The paper studied the online experimental design problem where there are temporal dependencies between the two control policies/treatments. The novelty of the problem setup and the theoretical analysis in the paper are appreciated by all the reviewers. Although the analysis is the main contribution, the paper would be much stronger if there are meaningful experiments on toy problems to showcase the performance the online MLE-based approach vs the standard experimental design approaches.

This paper contributes a new technique for the estimation of structure in continuous time Bayesian networks, and completes the picture with an accompanying inference method and an illustration on a real-world problem. There is agreement among reviewers that this is a high quality contribution, if one takes the confidence-weighted scores from reviewers into account. As a point for improvement for the paper, we could reiterate a comment that was raised in the reviewer discussion: "[the paper] is missing reasonable and helpful experimental comparisons that are not hard to do, given that the code exists already in CTBN-RLE" and the authors are encouraged to consider broadening their experimental comparisons for a final published version.

Variational autoencoders (VAEs) are a popular framework for modeling complex data distributions; they can be efficiently trained via variational inference by maximizing the evidence lower bound (ELBO), at the expense of a gap to the exact (log-)marginal likelihood. While VAEs are commonly used for representation learning, it is unclear why ELBO maximization would yield useful representations, since unregularized maximum likelihood estimation cannot invert the data-generating process. Yet, VAEs often succeed at this task. We seek to elucidate this apparent paradox by studying nonlinear VAEs in the limit of near-deterministic decoders. We first prove that, in this regime, the optimal encoder approximately inverts the decoder---a commonly used but unproven conjecture---which we refer to as self-consistency.

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.

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.

Active Learning (AL) is a sequential learning approach aiming at selecting the most informative data for model training. In many systems, safety constraints appear during data evaluation, requiring the development of safe AL methods. Key challenges of AL are the repeated model training and acquisition optimization required for data selection, which become particularly restrictive under safety constraints. This repeated effort often creates a bottleneck, especially in physical systems requiring real-time decision-making. In this paper, we propose a novel amortized safe AL framework. By leveraging a pretrained neural network policy, our method eliminates the need for repeated model training and acquisition optimization, achieving substantial speed improvements while maintaining competitive learning outcomes and safety awareness. The policy is trained entirely on synthetic data utilizing a novel safe AL objective. The resulting policy is highly versatile and adapts to a wide range of systems, as we demonstrate in our experiments. Furthermore, our framework is modular and we empirically show that we also achieve superior performance for unconstrained time-sensitive AL tasks if we omit the safety requirement.

Federated learning collaboratively trains a neural network on a global server, where each local client receives the current global model weights and sends back parameter updates (gradients) based on its local private data. The process of sending these model updates may leak client's private data information. Existing gradient inversion attacks can exploit this vulnerability to recover private training instances from a client's gradient vectors. Recently, researchers have proposed advanced gradient inversion techniques that existing defenses struggle to handle effectively. In this work, we present a novel defense tailored for large neural network models. Our defense capitalizes on the high dimensionality of the model parameters to perturb gradients within a subspace orthogonal to the original gradient. By leveraging cold posteriors over orthogonal subspaces, our defense implements a refined gradient update mechanism. This enables the selection of an optimal gradient that not only safeguards against gradient inversion attacks but also maintains model utility. We conduct comprehensive experiments across three different datasets and evaluate our defense against various state-of-the-art attacks and defenses. Code is available at https://censor-gradient.github.io.