Addressing uncertainty in Deep Learning (DL) is essential, as it enables the development of models that can make reliable predictions and informed decisions in complex, real-world environments where data may be incomplete or ambiguous. This paper introduces a novel algorithm leveraging Dempster-Shafer Theory (DST) to integrate multiple pre-trained models to form an ensemble capable of providing more reliable and enhanced classifications. The main steps of the proposed method include feature extraction, mass function calculation, fusion, and expected utility calculation. Several experiments have been conducted on CIFAR-10 and CIFAR-100 datasets, demonstrating superior classification accuracy of the proposed DST-based method, achieving improvements of 5.4% and 8.4%, respectively, compared to the best individual pre-trained models. Results highlight the potential of DST as a robust framework for managing uncertainties related to data when applying DL in real-world scenarios.

Adversarial examples pose a security threat to many critical systems built on neural networks. Given that deterministic robustness often comes with significantly reduced accuracy, probabilistic robustness (i.e., the probability of having the same label with a vicinity is $\ge 1-\kappa$) has been proposed as a promising way of achieving robustness whilst maintaining accuracy. However, existing training methods for probabilistic robustness still experience non-trivial accuracy loss. It is unclear whether there is an upper bound on the accuracy when optimising towards probabilistic robustness, and whether there is a certain relationship between $\kappa$ and this bound. This work studies these problems from a Bayes error perspective. We find that while Bayes uncertainty does affect probabilistic robustness, its impact is smaller than that on deterministic robustness. This reduced Bayes uncertainty allows a higher upper bound on probabilistic robust accuracy than that on deterministic robust accuracy. Further, we prove that with optimal probabilistic robustness, each probabilistically robust input is also deterministically robust in a smaller vicinity. We also show that voting within the vicinity always improves probabilistic robust accuracy and the upper bound of probabilistic robust accuracy monotonically increases as $\kappa$ grows. Our empirical findings also align with our results.

Effective large-scale process optimization in manufacturing industries requires close cooperation between different human expert parties who encode their knowledge of related domains as Bayesian network models. For instance, Bayesian networks for domains such as lithography equipment, processes, and auxiliary tools must be conjointly used to effectively identify process optimizations in the semiconductor industry. However, business confidentiality across domains hinders such collaboration, and encourages alternatives to centralized inference. We propose CCBNet, the first Confidentiality-preserving Collaborative Bayesian Network inference framework. CCBNet leverages secret sharing to securely perform analysis on the combined knowledge of party models by joining two novel subprotocols: (i) CABN, which augments probability distributions for features across parties by modeling them into secret shares of their normalized combination; and (ii) SAVE, which aggregates party inference result shares through distributed variable elimination. We extensively evaluate CCBNet via 9 public Bayesian networks. Our results show that CCBNet achieves predictive quality that is similar to the ones of centralized methods while preserving model confidentiality. We further demonstrate that CCBNet scales to challenging manufacturing use cases that involve 16-128 parties in large networks of 223-1003 features, and decreases, on average, computational overhead by 23%, while communicating 71k values per request. Finally, we showcase possible attacks and mitigations for partially reconstructing party networks in the two subprotocols.

Causal models are crucial for understanding complex systems and identifying causal relationships among variables. Even though causal models are extremely popular, conditional probability calculation of formulas involving interventions pose significant challenges. In case of Causal Bayesian Networks (CBNs), Pearl assumes autonomy of mechanisms that determine interventions to calculate a range of probabilities. We show that by making simple yet often realistic independence assumptions, it is possible to uniquely estimate the probability of an interventional formula (including the well-studied notions of probability of sufficiency and necessity). We discuss when these assumptions are appropriate. Importantly, in many cases of interest, when the assumptions are appropriate, these probability estimates can be evaluated using observational data, which carries immense significance in scenarios where conducting experiments is impractical or unfeasible.

Learning the unique directed acyclic graph corresponding to an unknown causal model is a challenging task. Methods based on functional causal models can identify a unique graph, but either suffer from the curse of dimensionality or impose strong parametric assumptions. To address these challenges, we propose a novel hybrid approach for global causal discovery in observational data that leverages local causal substructures. We first present a topological sorting algorithm that leverages ancestral relationships in linear structural equation models to establish a compact top-down hierarchical ordering, encoding more causal information than linear orderings produced by existing methods. We demonstrate that this approach generalizes to nonlinear settings with arbitrary noise. We then introduce a nonparametric constraint-based algorithm that prunes spurious edges by searching for local conditioning sets, achieving greater accuracy than current methods. We provide theoretical guarantees for correctness and worst-case polynomial time complexities, with empirical validation on synthetic data.

Bayesian networks are well-suited for clinical reasoning on tabular data, but are less compatible with natural language data, for which neural networks provide a successful framework. This paper compares and discusses strategies to augment Bayesian networks with neural text representations, both in a generative and discriminative manner. This is illustrated with simulation results for a primary care use case (diagnosis of pneumonia) and discussed in a broader clinical context.

In the context of reinforcement learning from human feedback (RLHF), the reward function is generally derived from maximum likelihood estimation of a random utility model based on pairwise comparisons made by humans. The problem of learning a reward function is one of preference aggregation that, we argue, largely falls within the scope of social choice theory. From this perspective, we can evaluate different aggregation methods via established axioms, examining whether these methods meet or fail well-known standards. We demonstrate that both the Bradley-Terry-Luce Model and its broad generalizations fail to meet basic axioms. In response, we develop novel rules for learning reward functions with strong axiomatic guarantees. A key innovation from the standpoint of social choice is that our problem has a linear structure, which greatly restricts the space of feasible rules and leads to a new paradigm that we call linear social choice.

Predicting cancer dynamics under treatment is challenging due to high inter-patient heterogeneity, lack of predictive biomarkers, and sparse and noisy longitudinal data. Mathematical models can summarize cancer dynamics by a few interpretable parameters per patient. Machine learning methods can then be trained to predict the model parameters from baseline covariates, but do not account for uncertainty in the parameter estimates. Instead, hierarchical Bayesian modeling can model the relationship between baseline covariates to longitudinal measurements via mechanistic parameters while accounting for uncertainty in every part of the model. The mapping from baseline covariates to model parameters can be modeled in several ways. A linear mapping simplifies inference but fails to capture nonlinear covariate effects and scale poorly for interaction modeling when the number of covariates is large. In contrast, Bayesian neural networks can potentially discover interactions between covariates automatically, but at a substantial cost in computational complexity. In this work, we develop a hierarchical Bayesian model of subpopulation dynamics that uses baseline covariate information to predict cancer dynamics under treatment, inspired by cancer dynamics in multiple myeloma (MM), where serum M protein is a well-known proxy of tumor burden. As a working example, we apply the model to a simulated dataset and compare its ability to predict M protein trajectories to a model with linear covariate effects. Our results show that the Bayesian neural network covariate effect model predicts cancer dynamics more accurately than a linear covariate effect model when covariate interactions are present. The framework can also be applied to other types of cancer or other time series prediction problems that can be described with a parametric model.

The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current machine learning approaches, however, mostly rely on rerunning simulations over a fixed set of designs available in the observed data, potentially neglecting informative correlations across the design space and requiring a large amount of simulations. Instead, we consider the calibration process from the perspective of Bayesian adaptive experimental design and propose a data-efficient algorithm to run maximally informative simulations within a batch-sequential process. At each round, the algorithm jointly estimates the parameters of the posterior distribution and optimal designs by maximising a variational lower bound of the expected information gain. The simulator is modelled as a sample from a Gaussian process, which allows us to correlate simulations and observed data with the unknown calibration parameters. We show the benefits of our method when compared to related approaches across synthetic and real-data problems.

Multi-dimensional parameter spaces are commonly encountered in astroparticle physics theories that attempt to capture novel phenomena. However, they often possess complicated posterior geometries that are expensive to traverse using techniques traditional to this community. Effectively sampling these spaces is crucial to bridge the gap between experiment and theory. Several recent innovations, which are only beginning to make their way into this field, have made navigating such complex posteriors possible. These include GPU acceleration, automatic differentiation, and neural-network-guided reparameterization. We apply these advancements to astroparticle physics experimental results in the context of novel neutrino physics and benchmark their performances against traditional nested sampling techniques. Compared to nested sampling alone, we find that these techniques increase performance for both nested sampling and Hamiltonian Monte Carlo, accelerating inference by factors of $\sim 100$ and $\sim 60$, respectively. As nested sampling also evaluates the Bayesian evidence, these advancements can be exploited to improve model comparison performance while retaining compatibility with existing implementations that are widely used in the natural sciences.