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.

Neurosymbolic AI aims to integrate deep learning with symbolic AI. This integration has many promises, such as decreasing the amount of data required to train a neural network, improving the explainability and interpretability of answers given by models and verifying the correctness of trained systems. We study neurosymbolic learning, where we have both data and background knowledge expressed using symbolic languages. How do we connect the symbolic and neural components to communicate this knowledge? One option is fuzzy reasoning, which studies degrees of truth. For example, being tall is not a binary concept. Instead, probabilistic reasoning studies the probability that something is true or will happen. Our first research question studies how different forms of fuzzy reasoning combine with learning. We find surprising results like a connection to the Raven paradox stating we confirm "ravens are black" when we observe a green apple. In this study, we did not use the background knowledge when we deployed our models after training. In our second research question, we studied how to use background knowledge in deployed models. We developed a new neural network layer based on fuzzy reasoning. Probabilistic reasoning is a natural fit for neural networks, which we usually train to be probabilistic. However, they are expensive to compute and do not scale well to large tasks. In our third research question, we study how to connect probabilistic reasoning with neural networks by sampling to estimate averages, while in the final research question, we study scaling probabilistic neurosymbolic learning to much larger problems than before. Our insight is to train a neural network with synthetic data to predict the result of probabilistic reasoning.

Bayesian Optimization (BO) is a powerful method for optimizing black-box functions by combining prior knowledge with ongoing function evaluations. BO constructs a probabilistic surrogate model of the objective function given the covariates, which is in turn used to inform the selection of future evaluation points through an acquisition function. For smooth continuous search spaces, Gaussian Processes (GPs) are commonly used as the surrogate model as they offer analytical access to posterior predictive distributions, thus facilitating the computation and optimization of acquisition functions. However, in complex scenarios involving optimizations over categorical or mixed covariate spaces, GPs may not be ideal. This paper introduces Simulation Based Bayesian Optimization (SBBO) as a novel approach to optimizing acquisition functions that only requires \emph{sampling-based} access to posterior predictive distributions. SBBO allows the use of surrogate probabilistic models tailored for combinatorial spaces with discrete variables. Any Bayesian model in which posterior inference is carried out through Markov chain Monte Carlo can be selected as the surrogate model in SBBO. In applications involving combinatorial optimization, we demonstrate empirically the effectiveness of SBBO method using various choices of surrogate models.

Fair machine learning aims to prevent discrimination against individuals or sub-populations based on sensitive attributes such as gender and race. In recent years, causal inference methods have been increasingly used in fair machine learning to measure unfairness by causal effects. However, current methods assume that the true causal graph is given, which is often not true in real-world applications. To address this limitation, this paper proposes a framework for achieving causal fairness based on the notion of interventions when the true causal graph is partially known. The proposed approach involves modeling fair prediction using a Partially Directed Acyclic Graph (PDAG), specifically, a class of causal DAGs that can be learned from observational data combined with domain knowledge. The PDAG is used to measure causal fairness, and a constrained optimization problem is formulated to balance between fairness and accuracy. Results on both simulated and real-world datasets demonstrate the effectiveness of this method.

Development of multi-modal, probabilistic prediction models has lead to a need for comprehensive evaluation metrics. While several metrics can characterize the accuracy of machine-learned models (e.g., negative log-likelihood, Jensen-Shannon divergence), these metrics typically operate on probability densities. Applying them to purely sample-based prediction models thus requires that the underlying density function is estimated. However, common methods such as kernel density estimation (KDE) have been demonstrated to lack robustness, while more complex methods have not been evaluated in multi-modal estimation problems. In this paper, we present ROME (RObust Multi-modal density Estimator), a non-parametric approach for density estimation which addresses the challenge of estimating multi-modal, non-normal, and highly correlated distributions. ROME utilizes clustering to segment a multi-modal set of samples into multiple uni-modal ones and then combines simple KDE estimates obtained for individual clusters in a single multi-modal estimate. We compared our approach to state-of-the-art methods for density estimation as well as ablations of ROME, showing that it not only outperforms established methods but is also more robust to a variety of distributions. Our results demonstrate that ROME can overcome the issues of over-fitting and over-smoothing exhibited by other estimators, promising a more robust evaluation of probabilistic machine learning models.

One important task in causal discovery is the recovery of a topological ordering of the underlying graph, which in the context of causality is an ordering of the nodes which places causes before effects. Other than the importance of such ordering in its own right, it is also highly useful for discovering the full graph [Teyssier and Koller, 2005]. A topological ordering which doesn't unnecessarily break all ties is called a layering [Tamassia, 2013]. Given a graph, repeated removal of sources or sinks yields a layering: we denote these algorithms as repeated-SOUrceRemoval (SOUR) and repeatedSInkRemoval (SIR), both are simple and probably known variants of Kahn's Algorithm [Kahn, 1962]. Of course, in causal discovery, we are not given the graph, so implementing SOUR/SIR is not straightforward. In this paper, we propose a new method for causal discovery of layerings of discrete random variables, which implements SOUR/SIR without direct access to the graph, but with access to a conditional entropy oracle for the data instead. We show that, under some assumptions, we can separate sources from non-sources and sinks from non-sinks by comparing their conditional entropy (with appropriate conditioning) to their unconditional noise entropy. Specifically, when repeatedly removing sources and conditioning on all removed variables, we show that the conditional entropy of new sources equals the conditional entropy of their noise, while the conditional entropy of non-sources is larger than the entropy of their noise.