We develop a statistical learning theory for gradient boosting applied to the estimation of covariate-dependent Generalized Pareto (GP) distributions in the context of Peaks-over-Threshold modeling. After an orthogonal reparametrization of the GP likelihood that diagonalizes its Fisher information matrix, we cast the estimation problem within the Empirical Risk Minimization (ERM) framework and derive non-asymptotic error bounds for the boosting estimator. Our analysis accounts for three distinct sources of error in the process: statistical fluctuations, the approximation bias inherent to the asymptotic nature of the GP model-controlled under second-order regular variation-and the approximation error associated with the finite number of boosting iterates, making explicit the resulting bias-variance trade-off. We illustrate the practical benefits of the reparametrization through simulations, showing that it significantly reduces gradient correlation during training and improves convergence stability. The methodology is applied to a medical malpractice insurance dataset from the Texas Department of Insurance, comprising over 18 000 closed claims. The gradient boosting approach yields a good fit for the tail of settlement cost distributions and reveals that the number of days to settlement is the dominant predictor of tail heaviness, consistent with earlier findings in the reserving literature.

Online inventory optimization (OIO) is online convex optimization with physical memory: inventory carryover makes the feasible action set depend on the past. A natural principle, used in stochastic inventory learning and recently in OIO under a single linear capacity constraint, is to maintain a hidden target chosen by an online learner and implement its projection onto the currently feasible order-up-to set. We prove that this simple principle is optimal for OIO on arbitrary bounded convex capacity sets. With online gradient descent as the base learner, the method improves the best known regret guarantee for OIO on general convex sets from inverse to inverse-square-root dependence on the common-demand probability, and we prove a matching lower bound. The same principle gives the first polylogarithmic regret guarantee for strongly convex losses and the first dynamic regret guarantee adapting to Euclidean path variation on general convex capacity sets. The analysis introduces a norm alignment principle: the right state variable is the distance from the hidden target to the feasible set, measured in the same norm as the projection. Under norm alignment, this distance evolves pathwise as a scalar queue, with target movement as arrival and common demand as service. This reduction to one-dimensional queue control resolves the state dependence and extends the guarantees to general convex capacity sets, beyond the reach of prior productwise approaches. Experiments on synthetic and real-world inventory data corroborate the theory.

Optimal Transport has become recently a powerful method for domain adaptation by aligning source and target distributions. We study a supervised domain adaptation problem where source and target domains are related by a rotation or a translation or a homothety in $\mathbb{R}^2$. We prove that the optimal transport map recovers the underlying map when using a $p-$norm cost with $p \geq 2$. Based on this insight, we develop a method combining $K-$means and optimal transport to estimate the underlying map, enabling adaptation of linear regression models when target data is scarce. Simulations demonstrate improved performance over baseline methods. Rather than relying on highly expressive deep learning architectures, we focus on classical machine learning models to emphasize interpretability and theoretical insight. This perspective allows us to explicitly characterize the role of optimal transport in recovering geometric transformations such as rotations, translations, and homotheties. Our contributions include a theoretical result linking optimal transport and rotations, translations and homothecies in $\mathbb{R}^2$, and a practical method for adaptation in linear regression offering both conceptual clarity and applied value in domain adaptation tasks in this space.

Understanding how a prediction model will perform in a new environment before deployment is essential to preventing harm when algorithms inform decision-making. Two common sources of model performance degradation are (i) covariate shift, where the target covariate distribution differs from the source, and (ii) selective labels, where the observability of outcomes depends on historical decisions. We study pre-deployment model evaluation under the joint presence of covariate shift and labeling of outcomes selectively based on observed features. In particular, we present a double machine learning procedure for estimating the target risk of an arbitrary black-box prediction model under a general loss function. We show identification of this estimand under standard assumptions and derive a bias-corrected estimator based on the influence function of the target risk. Finally, we evaluate our estimator through experiments using the eICU electronic health records database, showing that it tracks the true target risk more accurately than methods that address either selective labels or covariate shift alone, as well as baselines that combine standard plug-in approaches.

We study training-free fixed-length descriptors for multivariate time series and ask not merely whether such a descriptor performs well, but when it can be expected to work at all. Our object of study is $D(τ)$, built from a time-lagged correlation matrix truncated at the Marchenko-Pastur edge so that only signal-bearing eigenvalues survive and classified by cosine similarity to class centroids with zero learned parameters. The central contribution is not the descriptor but a falsifiable applicability criterion for it. Working from a stationary Gaussian VAR(1) model, we argue that $D(τ)$ separates two classes when the signals are approximately stationary and the class information lives in their cross-channel temporal coupling rather than in marginal per-channel power. We derive, semi-formally, three consequences: a distinguishability condition, why the static ($τ=0$) covariance collapses to chance, and why a stationary but power-discriminated paradigm defeats the descriptor. The criterion is operational: a two-part pre-flight test -- an augmented Dickey-Fuller stationarity check and a power-baseline saturation check -- predicts applicability before any training. We validate both halves on a mixed assortment. On four paradigms that satisfy the criterion (Sleep-EDF, BCI-IV-2a, MIT-BIH, ESC-50) the descriptor is competitive with strong baselines at a fraction of their cost, reaching $88.5\pm4.5\%$ under 20-subject leave-one-subject-out on Sleep-EDF on a single CPU thread. On three that violate it -- non-stationary ERPs, and financial-volatility and wearable-stress regimes that are power-discriminated -- it fails exactly as the pre-flight predicts, and these negatives are the more informative half. We are explicit that $D(τ)$ is not the most accurate representation; its value is a compact, training-free embedding whose domain of validity is known in advance.

Instance-dependent Partial Label Learning (ID-PLL) aims to learn a multi-class predictive model given training instances annotated with candidate labels related to features, among which correct labels are hidden fixed but unknown. The previous works involve leveraging the identification capability of the training model itself to iteratively refine supervision information. However, these methods overlook a critical aspect of ID-PLL: within the original label space, the model may fail to distinguish some incorrect candidate labels that are strongly correlated with features from correct labels. This leads to poor-quality supervision signals and creates a bottleneck in the training process. In this paper, we propose to leverage reduction-based pseudo-labels to alleviate the influence of incorrect candidate labels and train our predictive model to overcome this bottleneck. Specifically, reduction-based pseudo-labels are generated by performing weighted aggregation on the outputs of a multi-branch auxiliary model, with each branch trained in a label subspace that excludes certain labels. This approach ensures that each branch explicitly avoids the disturbance of the excluded labels, allowing the pseudo-labels provided for instances troubled by these excluded labels to benefit from the unaffected branches. Theoretically, we demonstrate that reduction-based pseudolabels exhibit greater consistency with the Bayes optimal classifier compared to pseudo-labels directly generated from the training predictive model.

Linear attention methods offer Transformers O(N) complexity but typically underperform standard softmax attention. We identify two fundamental limitations affecting these approaches: the restriction to convex combinations that only permits additive information blending, and uniform accumulated weight bias that dilutes attention in long contexts. We propose Zero-Sum Linear Attention (ZeroS), which addresses these limitations by removing the constant zero-order term 1/t and reweighting the remaining zero-sum softmax residuals. This modification creates mathematically stable weights, enabling both positive and negative values and allowing a single attention layer to perform contrastive operations. While maintaining O(N)complexity, ZeroS theoretically expands the set of representable functions compared to convex combinations. Empirically, it matches or exceeds standard softmax attention across various sequence modeling benchmarks. The code implementation is available at this link.

The shape of objects is an important source of visual information in a wide range of applications. One of the core challenges of shape quantification is to ensure that the extracted measurements remain invariant to transformations that preserve an object's intrinsic geometry, such as changing its size, orientation, and position in the image. In this work, we introduce ShapeEmbed, a self-supervised representation learning framework designed to encode the contour of objects in 2D images, represented as a Euclidean distance matrix, into a shape descriptor that is invariant to translation, scaling, rotation, reflection, and point indexing. Our approach overcomes the limitations of traditional shape descriptors while improving upon existing state-of-the-art autoencoder-based approaches. We demonstrate that the descriptors learned by our framework outperform their competitors in shape classification tasks on natural and biological images. We envision our approach to be of particular relevance to biological imaging applications.

Recent advancements have explored text-to-image diffusion models for synthesizing out-of-distribution (OOD) samples, substantially enhancing the performance of OOD detection. However, existing approaches typically rely on perturbing textconditioned embeddings, resulting in semantic instability and insufficient shift diversity, which limit generalization to realistic OOD. To address these challenges, we propose GOOD, a novel and flexible framework that directly guides diffusion sampling trajectories towards OOD regions using off-the-shelf in-distribution (ID) classifiers. GOOD incorporates dual-level guidance: (1) Image-level guidance based on the gradient of log partition to reduce input likelihood, drives samples toward low-density regions in pixel space.

Does vision-and-language (VL) training change the linguistic representations of language models in meaningful ways? Most results in the literature have shown inconsistent or marginal differences, both behaviorally and representationally. In this work, we start from the hypothesis that the domain in which VL training could have a significant effect is lexical-conceptual knowledge, in particular its taxonomic organization. Through comparing minimal pairs of text-only LMs and their VL-trained counterparts, we first show that the VL models often outperform their text-only counterparts on a text-only question-answering task that requires taxonomic understanding of concepts mentioned in the questions. Using an array of targeted behavioral and representational analyses, we show that the LMs and VLMs do not differ significantly in terms of their taxonomic knowledge itself, but they differ in how they represent questions that contain concepts in a taxonomic relation vs. a non-taxonomic relation. This implies that the taxonomic knowledge itself does not change substantially through additional VL training, but VL training does improve the deployment of this knowledge in the context of a specific task, even when the presentation of the task is purely linguistic.