In this paper, a hyperparameter tuning based Bayesian optimization of digital twins is carried out to diagnose various faults in grid connected inverters. As fault detection and diagnosis require very high precision, we channelize our efforts towards an online optimization of the digital twins, which, in turn, allows a flexible implementation with limited amount of data. As a result, the proposed framework not only becomes a practical solution for model versioning and deployment of digital twins design with limited data, but also allows integration of deep learning tools to improve the hyperparameter tuning capabilities. For classification performance assessment, we consider different fault cases in virtual synchronous generator (VSG) controlled grid-forming converters and demonstrate the efficacy of our approach. Our research outcomes reveal the increased accuracy and fidelity levels achieved by our digital twin design, overcoming the shortcomings of traditional hyperparameter tuning methods.

Time management under uncertainty is essential to large scale projects. From space exploration to industrial production, there is a need to schedule and perform activities. given complex specifications on timing. In order to generate schedules that are robust to uncertainty in the duration of activities, prior work has focused on a problem framing that uses an interval-bounded uncertainty representation. However, such approaches are unable to take advantage of known probability distributions over duration. In this paper we concentrate on a probabilistic formulation of temporal problems with uncertain duration, called the probabilistic simple temporal problem. As distributions often have an unbounded range of outcomes, we consider chance-constrained solutions, with guarantees on the probability of meeting temporal constraints. By considering distributions over uncertain duration, we are able to use risk as a resource, reason over the relative likelihood of outcomes, and derive higher utility solutions. We first demonstrate our approach by encoding the problem as a convex program. We then develop a more efficient hybrid algorithm whose parent solver generates risk allocations and whose child solver generates schedules for a particular risk allocation. The child is made efficient by leveraging existing interval-bounded scheduling algorithms, while the parent is made efficient by extracting conflicts over risk allocations. We perform numerical experiments to show the advantages of reasoning over probabilistic uncertainty, by comparing the utility of schedules generated with risk allocation against those generated from reasoning over bounded uncertainty. We also empirically show that solution time is greatly reduced by incorporating conflict-directed risk allocation.

From the perspective of machine learning and data science, probabilities and likelihoods are used to quantify uncertainty, or perhaps how probable it is that an observation belongs to one class or another. They crop up when looking at confusion matrices; and indeed, algorithms like Naive Bayes classification are pretty much probabilistic models. The reality is that data scientists cannot escape these concepts. In everyday language, though, we tend to use the terms probability and likelihood almost interchangeably. Indeed, it's not uncommon to hear things like'how likely is it to rain today?' or'what are the chances of this or that happening?'

One of the weaknesses of classical (fuzzy) rough sets is their sensitivity to noise, which is particularly undesirable for machine learning applications. One approach to solve this issue is by making use of fuzzy quantifiers, as done by the vaguely quantified fuzzy rough set (VQFRS) model. While this idea is intuitive, the VQFRS model suffers from both theoretical flaws as well as from suboptimal performance in applications. In this paper, we improve on VQFRS by introducing fuzzy quantifier-based fuzzy rough sets (FQFRS), an intuitive generalization of fuzzy rough sets that makes use of general unary and binary quantification models. We show how several existing models fit in this generalization as well as how it inspires novel ones. Several binary quantification models are proposed to be used with FQFRS. We conduct a theoretical study of their properties, and investigate their potential by applying them to classification problems. In particular, we highlight Yager's Weighted Implication-based (YWI) binary quantification model, which induces a fuzzy rough set model that is both a significant improvement on VQFRS, as well as a worthy competitor to the popular ordered weighted averaging based fuzzy rough set (OWAFRS) model.

Universal Approximation Theorems establish the density of various classes of neural network function approximators in $C(K, \mathbb{R}^m)$, where $K \subset \mathbb{R}^n$ is compact. In this paper, we aim to extend these guarantees by establishing conditions on learning tasks that guarantee their continuity. We consider learning tasks given by conditional expectations $x \mapsto \mathrm{E}\left[Y \mid X = x\right]$, where the learning target $Y = f \circ L$ is a potentially pathological transformation of some underlying data-generating process $L$. Under a factorization $L = T \circ W$ for the data-generating process where $T$ is thought of as a deterministic map acting on some random input $W$, we establish conditions (that might be easily verified using knowledge of $T$ alone) that guarantee the continuity of practically \textit{any} derived learning task $x \mapsto \mathrm{E}\left[f \circ L \mid X = x\right]$. We motivate the realism of our conditions using the example of randomized stable matching, thus providing a theoretical justification for the continuity of real-world learning tasks.

Deep learning models that leverage large datasets are often the state of the art for modelling molecular properties. When the datasets are smaller (< 2000 molecules), it is not clear that deep learning approaches are the right modelling tool. In this work we perform an extensive study of the calibration and generalizability of probabilistic machine learning models on small chemical datasets. Using different molecular representations and models, we analyse the quality of their predictions and uncertainties in a variety of tasks (binary, regression) and datasets. We also introduce two simulated experiments that evaluate their performance: (1) Bayesian optimization guided molecular design, (2) inference on out-of-distribution data via ablated cluster splits. We offer practical insights into model and feature choice for modelling small chemical datasets, a common scenario in new chemical experiments. We have packaged our analysis into the DIONYSUS repository, which is open sourced to aid in reproducibility and extension to new datasets.

Moving agents perceive streams of information, typically a mix of RGB images, depth and inertial measurements. Probabilistic generative models [1] are a principled way to formalise the synthesis of this data, and from these models inference can be derived through Bayes' rule. We focus on exactly such inference and target the agent states and the scene map, a problem known as simultaneous localisation and mapping (SLAM). We treat it as a posterior approximation for a given state-space model, such that the combination is useful for model-based control: the posterior inference serves as a state estimator and the predictive state-space model as a simulator with which to plan ahead [2]. To pave the way towards decision making, we believe an inference method should have: a compatible predictive model for both RGB-D images and 6-DoF dynamics; principled state and map uncertainty; real-time performance on commodity hardware; state-of-the-art localisation accuracy. We motivate these requirements further in appendix J. Prominent methods like LSD-SLAM [3], ORB-SLAM [4], DSO [5] have propelled visual SLAM forward, with heavy focus on large-scale localisation. The core of modern large-scale SLAM is maximum a-posteriori (MAP) smoothing in a probabilistic factor graph [6, 7]. At present this demands sparsity assumptions for computational feasibility, which obstructs the tight integration of dense maps and rendering.

We develop a simple framework to learn bio-inspired foraging policies using human data. We conduct an experiment where humans are virtually immersed in an open field foraging environment and are trained to collect the highest amount of rewards. A Markov Decision Process (MDP) framework is introduced to model the human decision dynamics. Then, Imitation Learning (IL) based on maximum likelihood estimation is used to train Neural Networks (NN) that map human decisions to observed states. The results show that passive imitation substantially underperforms humans. We further refine the human-inspired policies via Reinforcement Learning (RL) using the on-policy Proximal Policy Optimization (PPO) algorithm which shows better stability than other algorithms and can steadily improve the policies pretrained with IL. We show that the combination of IL and RL can match human results and that good performance strongly depends on combining the allocentric information with an egocentric representation of the environment.

This work addresses the problem of sharing partial information within social learning strategies. In traditional social learning, agents solve a distributed multiple hypothesis testing problem by performing two operations at each instant: first, agents incorporate information from private observations to form their beliefs over a set of hypotheses; second, agents combine the entirety of their beliefs locally among neighbors. Within a sufficiently informative environment and as long as the connectivity of the network allows information to diffuse across agents, these algorithms enable agents to learn the true hypothesis. Instead of sharing the entirety of their beliefs, this work considers the case in which agents will only share their beliefs regarding one hypothesis of interest, with the purpose of evaluating its validity, and draws conditions under which this policy does not affect truth learning. We propose two approaches for sharing partial information, depending on whether agents behave in a self-aware manner or not. The results show how different learning regimes arise, depending on the approach employed and on the inherent characteristics of the inference problem. Furthermore, the analysis interestingly points to the possibility of deceiving the network, as long as the evaluated hypothesis of interest is close enough to the truth.

This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian inference applications, a multielement Polynomial Chaos Expansion based Kriging metamodel is proposed. The developed surrogate model combines in a piecewise function an array of local Polynomial Chaos based Kriging metamodels constructed on a finite set of non-overlapping subdomains of the stochastic input space. Therewith, the presence of non-smoothness in the response of the forward model (e.g.~ nonlinearities and sparseness) can be reproduced by the proposed metamodel with minimum computational costs owing to its local adaptation capabilities. The model parameter inference is conducted through a Markov chain Monte Carlo approach comprising adaptive exploration and delayed rejection. The efficiency and accuracy of the proposed approach are validated through two case studies, including an analytical benchmark and a numerical case study. The latter relates the partial differential equation governing the hydrogen diffusion phenomenon of metallic materials in Thermal Desorption Spectroscopy tests.