Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm for selection continuous or categorical variables, but all estimates related to a selected factor usually differ. Therefore, a fitted model may not be sparse, which makes the model interpretation difficult. To obtain a sparse solution of the Group Lasso we propose the following two-step procedure: first, we reduce data dimensionality using the Group Lasso; then to choose the final model we use an information criterion on a small family of models prepared by clustering levels of individual factors. We investigate selection correctness of the algorithm in a sparse high-dimensional scenario. We also test our method on synthetic as well as real datasets and show that it performs better than the state of the art algorithms with respect to the prediction accuracy or model dimension.

The new wave of digitization induced by Industry 4.0 calls for ubiquitous and reliable connectivity to perform and automate industrial operations. 5G networks can afford the extreme requirements of heterogeneous vertical applications, but the lack of real data and realistic traffic statistics poses many challenges for the optimization and configuration of the network for industrial environments. In this paper, we investigate the network traffic data generated from a laser cutting machine deployed in a Trumpf factory in Germany. We analyze the traffic statistics, capture the dependencies between the internal states of the machine, and model the network traffic as a production state dependent stochastic process. The two-step model is proposed as follows: first, we model the production process as a multi-state semi-Markov process, then we learn the conditional distributions of the production state dependent packet interarrival time and packet size with generative models. We compare the performance of various generative models including variational autoencoder (VAE), conditional variational autoencoder (CVAE), and generative adversarial network (GAN). The numerical results show a good approximation of the traffic arrival statistics depending on the production state. Among all generative models, CVAE provides in general the best performance in terms of the smallest Kullback-Leibler divergence.

Learning causal structure is useful in many areas of artificial intelligence, including planning, robotics, and explanation. Constraint-based structure learning algorithms such as PC use conditional independence (CI) tests to infer causal structure. Traditionally, constraint-based algorithms perform CI tests with a preference for smaller-sized conditioning sets, partially because the statistical power of conventional CI tests declines rapidly as the size of the conditioning set increases. However, many modern conditional independence tests are model-based, and these tests use well-regularized models that maintain statistical power even with very large conditioning sets. This suggests an intriguing new strategy for constraint-based algorithms which may result in a reduction of the total number of CI tests performed: Test variable pairs with large conditioning sets first, as a pre-processing step that finds some conditional independencies quickly, before moving on to the more conventional strategy that favors small conditioning sets. We propose such a pre-processing step for the PC algorithm which relies on performing CI tests on a few randomly selected large conditioning sets. We perform an empirical analysis on directed acyclic graphs (DAGs) that correspond to real-world systems and both empirical and theoretical analyses for Erd\H{o}s-Renyi DAGs. Our results show that Pre-Processing Plus PC (P3PC) performs far fewer CI tests than the original PC algorithm, between 0.5% to 36%, and often less than 10%, of the CI tests that the PC algorithm alone performs. The efficiency gains are particularly significant for the DAGs corresponding to real-world systems.

Epistemic uncertainty quantification is a crucial part of drawing credible conclusions from predictive models, whether concerned about the prediction at a given point or any downstream evaluation that uses the model as input. When the predictive model is simple and its evaluation differentiable, this task is solved by the delta method, where we propagate the asymptotically-normal uncertainty in the predictive model through the evaluation to compute standard errors and Wald confidence intervals. However, this becomes difficult when the model and/or evaluation becomes more complex. Remedies include the bootstrap, but it can be computationally infeasible when training the model even once is costly. In this paper, we propose an alternative, the implicit delta method, which works by infinitesimally regularizing the training loss of the predictive model to automatically assess downstream uncertainty. We show that the change in the evaluation due to regularization is consistent for the asymptotic variance of the evaluation estimator, even when the infinitesimal change is approximated by a finite difference. This provides both a reliable quantification of uncertainty in terms of standard errors as well as permits the construction of calibrated confidence intervals. We discuss connections to other approaches to uncertainty quantification, both Bayesian and frequentist, and demonstrate our approach empirically.

Uncertainty quantification (UQ) has increasing importance in building robust high-performance and generalizable materials property prediction models. It can also be used in active learning to train better models by focusing on getting new training data from uncertain regions. There are several categories of UQ methods each considering different types of uncertainty sources. Here we conduct a comprehensive evaluation on the UQ methods for graph neural network based materials property prediction and evaluate how they truly reflect the uncertainty that we want in error bound estimation or active learning. Our experimental results over four crystal materials datasets (including formation energy, adsorption energy, total energy, and band gap properties) show that the popular ensemble methods for uncertainty estimation is NOT the best choice for UQ in materials property prediction. For the convenience of the community, all the source code and data sets can be accessed freely at \url{https://github.com/usccolumbia/materialsUQ}.

Here we aimed to use biologically relevant neuron models connected in a brain-like network structure to study its potential to achieve input separation in a robotic system interacting with real-world objects. The model network was inspired by local cortical networks in its recursive structure in principle, though with much fewer neurons and without the ambition to precisely mimick any assumed specific network structure. The aim was to explore if the inherent dynamic properties in such networks in themselves were enough to achieve efficient object classification. Our model system is reminiscent of Reservoir Computing networks (i.e. Gauthier et al 2020 Nature Communications), but our neurons have state memory, i.e. dynamics, which are biologically relevant. Moreover, the population of neurons are split into excitatory and inhibitory neurons. Combined with the neuronal output thresholding, i.e. imparting nonlinearity to the networks when inhibition drives the neurons below their thresholds, and combined with biologically relevant conduction delays, this setting creates extraordinarily rich network dynamics. Motivation for: what would be required in the robotics design to explore the questions we set out to explore? How well could we live up to those requirements with the robotics system used?

This paper considers centralized mission-planning for a heterogeneous multi-agent system with the aim of locating a hidden target. We propose a mixed observable setting, consisting of a fully observable state-space and a partially observable environment, using a hidden Markov model. First, we construct rapidly exploring random trees (RRTs) to introduce the mixed observable RRT for finding plausible mission plans giving way-points for each agent. Leveraging this construction, we present a path-selection strategy based on a dynamic programming approach, which accounts for the uncertainty from partial observations and minimizes the expected cost. Finally, we combine the high-level plan with model predictive control algorithms to evaluate the approach on an experimental setup consisting of a quadruped robot and a drone. It is shown that agents are able to make intelligent decisions to explore the area efficiently and to locate the target through collaborative actions.

Backpropagation applied to handwritten zip code recognition.

Motivated by the fragility of neural network (NN) controllers in safety-critical applications, we present a data-driven framework for verifying the risk of stochastic dynamical systems with NN controllers. Given a stochastic control system, an NN controller, and a specification equipped with a notion of trace robustness (e.g., constraint functions or signal temporal logic), we collect trajectories from the system that may or may not satisfy the specification. In particular, each of the trajectories produces a robustness value that indicates how well (severely) the specification is satisfied (violated). We then compute risk metrics over these robustness values to estimate the risk that the NN controller will not satisfy the specification. We are further interested in quantifying the difference in risk between two systems, and we show how the risk estimated from a nominal system can provide an upper bound the risk of a perturbed version of the system. In particular, the tightness of this bound depends on the closeness of the systems in terms of the closeness of their system trajectories. For Lipschitz continuous and incrementally input-to-state stable systems, we show how to exactly quantify system closeness with varying degrees of conservatism, while we estimate system closeness for more general systems from data in our experiments. We demonstrate our risk verification approach on two case studies, an underwater vehicle and an F1/10 autonomous car.

In many practical fields like engineering, finance and physics, we need to explore the effects of uncertainties borne by input or parameters, which is the task of the uncertainty quantification (UQ). In a specific UQ problem, if the system is represented as stochastic partial differential equations, then stochastic Galerkin methods like generalised polynomial chaos (gPC) [29] can be used to obtain statistics of the distribution of the unknown solution. As long as a numerical or analytical solver for the system is available, the renowned Monte Carlo (MC) method [8] can be applied to obtain a distribution of the quantities of interest. However, that is usually prohibitively expensive due to the slow convergence of the Monte Carlo method, despite the fact that the running of the computer code for solving some complicated systems one single time might take days. Thus, to some extent we may be willing to compromise accuracy to reduce running time through formulating a cheap surrogate [2].