Sequential Bayesian Learning Research Articles

Bayesian Sequential Learning and Decision Making in Bike‐Sharing Systems

Bayesian Sequential Learning and Decision Making in Bike‐Sharing Systems

Low-density parity-check codes: tracking non-stationary channel noise using sequential variational Bayesian estimates

We present a sequential Bayesian learning method for tracking non-stationary signal-to-noise ratios in low-density parity-check (LDPC) codes by way of probabilistic graphical models. We represent the LDPC code as a cluster graph using a general purpose cluster graph construction algorithm called the layered trees running intersection property (LTRIP) algorithm. The channel noise estimator is a global gamma cluster, which we extend to allow for Bayesian tracking of non-stationary noise variation. We evaluate our proposed model on real-world 5G drive-test data. Our results show that our model can track non-stationary channel noise accurately while adding performance benefits to the LDPC code, which outperforms an LDPC code with a fixed stationary knowledge of the actual channel noise.

Bayesian Sequential Learning for Clinical Trials of Multiple Correlated Medical Interventions

We propose and analyze the first model for clinical trial design that integrates each of three important trends intending to improve the effectiveness of clinical trials that inform health-technology adoption decisions: adaptive design, which dynamically adjusts the sample size and allocation of interventions to different patients; multiarm trial design, which compares multiple interventions simultaneously; and value-based design, which focuses on cost-benefit improvements of health interventions over a current standard of care. Example applications are to seamless phase II/III dose-finding trials and to trials that test multiple combinations of therapies. Our objective is to maximize the expected population health-economic benefit of health-technology adoption decisions less clinical trial costs. We show that unifying the adaptive, multiarm, and value-based approaches to trial design can reduce the cost and duration of multiarm trials with efficient adaptive look ahead policies that focus on value to patients and account for correlated rewards across arms. Features that differentiate our approach from much other work on stochastic optimization include stopping times that balance sampling costs and the expected value of information of those samples, performance guarantees offered by new asymptotic convergence proofs, and the modeling of arms’ potentially different sampling costs. Our proposed solution can be computed feasibly and can randomize patients. The class of trials for the base model assumes that health-economic data are collected and observed quickly. Related work from Bayesian optimization can enable the further inclusion of trials with intermediate duration delays between the time of treatment initiation and observation of outcomes.This paper was accepted by Stefan Scholtes, healthcare management.

Quantifying the impact of electric fields on single-cell motility

Cell motility in response to environmental cues forms the basis of many developmental processes in multicellular organisms. One such environmental cue is an electric field (EF), which induces a form of motility known as electrotaxis. Electrotaxis has evolved in a number of cell types to guide wound healing and has been associated with different cellular processes, suggesting that observed electrotactic behavior is likely a combination of multiple distinct effects arising from the presence of an EF. To determine the different mechanisms by which observed electrotactic behavior emerges, and thus to design EFs that can be applied to direct and control electrotaxis, researchers require accurate quantitative predictions of cellular responses to externally applied fields. Here, we use mathematical modeling to formulate and parameterize a variety of hypothetical descriptions of how cell motility may change in response to an EF. We calibrate our model to observed data using synthetic likelihoods and Bayesian sequential learning techniques and demonstrate that EFs bias cellular motility through only one of a selection of hypothetical mechanisms. We also demonstrate how the model allows us to make predictions about cellular motility under different EFs. The resulting model and calibration methodology will thus form the basis for future data-driven and model-based feedback control strategies based on electric actuation.

Multitask learning over shared subspaces.

This paper uses constructs from machine learning to define pairs of learning tasks that either shared or did not share a common subspace. Human subjects then learnt these tasks using a feedback-based approach and we hypothesised that learning would be boosted for shared subspaces. Our findings broadly supported this hypothesis with either better performance on the second task if it shared the same subspace as the first, or positive correlations over task performance for shared subspaces. These empirical findings were compared to the behaviour of a Neural Network model trained using sequential Bayesian learning and human performance was found to be consistent with a minimal capacity variant of this model. Networks with an increased representational capacity, and networks without Bayesian learning, did not show these transfer effects. We propose that the concept of shared subspaces provides a useful framework for the experimental study of human multitask and transfer learning.

Learning for infinitely divisible GARCH models in option pricing

Abstract This paper studies the option valuation problem of non-Gaussian and asymmetric GARCH models from a state-space structure perspective. Assuming innovations following an infinitely divisible distribution, we apply different estimation methods including filtering and learning approaches. We then investigate the performance in pricing S&P 500 index short-term options after obtaining a proper change of measure. We find that the sequential Bayesian learning approach (SBLA) significantly and robustly decreases the option pricing errors. Our theoretical and empirical findings also suggest that, when stock returns are non-Gaussian distributed, their innovations under the risk-neutral measure may present more non-normality, exhibit higher volatility, and have a stronger leverage effect than under the physical measure.

Spectrum Analysis of Filtering Technologies in Management Networks and Wireless Systems

Filtering technology has been widely applied in signal processing and object tracking for decades, and most recently it has become a useful instrument for time series analysis. In this article, we introduce several popular technologies developed for analysis of the dynamic state space model, including Kalman and particle filtering, Markov chain Monte Carlo algorithms, as well as the sequential Bayesian learning method. Their applications in fields of interest are also discussed. Filtering technologies have great superiority in solving the problems arising from management and communications, making them deserving of further exploration.

Bayesian Sequential Learning for Railway Cognitive Radio

Applying cognitive radio in the railway communication systems is a cutting-edge research area. The rapid motion of the train makes the spectrum access of the railway wireless environment instable. To address the issue, first we formulate the spectrum management of railway cognitive radio as a distributed sequential decision problem. Then, based on the available environmental information, we propose a multi-cognitive-base-station cascade collaboration algorithm by using naive Bayesian learning and agent theory. Finally, our experiment results reveal that the model can improve the performance of spectrum access. This cognitive-base-station multi-agent system scheme comprehensively solves the problem of low efficiency in the dynamic access of the railway cognitive radio. The article is also a typical case of artificial intelligence applied in the field of the smart city.

A Bayesian Sequential Learning Framework to Parameterise Continuum Models of Melanoma Invasion into Human Skin.

We present a novel framework to parameterise a mathematical model of cell invasion that describes how a population of melanoma cells invades into human skin tissue. Using simple experimental data extracted from complex experimental images, we estimate three model parameters: (i) the melanoma cell proliferation rate, [Formula: see text]; (ii) the melanoma cell diffusivity, D; and (iii) [Formula: see text], a constant that determines the rate that melanoma cells degrade the skin tissue. The Bayesian sequential learning framework involves a sequence of increasingly sophisticated experimental data from: (i) a spatially uniform cell proliferation assay; (ii) a two-dimensional circular barrier assay; and (iii) a three-dimensional invasion assay. The Bayesian sequential learning approach leads to well-defined parameter estimates. In contrast, taking a naive approach that attempts to estimate all parameters from a single set of images from the same experiment fails to produce meaningful results. Overall, our approach to inference is simple-to-implement, computationally efficient, and well suited for many cell biology phenomena that can be described by low-dimensional continuum models using ordinary differential equations and partial differential equations. We anticipate that this Bayesian sequential learning framework will be relevant in other biological contexts where it is challenging to extract detailed, quantitative biological measurements from experimental images and so we must rely on using relatively simple measurements from complex images.

Discussion of “Sequential Bayesian learning for stochastic volatility with variance‐gamma jumps in returns”

Discussion of “Sequential Bayesian learning for stochastic volatility with variance‐gamma jumps in returns”

Rejoinder to “Sequential Bayesian learning for stochastic volatility with variance‐gamma jumps in returns” Reply to the discussions by Nalini Ravishanker and Refik Soyer

Rejoinder to “Sequential Bayesian learning for stochastic volatility with variance‐gamma jumps in returns” Reply to the discussions by Nalini Ravishanker and Refik Soyer

Discussion of “Sequential Bayesian learning for stochastic volatility with variance‐gamma jumps in returns”

Discussion of “Sequential Bayesian learning for stochastic volatility with variance‐gamma jumps in returns”

Bayesian Sequential Learning for Clinical Trials of Multiple Correlated Medical Interventions

We propose and analyze the first model for clinical trial design that integrates each of three important trends intending to improve the effectiveness of clinical trials that inform health-technology adoption decisions: adaptive design, which dynamically adjusts the sample size and allocation of interventions to different patients; multi-arm trial design, which compares multiple interventions simultaneously; and value-based design, which focuses on cost-beneft improvements of health interventions over a current standard of care. Example applications are to seamless Phase II/III dose-finding trials and to trials that test multiple combinations of therapies. Our objective is to maximize the expected population health-economic benefit of health-technology adoption decisions less clinical trial costs. We show that unifying the adaptive, multi-arm, and value-based approaches to trial design can reduce the cost and duration of multi-arm trials with efficient adaptive lookahead policies that focus on value to patients, and account for correlated rewards across arms. Features that differentiate our approach from much other work on stochastic optimization include stopping times that balance sampling costs and the expected value of information of those samples, performance guarantees offered by new asymptotic convergence proofs, and the modeling of arms' potentially different sampling costs. Our proposed solution can be computed feasibly and can randomize patients. The class of trials for the base model assumes that health-economic data are collected and observed quickly. Related work from Bayesian optimization can enable the further inclusion of trials with intermediate duration delays between the time of treatment initiation and observation of outcomes.

A Bayesian Learning Method for Financial Time-Series Analysis

This article develops a sequential Bayesian learning method to estimate the parameters and recover the state variables for generalized autoregressive conditional heteroscedasticity (GARCH) models, which are commonly used in the financial time-series analysis. This simulation-based method combines particle-filtering technology with a Markov chain Monte Carlo algorithm when the model is non-linear and the number of observed variables is relatively sparse. We compare the performance of the sequential Bayesian learning approach with the numerical maximum likelihood estimation (NMLE) in estimating models based on S&P 500 return rates. Our research concludes that the sequential parameter learning approach performs more robustly and accurately than the NMLE, by taking into account the uncertainty of the model. We also carry out simulation studies to confirm that the sequential Bayesian learning method is extremely reliable for GARCH models.

Sequential Bayesian learning for stochastic volatility with variance‐gamma jumps in returns

In this work, we investigate sequential Bayesian estimation for inference of stochastic volatility with variance‐gamma (SVVG) jumps in returns. We develop an estimation algorithm that combines the sequential learning auxiliary particle filter with the particle learning filter. Simulation evidence and empirical estimation results indicate that this approach is able to filter latent variances, identify latent jumps in returns, and provide sequential learning about the static parameters of SVVG. We demonstrate comparative performance of the sequential algorithm and off‐line Markov Chain Monte Carlo in synthetic and real data applications.

Robust estimation of lake metabolism by coupling high frequency dissolved oxygen and chlorophyll fluorescence data in a Bayesian framework

Gross primary production (GPP) and community respiration (R) are increasingly calculated from high-frequency measurements of dissolved oxygen (DO) by fitting dynamic metabolic models to the observed DO time series. Because different combinations of metabolic components result in nearly the same DO time series, theoretical problems burden this inverse modeling approach. Bayesian parameter inference could improve identification of processes by including independent knowledge in the estimation procedure. This method, however, requires model development because parameters of existing metabolic models are too abstract to achieve a significant improvement. Because algal biomass is a key determinant of GPP and R, and high-frequency data on phytoplankton biomass are increasingly available, coupling DO and biomass time series within a Bayesian framework has a high potential to support identification of individual metabolic components. We demonstrate this potential in 3 lakes. Phytoplankton data were simulated via a sequential Bayesian learning procedure coupled with an error model that accounted for systematic errors caused by structural deficiencies of the metabolic model. This method provided ecologically coherent, and therefore presumably robust, estimates for biomass-specific metabolic rates and contributes to a better understanding of metabolic responses to natural and anthropogenic disturbances.

Particle swarm optimisation particle filtering for dual estimation

A new method for the dual estimation in dynamic state-space model was proposed in this study with a focus on sequential Bayesian learning about time-varying state and static parameter simultaneously. The proposed algorithm combines auxiliary particle filtering (APF) with particle swarm optimisation (PSO) to achieve computational efficiency and stability. The PSO provides the mechanism for generating new parameter values for the particle filtering at each time step. By properly choosing the fitness function of PSO, the algorithm produces the recursive maximum-likelihood estimation of the parameter. It is shown that PSO can be integrated with APF in the simulation-based sequential frame for dual estimation. The algorithm is tested on Markov switching stochastic volatility model with promising results compared with existing ones.

Of bits and wows: A Bayesian theory of surprise with applications to attention

The amount of information contained in a piece of data can be measured by the effect this data has on its observer. Fundamentally, this effect is to transform the observer's prior beliefs into posterior beliefs, according to Bayes theorem. Thus the amount of information can be measured in a natural way by the distance (relative entropy) between the prior and posterior distributions of the observer over the available space of hypotheses. This facet of information, termed "surprise", is important in dynamic situations where beliefs change, in particular during learning and adaptation. Surprise can often be computed analytically, for instance in the case of distributions from the exponential family, or it can be numerically approximated. During sequential Bayesian learning, surprise decreases as the inverse of the number of training examples. Theoretical properties of surprise are discussed, in particular how it differs and complements Shannon's definition of information. A computer vision neural network architecture is then presented capable of computing surprise over images and video stimuli. Hypothesizing that surprising data ought to attract natural or artificial attention systems, the output of this architecture is used in a psychophysical experiment to analyze human eye movements in the presence of natural video stimuli. Surprise is found to yield robust performance at predicting human gaze (ROC-like ordinal dominance score approximately 0.7 compared to approximately 0.8 for human inter-observer repeatability, approximately 0.6 for simpler intensity contrast-based predictor, and 0.5 for chance). The resulting theory of surprise is applicable across different spatio-temporal scales, modalities, and levels of abstraction.

Bayesian Analysis of Evidence from Studies of Warfarin v Aspirin for Symptomatic Intracranial Stenosis

Bayesian analyses of symptomatic intracranial stenosis studies were conducted to compare the benefits of long-term therapy with warfarin to aspirin. The synthesis of evidence of effect from previous nonrandomized studies in monitoring a randomized clinical trial was of particular interest. Sequential Bayesian learning analysis was conducted and Bayesian hierarchical random effects models were used to incorporate variability between studies. The posterior point estimates for the risk rate ratio (RRR) were similar between analyses, although the interval estimates resulting from the hierarchical analyses are larger than the corresponding Bayesian learning analyses. This demonstrated the difference between these methods in accounting for between-study variability. This study suggests that Bayesian synthesis can be a useful supplement to futility analysis in the process of monitoring randomized clinical trials.

A novel Bayesian learning method for information aggregation in modular neural networks

Modular neural network is a popular neural network model which has many successful applications. In this paper, a sequential Bayesian learning (SBL) is proposed for modular neural networks aiming at efficiently aggregating the outputs of members of the ensemble. The experimental results on eight benchmark problems have demonstrated that the proposed method can perform information aggregation efficiently in data modeling.