We show how to estimate a model's test error from unlabeled data, on distributions very different from the training distribution, while assuming only that certain conditional independencies are preserved between train and test. We do not need to assume that the optimal predictor is the same between train and test, or that the true distribution lies in any parametric family. We can also efficiently compute gradients of the estimated error and hence perform unsupervised discriminative learning. Our technical tool is the method of moments, which allows us to exploit conditional independencies in the absence of a fully-specified model. Our framework encompasses a large family of losses including the log and exponential loss, and extends to structured output settings such as conditional random fields.

Causal inference is a key research area in machine learning, yet confusion reigns over the tools needed to tackle it. There are prevalent claims in the machine learning literature that you need a bespoke causal framework or notation to answer causal questions. In this paper, we want to make it clear that you \emph{can} answer any causal inference question within the realm of probabilistic modelling and inference, without causal-specific tools or notation. Through concrete examples, we demonstrate how causal questions can be tackled by writing down the probability of everything. Lastly, we reinterpret causal tools as emerging from standard probabilistic modelling and inference, elucidating their necessity and utility.

We show how to estimate a model's test error from unlabeled data, on distributions very different from the training distribution, while assuming only that certain conditional independencies are preserved between train and test. We do not need to assume that the optimal predictor is the same between train and test, or that the true distribution lies in any parametric family. We can also efficiently compute gradients of the estimated error and hence perform unsupervised discriminative learning. Our technical tool is the method of moments, which allows us to exploit conditional independencies in the absence of a fully-specified model. Our framework encompasses a large family of losses including the log and exponential loss, and extends to structured output settings such as conditional random fields.

Psychological attributes rarely operate in isolation: coaches reason about networks of related traits. We analyze a new dataset of 164 female volleyball players from Italy's C and D leagues that combines standardized psychological profiling with background information. To learn directed relationships among mixed-type variables (ordinal questionnaire scores, categorical demographics, continuous indicators), we introduce latent MMHC, a hybrid structure learner that couples a latent Gaussian copula and a constraint-based skeleton with a constrained score-based refinement to return a single DAG. We also study a bootstrap-aggregated variant for stability. In simulations spanning sample size, sparsity, and dimension, latent Max-Min Hill-Climbing (MMHC) attains lower structural Hamming distance and higher edge recall than recent copula-based learners while maintaining high specificity. Applied to volleyball, the learned network organizes mental skills around goal setting and self-confidence, with emotional arousal linking motivation and anxiety, and locates Big-Five traits (notably neuroticism and extraversion) upstream of skill clusters. Scenario analyses quantify how improvements in specific skills propagate through the network to shift preparation, confidence, and self-esteem. The approach provides an interpretable, data-driven framework for profiling psychological traits in sport and for decision support in athlete development.

Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures non-parametrically, while maintaining interpretability through the identification of varying conditional independencies. GTMs extend multivariate transformation models by replacing the Gaussian copula with a custom-designed multivariate transformation, offering two major advantages. Firstly, GTMs can capture more complex interdependencies using penalized splines, which also provide an efficient regularization scheme. Secondly, we demonstrate how to approximately regularize GTMs using a lasso penalty towards pairwise conditional independencies, akin to Gaussian graphical models. The model's robustness and effectiveness are validated through simulations, showcasing its ability to accurately learn parametric vine copulas and identify conditional independencies. Additionally, the model is applied to a benchmark astrophysics dataset, where the GTM demonstrates favorable performance compared to non-parametric vine copulas in learning complex multivariate distributions.

We show how to estimate a model's test error from unlabeled data, on distributions very different from the training distribution, while assuming only that certain conditional independencies are preserved between train and test. We do not need to assume that the optimal predictor is the same between train and test, or that the true distribution lies in any parametric family. We can also efficiently compute gradients of the estimated error and hence perform unsupervised discriminative learning. Our technical tool is the method of moments, which allows us to exploit conditional independencies in the absence of a fully-specified model. Our framework encompasses a large family of losses including the log and exponential loss, and extends to structured output settings such as conditional random fields.

Over the last decades, conditional independence was shown to be a crucial concept supporting adequate modelling and efficient reasoning in probabilistics (Pearl, Geiger, and Verma, 1989). It is the fundamental concept underlying network-based reasoning in probabilistics, which has been arguably one of the most important factors in the rise of contemporary artificial intelligence. Even though many reasoning tasks on the basis of probabilistic information have a high worst-case complexity due to their semantic nature, network-based models allow an efficient computation of many concrete instances of these reasoning tasks thanks to local reasoning techniques. Therefore, conditional independence has also been investigated for several approaches in knowledge representation, such as propositional logic (Darwiche, 1997; Lang, Liberatore, and Marquis, 2002), belief revision (Kern-Isberner, Heyninck, and Beierle, 2022; Lynn, Delgrande, and Peppas, 2022) and conditional logics (Heyninck et al., 2023). For many other central formalisms in KR, such a study has not yet been undertaken. Due to the wide variety of formalisms studied in knowledge representation, it is often beneficial yet challenging to study a concept in a language-independent manner. Indeed, such languageindependent studies avoid having to define and investigate the same concept for different formalisms. In recent years, a promising framework for such language-independent investigations is the algebraic approximation fixpoint theory (AFT) Denecker, Marek, and Truszczyński (2003), which conceives of KR-formalisms as operators over a lattice (such as the immediate consequence operator from logic programming).

This paper presents a novel Integer Programming (IP) approach for discovering the Markov Equivalent Class (MEC) of Bayesian Networks (BNs) through observational data. The MEC-IP algorithm utilizes a unique clique-focusing strategy and Extended Maximal Spanning Graphs (EMSG) to streamline the search for MEC, thus overcoming the computational limitations inherent in other existing algorithms. Our numerical results show that not only a remarkable reduction in computational time is achieved by our algorithm but also an improvement in causal discovery accuracy is seen across diverse datasets. These findings underscore this new algorithm's potential as a powerful tool for researchers and practitioners in causal discovery and BNSL, offering a significant leap forward toward the efficient and accurate analysis of complex data structures.