In many robotics problems, there is a significant gain in collaborative information sharing between multiple robots, for exploration, search and rescue, tracking multiple targets, or mapping large environments. One of the key implicit assumptions when solving cooperative multi-robot problems is that all robots use the same (homogeneous) underlying algorithm. However, in practice, we want to allow collaboration between robots possessing different capabilities and that therefore must rely on heterogeneous algorithms. We present a system architecture and the supporting theory, to enable collaboration in a decentralized network of robots, where each robot relies on different estimation algorithms. To develop our approach, we focus on multi-robot simultaneous localization and mapping (SLAM) with multi-target tracking. Our theoretical framework builds on our idea of exploiting the conditional independence structure inherent to many robotics applications to separate between each robot's local inference (estimation) tasks and fuse only relevant parts of their non-equal, but overlapping probability density function (pdfs). We present a new decentralized graph-based approach to the multi-robot SLAM and tracking problem. We leverage factor graphs to split between different parts of the problem for efficient data sharing between robots in the network while enabling robots to use different local sparse landmark/dense/metric-semantic SLAM algorithms.

The reinforcement learning algorithm SARSA combined with linear function approximation has been shown to converge for infinite horizon discounted Markov decision problems (MDPs). In this paper, we investigate the convergence of the algorithm for random horizon MDPs, which has not previously been shown. We show, similar to earlier results for infinite horizon discounted MDPs, that if the behaviour policy is $\varepsilon$-soft and Lipschitz continuous with respect to the weight vector of the linear function approximation, with small enough Lipschitz constant, then the algorithm will converge with probability one when considering a random horizon MDP.

The Blackboard Architecture provides a mechanism for embodying data, decision making and actuation. Its versatility has been demonstrated across a wide number of application areas. However, it lacks the capability to directly model organizational, spatial and other relationships which may be useful in decision-making, in addition to the propositional logic embodied in the rule-fact-action network. Previous work has proposed the use of container objects and links as a mechanism to simultaneously model these organizational and other relationships, while leaving the operational logic modeled in the rules, facts and actions. While containers facilitate this modeling, their utility is limited by the need to manually define them. For systems which may have multiple instances of a particular type of object and which may build their network autonomously, based on sensing, the reuse of logical structures facilitates operations and reduces storage and processing needs. This paper, thus, presents and assesses two additional concepts to add to the Blackboard Architecture: common properties and generic rules. Common properties are facts associated with containers which are defined as representing the same information across the various objects that they are associated with. Generic rules provide logical propositions that use these generic rules across links and apply to any objects matching their definition. The potential uses of these two new concepts are discussed herein and their impact on system performance is characterized.

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

Control variates can be a powerful tool to reduce the variance of Monte Carlo estimators, but constructing effective control variates can be challenging when the number of samples is small. In this paper, we show that when a large number of related integrals need to be computed, it is possible to leverage the similarity between these integration tasks to improve performance even when the number of samples per task is very small. Our approach, called meta learning CVs (Meta-CVs), can be used for up to hundreds or thousands of tasks. Our empirical assessment indicates that Meta-CVs can lead to significant variance reduction in such settings, and our theoretical analysis establishes general conditions under which Meta-CVs can be successfully trained.

We propose a novel Bayesian inference framework for distributed differentially private linear regression. We consider a distributed setting where multiple parties hold parts of the data and share certain summary statistics of their portions in privacy-preserving noise. We develop a novel generative statistical model for privately shared statistics, which exploits a useful distributional relation between the summary statistics of linear regression. Bayesian estimation of the regression coefficients is conducted mainly using Markov chain Monte Carlo algorithms, while we also provide a fast version to perform Bayesian estimation in one iteration. The proposed methods have computational advantages over their competitors. We provide numerical results on both real and simulated data, which demonstrate that the proposed algorithms provide well-rounded estimation and prediction.

The initial alignment provides an accurate attitude for SINS (strapdown inertial navigation system). By further estimating the IMU's bias and misalignment angle, the recursive Bayesian filter is accurate. However, the prior heading error has significant influence on the convergence speed and accuracy. In addition, the accuracy will be limited by its iteration at a single time-step. Coarse alignment method OBA (optimization-based alignment) uses MLE (maximum likelihood estimation) to find the optimal attitude quickly. However, few methods consider the IMU bias and misalignment angle, which will reduce the attitude accuracy. In this paper, a unified method based on FGO (Factor graph optimization) and IBF (inertial base frame) is proposed. The attitude is estimated by MLE, IMU bias and misalignment angle are estimated by MAP estimation. The state of all time steps is optimized together to further improve the accuracy. Physical experiments on the rotation MEMS SINS show that the heading accuracy of this method is improved in limited alignment time.

Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss mutual information. Compared to the classical FSDR methods, such as functional sliced inverse regression and functional sliced average variance estimation, the proposed methods are appealing because they are capable of estimating multiple effective dimension reduction directions in the case of a relatively small number of categories, especially for the binary response. Moreover, the proposed methods do not require the restrictive linear conditional mean assumption and the constant covariance assumption. They avoid the inverse problem of the covariance operator which is often encountered in the functional sufficient dimension reduction. The functional principal component analysis with truncation be used as a regularization mechanism. Under some mild conditions, the statistical consistency of the proposed methods is established. It is demonstrated that the two methods are competitive compared with some existing FSDR methods by simulations and real data analyses.

We introduce MESSY estimation, a Maximum-Entropy based Stochastic and Symbolic densitY estimation method. The proposed approach recovers probability density functions symbolically from samples using moments of a Gradient flow in which the ansatz serves as the driving force. In particular, we construct a gradient-based drift-diffusion process that connects samples of the unknown distribution function to a guess symbolic expression. We then show that when the guess distribution has the maximum entropy form, the parameters of this distribution can be found efficiently by solving a linear system of equations constructed using the moments of the provided samples. Furthermore, we use Symbolic regression to explore the space of smooth functions and find optimal basis functions for the exponent of the maximum entropy functional leading to good conditioning. The cost of the proposed method in each iteration of the random search is linear with the number of samples and quadratic with the number of basis functions. We validate the proposed MESSY estimation method against other benchmark methods for the case of a bi-modal and a discontinuous density, as well as a density at the limit of physical realizability. We find that the addition of a symbolic search for basis functions improves the accuracy of the estimation at a reasonable additional computational cost. Our results suggest that the proposed method outperforms existing density recovery methods in the limit of a small to moderate number of samples by providing a low-bias and tractable symbolic description of the unknown density at a reasonable computational cost.

Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters just like standard neural network parameters using gradients and on the training data. However, estimating a single hyperparameter gradient requires a pass through the entire dataset, limiting the scalability of such algorithms. In this work, we overcome this issue by introducing lower bounds to the linearized Laplace approximation of the marginal likelihood. In contrast to previous estimators, these bounds are amenable to stochastic-gradient-based optimization and allow to trade off estimation accuracy against computational complexity. We derive them using the function-space form of the linearized Laplace, which can be estimated using the neural tangent kernel. Experimentally, we show that the estimators can significantly accelerate gradient-based hyperparameter optimization.