p(y|d,z)/p(y|d)$ between two Gaussian random fields can be learned by a kernel mixture network, so the optimal design maximizes $d^* = \arg\max_{d\in D} \mathbb{E}_{y_i\sim p_{\mathrm{GP}}(y|d),\, z_i\sim p(z)}[ (\hat{p}(y_i|d,z_i)/p(y_i|d)) \ln(\hat{p}(y_i|d,z_i)/p(y|d)) ]$, with $\hat{p}(y|d,z)=q_{\mathrm{CDE}}(y|d,z)p_{\mathrm{GP}}(y|d)$. Once $q_{\mathrm{CDE}}$ is trained, evaluating it is nearly free, and covariance-based screening keeps only the $z$-samples that affect each design candidate. The paper reports that this procedure reproduces the expected-information-gain landscape of standard BOED (Figure 1) and the RMSE trajectory of the constructed surrogate (Figure 2b), while running 6 to 13 times faster than basic BOED in six test cases.
Load-bearing premise
The method assumes that the conditional distribution $p(y|d,z)$ is a Gaussian obtained by conditioning the Gaussian process on a virtual observation at $z$, yet the value of that virtual observation is never specified; if $z$ is an unknown parameter, no such observation exists.
Editorial extensions
If this is right
- If Eq. (11) is right, the expected information gain can be maximized by independent Monte Carlo sampling over $y$ and $z$, eliminating the nested double integral that dominates basic BOED's cost.
- Because the trained $q_{\mathrm{CDE}}$ can be evaluated at any $(d,z)$ almost for free, the optimal-design search no longer requires fitting a separate constrained Gaussian process for every candidate design.
- The covariance-guided screening in Algorithms 1 and 2 removes $z$-samples whose Gaussian-process covariance with the design is below threshold, so both CDE training and integration concentrate on informative points; this is the claimed source of the 6-13x speedup.
- The same loop, with $p(z)$ redefined in Section 5.1, applies to surrogate construction, parameter estimation, and failure probability estimation, yielding one unified active-learning procedure.
Reading between the lines
- A testable consequence of Eq. (9) is that the normalizer $Z$ is only positive when $\Sigma_2-\Sigma_1$ is positive definite; this hidden restriction on kernel length scales and design spacing is not discussed in the paper.
- The covariance threshold $\epsilon_{\mathrm{cov}}$ acts as a bias-variance knob: raising it discards more $z$-samples and inflates the speedup, but the integral being maximized drifts away from the true expected information gain, so the 6-13x range in Table 1 should be paired with the thresholds actually used.
- Since $p(z)$ is updated every iteration, the amortized cost of $q_{\mathrm{CDE}}$ only holds if the new prior's support remains inside the training region; a shifted $p(z)$ would force retraining and reduce the speedup.
- The same ratio-approximation trick could be tested with normalizing flows instead of kernel mixture networks, which would separate the benefit of the reformulation from the choice of density estimator.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes an accelerated Bayesian optimal experimental design (BOED) method, Acc-BOED, based on three ingredients: a reformulation of the expected information gain as a double integral with independent sampling variables, an approximation of the likelihood ratio p(y|d,z)/p(y|d) by a conditional density estimator (a kernel mixture network), and a covariance-threshold criterion for selecting informative samples for both CDE training and Monte Carlo integration. The method is applied to surrogate construction, parameter estimation, and failure probability estimation, and the paper reports a speedup of 6–13x over a basic BOED implementation while claiming that the optimal designs are preserved. The numerical sections compare Acc-BOED with random sampling and Latin hypercube sampling in terms of RMSE, KL divergence, and failure probability, with several comparisons made against known ground-truth functions.
Significance. If the central estimator were well defined, the broad idea of using a learned density ratio to avoid repeated Gaussian-process refits in BOED would be timely and potentially useful. The reformulation leading to Eq. (6) is standard, and the empirical comparisons against ground truth in the failure-probability and RMSE examples are concrete and partially instructive. However, the central quantity p(y|d,z) is not actually defined in the paper, so the EIG estimates, the speedup numbers in Table 1, and the design-preservation claim in Figure 1 are not currently supported. The paper also does not provide code, KMN architecture details, or thresholds for the covariance criterion, which limits reproducibility. The contribution as written is therefore not ready for publication.
major comments (4)
- [Section 3, Section 4.1, Algorithm 1] The load-bearing quantity p(y|d,z) is never defined. Section 3 states that z lies in the same domain as d and that p(y|d,z) is determined by a 'virtual observation' {z,y_z}, but the value y_z is never specified and no likelihood for it is given. In the KdV parameter-estimation example in Section 6.2.2, z=(theta1,theta2) is a parameter vector rather than an input coordinate, so conditioning a GP on 'the observation at input z' has no meaning. Because Eq. (9), the CDE training targets in Algorithm 1 Step 9, and the estimator in Eq. (11) all depend on this undefined density, the central claim that Eq. (11) computes the BOED utility accurately and cheaply is not established. The authors need to specify a well-defined generative model or likelihood p(y|d,z) for each application class.
- [Algorithm 2, Eq. (13)] The informative-sample selection step replaces the Monte Carlo average over z ~ p(z) in Eq. (11) with an average over the subset {z : COV(y_d_i, y_z) > epsilon_cov} without any importance-weight correction. This changes the target expectation unless the selection probability is explicitly accounted for. The resulting EIG estimates and the designs d* derived from them are biased in a way that is not quantified in any of the experiments. A corrected estimator should either reweight retained samples by p(z)/P(selection | z) or justify that the retained subset is a sufficient statistic for the utility.
- [Eq. (8), Eq. (11), Algorithm 3 line 6] The normalizing constant Z is introduced but then omitted. Eq. (8) defines \hat p(y|d,z) = Z q_CDE(y|d,z) p(y|d), so \hat p/p = Z q_CDE, whereas Algorithm 3 line 6 and Eq. (11) use \hat p = q_CDE p_GP(y|d) and hence \hat p/p = q_CDE. If Z(d,z) is not constant in d and z, dropping it can change the argmax; if it is intended to be absorbed into q_CDE, that must be stated explicitly and the training objective must be reconciled with the actual target ratio p(y|d,z)/p(y|d).
- [Eq. (9), Algorithm 1 Step 9] The samples used to train q_CDE are drawn from N(\hat m, \hat Sigma), where \hat m and \hat Sigma are the mean and covariance of the Gaussian ratio in Eq. (9). These are not samples from p(y|d,z), nor from the normalized conditional density; they are samples from an unnormalized ratio density. The relation between this training target and the ratio p(y|d,z)/p(y|d) that q_CDE is supposed to approximate is never established. This also means the agreement shown in Figure 1 is partly self-consistent: both the CDE training target and the reference EIG computation are derived from the same Eq. (9), so the comparison is not an independent validation of the approximation.
minor comments (6)
- [Eq. (11)] The final denominator in the logarithm should be p(y_i|d), not p(y|d); the subscript is missing.
- [Section 4.3.2, Eq. (13)] The text says the method 'filter[s] out those z values that exhibit high covariance with the fixed design point', but Eq. (13) and Algorithm 2 retain exactly those high-covariance samples. The wording should be corrected to avoid the opposite reading.
- [Section 3.1, Matérn kernel] The Matérn kernel formula uses K_nu without defining it as the modified Bessel function of the second kind; also the RBF kernel notation |d_i - d_j|_L2 is ambiguous.
- [Section 6.3.1, Table 2] The relative error for Acc-BOED is given as 2.2764% in Table 2 but as 2.2784% in the main text; one of these numbers is a typo.
- [Section 6.2.2, Figure 10] The text says the KL divergence of Acc-BOED 'eventually converges to approximately 0.8' but also that parameter estimation is expected to be 'very satisfactory'; the gap between the approximate and true posterior should be quantified and discussed rather than described qualitatively.
- [Section 4.2] Section 4.1 defines q_CDE as an approximation to the ratio p(y|d,z)/p(y|d), but Section 4.2 describes the KMN as estimating the conditional density p(y|d,z). These are different targets and the inconsistency should be resolved.
Circularity Check
The EIG-accuracy validation is built in: q_CDE is trained on samples from the very GP-ratio density that Eq. (11) and the 'basic BOED' baseline both evaluate, and the anchoring density p(y|d,z) rests on a virtual observation {z,y_z} whose value is never specified.
-
fitted input called prediction
[Section 4.3.1, Algorithm 1 Steps 7-10; Eq. (9); Eq. (11); Section 6, Figure 1]
"Obtain ( ˆmij, ˆΣij) using Eq.(9). Sample ˆyij ∼ N( ˆmij, ˆΣij). Update Dcde ← Dcde ∪ { ˜d, zi, ˆyij}. ... The values of u(d) computed using the Acc-BOED method are compared with those obtained using the basic BOED approach ... The results reveal a high degree of similarity between the two plots, indicating that the numerical values remain consistent. This consistency confirms the effectiveness and feasibility of the Acc-BOED method in identifying optimal experimental designs."
The CDE q_CDE(y|d,z) is trained on triples {d, z, ŷ} whose target ŷ is sampled from the analytic ratio density of the two GPs via Eq. (9) (Algorithm 1, Steps 8-9). Equation (11) then estimates the utility as E_{y∼pGP(y|d), z∼p(z)}[q_CDE ln q_CDE] — a functional of precisely the ratio density that generated the training targets — and 'basic BOED' evaluates the same integrand from the same GPs. The 'high degree of similarity' of u(d) in Figure 1, and the near-identical RMSE curves in Figure 2(b), therefore reduce to the KMN reproducing the distribution it was trained on: agreement is by construction up to approximation error. The EIG-accuracy claim is statistically forced rather than independently predicted.
-
self definitional
[Section 3 (first paragraph), Section 4.1 (bulleted GPR types), Algorithm 1 Step 7; relied on in Section 6.2.2]
"Given that z is defined within the same domain as d, the conditional distribution p(y|d, z) is determined solely by the observation at the inputz, denoted as yz. These constraints, when embedded within the GPR framework, are equivalent to incorporating additional data pairs {z, yz}. ... Predict (m1,ij, Σ1,ij), (m2,ij, Σ2,ij) ← pGP(y| ˜d, zi), pGP(y| ˜d)."
Every use of p(y|d,z) — the ratio in Eq. (9), the CDE training targets in Algorithm 1, and the integrands of Eqs. (10)-(11) — rests on the definition that the conditional density 'is determined solely by the observation at the input z, denoted as yz', but the value yz is never specified anywhere, and Algorithm 1 Step 7 calls pGP(y|d̃, zi) without ever supplying it. In the KdV parameter-estimation example z = (θ1, θ2) is a parameter vector, not an input-space location, so an 'observation at the input z' cannot exist; in the surrogate examples z is an unobserved location whose value is unknown.
full rationale
The circularity is real but partial, hence 5 rather than 0 or 8. What is genuinely external and non-circular: Table 1's 6-13x speedup is wall-clock time comparing the covariance-filtered Monte Carlo (Algorithms 1-2) with the full nested BOED procedure, and the surrogate-model and failure-probability claims are checked against external targets: the true trigonometric function, the alanine free-energy surface, and the true circle/four-branch failure boundaries (ground-truth failure probability 0.002460 vs 0.002516, and 0.00225 vs 0.002342). These parts of the paper are self-contained against outside benchmarks and keep the score below 6-8. The circular part is the EIG-accuracy validation that is supposed to show Eq. (11) correctly evaluates the BOED utility: Algorithm 1 generates CDE training targets by sampling from the analytic GP ratio (Eq. 9), and Eq. (11) scores the same GP ratio through q_CDE; the 'basic BOED' comparator in Figure 1 is that same ratio, so agreement is the CDE reproducing its own training distribution, not an independent check. The paper's own Section 4.3.1 states that the CDE 'serves as an approximation for the ratio p(y|d,z)/p(y|d)' — the very quantity the baseline evaluates. The self-citation [31] (co-author Wang) is minor and not load-bearing for circularity: the GPRC device of a virtual observation {z, y_z} is the authors' own construction, and the cited work concerns derivative constraints and cannot supply the missing y_z. The never-specified value y_z makes p(y|d,z), and hence Eqs. (9)-(11), undefined for the parameter-estimation examples — a definitional/self-referential weakness more than a benchmark-validated result. Separately, Eq. (9)'s normalization (|Σ2−Σ1|, 1/N(m1|m2, Σ2−Σ1)) is questionable when Σ2−Σ1 is indefinite, since a ratio of Gaussians with different precisions need not be a valid density; that is a correctness risk, not circularity.
Assumptions & free parameters
free parameters (3)
- Covariance threshold epsilon_cov =
not reported
- Failure-boundary bandwidth lambda =
not reported
- KMN architecture and training hyperparameters =
not reported
assumptions (5)
- standard math The ratio p(y|d,z)/p(y|d) of two Gaussian predictive densities is an unnormalized Gaussian density with parameters given in Eq. (9).
- ad hoc to paper p(y|d,z) is obtained by conditioning the GP on a virtual observation at z, and is Gaussian with known mean and covariance.
- domain assumption Discarding low-covariance z samples leaves the Monte Carlo estimator consistent.
- domain assumption KMN can accurately approximate the density ratio from finite samples.
- domain assumption The adaptive p(z) definitions in Section 5.1 (variance-weighted, posterior-based, and limiting-state) approximate the true quantity of interest.
invented entities (1)
-
Virtual observation {z, y_z}
Cite this review
Pith. "Pith review of Accelerated Bayesian Optimal Experimental Design via Conditional Density Estimation and Informative Data." pith.science (2026). https://pith.science/paper/KRPL2SQA
@misc{pith2026250715235,
author = {Pith},
title = {Pith review of: Accelerated Bayesian Optimal Experimental Design via Conditional Density Estimation and Informative Data},
year = {2026},
howpublished = {\url{https://pith.science/paper/KRPL2SQA}},
note = {Machine review of arXiv:2507.15235}
}
read the original abstract
The Design of Experiments (DOEs) is a fundamental scientific methodology that provides researchers with systematic principles and techniques to enhance the validity, reliability, and efficiency of experimental outcomes. In this study, we explore optimal experimental design within a Bayesian framework, utilizing Bayes' theorem to reformulate the utility expectation--originally expressed as a nested double integral--into an independent double integral form, significantly improving numerical efficiency. To further accelerate the computation of the proposed utility expectation, conditional density estimation is employed to approximate the ratio of two Gaussian random fields, while covariance serves as a selection criterion to identify informative datasets during model fitting and integral evaluation. In scenarios characterized by low simulation efficiency and high costs of raw data acquisition, key challenges such as surrogate modeling, failure probability estimation, and parameter inference are systematically restructured within the Bayesian experimental design framework. The effectiveness of the proposed methodology is validated through both theoretical analysis and practical applications, demonstrating its potential for enhancing experimental efficiency and decision-making under uncertainty.
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Works this paper leans on
-
[1]
On the mathematical foundations of theoretical statistics
Ronald A Fisher. On the mathematical foundations of theoretical statistics. Philosophical transactions of the Royal Society of London. Series A, containing papers of a mathematical or physical character, 222(594-604):309–368, 1922
work page 1922
-
[2]
The usefulness of optimum experimental designs
Anthony C Atkinson. The usefulness of optimum experimental designs. Journal of the Royal Statistical Society Series B: Statistical Methodology, 58(1):59–76, 1996
work page 1996
-
[3]
Optimal design of experiments
Friedrich Pukelsheim. Optimal design of experiments. SIAM, 2006
2006
-
[4]
Valerii Vadimovich Fedorov. Theory of optimal experiments. Elsevier, 2013
work page 2013
-
[5]
Global a-optimal robot exploration in slam
Robert Sim and Nicholas Roy. Global a-optimal robot exploration in slam. In Proceedings of the 2005 IEEE international conference on robotics and automation, pages 661–666. IEEE, 2005
work page 2005
-
[6]
P Fernandes de Aguiar, B Bourguignon, MS Khots, DL Massart, and R Phan- Than-Luu. D-optimal designs. Chemometrics and intelligent laboratory systems, 30(2):199–210, 1995
work page 1995
-
[7]
The choice of variables in multiple regression
Dennis V Lindley. The choice of variables in multiple regression. Journal of the Royal Statistical Society: Series B (Methodological), 30(1):31–53, 1968
work page 1968
-
[8]
Bayesian statistics: A review
Dennis Victor Lindley. Bayesian statistics: A review. SIAM, 1972
1972
Show all 35 references
-
[9]
Optimal Bayesian experimental design for linear models
Kathryn Mary Chaloner. Optimal Bayesian experimental design for linear models. Carnegie Mellon University, 1982
1982
-
[10]
Bayesian estimation and experimental design in linear regression models
J¨ urgen Pilz. Bayesian estimation and experimental design in linear regression models. (No Title), 1991
1991
-
[11]
Institute of Statistics & Decision Sciences, Duke Univer- sity, 1995
Merlise A Clyde, Peter M¨ uller, and Giovanni Parmigiani.Exploring expected utility surfaces by markov chains. Institute of Statistics & Decision Sciences, Duke Univer- sity, 1995
1995
-
[12]
Decision analysis by augmented probability simulation
Concha Bielza, Peter M¨ uller, and David R ´ ıos Insua. Decision analysis by augmented probability simulation. Management Science, 45(7):995–1007, 1999. 30
1999
-
[13]
Optimal sampling times in population pharmacokinetic studies
Jonathan R Stroud, Peter M¨ uller, and Gary L Rosner. Optimal sampling times in population pharmacokinetic studies. Journal of the Royal Statistical Society Series C: Applied Statistics, 50(3):345–359, 2001
2001
-
[14]
Simulation based optimal design.Handbook of Statistics, 25:509–518, 2005
Peter M¨ uller. Simulation based optimal design.Handbook of Statistics, 25:509–518, 2005
2005
-
[15]
Bayesian- optimal design via interacting particle systems
Billy Amzal, Fr´ ed´ eric Y Bois, Eric Parent, and Christian P Robert. Bayesian- optimal design via interacting particle systems. Journal of the American Statistical association, 101(474):773–785, 2006
2006
-
[16]
A bayesian decision-theoretic dose-finding trial
Peter M¨ uller, Don A Berry, Andrew P Grieve, and Michael Krams. A bayesian decision-theoretic dose-finding trial. Decision analysis, 3(4):197–207, 2006
2006
-
[17]
Optimal observation times in experimental epidemic processes
Alex R Cook, Gavin J Gibson, and Christopher A Gilligan. Optimal observation times in experimental epidemic processes. Biometrics, 64(3):860–868, 2008
2008
-
[18]
Adaptive design optimization: A mutual information-based approach to model discrimination in cognitive science
Daniel R Cavagnaro, Jay I Myung, Mark A Pitt, and Janne V Kujala. Adaptive design optimization: A mutual information-based approach to model discrimination in cognitive science. Neural computation, 22(4):887–905, 2010
2010
-
[19]
Fully bayesian experimental design for pharmacokinetic studies
Elizabeth G Ryan, Christopher C Drovandi, and Anthony N Pettitt. Fully bayesian experimental design for pharmacokinetic studies. Entropy, 17(3):1063–1089, 2015
2015
-
[20]
Efficiency robust experimental design and estimation using a data-based prior
Blaza Toman and Joseph L Gastwirth. Efficiency robust experimental design and estimation using a data-based prior. Statistica Sinica, pages 603–615, 1994
1994
-
[21]
Bayesian methods and ethics in a clinical trial design
Joseph B Kadane. Bayesian methods and ethics in a clinical trial design. John Wiley & Sons, 2011
2011
-
[22]
Optimal experimental design for another’s analysis
Ruth Etzioni and Joseph B Kadane. Optimal experimental design for another’s analysis. Journal of the American Statistical Association, 88(424):1404–1411, 1993
1993
-
[23]
Bayesian experimental design for nonlinear mixed- effects models with application to hiv dynamics
Cong Han and Kathryn Chaloner. Bayesian experimental design for nonlinear mixed- effects models with application to hiv dynamics. Biometrics, 60(1):25–33, 2004
2004
-
[24]
Large-scale bayesian optimal experimental design with derivative-informed projected neural net- work
Keyi Wu, Thomas O’Leary-Roseberry, Peng Chen, and Omar Ghattas. Large-scale bayesian optimal experimental design with derivative-informed projected neural net- work. Journal of Scientific Computing, 95(1):30, 2023
2023
-
[25]
Online simulator-based experimental design for cognitive model selection
Alexander Aushev, Aini Putkonen, Gr´ egoire Clart´ e, Suyog Chandramouli, Luigi Acerbi, Samuel Kaski, and Andrew Howes. Online simulator-based experimental design for cognitive model selection. Computational Brain & Behavior, 6(4):719– 737, 2023
2023
-
[26]
Designing optimal behavioral experiments using machine learning
Simon Valentin, Steven Kleinegesse, Neil R Bramley, Peggy Seri` es, Michael U Gut- mann, and Christopher G Lucas. Designing optimal behavioral experiments using machine learning. Elife, 13:e86224, 2024
2024
-
[27]
Probabilistic bayesian op- timal experimental design using conditional normalizing flows
Rafael Orozco, Felix J Herrmann, and Peng Chen. Probabilistic bayesian op- timal experimental design using conditional normalizing flows. arXiv preprint arXiv:2402.18337, 2024. 31
2024 arXiv
-
[28]
Variational bayesian optimal experimental design
Adam Foster, Martin Jankowiak, Elias Bingham, Paul Horsfall, Yee Whye Teh, Thomas Rainforth, and Noah Goodman. Variational bayesian optimal experimental design. Advances in Neural Information Processing Systems, 32, 2019
2019
-
[29]
Variational bayesian optimal experimen- tal design with normalizing flows
Jiayuan Dong, Christian Jacobsen, Mehdi Khalloufi, Maryam Akram, Wanjiao Liu, Karthik Duraisamy, and Xun Huan. Variational bayesian optimal experimen- tal design with normalizing flows. Computer Methods in Applied Mechanics and Engineering, 433:117457, 2025
2025
-
[30]
Simulation-based optimal bayesian experimental design for nonlinear systems
Xun Huan and Youssef M Marzouk. Simulation-based optimal bayesian experimental design for nonlinear systems. Journal of Computational Physics, 232(1):288–317, 2013
2013
-
[31]
Explicit estimation of derivatives from data and differential equations by gaussian process regression
Hongqiao Wang and Xiang Zhou. Explicit estimation of derivatives from data and differential equations by gaussian process regression. International Journal for Uncertainty Quantification, 11(4), 2021
2021
-
[32]
The kernel mixture network: A nonparametric method for conditional density estimation of continuous random variables
Luca Ambrogioni, Umut G¨ u¸ cl¨ u, Marcel AJ van Gerven, and Eric Maris. The kernel mixture network: A nonparametric method for conditional density estimation of continuous random variables. arXiv preprint arXiv:1705.07111, 2017
2017 arXiv
-
[33]
Computing committor functions for the study of rare events using deep learning
Qianxiao Li, Bo Lin, and Weiqing Ren. Computing committor functions for the study of rare events using deep learning. The Journal of Chemical Physics, 151(5), 2019
2019
-
[34]
Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide
Weiqing Ren, Eric Vanden-Eijnden, Paul Maragakis, et al. Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide. The Journal of chemical physics, 123(13), 2005
2005
-
[35]
Scalable molecular dynamics with namd
James C Phillips, Rosemary Braun, Wei Wang, James Gumbart, Emad Tajkhor- shid, Elizabeth Villa, Christophe Chipot, Robert D Skeel, Laxmikant Kale, and Klaus Schulten. Scalable molecular dynamics with namd. Journal of computational chemistry, 26(16):1781–1802, 2005. 32
2005
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