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1. Inference of Protein-Protein Interaction Networks from Liquid-Chromatography Mass-Spectrometry Data by Approximate Bayesian Computation-Sequential Monte Carlo Sampling

   https://doi.org/10.1109/MLSP49062.2020.9231824  

   Tan, Yukun; Lima Neto, Fernando B.; Neto, Ulisses Braga (September 2020, 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP))

   null (Ed.)

   We propose a new algorithm for inference of protein-protein interaction (PPI) networks from noisy time series of Liquid- Chromatography Mass-Spectrometry (LC-MS) proteomic expression data based on Approximate Bayesian Computation - Sequential Monte Carlo sampling (ABC-SMC). The algorithm is an extension of our previous framework PALLAS. The proposed algorithm can be easily modified to handle other complex models of expression data, such as LC-MS data, for which the likelihood function is intractable. Results based on synthetic time series of cytokine LC-MS measurements cor- responding to a prototype immunomic network demonstrate that our algorithm is capable of inferring the network topology accurately. 

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2. Bayesian Parameter Estimation for Nonlinear Dynamics Using Sensitivity Analysis

   https://doi.org/10.24963/ijcai.2019/791  

   Chou, Yi; Sankaranarayanan, Sriram (August 2019, International Joint Conference on Artificial Intelligence (IJCAI))

   We investigate approximate Bayesian inference techniques for nonlinear systems described by ordinary differential equation (ODE) models. In particular, the approximations will be based on set-valued reachability analysis approaches, yielding approximate models for the posterior distribution. Nonlinear ODEs are widely used to mathematically describe physical and biological models. However, these models are often described by parameters that are not directly measurable and have an impact on the system behaviors. Often, noisy measurement data combined with physical/biological intuition serve as the means for finding appropriate values of these parameters.Our approach operates under a Bayesian framework, given prior distribution over the parameter space and noisy observations under a known sampling distribution. We explore subsets of the space of model parameters, computing bounds on the likelihood for each subset. This is performed using nonlinear set-valued reachability analysis that is made faster by means of linearization around a reference trajectory. The tiling of the parameter space can be adaptively refined to make bounds on the likelihood tighter. We evaluate our approach on a variety of nonlinear benchmarks and compare our results with Markov Chain Monte Carlo and Sequential Monte Carlo approaches. 

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3. Sequential Monte Carlo with model tempering

   https://doi.org/10.1515/snde-2022-0103  

   Mlikota, Marko; Schorfheide, Frank (May 2023, Studies in Nonlinear Dynamics & Econometrics)

   Abstract Modern macroeconometrics often relies on time series models for which it is time-consuming to evaluate the likelihood function. We demonstrate how Bayesian computations for such models can be drastically accelerated by reweighting and mutating posterior draws from an approximating model that allows for fast likelihood evaluations, into posterior draws from the model of interest, using a sequential Monte Carlo (SMC) algorithm. We apply the technique to the estimation of a vector autoregression with stochastic volatility and two nonlinear dynamic stochastic general equilibrium models. The runtime reductions we obtain range from 27 % to 88 %. 

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4. Unbiased Markov chain Monte Carlo for intractable target distributions

   Middleton, Lawrence; Deligiannidis, George; Doucet, Arnaud; Jacob, Pierre E (July 2020, Electronic journal of statistics)

   Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov chain Monte Carlo (MCMC) algorithms have been proposed for this setting, such as the pseudo-marginal method for latent variable models and the exchange algorithm for a class of undirected graphical models. As with any MCMC algorithm, the resulting estimators are justified asymptotically in the limit of the number of iterations, but exhibit a bias for any fixed number of iterations due to the Markov chains starting outside of stationarity. This "burn-in" bias is known to complicate the use of parallel processors for MCMC computations. We show how to use coupling techniques to generate unbiased estimators in finite time, building on recent advances for generic MCMC algorithms. We establish the theoretical validity of some of these procedures by extending existing results to cover the case of polynomially ergodic Markov chains. The efficiency of the proposed estimators is compared with that of standard MCMC estimators, with theoretical arguments and numerical experiments including state space models and Ising models. 

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5. Clustering time series with nonlinear dynamics: A Bayesian non-parametric and particle-based approach

   Lin, A.; Zhang, Y.; Heng, J.; Allsop, S.; Tye, K.; Jacob, P.; Ba, D. (April 2019, AISTATS)

   We propose a statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups that each comprise time series with similar dynamics. Our motivation comes from neuroscience where an important problem is to identify, within a large assembly of neurons, sub-groups that respond similarly to a stimulus or contingency. In the neural setting, conditioned on cluster membership and the parameters governing the dynamics, time series within a cluster are assumed independent and generated according to a nonlinear binomial state-space model. We derive a Metropolis-within-Gibbs algorithm for full Bayesian inference that alternates between sampling of cluster membership and sampling of parameters of interest. The Metropolis step is a PMMH iteration that requires an unbiased, low variance estimate of the likelihood function of a nonlinear state- space model. We leverage recent results on controlled sequential Monte Carlo to estimate likelihood functions more efficiently compared to the bootstrap particle filter. We apply the framework to time series acquired from the prefrontal cortex of mice in an experiment designed to characterize the neural underpinnings of fear. 

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