This paper considers the problem of evaluating an autonomous system's competency in performing a task, particularly when working in dynamic and uncertain environments. The inherent opacity of machine learning models, from the perspective of the user, often described as a `black box', poses a challenge. To overcome this, we propose using a measure called the Surprise index, which leverages available measurement data to quantify whether the dynamic system performs as expected. We show that the surprise index can be computed in closed form for dynamic systems when observed evidence in a probabilistic model if the joint distribution for that evidence follows a multivariate Gaussian marginal distribution. We then apply it to a nonlinear spacecraft maneuver problem, where actions are chosen by a reinforcement learning agent and show it can indicate how well the trajectory follows the required orbit.

Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the predictive distribution. For applications with spatiotemporal datasets, suitable kernels should model joint spatial and temporal dependence. Separable space-time covariance kernels offer simplicity and computational efficiency. However, non-separable kernels include space-time interactions that better capture observed correlations. Most non-separable kernels that admit explicit expressions are based on mathematical considerations (admissibility conditions) rather than first-principles derivations. We present a hybrid spectral approach for generating covariance kernels which is based on physical arguments. We use this approach to derive a new class of physically motivated, non-separable covariance kernels which have their roots in the stochastic, linear, damped, harmonic oscillator (LDHO). The new kernels incorporate functions with both monotonic and oscillatory decay of space-time correlations. The LDHO covariance kernels involve space-time interactions which are introduced by dispersion relations that modulate the oscillator coefficients. We derive explicit relations for the spatiotemporal covariance kernels in the three oscillator regimes (underdamping, critical damping, overdamping) and investigate their properties. We further illustrate the hybrid spectral method by deriving covariance kernels that are based on the Ornstein-Uhlenbeck model.

Recent Vision-Language Pretrained (VLP) models have become the backbone for many downstream tasks, but they are utilized as frozen model without learning. Prompt learning is a method to improve the pre-trained VLP model by adding a learnable context vector to the inputs of the text encoder. In a few-shot learning scenario of the downstream task, MLE training can lead the context vector to over-fit dominant image features in the training data. This overfitting can potentially harm the generalization ability, especially in the presence of a distribution shift between the training and test dataset. This paper presents a Bayesian-based framework of prompt learning, which could alleviate the overfitting issues on few-shot learning application and increase the adaptability of prompts on unseen instances. Specifically, modeling data-dependent prior enhances the adaptability of text features for both seen and unseen image features without the trade-off of performance between them. Based on the Bayesian framework, we utilize the Wasserstein Gradient Flow in the estimation of our target posterior distribution, which enables our prompt to be flexible in capturing the complex modes of image features. We demonstrate the effectiveness of our method on benchmark datasets for several experiments by showing statistically significant improvements on performance compared to existing methods. The code is available at https://github.com/youngjae-cho/APP.

Many researchers around the world are researching to get control solutions that enhance robots' ability to navigate in dynamic environments autonomously. However, until these days robots have limited capability and many navigation tasks on Earth and other planets have been difficult so far. This paperwork presents the development of a control system for a differential drive-wheeled mobile robot that autonomously controls its position, heading, and speed based on destination information given and surrounding data gathered through mounted proximity and GPS sensors. The intelligence of this control system is implemented by using a fuzzy logic algorithm which is a very powerful tool to handle un-modeled systems like the dynamically changing environment dealt with in this research. The fuzzy controller is used to address the problems associated with navigation in an obstacle-strewn environment. Such issues include position estimation, path planning, and obstacle avoidance. In this study modeling, design, and simulation of the system have been done. The simulation result shows that the developed mobile robot travels successfully from any location to the destination location without colliding with obstacles.

Sequences of labeled events observed at irregular intervals in continuous time are ubiquitous across various fields. Temporal Point Processes (TPPs) provide a mathematical framework for modeling these sequences, enabling inferences such as predicting the arrival time of future events and their associated label, called mark. However, due to model misspecification or lack of training data, these probabilistic models may provide a poor approximation of the true, unknown underlying process, with prediction regions extracted from them being unreliable estimates of the underlying uncertainty. This paper develops more reliable methods for uncertainty quantification in neural TPP models via the framework of conformal prediction. A primary objective is to generate a distribution-free joint prediction region for the arrival time and mark, with a finite-sample marginal coverage guarantee. A key challenge is to handle both a strictly positive, continuous response and a categorical response, without distributional assumptions. We first consider a simple but overly conservative approach that combines individual prediction regions for the event arrival time and mark. Then, we introduce a more effective method based on bivariate highest density regions derived from the joint predictive density of event arrival time and mark. By leveraging the dependencies between these two variables, this method exclude unlikely combinations of the two, resulting in sharper prediction regions while still attaining the pre-specified coverage level. We also explore the generation of individual univariate prediction regions for arrival times and marks through conformal regression and classification techniques. Moreover, we investigate the stronger notion of conditional coverage. Finally, through extensive experimentation on both simulated and real-world datasets, we assess the validity and efficiency of these methods.

Building machines capable of efficiently collaborating with humans has been a longstanding goal in artificial intelligence. Especially in the presence of uncertainties, optimal cooperation often requires that humans and artificial agents model each other's behavior and use these models to infer underlying goals, beliefs or intentions, potentially involving multiple levels of recursion. Empirical evidence for such higherorder Level 1 Level 2 Level 3 Level 2 cognition in human behavior is also provided by previous works in cognitive science, linguistics, and robotics. We advocate for a new paradigm for active learning for human feedback that utilises humans as active data sources while accounting for their higher levels of agency. In particular, we discuss how increasing level of agency results in qualitatively different forms of rational communication between an active learning system and a teacher. Additionally, we provide a practical example of active learning using a higher-order cognitive model. This is accompanied by a computational study Level 3 Level 4 Level 5 Level 4 that underscores the unique behaviors that this model produces.

This study introduces a novel methodology for modelling patient emotions from online patient experience narratives. We employed metadata network topic modelling to analyse patient-reported experiences from Care Opinion, revealing key emotional themes linked to patient-caregiver interactions and clinical outcomes. We develop a probabilistic, context-specific emotion recommender system capable of predicting both multilabel emotions and binary sentiments using a naive Bayes classifier using contextually meaningful topics as predictors. The superior performance of our predicted emotions under this model compared to baseline models was assessed using the information retrieval metrics nDCG and Q-measure, and our predicted sentiments achieved an F1 score of 0.921, significantly outperforming standard sentiment lexicons. This method offers a transparent, cost-effective way to understand patient feedback, enhancing traditional collection methods and informing individualised patient care. Our findings are accessible via an R package and interactive dashboard, providing valuable tools for healthcare researchers and practitioners.

In this work, we propose an original method for aggregating multiple clustering coming from different sources of information. Each partition is encoded by a co-membership matrix between observations. Our approach uses a mixture of multilayer Stochastic Block Models (SBM) to group co-membership matrices with similar information into components and to partition observations into different clusters, taking into account their specificities within the components. The identifiability of the model parameters is established and a variational Bayesian EM algorithm is proposed for the estimation of these parameters. The Bayesian framework allows for selecting an optimal number of clusters and components. The proposed approach is compared using synthetic data with consensus clustering and tensor-based algorithms for community detection in large-scale complex networks. Finally, the method is utilized to analyze global food trading networks, leading to structures of interest.

We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. Such settings have recently drawn considerable interest in the context of generative modelling. In this paper, we propose a generative model combining diffusion maps and Langevin dynamics. Diffusion maps are used to approximate the drift term from the available training samples, which is then implemented in a discrete-time Langevin sampler to generate new samples. By setting the kernel bandwidth to match the time step size used in the unadjusted Langevin algorithm, our method effectively circumvents any stability issues typically associated with time-stepping stiff stochastic differential equations. More precisely, we introduce a novel split-step scheme, ensuring that the generated samples remain within the convex hull of the training samples. Our framework can be naturally extended to generate conditional samples. We demonstrate the performance of our proposed scheme through experiments on synthetic datasets with increasing dimensions and on a stochastic subgrid-scale parametrization conditional sampling problem.

Federated Learning (FL) involves training a model over a dataset distributed among clients, with the constraint that each client's dataset is localized and possibly heterogeneous. In FL, small and noisy datasets are common, highlighting the need for well-calibrated models that represent the uncertainty of predictions. The closest FL techniques to achieving such goals are the Bayesian FL methods which collect parameter samples from local posteriors, and aggregate them to approximate the global posterior. To improve scalability for larger models, one common Bayesian approach is to approximate the global predictive posterior by multiplying local predictive posteriors. In this work, we demonstrate that this method gives systematically overconfident predictions, and we remedy this by proposing $\beta$-Predictive Bayes, a Bayesian FL algorithm that interpolates between a mixture and product of the predictive posteriors, using a tunable parameter $\beta$. This parameter is tuned to improve the global ensemble's calibration, before it is distilled to a single model. Our method is evaluated on a variety of regression and classification datasets to demonstrate its superiority in calibration to other baselines, even as data heterogeneity increases. Code available at https://github.com/hasanmohsin/betaPredBayesFL