We propose Expert Monitoring, an approach that leverages domain expertise to enhance the detection and mitigation of concept drift in machine learning (ML) models. Our approach supports practitioners by consolidating domain expertise related to concept drift-inducing events, making this expertise accessible to on-call personnel, and enabling automatic adaptability with expert oversight.

Robust evidence suggests that humans explore their environment using a combination of topological landmarks and coarse-grained path integration. This approach relies on identifiable environmental features (topological landmarks) in tandem with estimations of distance and direction (coarse-grained path integration) to construct cognitive maps of the surroundings. This cognitive map is believed to exhibit a hierarchical structure, allowing efficient planning when solving complex navigation tasks. Inspired by human behaviour, this paper presents a scalable hierarchical active inference model for autonomous navigation, exploration, and goal-oriented behaviour. The model uses visual observation and motion perception to combine curiosity-driven exploration with goal-oriented behaviour. Motion is planned using different levels of reasoning, i.e., from context to place to motion. This allows for efficient navigation in new spaces and rapid progress toward a target. By incorporating these human navigational strategies and their hierarchical representation of the environment, this model proposes a new solution for autonomous navigation and exploration. The approach is validated through simulations in a mini-grid environment.

Approximate Thompson sampling with Langevin Monte Carlo broadens its reach from Gaussian posterior sampling to encompass more general smooth posteriors. However, it still encounters scalability issues in high-dimensional problems when demanding high accuracy. To address this, we propose an approximate Thompson sampling strategy, utilizing underdamped Langevin Monte Carlo, where the latter is the go-to workhorse for simulations of high-dimensional posteriors. Based on the standard smoothness and log-concavity conditions, we study the accelerated posterior concentration and sampling using a specific potential function. This design improves the sample complexity for realizing logarithmic regrets from $\mathcal{\tilde O}(d)$ to $\mathcal{\tilde O}(\sqrt{d})$. The scalability and robustness of our algorithm are also empirically validated through synthetic experiments in high-dimensional bandit problems.

Nonparametric models have extensive applications across diverse fields, including biology (Mac-Farland et al. (2016)), economics (Ullah and Pagan (1999); Li and Racine (2023)), engineering (Lanzante (1996)), and machine learning (Hofmann et al. (2008); Schmidt-hieber (2020)). The most representative nonparametric approaches are kernel methods, known for their numerical robustness and statistical stability in lower-dimensional settings. However, kernel methods often suffer from the curse of dimensionality in higher-dimensional spaces. Recently, a number of significant studies have tackled various modern challenges in nonparametric models. For example, Ravikumar et al. (2009), Raskutti et al. (2012), and Yuan and Zhou (2016) have studied additive models for high-dimensional nonparametric regression; Zhang et al. (2015) and Yang et al. (2017) analyzed randomized algorithms for kernel regression estimation; and Liu et al. (2007) explored nonparametric density estimation in higher dimensions. Despite these contributions, the curse of dimensionality in nonparametric problems, particularly in aspects of statistical accuracy and computational efficiency, remains an open area for further exploration. In this paper, we aim to develop a new framework specifically designed for nonparametric estimation problems. Within this framework, we conceptualize functions as matrices or tensors and explore new methods for handling the bias-variance trade-off, aiming to reduce the curse of dimensionality in higher dimensions. Matrix approximation algorithms, such as singular value decomposition and QR decomposition, play a crucial role in computational mathematics and statistics.

We explore a stochastic contextual linear bandit problem where the agent observes a noisy, corrupted version of the true context through a noise channel with an unknown noise parameter. Our objective is to design an action policy that can approximate" that of an oracle, which has access to the reward model, the channel parameter, and the predictive distribution of the true context from the observed noisy context. In a Bayesian framework, we introduce a Thompson sampling algorithm for Gaussian bandits with Gaussian context noise. Adopting an information-theoretic analysis, we demonstrate the Bayesian regret of our algorithm concerning the oracle's action policy. We also extend this problem to a scenario where the agent observes the true context with some delay after receiving the reward and show that delayed true contexts lead to lower Bayesian regret. Finally, we empirically demonstrate the performance of the proposed algorithms against baselines.

In recent years, significant progress in generative AI has highlighted the important role of physics-inspired models that utilize advanced mathematical concepts based on fundamental physics principles to enhance artificial intelligence capabilities. Among these models, those based on diffusion equations have greatly improved image quality. This study aims to explore the potential uses of Maxwell-Boltzmann equation, which forms the basis of the kinetic theory of gases, and the Michaelis-Menten model in Marketing Mix Modelling (MMM) applications. We propose incorporating these equations into Hierarchical Bayesian models to analyse consumer behaviour in the context of advertising. These equation sets excel in accurately describing the random dynamics in complex systems like social interactions and consumer-advertising interactions.

We propose a weakly-supervised framework for the semantic segmentation of circular-scan synthetic-aperture-sonar (CSAS) imagery. The first part of our framework is trained in a supervised manner, on image-level labels, to uncover a set of semi-sparse, spatially-discriminative regions in each image. The classification uncertainty of each region is then evaluated. Those areas with the lowest uncertainties are then chosen to be weakly labeled segmentation seeds, at the pixel level, for the second part of the framework. Each of the seed extents are progressively resized according to an unsupervised, information-theoretic loss with structured-prediction regularizers. This reshaping process uses multi-scale, adaptively-weighted features to delineate class-specific transitions in local image content. Content-addressable memories are inserted at various parts of our framework so that it can leverage features from previously seen images to improve segmentation performance for related images. We evaluate our weakly-supervised framework using real-world CSAS imagery that contains over ten seafloor classes and ten target classes. We show that our framework performs comparably to nine fully-supervised deep networks. Our framework also outperforms eleven of the best weakly-supervised deep networks. We achieve state-of-the-art performance when pre-training on natural imagery. The average absolute performance gap to the next-best weakly-supervised network is well over ten percent for both natural imagery and sonar imagery. This gap is found to be statistically significant.

Root Cause Analysis (RCA) in the manufacturing of electric vehicles is the process of identifying fault causes. Traditionally, the RCA is conducted manually, relying on process expert knowledge. Meanwhile, sensor networks collect significant amounts of data in the manufacturing process. Using this data for RCA makes it more efficient. However, purely data-driven methods like Causal Bayesian Networks have problems scaling to large-scale, real-world manufacturing processes due to the vast amount of potential cause-effect relationships (CERs). Furthermore, purely data-driven methods have the potential to leave out already known CERs or to learn spurious CERs. The paper contributes by proposing an interactive and intelligent RCA tool that combines expert knowledge of an electric vehicle manufacturing process and a data-driven machine learning method. It uses reasoning over a large-scale Knowledge Graph of the manufacturing process while learning a Causal Bayesian Network. In addition, an Interactive User Interface enables a process expert to give feedback to the root cause graph by adding and removing information to the Knowledge Graph. The interactive and intelligent RCA tool reduces the learning time of the Causal Bayesian Network while decreasing the number of spurious CERs. Thus, the interactive and intelligent RCA tool closes the feedback loop between expert and machine learning method.

Document set expansion aims to identify relevant documents from a large collection based on a small set of documents that are on a fine-grained topic. Previous work shows that PU learning is a promising method for this task. However, some serious issues remain unresolved, i.e. typical challenges that PU methods suffer such as unknown class prior and imbalanced data, and the need for transductive experimental settings. In this paper, we propose a novel PU learning framework based on density estimation, called puDE, that can handle the above issues. The advantage of puDE is that it neither constrained to the SCAR assumption and nor require any class prior knowledge. We demonstrate the effectiveness of the proposed method using a series of real-world datasets and conclude that our method is a better alternative for the DSE task.

Variational families with full-rank covariance approximations are known not to work well in black-box variational inference (BBVI), both empirically and theoretically. In fact, recent computational complexity results for BBVI have established that full-rank variational families scale poorly with the dimensionality of the problem compared to e.g. mean field families. This is particularly critical to hierarchical Bayesian models with local variables; their dimensionality increases with the size of the datasets. Consequently, one gets an iteration complexity with an explicit $\mathcal{O}(N^2)$ dependence on the dataset size $N$. In this paper, we explore a theoretical middle ground between mean-field variational families and full-rank families: structured variational families. We rigorously prove that certain scale matrix structures can achieve a better iteration complexity of $\mathcal{O}(N)$, implying better scaling with respect to $N$. We empirically verify our theoretical results on large-scale hierarchical models.