Attribution modelling lies at the heart of marketing effectiveness, yet most existing approaches depend on user-level path data, which are increasingly inaccessible due to privacy regulations and platform restrictions. This paper introduces a Causal-Driven Attribution (CDA) framework that infers channel influence using only aggregated impression-level data, avoiding any reliance on user identifiers or click-path tracking. CDA integrates temporal causal discovery (using PCMCI) with causal effect estimation via a Structural Causal Model to recover directional channel relationships and quantify their contributions to conversions. Using large-scale synthetic data designed to replicate real marketing dynamics, we show that CDA achieves an average relative RMSE of 9.50% when given the true causal graph, and 24.23% when using the predicted graph, demonstrating strong accuracy under correct structure and meaningful signal recovery even under structural uncertainty. CDA captures cross-channel interdependencies while providing interpretable, privacy-preserving attribution insights, offering a scalable and future-proof alternative to traditional path-based models.

This technical note considers the sampling of outcomes that provide the greatest amount of information about the structure of underlying world models. This generalisation furnishes a principled approach to structure learning under a plausible set of generative models or hypotheses. In active inference, policies - i.e., combinations of actions - are selected based on their expected free energy, which comprises expected information gain and value. Information gain corresponds to the KL divergence between predictive posteriors with, and without, the consequences of action. Posteriors over models can be evaluated quickly and efficiently using Bayesian Model Reduction, based upon accumulated posterior beliefs about model parameters. The ensuing information gain can then be used to select actions that disambiguate among alternative models, in the spirit of optimal experimental design. We illustrate this kind of active selection or reasoning using partially observed discrete models; namely, a 'three-ball' paradigm used previously to describe artificial insight and 'aha moments' via (synthetic) introspection or sleep. We focus on the sample efficiency afforded by seeking outcomes that resolve the greatest uncertainty about the world model, under which outcomes are generated.

Diffusion models (Sohl-Dickstein et al., 2015; Ho et al., 2020; Song et al., 2020) have emerged as one of the most powerful classes of generative models for high-dimensional data, achieving state-of-the-art performance in image synthesis (Dhariwal and Nichol, 2021; Rombach et al., 2022) and other tasks such as action generation in robotic or protein design (Watson et al., 2023; Chi et al., 2025). However, sampling from these models is typically slow: many reverse-time steps are required to transform an initial Gaussian sample into a high-quality sample in data space (Ho et al., 2020; Song et al., 2020). This computational cost is especially problematic, and it restricts the practical deployment of diffusion models in real-time or resource-constrained settings (Salimans and Ho, 2022; Lu et al., 2022). Recent theoretical and empirical studies suggest that this inefficiency is closely related to a dynamical phase transition (bifurcation) that occurs during the reverse process (Raya and Ambrogioni, 2024; Biroli et al., 2024; Ambrogioni, 2025). In the early reverse steps, the trajectories stay near a stable fixed point whose distribution is close to the initial independent Gaussian, and little structure is present in the samples.

Modeling sparse count data, which arise across numerous scientific fields, presents significant statistical challenges. This chapter addresses these challenges in the context of infectious disease prediction, with a focus on predicting outbreaks in geographic regions that have historically reported zero cases. To this end, we present the detailed computational framework and experimental application of the Poisson Hierarchical Indian Buffet Process (PHIBP), with demonstrated success in handling sparse count data in microbiome and ecological studies. The PHIBP's architecture, grounded in the concept of absolute abundance, systematically borrows statistical strength from related regions and circumvents the known sensitivities of relative-rate methods to zero counts. Through a series of experiments on infectious disease data, we show that this principled approach provides a robust foundation for generating coherent predictive distributions and for the effective use of comparative measures such as alpha and beta diversity. The chapter's emphasis on algorithmic implementation and experimental results confirms that this unified framework delivers both accurate outbreak predictions and meaningful epidemiological insights in data-sparse settings.

A methodology is developed to extract $d$ invariant features $W=f(X)$ that predict a response variable $Y$ without being confounded by variables $Z$ that may influence both $X$ and $Y$. The methodology's main ingredient is the penalization of any statistical dependence between $W$ and $Z$ conditioned on $Y$, replaced by the more readily implementable plain independence between $W$ and the random variable $Z_Y = T(Z,Y)$ that solves the [Monge] Optimal Transport Barycenter Problem for $Z\mid Y$. In the Gaussian case considered in this article, the two statements are equivalent. When the true confounders $Z$ are unknown, other measurable contextual variables $S$ can be used as surrogates, a replacement that involves no relaxation in the Gaussian case if the covariance matrix $Σ_{ZS}$ has full range. The resulting linear feature extractor adopts a closed form in terms of the first $d$ eigenvectors of a known matrix. The procedure extends with little change to more general, non-Gaussian / non-linear cases.

We study the problem of subgroup discovery for survival analysis, where the goal is to find an interpretable subset of the data on which a Cox model is highly accurate. Our work is the first to study this particular subgroup problem, for which we make several contributions. Subgroup discovery methods generally require a "quality function" in order to sift through and select the most advantageous subgroups. We first examine why existing natural choices for quality functions are insufficient to solve the subgroup discovery problem for the Cox model. To address the shortcomings of existing metrics, we introduce two technical innovations: the *expected prediction entropy (EPE)*, a novel metric for evaluating survival models which predict a hazard function; and the *conditional rank statistics (CRS)*, a statistical object which quantifies the deviation of an individual point to the distribution of survival times in an existing subgroup. We study the EPE and CRS theoretically and show that they can solve many of the problems with existing metrics. We introduce a total of eight algorithms for the Cox subgroup discovery problem. The main algorithm is able to take advantage of both the EPE and the CRS, allowing us to give theoretical correctness results for this algorithm in a well-specified setting. We evaluate all of the proposed methods empirically on both synthetic and real data. The experiments confirm our theory, showing that our contributions allow for the recovery of a ground-truth subgroup in well-specified cases, as well as leading to better model fit compared to naively fitting the Cox model to the whole dataset in practical settings. Lastly, we conduct a case study on jet engine simulation data from NASA. The discovered subgroups uncover known nonlinearities/homogeneity in the data, and which suggest design choices which have been mirrored in practice.

Least-absolute-deviations (LAD) line fitting is robust to outliers but computationally more involved than least squares regression. Although the literature includes linear and near-linear time algorithms for the LAD line fitting problem, these methods are difficult to implement and, to our knowledge, lack maintained public implementations. As a result, practitioners often resort to linear programming (LP) based methods such as the simplex-based Barrodale-Roberts method and interior-point methods, or on iteratively reweighted least squares (IRLS) approximation which does not guarantee exact solutions. To close this gap, we propose the Piecewise Affine Lower-Bounding (PALB) method, an exact algorithm for LAD line fitting. PALB uses supporting lines derived from subgradients to build piecewise-affine lower bounds, and employs a subdivision scheme involving minima of these lower bounds. We prove correctness and provide bounds on the number of iterations. On synthetic datasets with varied signal types and noise including heavy-tailed outliers as well as a real dataset from the NOAA's Integrated Surface Database, PALB exhibits empirical log-linear scaling. It is consistently faster than publicly available implementations of LP based and IRLS based solvers. We provide a reference implementation written in Rust with a Python API.

We present a comprehensive study on fully automated pollen recognition across both conventional optical and digital in-line holographic microscopy (DIHM) images of sample slides. Visually recognizing pollen in unreconstructed holographic images remains challenging due to speckle noise, twin-image artifacts and substantial divergence from bright-field appearances. We establish the performance baseline by training YOLOv8s for object detection and MobileNetV3L for classification on a dual-modality dataset of automatically annotated optical and affinely aligned DIHM images. On optical data, detection mAP50 reaches 91.3% and classification accuracy reaches 97%, whereas on DIHM data, we achieve only 8.15% for detection mAP50 and 50% for classification accuracy. Expanding the bounding boxes of pollens in DIHM images over those acquired in aligned optical images achieves 13.3% for detection mAP50 and 54% for classification accuracy. To improve object detection in DIHM images, we employ a Wasserstein GAN with spectral normalization (WGAN-SN) to create synthetic DIHM images, yielding an FID score of 58.246. Mixing real-world and synthetic data at the 1.0 : 1.5 ratio for DIHM images improves object detection up to 15.4%. These results demonstrate that GAN-based augmentation can reduce the performance divide, bringing fully automated DIHM workflows for veterinary imaging a small but important step closer to practice.

Visual information arriving at the retina is transmitted to the brain by signals in the optic nerve, and the brain must rely solely on these signals to make inferences about the visual world. Previous work has probed the content of these signals by directly reconstructing images from retinal activity using linear regression or nonlinear regression with neural networks. Maximum a posteriori (MAP) reconstruction using retinal encoding models and separately-trained natural image priors offers a more general and principled approach. We develop a novel method for approximate MAP reconstruction that combines a generalized linear model for retinal responses to light, including their dependence on spike history and spikes of neighboring cells, with the image prior implicitly embedded in a deep convolutional neural network trained for image denoising. We use this method to reconstruct natural images from ex vivo simultaneously-recorded spikes of hundreds of retinal ganglion cells uniformly sampling a region of the retina. The method produces reconstructions that match or exceed the state-of-the-art in perceptual similarity and exhibit additional fine detail, while using substantially fewer model parameters than previous approaches. The use of more rudimentary encoding models (a linear-nonlinear-Poisson cascade) or image priors (a 1/f spectral model) significantly reduces reconstruction performance, indicating the essential role of both components in achieving high-quality reconstructed images from the retinal signal.

Geometric deep learning has broad applications in biology, a domain where relational structure in data is often intrinsic to modelling the underlying phenomena. Currently, efforts in both geometric deep learning and, more broadly, deep learning applied to biomolecular tasks have been hampered by a scarcity of appropriate datasets accessible to domain specialists and machine learning researchers alike. To address this, we introduce Graphein as a turn-key tool for transforming raw data from widely-used bioinformatics databases into machine learning-ready datasets in a high-throughput and flexible manner. Graphein is a Python library for constructing graph and surface-mesh representations of biomolecular structures, such as proteins, nucleic acids and small molecules, and biological interaction networks for computational analysis and machine learning. Graphein provides utilities for data retrieval from widely-used bioinformatics databases for structural data, including the Protein Data Bank, the AlphaFold Structure Database, chemical data from ZINC and ChEMBL, and for biomolecular interaction networks from STRINGdb, BioGrid, TRRUST and RegNetwork. The library interfaces with popular geometric deep learning libraries: DGL, Jraph, PyTorch Geometric and PyTorch3D though remains framework agnostic as it is built on top of the PyData ecosystem to enable inter-operability with scientific computing tools and libraries. Graphein is designed to be highly flexible, allowing the user to specify each step of the data preparation, scalable to facilitate working with large protein complexes and interaction graphs, and contains useful pre-processing tools for preparing experimental files.