We study the problem of diffeomorphometric geodesic landmark matching where the objective is to find a diffeomorphism that via its group action maps between two sets of landmarks. It is well-known that the motion of the landmarks, and thereby the diffeomorphism, can be encoded by an initial momentum leading to a formulation where the landmark matching problem can be solved as an optimisation problem over such momenta. The novelty of our work lies in the application of a derivative-free Bayesian inverse method for learning the optimal momentum encoding the diffeomorphic mapping between the template and the target. The method we apply is the ensemble Kalman filter, an extension of the Kalman filter to nonlinear observation operators. We describe an efficient implementation of the algorithm and show several numerical results for various target shapes.

While Shapley Values (SV) are one of the gold standard for interpreting machine learning models, we show that they are still poorly understood, in particular in the presence of categorical variables or of variables of low importance. For instance, we show that the popular practice that consists in summing the SV of dummy variables is false as it provides wrong estimates of all the SV in the model and implies spurious interpretations. Based on the identification of null and active coalitions, and a coalitional version of the SV, we provide a correct computation and inference of important variables. Moreover, a Python library (All the experiments and simulations can be reproduced with the publicly available library Active Coalition of Variables, https://www.github.com/salimamoukou/acv00) that computes reliably conditional expectations and SV for tree-based models, is implemented and compared with state-of-the-art algorithms on toy models and real data sets.

We consider the problem of estimating a particular type of linear non-Gaussian model. Without resorting to the overcomplete Independent Component Analysis (ICA), we show that under some mild assumptions, the model is uniquely identified by a hybrid method. Our method leverages the advantages of constraint-based methods and independent noise-based methods to handle both confounded and unconfounded situations. The first step of our method uses the FCI procedure, which allows confounders and is able to produce asymptotically correct results. The results, unfortunately, usually determine very few unconfounded direct causal relations, because whenever it is possible to have a confounder, it will indicate it. The second step of our procedure finds the unconfounded causal edges between observed variables among only those adjacent pairs informed by the FCI results. By making use of the so-called Triad condition, the third step is able to find confounders and their causal relations with other variables. Afterward, we apply ICA on a notably smaller set of graphs to identify remaining causal relationships if needed. Extensive experiments on simulated data and real-world data validate the correctness and effectiveness of the proposed method.

Causal induction, i.e., identifying unobservable mechanisms that lead to the observable relations among variables, has played a pivotal role in modern scientific discovery, especially in scenarios with only sparse and limited data. Humans, even young toddlers, can induce causal relationships surprisingly well in various settings despite its notorious difficulty. However, in contrast to the commonplace trait of human cognition is the lack of a diagnostic benchmark to measure causal induction for modern Artificial Intelligence (AI) systems. Therefore, in this work, we introduce the Abstract Causal REasoning (ACRE) dataset for systematic evaluation of current vision systems in causal induction. Motivated by the stream of research on causal discovery in Blicket experiments, we query a visual reasoning system with the following four types of questions in either an independent scenario or an interventional scenario: direct, indirect, screening-off, and backward-blocking, intentionally going beyond the simple strategy of inducing causal relationships by covariation. By analyzing visual reasoning architectures on this testbed, we notice that pure neural models tend towards an associative strategy under their chance-level performance, whereas neuro-symbolic combinations struggle in backward-blocking reasoning. These deficiencies call for future research in models with a more comprehensive capability of causal induction.

Spatial-temporal reasoning is a challenging task in Artificial Intelligence (AI) due to its demanding but unique nature: a theoretic requirement on representing and reasoning based on spatial-temporal knowledge in mind, and an applied requirement on a high-level cognitive system capable of navigating and acting in space and time. Recent works have focused on an abstract reasoning task of this kind -- Raven's Progressive Matrices (RPM). Despite the encouraging progress on RPM that achieves human-level performance in terms of accuracy, modern approaches have neither a treatment of human-like reasoning on generalization, nor a potential to generate answers. To fill in this gap, we propose a neuro-symbolic Probabilistic Abduction and Execution (PrAE) learner; central to the PrAE learner is the process of probabilistic abduction and execution on a probabilistic scene representation, akin to the mental manipulation of objects. Specifically, we disentangle perception and reasoning from a monolithic model. The neural visual perception frontend predicts objects' attributes, later aggregated by a scene inference engine to produce a probabilistic scene representation. In the symbolic logical reasoning backend, the PrAE learner uses the representation to abduce the hidden rules. An answer is predicted by executing the rules on the probabilistic representation. The entire system is trained end-to-end in an analysis-by-synthesis manner without any visual attribute annotations. Extensive experiments demonstrate that the PrAE learner improves cross-configuration generalization and is capable of rendering an answer, in contrast to prior works that merely make a categorical choice from candidates.

Normalizing flow models have risen as a popular solution to the problem of density estimation, enabling high-quality synthetic data generation as well as exact probability density evaluation. However, in contexts where individuals are directly associated with the training data, releasing such a model raises privacy concerns. In this work, we propose the use of normalizing flow models that provide explicit differential privacy guarantees as a novel approach to the problem of privacy-preserving density estimation. We evaluate the efficacy of our approach empirically using benchmark datasets, and we demonstrate that our method substantially outperforms previous state-of-the-art approaches. We additionally show how our algorithm can be applied to the task of differentially private anomaly detection.

Model-based planning and prospection are widely studied in both cognitive neuroscience and artificial intelligence (AI), but from different perspectives - and with different desiderata in mind (biological realism versus scalability) that are difficult to reconcile. Here, we introduce a novel method to plan in large POMDPs - Active Tree Search - that combines the normative character and biological realism of a leading planning theory in neuroscience (Active Inference) and the scalability of Monte-Carlo methods in AI. This unification is beneficial for both approaches. On the one hand, using Monte-Carlo planning permits scaling up the biologically grounded approach of Active Inference to large-scale problems. On the other hand, the theory of Active Inference provides a principled solution to the balance of exploration and exploitation, which is often addressed heuristically in Monte-Carlo methods. Our simulations show that Active Tree Search successfully navigates binary trees that are challenging for sampling-based methods, problems that require adaptive exploration, and the large POMDP problem Rocksample. Furthermore, we illustrate how Active Tree Search can be used to simulate neurophysiological responses (e.g., in the hippocampus and prefrontal cortex) of humans and other animals that contain large planning problems. These simulations show that Active Tree Search is a principled realisation of neuroscientific and AI theories of planning, which offers both biological realism and scalability.

We consider a sequential assortment selection problem where the user choice is given by a multinomial logit (MNL) choice model whose parameters are unknown. In each period, the learning agent observes a $d$-dimensional contextual information about the user and the $N$ available items, and offers an assortment of size $K$ to the user, and observes the bandit feedback of the item chosen from the assortment. We propose upper confidence bound based algorithms for this MNL contextual bandit. The first algorithm is a simple and practical method which achieves an $\tilde{\mathcal{O}}(d\sqrt{T})$ regret over $T$ rounds. Next, we propose a second algorithm which achieves a $\tilde{\mathcal{O}}(\sqrt{dT})$ regret. This matches the lower bound for the MNL bandit problem, up to logarithmic terms, and improves on the best known result by a $\sqrt{d}$ factor. To establish this sharper regret bound, we present a non-asymptotic confidence bound for the maximum likelihood estimator of the MNL model that may be of independent interest as its own theoretical contribution. We then revisit the simpler, significantly more practical, first algorithm and show that a simple variant of the algorithm achieves the optimal regret for a broad class of important applications.

We study active structure learning of Bayesian networks in an observational setting, in which there are external limitations on the number of variable values that can be observed from the same sample. Random samples are drawn from the joint distribution of the network variables, and the algorithm iteratively selects which variables to observe in the next sample. We propose a new active learning algorithm for this setting, that finds with a high probability a structure with a score that is $\epsilon$-close to the optimal score. We show that for a class of distributions that we term stable, a sample complexity reduction of up to a factor of $\widetilde{\Omega}(d^3)$ can be obtained, where $d$ is the number of network variables. We further show that in the worst case, the sample complexity of the active algorithm is guaranteed to be almost the same as that of a naive baseline algorithm. To supplement the theoretical results, we report experiments that compare the performance of the new active algorithm to the naive baseline and demonstrate the sample complexity improvements. Code for the algorithm and for the experiments is provided at https://github.com/noabdavid/activeBNSL.

The field of meta-learning seeks to improve the ability of today's machine learning systems to adapt efficiently to small amounts of data. Typically this is accomplished by training a system with a parametrized update rule to improve a task-relevant objective based on supervision or a reward function. However, in many domains of practical interest, task data is unlabeled, or reward functions are unavailable. In this paper we introduce a new approach to address the more general problem of generative meta-learning, which we argue is an important prerequisite for obtaining human-level cognitive flexibility in artificial agents, and can benefit many practical applications along the way. Our contribution leverages the AEVB framework and mean-field variational Bayes, and creates fast-adapting latent-space generative models. At the heart of our contribution is a new result, showing that for a broad class of deep generative latent variable models, the relevant VB updates do not depend on any generative neural network. The theoretical merits of our approach are reflected in empirical experiments.