Generalization under distribution shift remains a core challenge in modern machine learning, yet existing learning bound theory is limited to narrow, idealized settings and is non-estimable from samples. In this paper, we bridge the gap between theory and practical applications. We first show that existing bounds become loose and non-estimable because their concept shift definition breaks when the source and target supports mismatch. Leveraging entropic optimal transport, we propose new support-agnostic definitions for covariate and concept shifts, and derive a novel unified error bound that applies to broad loss functions, label spaces, and stochastic labeling. We further develop estimators for these shifts with concentration guarantees, and the DataShifts algorithm, which can quantify distribution shifts and estimate the error bound in most applications -- a rigorous and general tool for analyzing learning error under distribution shift.

Researchers in urban and regional studies increasingly deal with spatial data that reflects geographic location and spatial relationships. As a framework for dealing with the unique nature of spatial data, various spatial regression models have been introduced. In this article, a novel model-based gradient boosting algorithm for spatial regression models with autoregressive disturbances is proposed. Due to the modular nature, the approach provides an alternative estimation procedure which is feasible even in high-dimensional settings where established quasi-maximum likelihood or generalized method of moments estimators do not yield unique solutions. The approach additionally enables data-driven variable and model selection in low- as well as high-dimensional settings. Since the bias-variance trade-off is also controlled in the algorithm, implicit regularization is imposed which improves prediction accuracy on out-of-sample spatial data. Detailed simulation studies regarding the performance of estimation, prediction and variable selection in low- and high-dimensional settings confirm proper functionality of the proposed methodology. To illustrative the functionality of the model-based gradient boosting algorithm, a case study is presented where the life expectancy in German districts is modeled incorporating a potential spatial dependence structure.

We propose a graph semi-supervised learning framework for classification tasks on data manifolds. Motivated by the manifold hypothesis, we model data as points sampled from a low-dimensional manifold $\mathcal{M} \subset \mathbb{R}^F$. The manifold is approximated in an unsupervised manner using a variational autoencoder (VAE), where the trained encoder maps data to embeddings that represent their coordinates in $\mathbb{R}^F$. A geometric graph is constructed with Gaussian-weighted edges inversely proportional to distances in the embedding space, transforming the point classification problem into a semi-supervised node classification task on the graph. This task is solved using a graph neural network (GNN). Our main contribution is a theoretical analysis of the statistical generalization properties of this data-to-manifold-to-graph pipeline. We show that, under uniform sampling from $\mathcal{M}$, the generalization gap of the semi-supervised task diminishes with increasing graph size, up to the GNN training error. Leveraging a training procedure which resamples a slightly larger graph at regular intervals during training, we then show that the generalization gap can be reduced even further, vanishing asymptotically. Finally, we validate our findings with numerical experiments on image classification benchmarks, demonstrating the empirical effectiveness of our approach.

ADMM is a popular method for federated deep learning which originated in the 1970s and, even though many new variants of it have been proposed since then, its core algorithmic structure has remained unchanged. Here, we take a major departure from the old structure and present a fundamentally new way to derive and extend federated ADMM. We propose to use a structure called Bayesian Duality which exploits a duality of the posterior distributions obtained by solving a variational-Bayesian reformulation of the original problem. We show that this naturally recovers the original ADMM when isotropic Gaussian posteriors are used, and yields non-trivial extensions for other posterior forms. For instance, full-covariance Gaussians lead to Newton-like variants of ADMM, while diagonal covariances result in a cheap Adam-like variant. This is especially useful to handle heterogeneity in federated deep learning, giving up to 7% accuracy improvements over recent baselines. Our work opens a new Bayesian path to improve primal-dual methods.

The long horizon forecasting (LHF) problem has come up in the time series literature for over the last 35 years or so. This review covers aspects of LHF in this period and how deep learning has incorporated variants of trend, seasonality, fourier and wavelet transforms, misspecification bias reduction and bandpass filters while contributing using convolutions, residual connections, sparsity reduction, strided convolutions, attention masks, SSMs, normalization methods, low-rank approximations and gating mechanisms. We highlight time series decomposition techniques, input data preprocessing and dataset windowing schemes that improve performance. Multi-layer perceptron models, recurrent neural network hybrids, self-attention models that improve and/or address the performances of the LHF problem are described, with an emphasis on the feature space construction. Ablation studies are conducted over the ETTm2 dataset in the multivariate and univariate high useful load (HUFL) forecasting contexts, evaluated over the last 4 months of the dataset. The heatmaps of MSE averages per time step over test set series in the horizon show that there is a steady increase in the error proportionate to its length except with xLSTM and Triformer models and motivate LHF as an error propagation problem. The trained models are available here: https://bit.ly/LHFModelZoo

While contrastive multi-view clustering has achieved remarkable success, it implicitly assumes balanced class distribution. However, real-world multi-view data primarily exhibits class imbalance distribution. Consequently, existing methods suffer performance degradation due to their inability to perceive and model such imbalance. To address this challenge, we present the first systematic study of imbalanced multi-view clustering, focusing on two fundamental problems: i. perceiving class imbalance distribution, and ii. mitigating representation degradation of minority samples. We propose PROTOCOL, a novel PaRtial Optimal TranspOrt-enhanced COntrastive Learning framework for imbalanced multi-view clustering. First, for class imbalance perception, we map multi-view features into a consensus space and reformulate the imbalanced clustering as a partial optimal transport (POT) problem, augmented with progressive mass constraints and weighted KL divergence for class distributions. Second, we develop a POT-enhanced class-rebalanced contrastive learning at both feature and class levels, incorporating logit adjustment and class-sensitive learning to enhance minority sample representations. Extensive experiments demonstrate that PROTOCOL significantly improves clustering performance on imbalanced multi-view data, filling a critical research gap in this field.

Neural networks have revolutionized supervised learning, but their internal complexity often renders their learned functions opaque. In effect, they behave as black boxes. This lack of interpretability hinders trust, accountability, and transparency--especially in high-stakes domains such as healthcare, finance, and criminal justice, where understanding a model's decisions can be as important as their accuracy. While many techniques exist for interpreting classification networks--such as saliency maps, feature attribution methods like LIME [10] and SHAP [6], and probing approaches [1]--the interpretability of regression networks remains comparatively underexplored, especially at the level of input-output function behavior [6, 14]. One common strategy in model interpretability is to approximate a complex system with a simpler, interpretable surrogate, such as a linear model or decision tree [3, 12]. In classification settings, surrogate models are often applied to internal representations to evaluate the linear accessibility of information at each layer [1, 5]. However, in regression tasks, there has been limited work focused on assessing the linearity of a network's full input-output function. In this paper, we introduce a simple yet powerful idea: we quantify how linearly decodable a trained regression network's output function is.

Inorganic synthesis planning currently relies primarily on heuristic approaches or machine-learning models trained on limited datasets, which constrains its generality. We demonstrate that language models, without task-specific fine-tuning, can recall synthesis conditions. Off-the-shelf models, such as GPT-4.1, Gemini 2.0 Flash and Llama 4 Maverick, achieve a Top-1 precursor-prediction accuracy of up to 53.8 % and a Top-5 performance of 66.1 % on a held-out set of 1,000 reactions. They also predict calcination and sintering temperatures with mean absolute errors below 126 °C, matching specialized regression methods. Ensembling these language models further enhances predictive accuracy and reduces inference cost per prediction by up to 70 %. We subsequently employ language models to generate 28,548 synthetic reaction recipes, which we combine with literature-mined examples to pretrain a transformer-based model, SyntMTE. After fine-tuning on the combined dataset, SyntMTE reduces mean-absolute error in sintering temperature prediction to 73 °C and in calcination temperature to 98 °C. This strategy improves models by up to 8.7 % compared with baselines trained exclusively on experimental data. Finally, in a case study on Li7La3Zr2O12 solid-state electrolytes, we demonstrate that SyntMTE reproduces the experimentally observed dopant-dependent sintering trends. Our hybrid workflow enables scalable, data-efficient inorganic synthesis planning.

Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL) divergence. In this paper, we focus on the following parametric family: mixtures of isotropic Gaussians (i.e., with diagonal covariance matrices proportional to the identity) and uniform weights. We develop a variational framework and provide efficient algorithms suited for this family. In contrast with mixtures of Gaussian with generic covariance matrices, this choice presents a balance between accurate approximations of multimodal Bayesian posteriors, while being memory and computationally efficient. Our algorithms implement gradient descent on the location of the mixture components (the modes of the Gaussians), and either (an entropic) Mirror or Bures descent on their variance parameters. We illustrate the performance of our algorithms on numerical experiments.

In high-dimensional statistics, the primary goal is to derive computationally efficient estimation procedures, achieving the best possible statistical performance. Y et, in many problems, such as sparse PCA, planted clique or clustering, the best known algorithms with polynomial-time complexity are unable to match the performances provably achievable by the best estimators (without computational constraints). This observation has lead to several conjectures on the existence of gaps (called statistical-computational gaps) between the optimal statistical performance, i.e. the best performance achievable without computational constraints, and the best performance achievable by polynomial time algorithms. In particular, to assess the quality of a computationally efficient algorithm for a given task, the theoretical performance should not be compared to the optimal statistical performance (without computational constraints), but to the performance of the best poly-time algorithm. This raises the problem of establishing lower-bounds on the performance of the best poly-time algorithms for a wide range of problems. Since high-dimensional statistics deal with random instances, the classical notions of worst-case hardness, such as P, NP, etc are not suitable for the high-dimensional framework. Instead, lower bounds are obtained for some specific models of computations, such as SoS [38, 10], overlap gap property [32], statistical query [41, 13], and low-degree polynomials [37, 44, 66], possibly combined with reductions between different statistical problems [12, 11, 14].