Machine learning has matured to the point where we often take key design decisions for granted.

The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing statistical theory for OT map estimation is quite restricted, hinging on Brenier's theorem (quadratic cost, absolutely continuous source) to guarantee existence and uniqueness of a deterministic OT map, on which various additional regularity assumptions are imposed to obtain quantitative error bounds. In many real-world problems these conditions fail or cannot be certified, in which case optimal transportation is possible only via stochastic maps that can split mass. To broaden the scope of map estimation theory to such settings, this work introduces a novel metric for evaluating the transportation quality of stochastic maps. Under this metric, we develop computationally efficient map estimators with near-optimal finite-sample risk bounds, subject to easy-to-verify minimal assumptions. Our analysis further accommodates common forms of adversarial sample contamination, yielding estimators with robust estimation guarantees. Empirical experiments are provided which validate our theory and demonstrate the utility of the proposed framework in settings where existing theory fails. These contributions constitute the first general-purpose theory for map estimation, compatible with a wide spectrum of real-world applications where optimal transport may be intrinsically stochastic.

We thank all reviewers for their constructive feedback! We address reviewers comments below, and will incorporate all feedback. This explains why SD outperforms LS. Please refer to our response to [R3] for discussion on CD. One can alternatively compute the variance of prediction confidence.

Gaussian Cox processes are widely-used point process models that use a Gaussian process to describe the Bayesian a priori uncertainty present in latent intensity functions. In this paper, we propose a novel Bayesian inference scheme for Gaussian Cox processes by exploiting a conceptually-intuitive path integral formulation. The proposed scheme does not rely on domain discretization, scales linearly with the number of observed events, has a lower complexity than the state-of-the-art variational Bayesian schemes with respect to the number of inducing points, and is applicable to a wide range of Gaussian Cox processes with various types of link functions. Our scheme is especially beneficial under the multi-dimensional input setting, where the number of inducing points tends to be large. We evaluate our scheme on synthetic and real-world data, and show that it achieves comparable predictive accuracy while being tens of times faster than reference methods.

Educators teaching entry-level university engineering modules face the challenge of identifying which topics students find most difficult and how to support diverse student needs effectively. This study demonstrates a rigorous yet interpretable statistical approach -- hierarchical Bayesian modeling -- that leverages detailed student response data to quantify both skill difficulty and individual student abilities. Using a large-scale dataset from an undergraduate Statics course, we identified clear patterns of skill mastery and uncovered distinct student subgroups based on their learning trajectories. Our analysis reveals that certain concepts consistently present challenges, requiring targeted instructional support, while others are readily mastered and may benefit from enrichment activities. Importantly, the hierarchical Bayesian method provides educators with intuitive, reliable metrics without sacrificing predictive accuracy. This approach allows for data-informed decisions, enabling personalized teaching strategies to improve student engagement and success. By combining robust statistical methods with clear interpretability, this study equips educators with actionable insights to better support diverse learner populations.

We propose a general and versatile framework that significantly speeds-up graphical model optimization while maintaining an excellent solution accuracy. The proposed approach, refereed as Inference by Learning or in short as IbyL, relies on a multi-scale pruning scheme that progressively reduces the solution space by use of a coarse-to-fine cascade of learnt classifiers. We thoroughly experiment with classic computer vision related MRF problems, where our novel framework constantly yields a significant time speed-up (with respect to the most efficient inference methods) and obtains a more accurate solution than directly optimizing the MRF. We make our code available on-line [4].

Summary and Contributions: Discrete Determinantal Point Processes (DPPs) are probability distributions over subsets of a finite set of (feature) vectors where the probability of each subset is proportional to the volume of the parallelogram that they span. Since these distributions capture the negative correlations between items, they have been extensively employed in subset selection tasks where diversity is preferred. MAP estimation for DPPs is a well-studied problem which formally given a set of vectors and an integer k asks a for a subset of k items with (approximately) highest volume (probability); this objective functions can be translated as the most diverse subset of size k . The problem is shown to be hard. In particular, there is an exponential O(1) k lower bound on the approximation factor in the offline setting. This work studies the MAP estimation for DPPs in a specific streaming setting as follows: Vectors arrive in a stream and upon arrival of any vectors, the algorithm has to decide either store it (permanently) in the memory or erase it.

Radio map estimation (RME) involves spatial interpolation of radio measurements to predict metrics such as the received signal strength at locations where no measurements were collected. The most popular estimators nowadays project the measurement locations to a regular grid and complete the resulting measurement tensor with a convolutional deep neural network. Unfortunately, these approaches suffer from poor spatial resolution and require a great number of parameters. The first contribution of this paper addresses these limitations by means of an attention-based estimator named Spatial TransfOrmer for Radio Map estimation (STORM). This scheme not only outperforms the existing estimators, but also exhibits lower computational complexity, translation equivariance, rotation equivariance, and full spatial resolution. The second contribution is an extended transformer architecture that allows STORM to perform active sensing, by which the next measurement location is selected based on the previous measurements. This is particularly useful for minimization of drive tests (MDT) in cellular networks, where operators request user equipment to collect measurements. Finally, STORM is extensively validated by experiments with one ray-tracing and two real-measurement datasets.