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1. Predictive Runtime Monitoring of Vehicle Models Using Bayesian Estimation and Reachability Analysis

   https://doi.org/10.1109/IROS45743.2020.9340755  

   Chou, Yi ; Yoon, Hansol ; Sankaranarayanan, Sriram ( October 2020 , 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS))

   null (Ed.)

   We present a predictive runtime monitoring technique for estimating future vehicle positions and the probability of collisions with obstacles. Vehicle dynamics model how the position and velocity change over time as a function of external inputs. They are commonly described by discrete-time stochastic models. Whereas positions and velocities can be measured, the inputs (steering and throttle) are not directly measurable in these models. In our paper, we apply Bayesian inference techniques for real-time estimation, given prior distribution over the unknowns and noisy state measurements. Next, we pre-compute the set-valued reachability analysis to approximate future positions of a vehicle. The pre-computed reachability sets are combined with the posterior probabilities computed through Bayesian estimation to provided a predictive verification framework that can be used to detect impending collisions with obstacles. Our approach is evaluated using the coordinated-turn vehicle model for a UAV using on-board measurement data obtained from a flight test of a Talon UAV. We also compare the results with sampling-based approaches. We find that precomputed reachability analysis can provide accurate warnings up to 6 seconds in advance and the accuracy of the warnings improve as the time horizon is narrowed from 6 to 2 seconds. The approach also outperforms samplingmore »in terms of on-board computation cost and accuracy measures.« less
2. MFBO-SSM: Multi-Fidelity Bayesian Optimization for Fast Inference in State-Space Models

   Imani, M ; Ghoreishi, S.F. ; Allaire, D. ; Braga-Neto, U ( July 2019 , Proceedings of the ... AAAI Conference on Artificial Intelligence)

   Nonlinear state-space models are ubiquitous in modeling real-world dynamical systems. Sequential Monte Carlo (SMC) techniques, also known as particle methods, are a well-known class of parameter estimation methods for this general class of state-space models. Existing SMC-based techniques rely on excessive sampling of the parameter space, which makes their computation intractable for large systems or tall data sets. Bayesian optimization techniques have been used for fast inference in state-space models with intractable likelihoods. These techniques aim to find the maximum of the likelihood function by sequential sampling of the parameter space through a single SMC approximator. Various SMC approximators with different fidelities and computational costs are often available for sample- based likelihood approximation. In this paper, we propose a multi-fidelity Bayesian optimization algorithm for the inference of general nonlinear state-space models (MFBO-SSM), which enables simultaneous sequential selection of parameters and approximators. The accuracy and speed of the algorithm are demonstrated by numerical experiments using synthetic gene expression data from a gene regulatory network model and real data from the VIX stock price index.
3. Bayesian Decision Making in Uncertain MDPs with Large or Infinite-Dimensional Spaces

   Imani, Mandi ; Ghoreishi, Seyede ; Braga-Neto, Ulisses ( December 2018 , Advances in Neural Information Processing Systems 31 (NeurIPS’2018))

   We propose a Bayesian decision making framework for control of Markov Decision Processes (MDPs) with unknown dynamics and large, possibly continuous, state, action, and parameter spaces in data-poor environments. Most of the existing adaptive controllers for MDPs with unknown dynamics are based on the reinforcement learning framework and rely on large data sets acquired by sustained direct interaction with the system or via a simulator. This is not feasible in many applications, due to ethical, economic, and physical constraints. The proposed framework addresses the data poverty issue by decomposing the problem into an offline planning stage that does not rely on sustained direct interaction with the system or simulator and an online execution stage. In the offline process, parallel Gaussian process temporal difference (GPTD) learning techniques are employed for near-optimal Bayesian approximation of the expected discounted reward over a sample drawn from the prior distribution of unknown parameters. In the online stage, the action with the maximum expected return with respect to the posterior distribution of the parameters is selected. This is achieved by an approximation of the posterior distribution using a Markov Chain Monte Carlo (MCMC) algorithm, followed by constructing multiple Gaussian processes over the parameter space for efficientmore »prediction of the means of the expected return at the MCMC sample. The effectiveness of the proposed framework is demonstrated using a simple dynamical system model with continuous state and action spaces, as well as a more complex model for a metastatic melanoma gene regulatory network observed through noisy synthetic gene expression data.« less
4. Neural networks enable efficient and accurate simulation-based inference of evolutionary parameters from adaptation dynamics

   https://doi.org/10.1371/journal.pbio.3001633  

   Avecilla, Grace ; Chuong, Julie N. ; Li, Fangfei ; Sherlock, Gavin ; Gresham, David ; Ram, Yoav ( May 2022 , PLOS Biology)

   de Visser, J. Arjan (Ed.)

   The rate of adaptive evolution depends on the rate at which beneficial mutations are introduced into a population and the fitness effects of those mutations. The rate of beneficial mutations and their expected fitness effects is often difficult to empirically quantify. As these 2 parameters determine the pace of evolutionary change in a population, the dynamics of adaptive evolution may enable inference of their values. Copy number variants (CNVs) are a pervasive source of heritable variation that can facilitate rapid adaptive evolution. Previously, we developed a locus-specific fluorescent CNV reporter to quantify CNV dynamics in evolving populations maintained in nutrient-limiting conditions using chemostats. Here, we use CNV adaptation dynamics to estimate the rate at which beneficial CNVs are introduced through de novo mutation and their fitness effects using simulation-based likelihood–free inference approaches. We tested the suitability of 2 evolutionary models: a standard Wright–Fisher model and a chemostat model. We evaluated 2 likelihood-free inference algorithms: the well-established Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) algorithm, and the recently developed Neural Posterior Estimation (NPE) algorithm, which applies an artificial neural network to directly estimate the posterior distribution. By systematically evaluating the suitability of different inference methods and models, we show thatmore »NPE has several advantages over ABC-SMC and that a Wright–Fisher evolutionary model suffices in most cases. Using our validated inference framework, we estimate the CNV formation rate at the GAP1 locus in the yeast Saccharomyces cerevisiae to be 10 −4.7 to 10 −4 CNVs per cell division and a fitness coefficient of 0.04 to 0.1 per generation for GAP1 CNVs in glutamine-limited chemostats. We experimentally validated our inference-based estimates using 2 distinct experimental methods—barcode lineage tracking and pairwise fitness assays—which provide independent confirmation of the accuracy of our approach. Our results are consistent with a beneficial CNV supply rate that is 10-fold greater than the estimated rates of beneficial single-nucleotide mutations, explaining the outsized importance of CNVs in rapid adaptive evolution. More generally, our study demonstrates the utility of novel neural network–based likelihood–free inference methods for inferring the rates and effects of evolutionary processes from empirical data with possible applications ranging from tumor to viral evolution.« less
5. Efficient derivative-free Bayesian inference for large-scale inverse problems

   https://doi.org/10.1088/1361-6420/ac99fa  

   Huang, Daniel Zhengyu ; Huang, Jiaoyang ; Reich, Sebastian ; Stuart, Andrew M ( October 2022 , Inverse Problems)

   Abstract We consider Bayesian inference for large-scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible, since they typically require O ( 1 0 4 ) model runs, or more. Moreover, the forward model is often given as a black box or is impractical to differentiate. Therefore derivative-free algorithms are highly desirable. We propose a framework, which is built on Kalman methodology, to efficiently perform Bayesian inference in such inverse problems. The basic method is based on an approximation of the filtering distribution of a novel mean-field dynamical system, into which the inverse problem is embedded as an observation operator. Theoretical properties are established for linear inverse problems, demonstrating that the desired Bayesian posterior is given by the steady state of the law of the filtering distribution of the mean-field dynamical system, and proving exponential convergence to it. This suggests that, for nonlinear problems which are close to Gaussian, sequentially computing this law provides the basis for efficient iterative methods to approximate the Bayesian posterior. Ensemble methods are applied to obtain interacting particle system approximations of the filtering distribution of the mean-field model;more »and practical strategies to further reduce the computational and memory cost of the methodology are presented, including low-rank approximation and a bi-fidelity approach. The effectiveness of the framework is demonstrated in several numerical experiments, including proof-of-concept linear/nonlinear examples and two large-scale applications: learning of permeability parameters in subsurface flow; and learning subgrid-scale parameters in a global climate model. Moreover, the stochastic ensemble Kalman filter and various ensemble square-root Kalman filters are all employed and are compared numerically. The results demonstrate that the proposed method, based on exponential convergence to the filtering distribution of a mean-field dynamical system, is competitive with pre-existing Kalman-based methods for inverse problems.« less