Polynomial chaos expansion (PCE) is a versatile tool widely used in uncertainty quantification and machine learning, but its successful application depends strongly on the accuracy and reliability of the resulting PCE-based response surface. High accuracy typically requires high polynomial degrees, demanding many training points especially in high-dimensional problems through the curse of dimensionality. So-called sparse PCE concepts work with a much smaller selection of basis polynomials compared to conventional PCE approaches and can overcome the curse of dimensionality very efficiently, but have to pay specific attention to their strategies of choosing training points. Furthermore, the approximation error resembles an uncertainty that most existing PCE-based methods do not estimate. In this study, we develop and evaluate a fully Bayesian approach to establish the PCE representation via joint shrinkage priors and Markov chain Monte Carlo. The suggested Bayesian PCE model directly aims to solve the two challenges named above: achieving a sparse PCE representation and estimating uncertainty of the PCE itself. The embedded Bayesian regularizing via the joint shrinkage prior allows using higher polynomial degrees for given training points due to its ability to handle underdetermined situations, where the number of considered PCE coefficients could be much larger than the number of available training points. We also explore multiple variable selection methods to construct sparse PCE expansions based on the established Bayesian representations, while globally selecting the most meaningful orthonormal polynomials given the available training data. We demonstrate the advantages of our Bayesian PCE and the corresponding sparsity-inducing methods on several benchmarks.
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We introduce Sparse Variational Bayesian Monte Carlo (SVBMC), a method for fast "post-process" Bayesian inference for models with black-box and potentially noisy likelihoods. SVBMC reuses all existing target density evaluations -- for example, from previous optimizations or partial Markov Chain Monte Carlo runs -- to build a sparse Gaussian process (GP) surrogate model of the log posterior density. Uncertain regions of the surrogate are then refined via active learning as needed. Our work builds on the Variational Bayesian Monte Carlo (VBMC) framework for sample-efficient inference, with several novel contributions. First, we make VBMC scalable to a large number of pre-existing evaluations via sparse GP regression, deriving novel Bayesian quadrature formulae and acquisition functions for active learning with sparse GPs. Second, we introduce noise shaping, a general technique to induce the sparse GP approximation to focus on high posterior density regions. Third, we prove theoretical results in support of the SVBMC refinement procedure. We validate our method on a variety of challenging synthetic scenarios and real-world applications. We find that SVBMC consistently builds good posterior approximations by post-processing of existing model evaluations from different sources, often requiring only a small number of additional density evaluations.
The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures of two competing densities, the null and the alternative distributions. We investigate the use of weighted densities and, in particular, non-local densities as working alternative distributions, to enforce separation from the null and thus refine the screening procedure. We show how these weighted alternatives improve various operating characteristics, such as the Bayesian False Discovery rate, of the resulting tests for a fixed mixture proportion with respect to a local, unweighted likelihood approach. Parametric and nonparametric model specifications are proposed, along with efficient samplers for posterior inference. By means of a simulation study, we exhibit how our model compares with both well-established and state-of-the-art alternatives in terms of various operating characteristics. Finally, to illustrate the versatility of our method, we conduct three differential expression analyses with publicly-available datasets from genomic studies of heterogeneous nature.
When robots are deployed in the field for environmental monitoring they typically execute pre-programmed motions, such as lawnmower paths, instead of adaptive methods, such as informative path planning. One reason for this is that adaptive methods are dependent on parameter choices that are both critical to set correctly and difficult for the non-specialist to choose. Here, we show how to automatically configure a planner for informative path planning by training a reinforcement learning agent to select planner parameters at each iteration of informative path planning. We demonstrate our method with 37 instances of 3 distinct environments, and compare it against pure (end-to-end) reinforcement learning techniques, as well as approaches that do not use a learned model to change the planner parameters. Our method shows a 9.53% mean improvement in the cumulative reward across diverse environments when compared to end-to-end learning based methods; we also demonstrate via a field experiment how it can be readily used to facilitate high performance deployment of an information gathering robot.
Dynamic treatment regimens (DTRs), also known as treatment algorithms or adaptive interventions, play an increasingly important role in many health domains. DTRs are motivated to address the unique and changing needs of individuals by delivering the type of treatment needed, when needed, while minimizing unnecessary treatment. Practically, a DTR is a sequence of decision rules that specify, for each of several points in time, how available information about the individual's status and progress should be used in practice to decide which treatment (e.g., type or intensity) to deliver. The sequential multiple assignment randomized trial (SMART) is an experimental design widely used to empirically inform the development of DTRs. Sample size planning resources for SMARTs have been developed for continuous, binary, and survival outcomes. However, an important gap exists in sample size estimation methodology for SMARTs with longitudinal count outcomes. Further, in many health domains, count data are overdispersed - having variance greater than their mean. We propose a Monte Carlo-based approach to sample size estimation applicable to many types of longitudinal outcomes and provide a case study with longitudinal overdispersed count outcomes. A SMART for engaging alcohol and cocaine-dependent patients in treatment is used as motivation.
The precision matrix that encodes conditional linear dependency relations among a set of variables forms an important object of interest in multivariate analysis. Sparse estimation procedures for precision matrices such as the graphical lasso (Glasso) gained popularity as they facilitate interpretability, thereby separating pairs of variables that are conditionally dependent from those that are independent (given all other variables). Glasso lacks, however, robustness to outliers. To overcome this problem, one typically applies a robust plug-in procedure where the Glasso is computed from a robust covariance estimate instead of the sample covariance, thereby providing protection against outliers. In this paper, we study such estimators theoretically, by deriving and comparing their influence function, sensitivity curves and asymptotic variances.
Crowdsourcing is the outsourcing of tasks to a crowd of contributors on a dedicated platform. The crowd on these platforms is very diversified and includes various profiles of contributors which generates data of uneven quality. However, majority voting, which is the aggregating method commonly used in platforms, gives equal weight to each contribution. To overcome this problem, we propose a method, MONITOR, which estimates the contributor's profile and aggregates the collected data by taking into account their possible imperfections thanks to the theory of belief functions. To do so, MONITOR starts by estimating the profile of the contributor through his qualification for the task and his behavior.Crowdsourcing campaigns have been carried out to collect the necessary data to test MONITOR on real data in order to compare it to existing approaches. The results of the experiments show that thanks to the use of the MONITOR method, we obtain a better rate of correct answer after aggregation of the contributions compared to the majority voting. Our contributions in this article are for the first time the proposal of a model that takes into account both the qualification of the contributor and his behavior in the estimation of his profile. For the second one, the weakening and the aggregation of the answers according to the estimated profiles.
This paper explores how the personality traits of robot operators can impact their task performance during remote control of robots. The influence of personal dispositions on information processing, either directly or indirectly, needs to be examined when working with robots on specific tasks. To investigate this relationship, we utilize the open-access multi-modal dataset MOCAS to examine the operator's personality, affect, cognitive load, and task performance. Our objective is to confirm if personal traits have a total effect, including both direct and indirect effects, that could significantly impact operator performance level. We specifically examine the relationship between personality traits such as extroversion, conscientiousness, and agreeableness, and task performance. We analyze the correlation between cognitive load, self-ratings of workload and affect, and the quantified individual personality traits and their experimental scores. As a result, we confirm that personality traits have no total effect on task performance.
Distance estimation from vision is fundamental for a myriad of robotic applications such as navigation, manipulation, and planning. Inspired by the mammal's visual system, which gazes at specific objects, we develop two novel constraints relating time-to-contact, acceleration, and distance that we call the $\tau$-constraint and $\Phi$-constraint. They allow an active (moving) camera to estimate depth efficiently and accurately while using only a small portion of the image. The constraints are applicable to range sensing, sensor fusion, and visual servoing. We successfully validate the proposed constraints with two experiments. The first applies both constraints in a trajectory estimation task with a monocular camera and an Inertial Measurement Unit (IMU). Our methods achieve 30-70% less average trajectory error while running 25$\times$ and 6.2$\times$ faster than the popular Visual-Inertial Odometry methods VINS-Mono and ROVIO respectively. The second experiment demonstrates that when the constraints are used for feedback with efference copies the resulting closed loop system's eigenvalues are invariant to scaling of the applied control signal. We believe these results indicate the $\tau$ and $\Phi$ constraint's potential as the basis of robust and efficient algorithms for a multitude of robotic applications.
Joint modeling longitudinal and survival data offers many advantages such as addressing measurement error and missing data in the longitudinal processes, understanding and quantifying the association between the longitudinal markers and the survival events and predicting the risk of events based on the longitudinal markers. A joint model involves multiple submodels (one for each longitudinal/survival outcome) usually linked together through correlated or shared random effects. Their estimation is computationally expensive (particularly due to a multidimensional integration of the likelihood over the random effects distribution) so that inference methods become rapidly intractable, and restricts applications of joint models to a small number of longitudinal markers and/or random effects. We introduce a Bayesian approximation based on the Integrated Nested Laplace Approximation algorithm implemented in the R package R-INLA to alleviate the computational burden and allow the estimation of multivariate joint models with less restrictions. Our simulation studies show that R-INLA substantially reduces the computation time and the variability of the parameter estimates compared to alternative estimation strategies. We further apply the methodology to analyze 5 longitudinal markers (3 continuous, 1 count, 1 binary, and 16 random effects) and competing risks of death and transplantation in a clinical trial on primary biliary cholangitis. R-INLA provides a fast and reliable inference technique for applying joint models to the complex multivariate data encountered in health research.
Aligning a robot's trajectory or map to the inertial frame is a critical capability that is often difficult to do accurately even though inertial measurement units (IMUs) can observe absolute roll and pitch with respect to gravity. Accelerometer biases and scale factor errors from the IMU's initial calibration are often the major source of inaccuracies when aligning the robot's odometry frame with the inertial frame, especially for low-grade IMUs. Practically, one would simultaneously estimate the true gravity vector, accelerometer biases, and scale factor to improve measurement quality but these quantities are not observable unless the IMU is sufficiently excited. While several methods estimate accelerometer bias and gravity, they do not explicitly address the observability issue nor do they estimate scale factor. We present a fixed-lag factor-graph-based estimator to address both of these issues. In addition to estimating accelerometer scale factor, our method mitigates limited observability by optimizing over a time window an order of magnitude larger than existing methods with significantly lower computational burden. The proposed method, which estimates accelerometer intrinsics and gravity separately from the other states, is enabled by a novel, velocity-agnostic measurement model for intrinsics and gravity, as well as a new method for gravity vector optimization on S2. Accurate IMU state prediction, gravity-alignment, and roll/pitch drift correction are experimentally demonstrated on public and self-collected datasets in diverse environments.
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