Federated Graph Learning (FGL) is tasked with training machine learning models, such as Graph Neural Networks (GNNs), for multiple clients, each with its own graph data. Existing methods usually assume that each client has both node features and graph structure of its graph data. In real-world scenarios, however, there exist federated systems where only a part of the clients have such data while other clients (i.e. graphless clients) may only have node features. This naturally leads to a novel problem in FGL: how to jointly train a model over distributed graph data with graphless clients? In this paper, we propose a novel framework FedGLS to tackle the problem in FGL with graphless clients. In FedGLS, we devise a local graph learner on each graphless client which learns the local graph structure with the structure knowledge transferred from other clients. To enable structure knowledge transfer, we design a GNN model and a feature encoder on each client. During local training, the feature encoder retains the local graph structure knowledge together with the GNN model via knowledge distillation, and the structure knowledge is transferred among clients in global update. Our extensive experiments demonstrate the superiority of the proposed FedGLS over five baselines.

This paper presents a novel feature selection method leveraging the Wasserstein distance to improve feature selection in machine learning. Unlike traditional methods based on correlation or Kullback-Leibler (KL) divergence, our approach uses the Wasserstein distance to assess feature similarity, inherently capturing class relationships and making it robust to noisy labels. We introduce a Markov blanket-based feature selection algorithm and demonstrate its effectiveness. Our analysis shows that the Wasserstein distance-based feature selection method effectively reduces the impact of noisy labels without relying on specific noise models. We provide a lower bound on its effectiveness, which remains meaningful even in the presence of noise. Experimental results across multiple datasets demonstrate that our approach consistently outperforms traditional methods, particularly in noisy settings.

Tsetlin Machines (TMs) have emerged as a compelling alternative to conventional deep learning methods, offering notable advantages such as smaller memory footprint, faster inference, fault-tolerant properties, and interpretability. Although various adaptations of TMs have expanded their applicability across diverse domains, a fundamental gap remains in understanding how TMs quantify uncertainty in their predictions. In response, this paper introduces the Probabilistic Tsetlin Machine (PTM) framework, aimed at providing a robust, reliable, and interpretable approach for uncertainty quantification. Unlike the original TM, the PTM learns the probability of staying on each state of each Tsetlin Automaton (TA) across all clauses. These probabilities are updated using the feedback tables that are part of the TM framework: Type I and Type II feedback. During inference, TAs decide their actions by sampling states based on learned probability distributions, akin to Bayesian neural networks when generating weight values. In our experimental analysis, we first illustrate the spread of the probabilities across TA states for the noisy-XOR dataset. Then we evaluate the PTM alongside benchmark models using both simulated and real-world datasets. The experiments on the simulated dataset reveal the PTM's effectiveness in uncertainty quantification, particularly in delineating decision boundaries and identifying regions of high uncertainty. Moreover, when applied to multiclass classification tasks using the Iris dataset, the PTM demonstrates competitive performance in terms of predictive entropy and expected calibration error, showcasing its potential as a reliable tool for uncertainty estimation. Our findings underscore the importance of selecting appropriate models for accurate uncertainty quantification in predictive tasks, with the PTM offering a particularly interpretable and effective solution.

We consider the problem of sampling a multimodal distribution with a Markov chain given a small number of samples from the stationary measure. Although mixing can be arbitrarily slow, we show that if the Markov chain has a $k$th order spectral gap, initialization from a set of $\tilde O(k/\varepsilon^2)$ samples from the stationary distribution will, with high probability over the samples, efficiently generate a sample whose conditional law is $\varepsilon$-close in TV distance to the stationary measure. In particular, this applies to mixtures of $k$ distributions satisfying a Poincar\'e inequality, with faster convergence when they satisfy a log-Sobolev inequality. Our bounds are stable to perturbations to the Markov chain, and in particular work for Langevin diffusion over $\mathbb R^d$ with score estimation error, as well as Glauber dynamics combined with approximation error from pseudolikelihood estimation. This justifies the success of data-based initialization for score matching methods despite slow mixing for the data distribution, and improves and generalizes the results of Koehler and Vuong (2023) to have linear, rather than exponential, dependence on $k$ and apply to arbitrary semigroups. As a consequence of our results, we show for the first time that a natural class of low-complexity Ising measures can be efficiently learned from samples.

Stability selection is a widely adopted resampling-based framework for high-dimensional structure estimation and variable selection. However, the concept of 'stability' is often narrowly addressed, primarily through examining selection frequencies, or 'stability paths'. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability selection framework, moving beyond single-variable analysis. We suggest that the stability estimator offers two advantages: it can serve as a reference to reflect the robustness of the outcomes obtained and help identify an optimal regularization value to improve stability. By determining this value, we aim to calibrate key stability selection parameters, namely, the decision threshold and the expected number of falsely selected variables, within established theoretical bounds. Furthermore, we explore a novel selection criterion based on this regularization value. With the asymptotic distribution of the stability estimator previously established, convergence to true stability is ensured, allowing us to observe stability trends over successive sub-samples. This approach sheds light on the required number of sub-samples addressing a notable gap in prior studies. The 'stabplot' package is developed to facilitate the use of the plots featured in this manuscript, supporting their integration into further statistical analysis and research workflows.

Often in prediction tasks, the predictive model itself can influence the distribution of the target variable, a phenomenon termed performative prediction. Generally, this influence stems from strategic actions taken by stakeholders with a vested interest in predictive models. A key challenge that hinders the widespread adaptation of performative prediction in machine learning is that practitioners are generally unaware of the social impacts of their predictions. To address this gap, we propose a methodology for learning the distribution map that encapsulates the long-term impacts of predictive models on the population. Specifically, we model agents' responses as a cost-adjusted utility maximization problem and propose estimates for said cost. Our approach leverages optimal transport to align pre-model exposure (ex ante) and post-model exposure (ex post) distributions. We provide a rate of convergence for this proposed estimate and assess its quality through empirical demonstrations on a credit-scoring dataset.

Current implementations of Bayesian Additive Regression Trees (BART) are based on axis-aligned decision rules that recursively partition the feature space using a single feature at a time. Several authors have demonstrated that oblique trees, whose decision rules are based on linear combinations of features, can sometimes yield better predictions than axis-aligned trees and exhibit excellent theoretical properties. We develop an oblique version of BART that leverages a data-adaptive decision rule prior that recursively partitions the feature space along random hyperplanes. Using several synthetic and real-world benchmark datasets, we systematically compared our oblique BART implementation to axis-aligned BART and other tree ensemble methods, finding that oblique BART was competitive with -- and sometimes much better than -- those methods.

An oblivious subspace embedding is a random $m\times n$ matrix $\Pi$ such that, for any $d$-dimensional subspace, with high probability $\Pi$ preserves the norms of all vectors in that subspace within a $1\pm\epsilon$ factor. In this work, we give an oblivious subspace embedding with the optimal dimension $m=\Theta(d/\epsilon^2)$ that has a near-optimal sparsity of $\tilde O(1/\epsilon)$ non-zero entries per column of $\Pi$. This is the first result to nearly match the conjecture of Nelson and Nguyen [FOCS 2013] in terms of the best sparsity attainable by an optimal oblivious subspace embedding, improving on a prior bound of $\tilde O(1/\epsilon^6)$ non-zeros per column [Chenakkod et al., STOC 2024]. We further extend our approach to the non-oblivious setting, proposing a new family of Leverage Score Sparsified embeddings with Independent Columns, which yield faster runtimes for matrix approximation and regression tasks. In our analysis, we develop a new method which uses a decoupling argument together with the cumulant method for bounding the edge universality error of isotropic random matrices. To achieve near-optimal sparsity, we combine this general-purpose approach with new traces inequalities that leverage the specific structure of our subspace embedding construction.

We consider data-driven inventory and pricing decisions in the feature-based newsvendor problem, where demand is influenced by both price and contextual features and is modeled without any structural assumptions. The unknown demand distribution results in a challenging conditional stochastic optimization problem, further complicated by decision-dependent uncertainty and the integration of features. Inspired by recent advances in deep generative learning, we propose a novel approach leveraging conditional deep generative models (cDGMs) to address these challenges. cDGMs learn the demand distribution and generate probabilistic demand forecasts conditioned on price and features. This generative approach enables accurate profit estimation and supports the design of algorithms for two key objectives: (1) optimizing inventory for arbitrary prices, and (2) jointly determining optimal pricing and inventory levels. We provide theoretical guarantees for our approach, including the consistency of profit estimation and convergence of our decisions to the optimal solution. Extensive simulations-ranging from simple to complex scenarios, including one involving textual features-and a real-world case study demonstrate the effectiveness of our approach. Our method opens a new paradigm in management science and operations research, is adaptable to extensions of the newsvendor and pricing problems, and holds potential for solving other conditional stochastic optimization problems.

This study investigates the impact of quantity and diversity of data on the performance of various machine-learning models for detecting general EEG pathology. We utilized an EEG dataset of 2,993 recordings from Temple University Hospital and a dataset of 55,787 recordings from Elmiko Biosignals sp. z o.o. The latter contains data from 39 hospitals and a diverse patient set with varied conditions. Thus, we introduce the Elmiko dataset - the largest publicly available EEG corpus. Our findings show that small and consistent datasets enable a wide range of models to achieve high accuracy; however, variations in pathological conditions, recording protocols, and labeling standards lead to significant performance degradation. Nonetheless, increasing the number of available recordings improves predictive accuracy and may even compensate for data diversity, particularly in neural networks based on attention mechanism or transformer architecture. A meta-model that combined these networks with a gradient-boosting approach using handcrafted features demonstrated superior performance across varied datasets.