Counterfactual explanations have emerged as an important tool to understand, debug, and audit complex machine learning models. To offer global counterfactual explainability, state-of-the-art methods construct summaries of local explanations, offering a trade-off among conciseness, counterfactual effectiveness, and counterfactual cost or burden imposed on instances. In this work, we provide a concise formulation of the problem of identifying global counterfactuals and establish principled criteria for comparing solutions, drawing inspiration from Pareto dominance. We introduce innovative algorithms designed to address the challenge of finding global counterfactuals for either the entire input space or specific partitions, employing clustering and decision trees as key components. Additionally, we conduct a comprehensive experimental evaluation, considering various instances of the problem and comparing our proposed algorithms with state-of-the-art methods. The results highlight the consistent capability of our algorithms to generate meaningful and interpretable global counterfactual explanations.

Partially class-disjoint data (PCDD), a common yet under-explored data formation where each client contributes a part of classes (instead of all classes) of samples, severely challenges the performance of federated algorithms. Without full classes, the local objective will contradict the global objective, yielding the angle collapse problem for locally missing classes and the space waste problem for locally existing classes. As far as we know, none of the existing methods can intrinsically mitigate PCDD challenges to achieve holistic improvement in the bilateral views (both global view and local view) of federated learning. To address this dilemma, we are inspired by the strong generalization of simplex Equiangular Tight Frame (ETF) on the imbalanced data, and propose a novel approach called FedGELA where the classifier is globally fixed as a simplex ETF while locally adapted to the personal distributions. Globally, FedGELA provides fair and equal discrimination for all classes and avoids inaccurate updates of the classifier, while locally it utilizes the space of locally missing classes for locally existing classes. We conduct extensive experiments on a range of datasets to demonstrate that our FedGELA achieves promising performance (averaged improvement of 3.9% to FedAvg and 1.5% to best baselines) and provide both local and global convergence guarantees.

Handling missing data is crucial in machine learning, but many datasets contain gaps due to errors or non-response. Unlike traditional methods such as listwise deletion, which are simple but inadequate, the literature offers more sophisticated and effective methods, thereby improving sample size and accuracy. However, these methods require accessing the whole dataset, which contradicts the privacy regulations when the data is distributed among multiple sources. Especially in the medical and healthcare domain, such access reveals sensitive information about patients. This study addresses privacy-preserving imputation methods for sensitive data using secure multi-party computation, enabling secure computations without revealing any party's sensitive information. In this study, we realized the mean, median, regression, and kNN imputation methods in a privacy-preserving way. We specifically target the medical and healthcare domains considering the significance of protection of the patient data, showcasing our methods on a diabetes dataset. Experiments on the diabetes dataset validated the correctness of our privacy-preserving imputation methods, yielding the largest error around $3 \times 10^{-3}$, closely matching plaintext methods. We also analyzed the scalability of our methods to varying numbers of samples, showing their applicability to real-world healthcare problems. Our analysis demonstrated that all our methods scale linearly with the number of samples. Except for kNN, the runtime of all our methods indicates that they can be utilized for large datasets.

Unsupervised Continual Learning (UCL) is a burgeoning field in machine learning, focusing on enabling neural networks to sequentially learn tasks without explicit label information. Catastrophic Forgetting (CF), where models forget previously learned tasks upon learning new ones, poses a significant challenge in continual learning, especially in UCL, where labeled information of data is not accessible. CF mitigation strategies, such as knowledge distillation and replay buffers, often face memory inefficiency and privacy issues. Although current research in UCL has endeavored to refine data representations and address CF in streaming data contexts, there is a noticeable lack of algorithms specifically designed for unsupervised clustering. To fill this gap, in this paper, we introduce the concept of Unsupervised Continual Clustering (UCC). We propose Forward-Backward Knowledge Distillation for unsupervised Continual Clustering (FBCC) to counteract CF within the context of UCC. FBCC employs a single continual learner (the ``teacher'') with a cluster projector, along with multiple student models, to address the CF issue. The proposed method consists of two phases: Forward Knowledge Distillation, where the teacher learns new clusters while retaining knowledge from previous tasks with guidance from specialized student models, and Backward Knowledge Distillation, where a student model mimics the teacher's behavior to retain task-specific knowledge, aiding the teacher in subsequent tasks. FBCC marks a pioneering approach to UCC, demonstrating enhanced performance and memory efficiency in clustering across various tasks, outperforming the application of clustering algorithms to the latent space of state-of-the-art UCL algorithms.

This work introduces the Supervised Expectation-Maximization Framework (SEMF), a versatile and model-agnostic framework that generates prediction intervals for datasets with complete or missing data. SEMF extends the Expectation-Maximization (EM) algorithm, traditionally used in unsupervised learning, to a supervised context, enabling it to extract latent representations for uncertainty estimation. The framework demonstrates robustness through extensive empirical evaluation across 11 tabular datasets, achieving$\unicode{x2013}$in some cases$\unicode{x2013}$narrower normalized prediction intervals and higher coverage than traditional quantile regression methods. Furthermore, SEMF integrates seamlessly with existing machine learning algorithms, such as gradient-boosted trees and neural networks, exemplifying its usefulness for real-world applications. The experimental results highlight SEMF's potential to advance state-of-the-art techniques in uncertainty quantification.

Deep neural networks based on state space models (SSMs) are attracting much attention in sequence modeling since their computational cost is significantly smaller than that of Transformers. While the capabilities of SSMs have been primarily investigated through experimental comparisons, theoretical understanding of SSMs is still limited. In particular, there is a lack of statistical and quantitative evaluation of whether SSM can replace Transformers. In this paper, we theoretically explore in which tasks SSMs can be alternatives of Transformers from the perspective of estimating sequence-to-sequence functions. We consider the setting where the target function has direction-dependent smoothness and prove that SSMs can estimate such functions with the same convergence rate as Transformers. Additionally, we prove that SSMs can estimate the target function, even if the smoothness changes depending on the input sequence, as well as Transformers. Our results show the possibility that SSMs can replace Transformers when estimating the functions in certain classes that appear in practice.

In deterministic optimization, adaptive stepsize strategies, such as line search (see [39], therein), AdaGrad-Norm [55], Polyak stepsize [46], and others were developed to provide stability and improve efficiency and adaptivity to unknown parameters. While the practical benefits for deterministic optimization problems are well-documented, much of our understanding of adaptive learning rate strategies for stochastic algorithms are still in their infancy. There are many adaptive learning rate strategies used in machine learning with many design goals. Some are known to adapt to SGD gradient noise while others are robust to hyper-parameters (e.g., [4, 59]). Theoretical results for adaptive algorithms tend to focus on guaranteeing minimax-optimal rates, but this theory is not engineered to provide realistic performance comparisons; indeed many adaptive algorithms are minimax-optimal, and so more precise statements are needed to distinguish them. For instance, the exact learning rates (or rate schedules) to which these strategies converge are unknown, nor their dependence on the geometry of the problem. Moreover, we often do not know how these adaptive stepsizes compare with well-tuned constant or decaying fixed learning rate stochastic gradient descent (SGD), which can be viewed as a cost associated with selecting the adaptive strategy in comparison to tuning by hand.

In applied statistics and machine learning, the "gold standards" used for training are often biased and almost always noisy. Dawid and Skene's justifiably popular crowdsourcing model adjusts for rater (coder, annotator) sensitivity and specificity, but fails to capture distributional properties of rating data gathered for training, which in turn biases training. In this study, we introduce a general purpose measurement-error model with which we can infer consensus categories by adding item-level effects for difficulty, discriminativeness, and guessability. We further show how to constrain the bimodal posterior of these models to avoid (or if necessary, allow) adversarial raters. We validate our model's goodness of fit with posterior predictive checks, the Bayesian analogue of $\chi^2$ tests. Dawid and Skene's model is rejected by goodness of fit tests, whereas our new model, which adjusts for item heterogeneity, is not rejected. We illustrate our new model with two well-studied data sets, binary rating data for caries in dental X-rays and implication in natural language.

The effectiveness of anomaly signal detection can be significantly undermined by the inherent uncertainty of relying on one specified model. Under the framework of model average methods, this paper proposes a novel criterion to select the weights on aggregation of multiple models, wherein the focal loss function accounts for the classification of extremely imbalanced data. This strategy is further integrated into Random Forest algorithm by replacing the conventional voting method. We have evaluated the proposed method on benchmark datasets across various domains, including network intrusion. The findings indicate that our proposed method not only surpasses the model averaging with typical loss functions but also outstrips common anomaly detection algorithms in terms of accuracy and robustness.

We develop algorithms for online linear regression which achieve optimal static and dynamic regret guarantees \emph{even in the complete absence of prior knowledge}. We present a novel analysis showing that a discounted variant of the Vovk-Azoury-Warmuth forecaster achieves dynamic regret of the form $R_{T}(\vec{u})\le O\left(d\log(T)\vee \sqrt{dP_{T}^{\gamma}(\vec{u})T}\right)$, where $P_{T}^{\gamma}(\vec{u})$ is a measure of variability of the comparator sequence, and show that the discount factor achieving this result can be learned on-the-fly. We show that this result is optimal by providing a matching lower bound. We also extend our results to \emph{strongly-adaptive} guarantees which hold over every sub-interval $[a,b]\subseteq[1,T]$ simultaneously.