The ability to perceive and reason about social interactions in the context of physical environments is core to human social intelligence and human-machine cooperation. However, no prior dataset or benchmark has systematically evaluated physically grounded perception of complex social interactions that go beyond short actions, such as high-fiving, or simple group activities, such as gathering. In this work, we create a dataset of physically-grounded abstract social events, PHASE, that resemble a wide range of real-life social interactions by including social concepts such as helping another agent. PHASE consists of 2D animations of pairs of agents moving in a continuous space generated procedurally using a physics engine and a hierarchical planner. Agents have a limited field of view, and can interact with multiple objects, in an environment that has multiple landmarks and obstacles. Using PHASE, we design a social recognition task and a social prediction task. PHASE is validated with human experiments demonstrating that humans perceive rich interactions in the social events, and that the simulated agents behave similarly to humans. As a baseline model, we introduce a Bayesian inverse planning approach, SIMPLE (SIMulation, Planning and Local Estimation), which outperforms state-of-the-art feed-forward neural networks. We hope that PHASE can serve as a difficult new challenge for developing new models that can recognize complex social interactions.

Since the seminal work of Venkatakrishnan et al. (2013), Plug & Play (PnP) methods have become ubiquitous in Bayesian imaging. These methods derive Minimum Mean Square Error (MMSE) or Maximum A Posteriori (MAP) estimators for inverse problems in imaging by combining an explicit likelihood function with a prior that is implicitly defined by an image denoising algorithm. The PnP algorithms proposed in the literature mainly differ in the iterative schemes they use for optimisation or for sampling. In the case of optimisation schemes, some recent works guarantee the convergence to a fixed point, albeit not necessarily a MAP estimate. In the case of sampling schemes, to the best of our knowledge, there is no known proof of convergence. There also remain important open questions regarding whether the underlying Bayesian models and estimators are well defined, well-posed, and have the basic regularity properties required to support these numerical schemes. To address these limitations, this paper develops theory, methods, and provably convergent algorithms for performing Bayesian inference with PnP priors. We introduce two algorithms: 1) PnP-ULA (Unadjusted Langevin Algorithm) for Monte Carlo sampling and MMSE inference; and 2) PnP-SGD (Stochastic Gradient Descent) for MAP inference. Using recent results on the quantitative convergence of Markov chains, we establish detailed convergence guarantees for these two algorithms under realistic assumptions on the denoising operators used, with special attention to denoisers based on deep neural networks. We also show that these algorithms approximately target a decision-theoretically optimal Bayesian model that is well-posed. The proposed algorithms are demonstrated on several canonical problems such as image deblurring, inpainting, and denoising, where they are used for point estimation as well as for uncertainty visualisation and quantification.

The main goal in task planning is to build a sequence of actions that takes an agent from an initial state to a goal state. In robotics, this is particularly difficult because actions usually have several possible results, and sensors are prone to produce measurements with error. Partially observable Markov decision processes (POMDPs) are commonly employed, thanks to their capacity to model the uncertainty of actions that modify and monitor the state of a system. However, since solving a POMDP is computationally expensive, their usage becomes prohibitive for most robotic applications. In this paper, we propose a task planning architecture for service robotics. In the context of service robot design, we present a scheme to encode knowledge about the robot and its environment, that promotes the modularity and reuse of information. Also, we introduce a new recursive definition of a POMDP that enables our architecture to autonomously build a hierarchy of POMDPs, so that it can be used to generate and execute plans that solve the task at hand. Experimental results show that, in comparison to baseline methods, by following a recursive hierarchical approach the architecture is able to significantly reduce the planning time, while maintaining (or even improving) the robustness under several scenarios that vary in uncertainty and size.

We generalize the'bits back with ANS' method to time-series models with a latent Markov structure. This family of models includes hidden Markov models (HMMs), linear Gaussian state space models (LGSSMs) and many more. We provide experimental evidence that our method is effective for small scale models, and discuss its applicability to larger scale settings such as video compression. Recent work by Townsend et al. (2019) shows the existence of a practical method, called'bits back with ANS' (BB-ANS), for doing lossless compression with a latent variable model, at rates close to the negative variational free energy of the model (this quantity bounds the model's marginal log-likelihood and is often referred to as the'evidence lower bound', or ELBO). BB-ANS depends on a last-in-first-out (LIFO) source coding algorithm called Asymmetric Numeral Systems (ANS; Duda, 2009), and also uses an idea called bits back coding (Wallace, 1990; Hinton & van Camp, 1993).

There are numerous examples in machine learning, statistics, mathematics and deep learning, requiring an algorithm to solve some complicated equations: for instance, maximum likelihood estimation (think about logistic regression or the EM algorithm) or gradient methods (think about stochastic or swarm optimization). Here we are dealing with even more difficult problems, where the solution is not a set of optimal parameters (a finite dimensional object), but a function (an infinite dimensional object). The context is discrete, chaotic dynamical systems, with applications to weather forecasting, population growth models, complex econometric systems, image encryption, chemistry (mixtures), physics (how matter reaches an equilibrium temperature), astronomy (how celestial man-made or natural bodies end up having stable or unstable orbits), or stock market prices, to name a few. These are referred to as complex systems. The solutions to the problems discussed here requires numerical methods, as usually no exact solution is known.

Inductive inference in supervised classification context constitutes to methods and approaches to assign some objects or items into different predefined classes using a formal rule that is derived from training data and possibly some additional auxiliary information. The optimality of such an assignment varies under different conditions due to intrinsic attributes of the objects being considered for such a task. One of these cases is when all the objects' features are discrete variables with a priori known categories. As another example, one can consider a modification of this case with a priori unknown categories. These two cases are the main focus of this thesis and based on Bayesian inductive theories, de Finetti type exchangeability is a suitable assumption that facilitates the derivation of classifiers in the former scenario. On the contrary, this type of exchangeability is not applicable in the latter case, instead, it is possible to utilise the partition exchangeability due to John Kingman. These two types of exchangeabilities are discussed and furthermore here I investigate inductive supervised classifiers based on both types of exchangeabilities. I further demonstrate that the classifiers based on de Finetti type exchangeability can optimally handle test items independently of each other in the presence of infinite amounts of training data while on the other hand, classifiers based on partition exchangeability still continue to benefit from joint labelling of all the test items. Additionally, it is shown that the inductive learning process for the simultaneous classifier saturates when the amount of test data tends to infinity.

This paper proposes a new methodology for performing Bayesian inference in imaging inverse problems where the prior knowledge is available in the form of training data. Following the manifold hypothesis and adopting a generative modelling approach, we construct a data-driven prior that is supported on a sub-manifold of the ambient space, which we can learn from the training data by using a variational autoencoder or a generative adversarial network. We establish the existence and well-posedness of the associated posterior distribution and posterior moments under easily verifiable conditions, providing a rigorous underpinning for Bayesian estimators and uncertainty quantification analyses. Bayesian computation is performed by using a parallel tempered version of the preconditioned Crank-Nicolson algorithm on the manifold, which is shown to be ergodic and robust to the non-convex nature of these data-driven models. In addition to point estimators and uncertainty quantification analyses, we derive a model misspecification test to automatically detect situations where the data-driven prior is unreliable, and explain how to identify the dimension of the latent space directly from the training data. The proposed approach is illustrated with a range of experiments with the MNIST dataset, where it outperforms alternative image reconstruction approaches from the state of the art. A model accuracy analysis suggests that the Bayesian probabilities reported by the data-driven models are also remarkably accurate under a frequentist definition of probability.

Machine Learning (ML) seems to be one of the most promising solution to automate partially or completely some of the complex tasks currently realized by humans, such as driving vehicles, recognizing voice, etc. It is also an opportunity to implement and embed new capabilities out of the reach of classical implementation techniques. However, ML techniques introduce new potential risks. Therefore, they have only been applied in systems where their benefits are considered worth the increase of risk. In practice, ML techniques raise multiple challenges that could prevent their use in systems submitted to certification constraints. But what are the actual challenges? Can they be overcome by selecting appropriate ML techniques, or by adopting new engineering or certification practices? These are some of the questions addressed by the ML Certification 3 Workgroup (WG) set-up by the Institut de Recherche Technologique Saint Exup\'ery de Toulouse (IRT), as part of the DEEL Project.

Direct decoding for task-oriented dialogue is known to suffer from the explaining-away effect, manifested in models that prefer short and generic responses. Here we argue for the use of Bayes' theorem to factorize the dialogue task into two models, the distribution of the context given the response, and the prior for the response itself. This approach, an instantiation of the noisy channel model, both mitigates the explaining-away effect and allows the principled incorporation of large pretrained models for the response prior. We present extensive experiments showing that a noisy channel model decodes better responses compared to direct decoding and that a two stage pretraining strategy, employing both open-domain and task-oriented dialogue data, improves over randomly initialized models.

We study planning problems for continuous control systems with uncertainty caused by measurement and process noise. The goal is to find an optimal plan that guarantees that the system reaches a desired goal state within finite time. Measurement noise causes limited observability of system states, and process noise causes uncertainty in the outcome of a given plan. These factors render the problem undecidable in general. Our key contribution is a novel abstraction scheme that employs Kalman filtering as a state estimator to obtain a finite-state model, which we formalize as a Markov decision process (MDP). For this MDP, we employ state-of-the-art model checking techniques to efficiently compute plans that maximize the probability of reaching goal states. Moreover, we account for numerical imprecision in computing the abstraction by extending the MDP with intervals of probabilities as a more robust model. We show the correctness of the abstraction and provide several optimizations that aim to balance the quality of the plan and the scalability of the approach. We demonstrate that our method can handle systems that result in MDPs with thousands of states and millions of transitions.