Likelihood-free inference methods based on neural conditional density estimation were shown to drastically reduce the simulation burden in comparison to classical methods such as ABC. When applied in the context of any latent variable model, such as a Hidden Markov model (HMM), these methods are designed to only estimate the parameters, rather than the joint distribution of the parameters and the hidden states. Naive application of these methods to a HMM, ignoring the inference of this joint posterior distribution, will thus produce an inaccurate estimate of the posterior predictive distribution, in turn hampering the assessment of goodness-of-fit. To rectify this problem, we propose a novel, sample-efficient likelihood-free method for estimating the high-dimensional hidden states of an implicit HMM. Our approach relies on learning directly the intractable posterior distribution of the hidden states, using an autoregressive-flow, by exploiting the Markov property. Upon evaluating our approach on some implicit HMMs, we found that the quality of the estimates retrieved using our method is comparable to what can be achieved using a much more computationally expensive SMC algorithm.

We present new Bayesian Last Layer models in the setting of multivariate regression under heteroscedastic noise, and propose an optimization algorithm for parameter learning. Bayesian Last Layer combines Bayesian modelling of the predictive distribution with neural networks for parameterization of the prior, and has the attractive property of uncertainty quantification with a single forward pass. The proposed framework is capable of disentangling the aleatoric and epistemic uncertainty, and can be used to transfer a canonically trained deep neural network to new data domains with uncertainty-aware capability.

Practical Bayesian learning often requires (1) online inference, (2) dynamic models, and (3) ensembling over multiple different models. Recent advances have shown how to use random feature approximations to achieve scalable, online ensembling of Gaussian processes with desirable theoretical properties and fruitful applications. One key to these methods' success is the inclusion of a random walk on the model parameters, which makes models dynamic. We show that these methods can be generalized easily to any basis expansion model and that using alternative basis expansions, such as Hilbert space Gaussian processes, often results in better performance. To simplify the process of choosing a specific basis expansion, our method's generality also allows the ensembling of several entirely different models, for example, a Gaussian process and polynomial regression. Finally, we propose a novel method to ensemble static and dynamic models together.

Recently, there has been a significant focus on exploring the theoretical aspects of deep learning, especially regarding its performance in classification tasks. Bayesian deep learning has emerged as a unified probabilistic framework, seeking to integrate deep learning with Bayesian methodologies seamlessly. However, there exists a gap in the theoretical understanding of Bayesian approaches in deep learning for classification. This study presents an attempt to bridge that gap. By leveraging PAC-Bayes bounds techniques, we present theoretical results on the prediction or misclassification error of a probabilistic approach utilizing Spike-and-Slab priors for sparse deep learning in classification. We establish non-asymptotic results for the prediction error. Additionally, we demonstrate that, by considering different architectures, our results can achieve minimax optimal rates in both low and high-dimensional settings, up to a logarithmic factor. Moreover, our additional logarithmic term yields slight improvements over previous works. Additionally, we propose and analyze an automated model selection approach aimed at optimally choosing a network architecture with guaranteed optimality.

In the realm of multi-arm bandit problems, the Gittins index policy is known to be optimal in maximizing the expected total discounted reward obtained from pulling the Markovian arms. In most realistic scenarios however, the Markovian state transition probabilities are unknown and therefore the Gittins indices cannot be computed. One can then resort to reinforcement learning (RL) algorithms that explore the state space to learn these indices while exploiting to maximize the reward collected. In this work, we propose tabular (QGI) and Deep RL (DGN) algorithms for learning the Gittins index that are based on the retirement formulation for the multi-arm bandit problem. When compared with existing RL algorithms that learn the Gittins index, our algorithms have a lower run time, require less storage space (small Q-table size in QGI and smaller replay buffer in DGN), and illustrate better empirical convergence to the Gittins index. This makes our algorithm well suited for problems with large state spaces and is a viable alternative to existing methods. As a key application, we demonstrate the use of our algorithms in minimizing the mean flowtime in a job scheduling problem when jobs are available in batches and have an unknown service time distribution. Markov decision processes (MDPs) are controlled stochastic processes where a decision maker is required to control the evolution of a Markov chain over its states space by suitably choosing actions that maximize the long-term payoffs. An interesting class of MDPs are the multi-armed bandits (MAB) where given K Markov chains (each Markov chain corresponds to a bandit arm), the decision maker is confronted with a K-tuple (state of each arm) and must choose to pull or activate exactly one arm and collect a corresponding reward.

Consider numerical observations; it is common to calculate their mean and refer to it as central tendency. There are, however, different measures of mean [4]. These measurements are sometimes grouped into families, like Lehmer and Hölder. Distinguishing these measures and better understanding their use involves identifying the link between them and probability density functions (PDFs). For example, the arithmetic mean is the maximum likelihood estimator (MLE) of the position parameter for the normal PDF and the scale parameter for the exponential PDF. For the families of Lehmer and Hölder means, such an interpretation has only recently been proposed for the case of PDFs in the case of the univariate exponential family Let's consider digital observations; it is often common to calculate their mean and designate it as a central tendency. However, there are various measures of the average [2]. These measures are sometimes grouped into families, such as Lehmer and Hölder.

Humans have exceptional tactile sensing capabilities, which they can leverage to solve challenging, partially observable tasks that cannot be solved from visual observation alone. Research in tactile sensing attempts to unlock this new input modality for robots. Lately, these sensors have become cheaper and, thus, widely available. At the same time, the question of how to integrate them into control loops is still an active area of research, with central challenges being partial observability and the contact-rich nature of manipulation tasks. In this study, we propose to use Reinforcement Learning to learn an end-to-end policy, mapping directly from tactile sensor readings to actions. Specifically, we use Dreamer-v3 on a challenging, partially observable robotic insertion task with a Franka Research 3, both in simulation and on a real system. For the real setup, we built a robotic platform capable of resetting itself fully autonomously, allowing for extensive training runs without human supervision. Our preliminary results indicate that Dreamer is capable of utilizing tactile inputs to solve robotic manipulation tasks in simulation and reality. Furthermore, we find that providing the robot with tactile feedback generally improves task performance, though, in our setup, we do not yet include other sensing modalities. In the future, we plan to utilize our platform to evaluate a wide range of other Reinforcement Learning algorithms on tactile tasks.

Prediction of road users' behaviors in the context of autonomous driving has gained considerable attention by the scientific community in the last years. Most works focus on predicting behaviors based on kinematic information alone, a simplification of the reality since road users are humans, and as such they are highly influenced by their surrounding context. In addition, a large plethora of research works rely on powerful Deep Learning techniques, which exhibit high performance metrics in prediction tasks but may lack the ability to fully understand and exploit the contextual semantic information contained in the road scene, not to mention their inability to provide explainable predictions that can be understood by humans. In this work, we propose an explainable road users' behavior prediction system that integrates the reasoning abilities of Knowledge Graphs (KG) and the expressiveness capabilities of Large Language Models (LLM) by using Retrieval Augmented Generation (RAG) techniques. For that purpose, Knowledge Graph Embeddings (KGE) and Bayesian inference are combined to allow the deployment of a fully inductive reasoning system that enables the issuing of predictions that rely on legacy information contained in the graph as well as on current evidence gathered in real time by onboard sensors. Two use cases have been implemented following the proposed approach: 1) Prediction of pedestrians' crossing actions; 2) Prediction of lane change maneuvers. In both cases, the performance attained surpasses the current state of the art in terms of anticipation and F1-score, showing a promising avenue for future research in this field.

Questions combine our mastery of language with our remarkable facility for reasoning about uncertainty. How do people navigate vast hypothesis spaces to pose informative questions given limited cognitive resources? We study these tradeoffs in a classic grounded question-asking task based on the board game Battleship. Our language-informed program sampling (LIPS) model uses large language models (LLMs) to generate natural language questions, translate them into symbolic programs, and evaluate their expected information gain. We find that with a surprisingly modest resource budget, this simple Monte Carlo optimization strategy yields informative questions that mirror human performance across varied Battleship board scenarios. In contrast, LLM-only baselines struggle to ground questions in the board state; notably, GPT-4V provides no improvement over non-visual baselines. Our results illustrate how Bayesian models of question-asking can leverage the statistics of language to capture human priors, while highlighting some shortcomings of pure LLMs as grounded reasoners.

To plan safely in uncertain environments, agents must balance utility with safety constraints. Safe planning problems can be modeled as a chance-constrained partially observable Markov decision process (CC-POMDP) and solutions often use expensive rollouts or heuristics to estimate the optimal value and action-selection policy. This work introduces the ConstrainedZero policy iteration algorithm that solves CC-POMDPs in belief space by learning neural network approximations of the optimal value and policy with an additional network head that estimates the failure probability given a belief. This failure probability guides safe action selection during online Monte Carlo tree search (MCTS). To avoid overemphasizing search based on the failure estimates, we introduce $\Delta$-MCTS, which uses adaptive conformal inference to update the failure threshold during planning. The approach is tested on a safety-critical POMDP benchmark, an aircraft collision avoidance system, and the sustainability problem of safe CO$_2$ storage. Results show that by separating safety constraints from the objective we can achieve a target level of safety without optimizing the balance between rewards and costs.