In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as is the case with text data. Sequential Monte Carlo (SMC) methods give a natural way of representing and updating this uncertainty over time, but have prohibitive memory requirements for large-scale problems. We propose a novel SMC algorithm that decomposes clustering problems into approximately independent subproblems, allowing a more compact representation of the algorithm state. Our approach is motivated by the knowledge base construction problem, and we show that our method is able to accurately and efficiently solve clustering problems in this setting and others where traditional SMC struggles.

Neural network classifiers trained with cross-entropy loss achieve strong predictive accuracy but lack the capability to provide inherent predictive uncertainty estimates, thus requiring external techniques to obtain these estimates. In addition, softmax scores for the true class can vary substantially across independent training runs, which limits the reliability of uncertainty-based decisions in downstream tasks. Evidential Deep Learning aims to address these limitations by producing uncertainty estimates in a single pass, but evidential training is highly sensitive to design choices including loss formulation, prior regularization, and activation functions. Therefore, this work introduces an alternative Dirichlet parameter estimation strategy by applying a method of moments estimator to ensembles of softmax outputs, with an optional maximum-likelihood refinement step. This ensemble-based construction decouples uncertainty estimation from the fragile evidential loss design while also mitigating the variability of single-run cross-entropy training, producing explicit Dirichlet predictive distributions. Across multiple datasets, we show that the improved stability and predictive uncertainty behavior of these ensemble-derived Dirichlet estimates translate into stronger performance in downstream uncertainty-guided applications such as prediction confidence scoring and selective classification.

We consider the problem of recommending relevant labels (items) for a given data point (user). In particular, we are interested in the practically important setting where the evaluation is with respect to non-decomposable (over labels) performance metrics like the $F_1$ measure, \emph{and} training data has missing labels. To this end, we propose a generic framework that given a performance metric $\Psi$, can devise a regularized objective function and a threshold such that all the values in the predicted score vector above and only above the threshold are selected to be positive. We show that the regret or generalization error in the given metric $\Psi$ is bounded ultimately by estimation error of certain underlying parameters. In particular, we derive regret bounds under three popular settings: a) collaborative filtering, b) multilabel classification, and c) PU (positive-unlabeled) learning. For each of the above problems, we can obtain precise non-asymptotic regret bound which is small even when a large fraction of labels is missing. Our empirical results on synthetic and benchmark datasets demonstrate that by explicitly modeling for missing labels and optimizing the desired performance metric, our algorithm indeed achieves significantly better performance (like $F_1$ score) when compared to methods that do not model missing label information carefully.

The process for calculating these metrics is described in Appendix C. Moreover, to ensure the comparability between prediction performance metrics and driving performance metrics in the radar plot, we normalize all metrics to the scale of [0, 1]. In the subsequent section, we provide an overview of the DESPOT planner. These two values can only be inferred from history. The safety is represented by the normalized collision rate.

We proceed to compute the variances of each estimator. The proof also holds for the non-zero mean case trivially. Causal model details for Section 5.2 In Section 5.2, We include a wide range of machine learning-based causal inference methods to evaluate the performance of causal error estimators. Others configs are kept as default. The others are kept as default.

This raises an obvious question,how should the cost-tradeoffs be chosen so that it reflects the expert'sdecision-making?