Reasoning about uncertainty is vital in many real-life autonomous systems. However, current state-of-the-art planning algorithms cannot either reason about uncertainty explicitly, or do so with a high computational burden. Here, we focus on making informed decisions efficiently, using reward functions that explicitly deal with uncertainty. We formulate an approximation, namely an abstract observation model, that uses an aggregation scheme to alleviate computational costs. We derive bounds on the expected information-theoretic reward function and, as a consequence, on the value function. We then propose a method to refine aggregation to achieve identical action selection with a fraction of the computational time.

Learning generalizeable policies from visual input in the presence of visual distractions is a challenging problem in reinforcement learning. Recently, there has been renewed interest in bisimulation metrics as a tool to address this issue; these metrics can be used to learn representations that are, in principle, invariant to irrelevant distractions by measuring behavioural similarity between states. An accurate, unbiased, and scalable estimation of these metrics has proved elusive in continuous state and action scenarios. We propose entangled bisimulation, a bisimulation metric that allows the specification of the distance function between states, and can be estimated without bias in continuous state and action spaces. We show how entangled bisimulation can meaningfully improve over previous methods on the Distracting Control Suite (DCS), even when added on top of data augmentation techniques.

Molecular optimization aims to discover novel molecules with improved properties, which is often formulated as a reinforcement learning problem by modeling the construction of a molecule using a Markov decision process. The performance of such agents is measured by the quality of generated molecules. In the community of machine learning, most of the molecular optimization methods have been verified in silico, i.e., in computer simulation. Since most of the generated molecules are novel, their properties are unknown and we have to resort to a predictor to estimate the properties. However, little attention has been paid to how reliable such estimates are, which makes the existing performance estimates less reliable. In this paper, we study the statistical performance of such performance estimators to enhance our understanding of the evaluation protocol and we discuss several directions to improve it. Let us first introduce a common practice to estimate the performance in silico.

Approximate Bayesian computation (ABC) is a popular likelihood-free inference method for models with intractable likelihood functions. As ABC methods usually rely on comparing summary statistics of observed and simulated data, the choice of the statistics is crucial. This choice involves a trade-off between loss of information and dimensionality reduction, and is often determined based on domain knowledge. However, handcrafting and selecting suitable statistics is a laborious task involving multiple trial-and-error steps. In this work, we introduce an active learning method for ABC statistics selection which reduces the domain expert's work considerably. By involving the experts, we are able to handle misspecified models, unlike the existing dimension reduction methods. Moreover, empirical results show better posterior estimates than with existing methods, when the simulation budget is limited.

For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set of summary statistics. These statistics need to retain the information that is relevant for constraining the parameters but cancel out the noise. They can thus be seen as thermodynamic state variables, for general stochastic models. For many scientific applications, we need strictly more summary statistics than model parameters to reach a satisfactory approximation of the posterior. Therefore, we propose to use the inner dimension of deep neural network based Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information on the noise that has been used to generate the training data. We validate the approach empirically on two types of stochastic models.

Directed Acyclic Graphs (DAGs) provide a powerful framework to model causal relationships among variables in multivariate settings; in addition, through the do-calculus theory, they allow for the identification and estimation of causal effects between variables also from pure observational data. In this setting, the process of inferring the DAG structure from the data is referred to as causal structure learning or causal discovery. We introduce BCDAG, an R package for Bayesian causal discovery and causal effect estimation from Gaussian observational data, implementing the Markov chain Monte Carlo (MCMC) scheme proposed by Castelletti & Mascaro (2021). Our implementation scales efficiently with the number of observations and, whenever the DAGs are sufficiently sparse, with the number of variables in the dataset. The package also provides functions for convergence diagnostics and for visualizing and summarizing posterior inference. In this paper, we present the key features of the underlying methodology along with its implementation in BCDAG. We then illustrate the main functions and algorithms on both real and simulated datasets.

As a structured prediction task, scene graph generation aims to build a visually-grounded scene graph to explicitly model objects and their relationships in an input image. Currently, the mean field variational Bayesian framework is the de facto methodology used by the existing methods, in which the unconstrained inference step is often implemented by a message passing neural network. However, such formulation fails to explore other inference strategies, and largely ignores the more general constrained optimization models. In this paper, we present a constrained structure learning method, for which an explicit constrained variational inference objective is proposed. Instead of applying the ubiquitous message-passing strategy, a generic constrained optimization method - entropic mirror descent - is utilized to solve the constrained variational inference step. We validate the proposed generic model on various popular scene graph generation benchmarks and show that it outperforms the state-of-the-art methods.

In this thesis a probabilistic framework is developed and proposed for Dynamic Object Recognition in 3D Environments. A software package is developed using C++ and Python in ROS that performs the detection and tracking task. Furthermore, a novel Gaussian Process Regression (GPR) based method is developed to detect ground points in different urban scenarios of regular, sloped and rough. The ground surface behavior is assumed to only demonstrate local input-dependent smoothness. kernel's length-scales are obtained. Bayesian inference is implemented sing \textit{Maximum a Posteriori} criterion. The log-marginal likelihood function is assumed to be a multi-task objective function, to represent a whole-frame unbiased view of the ground at each frame because adjacent segments may not have similar ground structure in an uneven scene while having shared hyper-parameter values. Simulation results shows the effectiveness of the proposed method in uneven and rough scenes which outperforms similar Gaussian process based ground segmentation methods.

How can we plan efficiently in a large and complex environment when the time budget is limited? However, there are three main limitations of this "twophase" Given the original simulator of the environment, paradigm, where a simulator is learned offline and which may be computationally very demanding, we then used as-is for online simulation and planning. First, no propose to learn online an approximate but much planning is possible until the offline learning phase finishes, faster simulator that improves over time. To plan which can take a long time. Second, the separation of learning reliably and efficiently while the approximate simulator and planning raises a question on what data collection policy is learning, we develop a method that adaptively should be used during training to ensure good online prediction decides which simulator to use for every simulation, during planning. We empirically demonstrate that when based on a statistic that measures the accuracy the training data is collected by a uniform random policy, the of the approximate simulator. This allows us to learned influence predictors can perform poorly during online use the approximate simulator to replace the original planning, due to distribution shift. Third, completely replacing simulator for faster simulations when it is accurate the original simulator with the approximate one after enough under the current context, thus trading training implies a risk of poor planning performance in certain off simulation speed and accuracy. Experimental situations, which is hard to detect in advance.

In this paper, we derive upper bounds on generalization errors for deep neural networks with Markov datasets. These bounds are developed based on Koltchinskii and Panchenko's approach for bounding the generalization error of combined classifiers with i.i.d. datasets. The development of new symmetrization inequalities in high-dimensional probability for Markov chains is a key element in our extension, where the pseudo-spectral gap of the infinitesimal generator of the Markov chain plays as a key parameter in these inequalities. We also propose a simple method to convert these bounds and other similar ones in traditional deep learning and machine learning to Bayesian counterparts for both i.i.d. and Markov datasets. Extensions to $m$-order homogeneous Markov chains such as AR and ARMA models and mixtures of several Markov data services are given, where the spectral method in functional analysis is used to derive these results.