Healthcare decision-making requires not only accurate predictions but also insights into how factors influence patient outcomes. While traditional Machine Learning (ML) models excel at predicting outcomes, such as identifying high risk patients, they are limited in addressing what-if questions about interventions. This study introduces the Probabilistic Causal Fusion (PCF) framework, which integrates Causal Bayesian Networks (CBNs) and Probability Trees (PTrees) to extend beyond predictions. PCF leverages causal relationships from CBNs to structure PTrees, enabling both the quantification of factor impacts and simulation of hypothetical interventions. PCF was validated on three real-world healthcare datasets i.e. MIMIC-IV, Framingham Heart Study, and Diabetes, chosen for their clinically diverse variables. It demonstrated predictive performance comparable to traditional ML models while providing additional causal reasoning capabilities. To enhance interpretability, PCF incorporates sensitivity analysis and SHapley Additive exPlanations (SHAP). Sensitivity analysis quantifies the influence of causal parameters on outcomes such as Length of Stay (LOS), Coronary Heart Disease (CHD), and Diabetes, while SHAP highlights the importance of individual features in predictive modeling. By combining causal reasoning with predictive modeling, PCF bridges the gap between clinical intuition and data-driven insights. Its ability to uncover relationships between modifiable factors and simulate hypothetical scenarios provides clinicians with a clearer understanding of causal pathways. This approach supports more informed, evidence-based decision-making, offering a robust framework for addressing complex questions in diverse healthcare settings.

In statistical classification and machine learning, classification error is an important performance measure, which is minimized by the Bayes decision rule. In practice, the unknown true distribution is usually replaced with a model distribution estimated from the training data in the Bayes decision rule. This substitution introduces a mismatch between the Bayes error and the model-based classification error. In this work, we apply classification error bounds to study the relationship between the error mismatch and the Kullback-Leibler divergence in machine learning. Motivated by recent observations of low model-based classification errors in many machine learning tasks, bounding the Bayes error to be lower, we propose a linear approximation of the classification error bound for low Bayes error conditions. Then, the bound for class priors are discussed. Moreover, we extend the classification error bound for sequences. Using automatic speech recognition as a representative example of machine learning applications, this work analytically discusses the correlations among different performance measures with extended bounds, including cross-entropy loss, language model perplexity, and word error rate.

We tackle the problem of informative input design for system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a methodology that is compatible with any system and parametric family of models. Our approach only requires input-output data from the system and first-order information from the model with respect to the parameters. Our algorithm consists of two modules. First, we formulate the problem of system identification from a Bayesian perspective and propose an approximate iterative method to optimize the model's parameters. Based on this Bayesian formulation, we are able to define a Gaussian-based uncertainty measure for the model parameters, which we can then minimize with respect to the next selected input. Our method outperforms model-free baselines with various linear and nonlinear dynamics.

Depending on their sophistication level, sensors can be classified ranging from simple sensors that directly measure single physical parameters (e.g., ambient light sensors and temperature sensors) to complex intelligent sensors, which determine parameters of the surrounding environment through wide spectrum signals (e.g., radio frequency/radar and light/video); besides measuring, they perform data processing and are enabled to carry out actuations. Whereas intelligent sensors make use of data of a different nature underneath, in which complex and nonlinear behaviors are codified; data-mining techniques used jointly with machine learning (ML) algorithms have shown adequate performance for modeling this hidden information. As intelligent sensors often rely on complex sensors and sensor fusion techniques, the data processing power they need can only be provided by high-performance computational platforms such as microprocessors, graphics-processing units (GPUs), or field-programmable gate arrays (FPGAs). In particular, FPGA-based implementations stand out due to the extremely high operational frequencies and low power consumption they can achieve, even for complex, multilayered algorithms [1]. In the context of the automotive field, intelligent sensors are key components of current assistance systems.

As one of the most fundamental models, meta learning aims to effectively address few-shot learning challenges. However, it still faces significant issues related to the training data, such as training inefficiencies due to numerous low-contribution tasks in large datasets and substantial noise from incorrect labels. Thus, training data attribution methods are needed for meta learning. However, the dual-layer structure of mata learning complicates the modeling of training data contributions because of the interdependent influence between meta-parameters and task-specific parameters, making existing data influence evaluation tools inapplicable or inaccurate. To address these challenges, based on the influence function, we propose a general data attribution evaluation framework for meta-learning within the bilevel optimization framework. Our approach introduces task influence functions (task-IF) and instance influence functions (instance-IF) to accurately assess the impact of specific tasks and individual data points in closed forms. This framework comprehensively models data contributions across both the inner and outer training processes, capturing the direct effects of data points on meta-parameters as well as their indirect influence through task-specific parameters. We also provide several strategies to enhance computational efficiency and scalability. Experimental results demonstrate the framework's effectiveness in training data evaluation via several downstream tasks.

Minor comments: - The panel labels have inconsistent styles. Some are just the label with a period, some have parentheses with a period, some have parentheses without a period.

The article considers a novel application of the recurrent switching linear dynamical system model to denoising dendritic voltages. The paper is very well written, the problem well motivated with compelling experiments.

The authors compare the ranks of tensor representations of HMM, and outputs of quantum circuits with two qubit unitary gates yielding Matrix product States (MPS) and so-called Locally Purified States (LPS) when ancillary unmeasured bits are present. A general comment: Born machines automaticaly enforce positivity but is it clear that 83) and (4) are less than 1? The A's come from some unitary circuits in SM? If yes the main problem formulation seems not selfcontained in sect.2. Some are more surprizing namely the very large (at least of the order of the number of qubits) difference in rank when one works in the real field versus complex field.

There's some space to improve for the experiments. I think the main contribution of this paper is proposing a method to transform the complicated neural network structure to a nonlinear feature mapping function, so that they can linearly separate the weight and feature mapping. Given the feature mapping, kernels/correlations and posterior distributions over output functions can be explicitly built for BNN (or DNN). Therefore, I would expect to see 1. What does this feature mapping look like? I think the authors show the kernel instead of the mapping itself.

This paper demonstrates theoretically that multiple forms of approximate Bayesian inference (Laplace approximation and variational inference) for deep neural networks are equivalent to Gaussian processes. The authors formalize this connection and write out the GP covariance function corresponding to these networks, which surprisingly turns out to be the neural tangent kernel. The authors also establish a connection to the training procedure of the neural network and GPs, which is a novel contribution. There is a growing literature on the connection between neural networks and Gaussian processes, with a variety of papers establishing the connection in the infinite limit of hidden units. This paper adds nicely to that literature, developing a connection to approximate Bayesian inference.