Continuous normalizing flows (CNFs) learn the probability path between a reference and a target density by modeling the vector field generating said path using neural networks. Recently, Lipman et al. (2022) introduced a simple and inexpensive method for training CNFs in generative modeling, termed flow matching (FM). In this paper, we re-purpose this method for probabilistic inference by incorporating Markovian sampling methods in evaluating the FM objective and using the learned probability path to improve Monte Carlo sampling. We propose a sequential method, which uses samples from a Markov chain to fix the probability path defining the FM objective. We augment this scheme with an adaptive tempering mechanism that allows the discovery of multiple modes in the target. Under mild assumptions, we establish convergence to a local optimum of the FM objective, discuss improvements in the convergence rate, and illustrate our methods on synthetic and real-world examples.

This work investigates the offline formulation of the contextual bandit problem, where the goal is to leverage past interactions collected under a behavior policy to evaluate, select, and learn new, potentially better-performing, policies. Motivated by critical applications, we move beyond point estimators. Instead, we adopt the principle of pessimism where we construct upper bounds that assess a policy's worst-case performance, enabling us to confidently select and learn improved policies. Precisely, we introduce novel, fully empirical concentration bounds for a broad class of importance weighting risk estimators. These bounds are general enough to cover most existing estimators and pave the way for the development of new ones. In particular, our pursuit of the tightest bound within this class motivates a novel estimator (LS), that logarithmically smooths large importance weights. The bound for LS is provably tighter than all its competitors, and naturally results in improved policy selection and learning strategies. Extensive policy evaluation, selection, and learning experiments highlight the versatility and favorable performance of LS.

The Intrinsic Dimension (ID) is a key concept in unsupervised learning and feature selection, as it is a lower bound to the number of variables which are necessary to describe a system. However, in almost any real-world dataset the ID depends on the scale at which the data are analysed. Quite typically at a small scale, the ID is very large, as the data are affected by measurement errors. At large scale, the ID can also be erroneously large, due to the curvature and the topology of the manifold containing the data. In this work, we introduce an automatic protocol to select the sweet spot, namely the correct range of scales in which the ID is meaningful and useful. This protocol is based on imposing that for distances smaller than the correct scale the density of the data is constant. Since to estimate the density it is necessary to know the ID, this condition is imposed self-consistently. We illustrate the usefulness and robustness of this procedure by benchmarks on artificial and real-world datasets.

Fairness is a critical objective in policy design and algorithmic decision-making. Identifying the causal pathways of unfairness requires knowledge of the underlying structural causal model, which may be incomplete or unavailable. This limits the practicality of causal fairness analysis in complex or low-knowledge domains. To mitigate this practicality gap, we advocate for developing efficient causal discovery methods for fairness applications. To this end, we introduce local discovery for direct discrimination (LD3): a polynomial-time algorithm that recovers structural evidence of direct discrimination. LD3 performs a linear number of conditional independence tests with respect to variable set size. Moreover, we propose a graphical criterion for identifying the weighted controlled direct effect (CDE), a qualitative measure of direct discrimination. We prove that this criterion is satisfied by the knowledge returned by LD3, increasing the accessibility of the weighted CDE as a causal fairness measure. Taking liver transplant allocation as a case study, we highlight the potential impact of LD3 for modeling fairness in complex decision systems. Results on real-world data demonstrate more plausible causal relations than baselines, which took 197x to 5870x longer to execute.

Preferential Bayesian optimization (PBO) is a sample-efficient framework for learning human preferences between candidate designs. PBO classically relies on homoscedastic noise models to represent human aleatoric uncertainty. Yet, such noise fails to accurately capture the varying levels of human aleatoric uncertainty, particularly when the user possesses partial knowledge among different pairs of candidates. For instance, a chemist with solid expertise in glucose-related molecules may easily compare two compounds from that family while struggling to compare alcohol-related molecules. Currently, PBO overlooks this uncertainty during the search for a new candidate through the maximization of the acquisition function, consequently underestimating the risk associated with human uncertainty. To address this issue, we propose a heteroscedastic noise model to capture human aleatoric uncertainty. This model adaptively assigns noise levels based on the distance of a specific input to a predefined set of reliable inputs known as anchors provided by the human. Anchors encapsulate partial knowledge and offer insight into the comparative difficulty of evaluating different candidate pairs. Such a model can be seamlessly integrated into the acquisition function, thus leading to candidate design pairs that elegantly trade informativeness and ease of comparison for the human expert. We perform an extensive empirical evaluation of the proposed approach, demonstrating a consistent improvement over homoscedastic PBO.

We re-examine the problem of reconstructing a high-dimensional signal from a small set of linear measurements, in combination with image prior from a diffusion probabilistic model. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component analysis (ICA) and compressed sensing (CS), all of which rely on axis- or subspace-aligned statistical characterization. But many naturally occurring signals, including photographic images, contain richer statistical structure. To exploit such structure, we introduce a general method for obtaining an optimized set of linear measurements, assuming a Bayesian inverse solution that leverages the prior implicit in a neural network trained to perform denoising. We demonstrate that these measurements are distinct from those of PCA and CS, with significant improvements in minimizing squared reconstruction error. In addition, we show that optimizing the measurements for the SSIM perceptual loss leads to perceptually improved reconstruction. Our results highlight the importance of incorporating the specific statistical regularities of natural signals when designing effective linear measurements.

I generalize acyclic deterministic structural equation models to the nondeterministic case and argue that it offers an improved semantics for counterfactuals. The standard, deterministic, semantics developed by Halpern (and based on the initial proposal of Galles & Pearl) assumes that for each assignment of values to parent variables there is a unique assignment to their child variable, and it assumes that the actual world (an assignment of values to all variables of a model) specifies a unique counterfactual world for each intervention. Both assumptions are unrealistic, and therefore I drop both of them in my proposal. I do so by allowing multi-valued functions in the structural equations. In addition, I adjust the semantics so that the solutions to the equations that obtained in the actual world are preserved in any counterfactual world. I motivate the resulting logic by comparing it to the standard one by Halpern and to more recent proposals that are closer to mine. Finally, I extend these models to the probabilistic case and show that they open up the way to identifying counterfactuals even in Causal Bayesian Networks.

We study the identification of causal effects, motivated by two improvements to identifiability which can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable causal effect may become identifiable when certain variables are functional. Second, certain functional variables can be excluded from being observed without affecting the identifiability of a causal effect, which may significantly reduce the number of needed variables in observational data. Our results are largely based on an elimination procedure which removes functional variables from a causal graph while preserving key properties in the resulting causal graph, including the identifiability of causal effects.

Next-generation (xG) wireless networks, with their complex and dynamic nature, present significant challenges to using traditional optimization techniques. Generative AI (GAI) emerges as a powerful tool due to its unique strengths. Unlike traditional optimization techniques and other machine learning methods, GAI excels at learning from real-world network data, capturing its intricacies. This enables safe, offline exploration of various configurations and generation of diverse, unseen scenarios, empowering proactive, data-driven exploration and optimization for xG networks. Additionally, GAI's scalability makes it ideal for large-scale xG networks. This paper surveys how GAI-based models unlock optimization opportunities in xG wireless networks. We begin by providing a review of GAI models and some of the major communication paradigms of xG (e.g., 6G) wireless networks. We then delve into exploring how GAI can be used to improve resource allocation and enhance overall network performance. Additionally, we briefly review the networking requirements for supporting GAI applications in xG wireless networks. The paper further discusses the key challenges and future research directions in leveraging GAI for network optimization. Finally, a case study demonstrates the application of a diffusion-based GAI model for load balancing, carrier aggregation, and backhauling optimization in non-terrestrial networks, a core technology of xG networks. This case study serves as a practical example of how the combination of reinforcement learning and GAI can be implemented to address real-world network optimization problems.

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in probabilistic graphical models (PGMs) still lack corresponding TN-based adaptations. In this work, we advance the connection between PGMs and TNs by formulating and implementing tensor-based solutions for the following inference tasks: (i) computing the partition function, (ii) computing the marginal probability of sets of variables in the model, (iii) determining the most likely assignment to a set of variables, and (iv) the same as (iii) but after having marginalized a different set of variables. We also present a generalized method for generating samples from a learned probability distribution. Our work is motivated by recent technical advances in the fields of quantum circuit simulation, quantum many-body physics, and statistical physics. Through an experimental evaluation, we demonstrate that the integration of these quantum technologies with a series of algorithms introduced in this study significantly improves the effectiveness of existing methods for solving probabilistic inference tasks.