Formal model evaluation methods typically certify that a model satisfies a prescribed target key performance indicator (KPI) level. However, in many applications, the relevant target KPI level may not be known a priori, and the user may instead wish to compare candidate models by analyzing the full trade-offs between performance and reliability achievable at test time by the models. This task, requiring the reliable estimate of the test-time KPI distributions, is made more complicated by the fact that the same data must often be used both to pre-select a subset of candidate models and to estimate their KPI distributions, causing a potential post-selection bias. In this work, we introduce post-selection distributional model evaluation (PS-DME), a general framework for statistically valid distributional model assessment after arbitrary data-dependent model pre-selection. Building on e-values, PS-DME controls post-selection false coverage rate (FCR) for the distributional KPI estimates and is proved to be more sample efficient than a baseline method based on sample splitting. Experiments on synthetic data, text-to-SQL decoding with large language models, and telecom network performance evaluation demonstrate that PS-DME enables reliable comparison of candidate configurations across a range of reliability levels, supporting the statistically reliable exploration of performance--reliability trade-offs.

We propose a method for non-parametric conditional distribution estimation based on partitioning covariate-sorted observations into contiguous bins and using the within-bin empirical CDF as the predictive distribution. Bin boundaries are chosen to minimise the total leave-one-out Continuous Ranked Probability Score (LOO-CRPS), which admits a closed-form cost function with $O(n^2 \log n)$ precomputation and $O(n^2)$ storage; the globally optimal $K$-partition is recovered by a dynamic programme in $O(n^2 K)$ time. Minimisation of within-sample LOO-CRPS turns out to be inappropriate for selecting $K$ as it results in in-sample optimism. We instead select $K$ by $K$-fold cross-validation of test CRPS, which yields a U-shaped criterion with a well-defined minimum. Having selected $K^*$ and fitted the full-data partition, we form two complementary predictive objects: the Venn prediction band and a conformal prediction set based on CRPS as the nonconformity score, which carries a finite-sample marginal coverage guarantee at any prescribed level $\varepsilon$. The conformal prediction is transductive and data-efficient, as all observations are used for both partitioning and p-value calculation, with no need to reserve a hold-out set. On real benchmarks against split-conformal competitors (Gaussian split conformal, CQR, CQR-QRF, and conformalized isotonic distributional regression), the method produces substantially narrower prediction intervals while maintaining near-nominal coverage.

This paper proposes a competitive and computationally efficient approach to probabilistic rainfall nowcasting. A video projector (V-JEPA Vision Transformer) associated to a lightweight probabilistic head is attached to a pre-trained satellite vision encoder (DINOv3-SAT493M) to map encoder tokens into a discrete empirical CDF (eCDF) over 4-hour accumulated rainfall. The projector-head is optimized end-to-end over the Ranked Probability Score (RPS). As an alternative, 3D-UNET baselines trained with an aggregate Rank Probability Score and a per-pixel Gamma-Hurdle objective are used. On the Weather4Cast 2025 benchmark, the proposed method achieved a promising performance, with a CRPS of 3.5102, which represents $\approx$ 26% in effectiveness gain against the best 3D-UNET.

Conformal prediction quantifies the uncertainty of machine learning models by augmenting point predictions with valid prediction sets, assuming exchangeability. For complex scenarios involving multiple trials, models, or data sources, conformal prediction sets can be aggregated to create a prediction set that captures the overall uncertainty, often improving precision. However, aggregating multiple prediction sets with individual $1-α$ coverage inevitably weakens the overall guarantee, typically resulting in $1-2α$ worst-case coverage. In this work, we propose a framework for the weighted aggregation of prediction sets, where weights are assigned to each prediction set based on their contribution. Our framework offers flexible control over how the sets are aggregated, achieving tighter coverage bounds that interpolate between the $1-2α$ guarantee of the combined models and the $1-α$ guarantee of an individual model depending on the distribution of weights. We extend our framework to data-dependent weights, and we derive a general procedure for data-dependent weight aggregation that maintains finite-sample validity. We demonstrate the effectiveness of our methods through experiments on synthetic and real data in the mixture-of-experts setting, and we show that aggregation with data-dependent weights provides a form of adaptive coverage.

In solid-state materials science, substantial efforts have been devoted to the calculation and modeling of the electronic band gap. While a wide range of ab initio methods and machine learning algorithms have been created that can predict this quantity, the development of new computational approaches for studying the band gap remains an active area of research. Here we introduce a simple machine learning model for predicting the band gap using only the chemical composition of the crystalline material. To motivate the form of the model, we first analyze the empirical distribution of the band gap, which sheds new light on its atypical statistics. Specifically, our analysis enables us to frame band gap prediction as a task of modeling a mixed random variable, and we design our model accordingly. Our model formulation incorporates thematic ideas from chemical heuristic models for other material properties in a manner that is suited towards the band gap modeling task. The model has exactly one parameter corresponding to each element, which is fit using data. To predict the band gap for a given material, the model computes a weighted average of the parameters associated with its constituent elements and then takes the maximum of this quantity and zero. The model provides heuristic chemical interpretability by intuitively capturing the associations between the band gap and individual chemical elements.

Automatic differentiation (see, for example, Ref.[1]) has revolutionized machine learning, permitting the routine application of gradient descent algorithms to fit to data models of essentially unlimited complexity. The same technology can be used to take the derivative of these models with respect to their inputs without the need to explicitly calculate the derivatives [2]. A potentially useful application of this capability is approximating the probability density function (pdf), f(x | θ), given an accurate neural network model of the associated conditional cumulative distribution function (cdf), F (x | θ), using the fact that F (x | θ) f(x | θ) =, (1) x where θ are the parameters of the data-generation mechanism, which we distinguish from the parameters w of the neural network model. This paper explores this possibility in the context of simulation-based frequentist inference [3-7]. Equation (1) furnishes an approximation of the pdf f(x | θ) whether x is a function of the underlying observations D only or if x = λ(D; θ) is a test statistic that depends on D as well as on the parameters θ. Moreover, computing the derivative of the cdf using autograd to obtain the pdf is exact; autograd does not use finite difference approximations.

Generalization error bounds from learning theory provide statistical guarantees on how well an algorithm will perform on previously unseen data. In this paper, we characterize the impacts of data non-IIDness due to censored feedback (a.k.a. selective labeling bias) on such bounds. We first derive an extension of the well-known Dvoretzky-Kiefer-Wolfowitz (DKW) inequality, which characterizes the gap between empirical and theoretical CDFs given IID data, to problems with non-IID data due to censored feedback. We then use this CDF error bound to provide a bound on the generalization error guarantees of a classifier trained on such non-IID data. We show that existing generalization error bounds (which do not account for censored feedback) fail to correctly capture the model's generalization guarantees, verifying the need for our bounds. We further analyze the effectiveness of (pure and bounded) exploration techniques, proposed by recent literature as a way to alleviate censored feedback, on improving our error bounds. Together, our findings illustrate how a decision maker should account for the trade-off between strengthening the generalization guarantees of an algorithm and the costs incurred in data collection when future data availability is limited by censored feedback.

Tabular data is common yet typically incomplete, small in volume, and access-restricted due to privacy concerns. Synthetic data generation offers potential solutions. Many metrics exist for evaluating the quality of synthetic tabular data; however, we lack an objective, coherent interpretation of the many metrics. To address this issue, we propose an evaluation framework with a single, mathematical objective that posits that the synthetic data should be drawn from the same distribution as the observed data. Through various structural decomposition of the objective, this framework allows us to reason for the first time the completeness of any set of metrics, as well as unifies existing metrics, including those that stem from fidelity considerations, downstream application, and model-based approaches. Moreover, the framework motivates model-free baselines and a new spectrum of metrics. We evaluate structurally informed synthesizers and synthesizers powered by deep learning. Using our structured framework, we show that synthetic data generators that explicitly represent tabular structure outperform other methods, especially on smaller datasets.

Offline change point detection retrospectively locates change points in a time series. Many nonparametric methods that target i.i.d. mean and variance changes fail in the presence of nonlinear temporal dependence, and model based methods require a known, rigid structure. For the at most one change point problem, we propose use of a conceptor matrix to learn the characteristic dynamics of a baseline training window with arbitrary dependence structure. The associated echo state network acts as a featurizer of the data, and change points are identified from the nature of the interactions between the features and their relationship to the baseline state. This model agnostic method can suggest potential locations of interest that warrant further study. We prove that, under mild assumptions, the method provides a consistent estimate of the true change point, and quantile estimates are produced via a moving block bootstrap of the original data. The method is evaluated with clustering metrics and Type 1 error control on simulated data, and applied to publicly available neural data from rats experiencing bouts of non-REM sleep prior to exploration of a radial maze. With sufficient spacing, the framework provides a simple extension to the sparse, multiple change point problem.