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.

Weaknesses: Overall, I thought this was a strong paper. The main concerns I had were as follows: (1) Mode-seeking versus showing the distribution: The aggregated results in the first experiment seem to show much more homogeneity than the results for GSP or MCMCP. It seems like one limitation of this approach might be that there is limited exploration of the space, perhaps making it hard to move between modes, and also makes it more difficult to see the full shape of the distribution, which I have often taken to be a goal in work using MCMCP. The movement between optimization and seeking a distribution is discussed to some extent in the paper, but I would be interested in seeing this discussed more (and perhaps whether GP without aggregation is likely to lead to more optimization than MCMCP). In the author response, they have shown additional information suggesting that GSP is more mode-seeking but also does a better job of capturing the distribution.

This paper introduces a new method for eliciting human representations of perceptual concepts, such as what RGB values people think correspond to the color "sunset" or what auditory dimensions (e.g. Rather than eliciting representations via guess-and-check (i.e., start with a dataset and then apply human-generated labels), this method (Gibbs Sampling with People, or GSP) enables inference to go in the other direction (i.e., start with labels, and then identify percepts that match those labels). GSP extends prior work (MCMC with People) to allow eliciting representations of much higher-dimensional stimuli. The reviewers unanimously praised this paper for tackling an important and relevant problem in cognitive science, for its breadth of empirical results, and for its novelty over prior work. R2 stated that the paper is "impressive in scale, scope, and results", R3 stated that it was "very relevant to the NeurIPS community and very novel", and R4 felt there could be "a potentially large impact of this work" with "substantial interest" amongst the NeurIPS community.

Recent years have witnessed an upsurge of interest in employing flexible machine learning models for instrumental variable (IV) regression, but the development of uncertainty quantification methodology is still lacking. In this work we present a scalable quasi-Bayesian procedure for IV regression, building upon the recently developed kernelized IV models. Contrary to Bayesian modeling for IV, our approach does not require additional assumptions on the data generating process, and leads to a scalable approximate inference algorithm with time cost comparable to the corresponding point estimation methods. Our algorithm can be further extended to work with neural network models. We analyze the theoretical properties of the proposed quasi-posterior, and demonstrate through empirical evaluation the competitive performance of our method.

Weaknesses: My main questions regarding the paper: 1) When computing the Laplace approximation, this still requires calculation of the Hessian, which I believe is with respect to the latent (theta). This is referred to as W in Algorithm 1. Would it be possible to comment further on the kind of trade-off between implementing full-HMC, versus the overhead of calculating the Hessian. I think this is the issue you are referring to in the second paragraph of the discussion section, whereby you mention higher-order automatic differentiation. I assume you stick to analytical Hessians (e.g. For example "Semi-Separable Hamiltonian Monte Carlo for Inference in Bayesian Hierarchical Models" by Zhang and Sutton jointly sample over hyperparameters and parameters to overcome similar funnel-like behaviours to that of the Gaussian latent variable models that you explore.