Fast inference of numerical model parameters from data is an important prerequisite to generate predictive models for a wide range of applications. Use of sampling-based approaches such as Markov chain Monte Carlo may become intractable when each likelihood evaluation is computationally expensive. New approaches combining variational inference with normalizing flow are characterized by a computational cost that grows only linearly with the dimensionality of the latent variable space, and rely on gradient-based optimization instead of sampling, providing a more efficient approach for Bayesian inference about the model parameters. Moreover, the cost of frequently evaluating an expensive likelihood can be mitigated by replacing the true model with an offline trained surrogate model, such as neural networks. However, this approach might generate significant bias when the surrogate is insufficiently accurate around the posterior modes. To reduce the computational cost without sacrificing inferential accuracy, we propose Normalizing Flow with Adaptive Surrogate (NoFAS), an optimization strategy that alternatively updates the normalizing flow parameters and surrogate model parameters. We also propose an efficient sample weighting scheme for surrogate model training that preserves global accuracy while effectively capturing high posterior density regions. We demonstrate the inferential and computational superiority of NoFAS against various benchmarks, including cases where the underlying model lacks identifiability. The source code and numerical experiments used for this study are available at https://github.com/cedricwangyu/NoFAS.
more »
« less
Adaptive Metrics for Adaptive Samples
We generalize the local-feature size definition of adaptive sampling used in surface reconstruction to relate it to an alternative metric on Euclidean space. In the new metric, adaptive samples become uniform samples, making it simpler both to give adaptive sampling versions of homological inference results and to prove topological guarantees using the critical points theory of distance functions. This ultimately leads to an algorithm for homology inference from samples whose spacing depends on their distance to a discrete representation of the complement space.
more »
« less
- Award ID(s):
- 2017980
- NSF-PAR ID:
- 10211933
- Date Published:
- Journal Name:
- Algorithms
- Volume:
- 13
- Issue:
- 8
- ISSN:
- 1999-4893
- Page Range / eLocation ID:
- 200
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past observations, adaptive approaches adjust sampling constraints online as model parameter estimates are refined, continually maximizing expected information gained or variance reduced. We apply adaptive Bayesian inference to estimate transition rates of Markov chains, a common class of models for stochastic processes in nature. Unlike most previous studies, our sequential Bayesian optimal design is updated with each observation and can be simply extended beyond two-state models to birth–death processes and multistate models. By iteratively finding the best time to obtain each sample, our adaptive algorithm maximally reduces variance, resulting in lower overall error in ground truth parameter estimates across a wide range of Markov chain parameterizations and conformations.more » « less
-
null (Ed.)Abstract In this study, we propose a scalable batch sampling scheme for optimization of simulation models with spatially varying noise. The proposed scheme has two primary advantages: (i) reduced simulation cost by recommending batches of samples at carefully selected spatial locations and (ii) improved scalability by actively considering replicating at previously observed sampling locations. Replication improves the scalability of the proposed sampling scheme as the computational cost of adaptive sampling schemes grow cubicly with the number of unique sampling locations. Our main consideration for the allocation of computational resources is the minimization of the uncertainty in the optimal design. We analytically derive the relationship between the “exploration versus replication decision” and the posterior variance of the spatial random process used to approximate the simulation model’s mean response. Leveraging this reformulation in a novel objective-driven adaptive sampling scheme, we show that we can identify batches of samples that minimize the prediction uncertainty only in the regions of the design space expected to contain the global optimum. Finally, the proposed sampling scheme adopts a modified preposterior analysis that uses a zeroth-order interpolation of the spatially varying simulation noise to identify sampling batches. Through the optimization of three numerical test functions and one engineering problem, we demonstrate (i) the efficacy and of the proposed sampling scheme to deal with a wide array of stochastic functions, (ii) the superior performance of the proposed method on all test functions compared to existing methods, (iii) the empirical validity of using a zeroth-order approximation for the allocation of sampling batches, and (iv) its applicability to molecular dynamics simulations by optimizing the performance of an organic photovoltaic cell as a function of its processing settings.more » « less
-
null (Ed.)A novel simulation-based framework that applies classification with adaptive labeling thresholds (CALT) is developed that auto-generates the component sizes of an analog integrated circuit. Classifiers are applied to predict whether the target specifications are satisfied. To address the lack of data points with positive labels due to the large dimensionality of the parameter space, the labeling threshold is adaptively set to a certain percentile of the distribution of a given circuit performance metric in the dataset. Random forest classifiers are executed for surrogate prediction modeling that provide a ranking of the design parameters. For each iteration of the simulation loop, optimization is utilized to determine new query points. CALT is applied to the design of a low noise amplifier (LNA) in a 65 nm technology. Qualified design solutions are generated for two sets of specifications with an average execution of 4 and 17 iterations of the optimization loop, which require an average of 1287 and 2190 simulation samples, and an average execution time of 5.4 hours and 23.2 hours, respectively. CALT is a specification-driven design framework to automate the sizing of the components (transistors, capacitors, inductors, etc.) of an analog circuit. CALT generates interpretable models and achieves high sample efficiency without requiring the use of prior circuit models.more » « less
-
more » « less
Abstract We investigate the performance of a class of particle filters (PFs) that can automatically tune their computational complexity by evaluating online certain predictive statistics which are invariant for a broad class of state-space models. To be specific, we propose a family of block-adaptive PFs based on the methodology of Elvira et al. (IEEE Trans Signal Process 65(7):1781–1794, 2017). In this class of algorithms, the number of Monte Carlo samples (known as
particles ) is adjusted periodically, and we prove that the theoretical error bounds of the PF actually adapt to the updates in the number of particles. The evaluation of the predictive statistics that lies at the core of the methodology is done by generatingfictitious observations , i.e., particles in the observation space. We study, both analytically and numerically, the impact of the numberK of these particles on the performance of the algorithm. In particular, we prove that if the predictive statistics withK fictitious observations converged exactly, then the particle approximation of the filtering distribution would match the firstK elements in a series of moments of the true filter. This result can be understood as a converse to some convergence theorems for PFs. From this analysis, we deduce an alternative predictive statistic that can be computed (for some models) without sampling any fictitious observations at all. Finally, we conduct an extensive simulation study that illustrates the theoretical results and provides further insights into the complexity, performance and behavior of the new class of algorithms.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/a13080200
