Function Classes for Identifiable Nonlinear Independent Component Analysis

Unsupervised learning of latent variable models (LVMs) is widely used to represent data in machine learning. When such models reflect the ground truth factors and the mechanisms mapping them to observations, there is reason to expect that they allow generalization in downstream tasks. It is however well known that such identifiability guaranties are typically not achievable without putting constraints on the model class. This is notably the case for nonlinear Independent Component Analysis, in which the LVM maps statistically independent variables to observations via a deterministic nonlinear function. Several families of spurious solutions fitting perfectly the data, but that do not correspond to the ground truth factors can be constructed in generic settings. However, recent work suggests that constraining the function class of such models may promote identifiability. Specifically, function classes with constraints on their partial derivatives, gathered in the Jacobian matrix, have been proposed, such as orthogonal coordinate transformations (OCT), which impose orthogonality of the Jacobian columns. In the present work, we prove that a subclass of these transformations, conformal maps, is identifiable and provide novel theoretical results suggesting that OCTs have properties that prevent families of spurious solutions to spoil identifiability in a generic setting.Comment: 43 page

Multi armed bandits and quantum channel oracles

Multi armed bandits are one of the theoretical pillars of reinforcement learning. Recently, the investigation of quantum algorithms for multi armed bandit problems was started, and it was found that a quadratic speed-up is possible when the arms and the randomness of the rewards of the arms can be queried in superposition. Here we introduce further bandit models where we only have limited access to the randomness of the rewards, but we can still query the arms in superposition. We show that this impedes any speed-up of quantum algorithms.Comment: 44 page

A Measure-Theoretic Axiomatisation of Causality

Causality is a central concept in a wide range of research areas, yet there is still no universally agreed axiomatisation of causality. We view causality both as an extension of probability theory and as a study of \textit{what happens when one intervenes on a system}, and argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. To that end, we propose the notion of a \textit{causal space}, consisting of a probability space along with a collection of transition probability kernels, called \textit{causal kernels}, that encode the causal information of the space. Our proposed framework is not only rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks including, for example, cycles, latent variables and stochastic processes

Absolute, pressure-dependent validation of a calibration-free, airborne laser hygrometer transfer standard (SEALDH-II) from 5 to 1200 ppmv using a metrological humidity generator

Highly accurate water vapor measurements are indispensable for understanding a variety of scientific questions as well as industrial processes. While in metrology water vapor concentrations can be defined, generated, and measured with relative uncertainties in the single percentage range, field-deployable airborne instruments deviate even under quasistatic laboratory conditions up to 10–20 %. The novel SEALDH-II hygrometer, a calibration-free, tuneable diode laser spectrometer, bridges this gap by implementing a new holistic concept to achieve higher accuracy levels in the field. We present in this paper the absolute validation of SEALDH-II at a traceable humidity generator during 23 days of permanent operation at 15 different H₂O mole fraction levels between 5 and 1200 ppmv. At each mole fraction level, we studied the pressure dependence at six different gas pressures between 65 and 950 hPa. Further, we describe the setup for this metrological validation, the challenges to overcome when assessing water vapor measurements on a high accuracy level, and the comparison results. With this validation, SEALDH-II is the first airborne, metrologically validated humidity transfer standard which links several scientific airborne and laboratory measurement campaigns to the international metrological water vapor scale

Learning Linear Causal Representations from Interventions under General Nonlinear Mixing

We study the problem of learning causal representations from unknown, latent interventions in a general setting, where the latent distribution is Gaussian but the mixing function is completely general. We prove strong identifiability results given unknown single-node interventions, i.e., without having access to the intervention targets. This generalizes prior works which have focused on weaker classes, such as linear maps or paired counterfactual data. This is also the first instance of causal identifiability from non-paired interventions for deep neural network embeddings. Our proof relies on carefully uncovering the high-dimensional geometric structure present in the data distribution after a non-linear density transformation, which we capture by analyzing quadratic forms of precision matrices of the latent distributions. Finally, we propose a contrastive algorithm to identify the latent variables in practice and evaluate its performance on various tasks.Comment: 38 page

Flow Matching for Scalable Simulation-Based Inference

Neural posterior estimation methods based on discrete normalizing flows have become established tools for simulation-based inference (SBI), but scaling them to high-dimensional problems can be challenging. Building on recent advances in generative modeling, we here present flow matching posterior estimation (FMPE), a technique for SBI using continuous normalizing flows. Like diffusion models, and in contrast to discrete flows, flow matching allows for unconstrained architectures, providing enhanced flexibility for complex data modalities. Flow matching, therefore, enables exact density evaluation, fast training, and seamless scalability to large architectures--making it ideal for SBI. We show that FMPE achieves competitive performance on an established SBI benchmark, and then demonstrate its improved scalability on a challenging scientific problem: for gravitational-wave inference, FMPE outperforms methods based on comparable discrete flows, reducing training time by 30% with substantially improved accuracy. Our work underscores the potential of FMPE to enhance performance in challenging inference scenarios, thereby paving the way for more advanced applications to scientific problems

Causal Component Analysis

Independent Component Analysis (ICA) aims to recover independent latent variables from observed mixtures thereof. Causal Representation Learning (CRL) aims instead to infer causally related (thus often statistically dependent) latent variables, together with the unknown graph encoding their causal relationships. We introduce an intermediate problem termed Causal Component Analysis (CauCA). CauCA can be viewed as a generalization of ICA, modelling the causal dependence among the latent components, and as a special case of CRL. In contrast to CRL, it presupposes knowledge of the causal graph, focusing solely on learning the unmixing function and the causal mechanisms. Any impossibility results regarding the recovery of the ground truth in CauCA also apply for CRL, while possibility results may serve as a stepping stone for extensions to CRL. We characterize CauCA identifiability from multiple datasets generated through different types of interventions on the latent causal variables. As a corollary, this interventional perspective also leads to new identifiability results for nonlinear ICA -- a special case of CauCA with an empty graph -- requiring strictly fewer datasets than previous results. We introduce a likelihood-based approach using normalizing flows to estimate both the unmixing function and the causal mechanisms, and demonstrate its effectiveness through extensive synthetic experiments in the CauCA and ICA setting

Functional Plasticity after Unilateral Vestibular Midbrain Infarction in Human Positron Emission Tomography

The aim of the study was to uncover mechanisms of central compensation of vestibular function at brainstem, cerebellar, and cortical levels in patients with acute unilateral midbrain infarctions presenting with an acute vestibular tone imbalance. Eight out of 17 patients with unilateral midbrain infarctions were selected on the basis of signs of a vestibular tone imbalance, e.g., graviceptive (tilts of perceived verticality) and oculomotor dysfunction (skew deviation, ocular torsion) in F18-fluordeoxyglucose (FDG)-PET at two time points: A) in the acute stage, and B) after recovery 6 months later. Lesion-behavior mapping analyses with MRI verified the exact structural lesion sites. Group subtraction analyses and comparisons with healthy controls were performed with Statistic Parametric Mapping for the PET data. A comparison of PET A of acute-stage patients with that of healthy controls showed increases in glucose metabolism in the cerebellum, motion-sensitive visual cortex areas, and inferior temporal lobe, but none in vestibular cortex areas. At the supratentorial level bilateral signal decreases dominated in the thalamus, frontal eye fields, and anterior cingulum. These decreases persisted after clinical recovery in contrast to the increases. The transient activations can be attributed to ocular motor and postural recovery (cerebellum) and sensory substitution of vestibular function for motion perception (visual cortex). The persisting deactivation in the thalamic nuclei and frontal eye fields allows alternative functional interpretations of the thalamic nuclei: either a disconnection of ascending sensory input occurs or there is a functional mismatch between expected and actual vestibular activity. Our data support the view that both thalami operate separately for each hemisphere but receive vestibular input from ipsilateral and contralateral midbrain integration centers. Normally they have gatekeeper functions for multisensory input to the cortex and automatic motor output to subserve balance and locomotion, as well as sensorimotor integration