A reliable knowledge structure is a prerequisite for building effective adaptive learning systems and intelligent tutoring systems. Pursuing an explainable and trustworthy knowledge structure, we propose a method for constructing causal knowledge networks. This approach leverages Bayesian networks as a foundation and incorporates causal relationship analysis to derive a causal network. Additionally, we introduce a dependable knowledge-learning path recommendation technique built upon this framework, improving teaching and learning quality while maintaining transparency in the decision-making process.

Test-time augmentation (TTA) is a well-known technique employed during the testing phase of computer vision tasks. It involves aggregating multiple augmented versions of input data. Combining predictions using a simple average formulation is a common and straightforward approach after performing TTA. This paper introduces a novel framework for optimizing TTA, called BayTTA (Bayesian-based TTA), which is based on Bayesian Model Averaging (BMA). First, we generate a model list associated with different variations of the input data created through TTA. Then, we use BMA to combine model predictions weighted by their respective posterior probabilities. Such an approach allows one to take into account model uncertainty, and thus to enhance the predictive performance of the related machine learning or deep learning model. We evaluate the performance of BayTTA on various public data, including three medical image datasets comprising skin cancer, breast cancer, and chest X-ray images and two well-known gene editing datasets, CRISPOR and GUIDE-seq. Our experimental results indicate that BayTTA can be effectively integrated into state-of-the-art deep learning models used in medical image analysis as well as into some popular pre-trained CNN models such as VGG-16, MobileNetV2, DenseNet201, ResNet152V2, and InceptionRes-NetV2, leading to the enhancement in their accuracy and robustness performance.

In this paper, we present a guide to the foundations of learning Dynamic Bayesian Networks (DBNs) from data in the form of multiple samples of trajectories for some length of time. We present the formalism for a generic as well as a set of common types of DBNs for particular variable distributions. We present the analytical form of the models, with a comprehensive discussion on the interdependence between structure and weights in a DBN model and their implications for learning. Next, we give a broad overview of learning methods and describe and categorize them based on the most important statistical features, and how they treat the interplay between learning structure and weights. We give the analytical form of the likelihood and Bayesian score functions, emphasizing the distinction from the static case. We discuss functions used in optimization to enforce structural requirements. We briefly discuss more complex extensions and representations. Finally we present a set of comparisons in different settings for various distinct but representative algorithms across the variants.

Specifying a prior distribution is an essential part of solving Bayesian inverse problems. The prior encodes a belief on the nature of the solution and this regularizes the problem. In this article we completely characterize a Gaussian prior that encodes the belief that the solution is a structured tensor. We first define the notion of (A,b)-constrained tensors and show that they describe a large variety of different structures such as Hankel, circulant, triangular, symmetric, and so on. Then we completely characterize the Gaussian probability distribution of such tensors by specifying its mean vector and covariance matrix. Furthermore, explicit expressions are proved for the covariance matrix of tensors whose entries are invariant under a permutation. These results unlock a whole new class of priors for Bayesian inverse problems. We illustrate how new kernel functions can be designed and efficiently computed and apply our results on two particular Bayesian inverse problems: completing a Hankel matrix from a few noisy measurements and learning an image classifier of handwritten digits. The effectiveness of the proposed priors is demonstrated for both problems. All applications have been implemented as reactive Pluto notebooks in Julia.

In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and engineering applications. The computational challenges we address with the proposed methodology are: (i) the need for repeated evaluations of expensive forward models; (ii) the potential existence of multiple modes; and (iii) the fact that gradient of, or adjoint solver for, the forward model might not be feasible. While existing Bayesian inference methods meet some of these challenges individually, we propose a framework that tackles all three systematically. Our approach builds upon the Fisher-Rao gradient flow in probability space, yielding a dynamical system for probability densities that converges towards the target distribution at a uniform exponential rate. This rapid convergence is advantageous for the computational burden outlined in (i). We apply Gaussian mixture approximations with operator splitting techniques to simulate the flow numerically; the resulting approximation can capture multiple modes thus addressing (ii). Furthermore, we employ the Kalman methodology to facilitate a derivative-free update of these Gaussian components and their respective weights, addressing the issue in (iii). The proposed methodology results in an efficient derivative-free sampler flexible enough to handle multi-modal distributions: Gaussian Mixture Kalman Inversion (GMKI). The effectiveness of GMKI is demonstrated both theoretically and numerically in several experiments with multimodal target distributions, including proof-of-concept and two-dimensional examples, as well as a large-scale application: recovering the Navier-Stokes initial condition from solution data at positive times.

Temporal causal discovery is a crucial task aimed at uncovering the causal relations within time series data. The latest temporal causal discovery methods usually train deep learning models on prediction tasks to uncover the causality between time series. They capture causal relations by analyzing the parameters of some components of the trained models, e.g., attention weights and convolution weights. However, this is an incomplete mapping process from the model parameters to the causality and fails to investigate the other components, e.g., fully connected layers and activation functions, that are also significant for causal discovery. To facilitate the utilization of the whole deep learning models in temporal causal discovery, we proposed an interpretable transformer-based causal discovery model termed CausalFormer, which consists of the causality-aware transformer and the decomposition-based causality detector. The causality-aware transformer learns the causal representation of time series data using a prediction task with the designed multi-kernel causal convolution which aggregates each input time series along the temporal dimension under the temporal priority constraint. Then, the decomposition-based causality detector interprets the global structure of the trained causality-aware transformer with the proposed regression relevance propagation to identify potential causal relations and finally construct the causal graph. Experiments on synthetic, simulated, and real datasets demonstrate the state-of-the-art performance of CausalFormer on discovering temporal causality. Our code is available at https://github.com/lingbai-kong/CausalFormer.

As large language models (LLMs) become increasingly prevalent in a wide variety of applications, concerns about the safety of their outputs have become more significant. Most efforts at safety-tuning or moderation today take on a predominantly Western-centric view of safety, especially for toxic, hateful, or violent speech. In this paper, we describe LionGuard, a Singapore-contextualized moderation classifier that can serve as guardrails against unsafe LLM outputs. When assessed on Singlish data, LionGuard outperforms existing widely-used moderation APIs, which are not finetuned for the Singapore context, by 14% (binary) and up to 51% (multi-label). Our work highlights the benefits of localization for moderation classifiers and presents a practical and scalable approach for low-resource languages.

This paper addresses the challenge of representing complex human action (HA) in a nuclear power plant (NPP) digital twin (DT) and minimizing latency in partial computation offloading (PCO) in sixth-generation-enabled computing in the network (COIN) assisted multiaccess edge computing (MEC). Accurate HA representation in the DT-HA model is vital for modeling human interventions that are crucial for the safe and efficient operation of NPPs. In this context, DT-enabled COIN-assisted MEC harnesses DT (known as a cybertwin) capabilities to optimize resource allocation and reduce latency effectively. A two-stage approach is employed to address system complexity. First, a probabilistic graphical model (PGM) is introduced to capture HAs in the DT abstraction. In the PGM, HA and NPP asset-twin abstractions form coupled systems that evolve and interact through observable data and control input. Next, the underlying PCO problem is formulated as a multiuser game, where NPP assets can partially offload tasks to COIN and MEC. We propose a decentralized algorithm to optimize offloading decisions, offloading ratios, and resource allocation. The simulation results demonstrate the effectiveness of the proposed method in capturing complex HAs and optimal resource allocation in DT-enabled NPPs.

Mixture of experts is a prediction aggregation method in machine learning that aggregates the predictions of specialized experts. This method often outperforms Bayesian methods despite the Bayesian having stronger inductive guarantees. We argue that this is due to the greater functional capacity of mixture of experts. We prove that in a limiting case of mixture of experts will have greater capacity than equivalent Bayesian methods, which we vouchsafe through experiments on non-limiting cases. Finally, we conclude that mixture of experts is a type of abductive reasoning in the Peircian sense of hypothesis construction.

Reliable uncertainty estimation plays a crucial role in various safety-critical applications such as medical diagnosis and autonomous driving. In recent years, Bayesian neural networks (BayesNNs) have gained substantial research and industrial interests due to their capability to make accurate predictions with reliable uncertainty estimation. However, the algorithmic complexity and the resulting hardware performance of BayesNNs hinder their adoption in real-life applications. To bridge this gap, this paper proposes an algorithm and hardware co-design framework that can generate field-programmable gate array (FPGA)-based accelerators for efficient BayesNNs. At the algorithm level, we propose novel multi-exit dropout-based BayesNNs with reduced computational and memory overheads while achieving high accuracy and quality of uncertainty estimation. At the hardware level, this paper introduces a transformation framework that can generate FPGA-based accelerators for the proposed efficient multi-exit BayesNNs. Several optimization techniques such as the mix of spatial and temporal mappings are introduced to reduce resource consumption and improve the overall hardware performance. Comprehensive experiments demonstrate that our approach can achieve higher energy efficiency compared to CPU, GPU, and other state-of-the-art hardware implementations. To support the future development of this research, we have open-sourced our code at: https://github.com/os-hxfan/MCME_FPGA_Acc.git