contour

Sequential design functions for contour finding

crit_ICU(x, model, thres=0, Xref=None, w=None, preds=None, kxprime=None)[source]

Computes ICU infill criterion

Integrated Contour Uncertainty criterion

Parameters:

  • x (nd_array) – matrix of new designs, one point per row (size n x d)

  • model (homGP or hetGP) – including inverse matrices

  • Xref (nd_array) – matrix of input locations to approximate the integral by a sum

  • w (nd_array) – optional weights vector of weights for code{Xref} locations

  • thres (float) – for contour finding

  • preds (dict) – optional predictions at Xref to avoid recomputing if already done

  • kxprime (nd_array) – optional covariance matrix between model.X0 and Xref to avoid its recomputation

References

Lyu, X., Binois, M. & Ludkovski, M. (2018+). Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation. arXiv:1807.06712.

crit_MCU(x, model, thres=0, gamma=2, preds=None)[source]
Parameters:

  • x (nd_array) – matrix of new designs, one point per row (size n x d)

  • model (homGP or hetGP) – including inverse matrices

  • thres (float) – for contour finding

  • gamma (float) – optional weight in -|f(x) - thres| + gamma * s(x). Default to 2

  • preds (dict) – optional predictions at x to avoid recomputing if already done (must contain cov)

References

Srinivas, N., Krause, A., Kakade, S, & Seeger, M. (2012). Information-theoretic regret bounds for Gaussian process optimization in the bandit setting, IEEE Transactions on Information Theory, 58, pp. 3250-3265.

Bogunovic, J., Scarlett, J., Krause, A. & Cevher, V. (2016). Truncated variance reduction: A unified approach to Bayesian optimization and level-set estimation, in Advances in neural information processing systems, pp. 1507-1515.

Lyu, X., Binois, M. & Ludkovski, M. (2018+). Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation. arXiv:1807.06712.

crit_MEE(x, model, thres=0, preds=None)[source]

Computes MEE infill criterion Maximum Empirical Error criterion

Parameters:

  • x (nd_array) – matrix of new designs, one point per row (size n x d)

  • model (homGP or hetGP) – including inverse matrices

  • thres (float) – for contour finding

  • preds (dict) – optional predictions at x to avoid recomputing if already done

References

Ranjan, P., Bingham, D. & Michailidis, G (2008). Sequential experiment design for contour estimation from complex computer codes, Technometrics, 50, pp. 527-541. cr cr

Bichon, B., Eldred, M., Swiler, L., Mahadevan, S. & McFarland, J. (2008). Efficient global reliability analysis for nonlinear implicit performance functions, AIAA Journal, 46, pp. 2459-2468. cr cr

Lyu, X., Binois, M. & Ludkovski, M. (2018+). Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation. arXiv:1807.06712.

crit_cSUR(x, model, thres=0, preds=None)[source]

Computes cSUR infill criterion

Contour Stepwise Uncertainty Reduction criterion

Parameters:

  • x (nd_array) – matrix of new designs, one point per row (size n x d)

  • model (homGP or hetGP) – including inverse matrices

  • thres (float) – for contour finding

  • preds (dict) – optional predictions at x to avoid recomputing if already done

References

Lyu, X., Binois, M. & Ludkovski, M. (2018+). Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation. arXiv:1807.06712.

crit_tMSE(x, model, thres=0, preds=None, seps=0.05)[source]

Computes targeted mean squared error infill criterion

t-MSE criterion

Parameters:

  • x (nd_array) – matrix of new designs, one point per row (size n x d)

  • model (homGP or hetGP) – including inverse matrices

  • thres (float) – for contour finding

  • preds (dict) – optional predictions at x to avoid recomputing if already done (must contain cov)

  • seps (float) – parameter for the target window

References

Picheny, V., Ginsbourger, D., Roustant, O., Haftka, R., Kim, N. (2010). Adaptive designs of experiments for accurate approximation of a target region, Journal of Mechanical Design (132), p. 071008.

Lyu, X., Binois, M. & Ludkovski, M. (2018+). Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation. arXiv:1807.06712.