Conditional Independence (CI) graph is a special type of a Probabilistic Graphical Model (PGM) where the feature connections are modeled using an undirected graph and the edge weights show the partial correlation strength between the features. Since the CI graphs capture direct dependence between features, they have been garnering increasing interest within the research community for gaining insights into the systems from various domains, in particular discovering the domain topology. In this work, we propose algorithms for performing knowledge propagation over the CI graphs. Our experiments demonstrate that our techniques improve upon the state-of-the-art on the publicly available Cora and PubMed datasets.

Human-Robot Interaction (HRI) becomes more and more important in a world where robots integrate fast in all aspects of our lives but HRI applications depend massively on the utilized robotic system as well as the deployment environment and cultural differences. Because of these variable dependencies it is often not feasible to use a data-driven approach to train a model for human intent recognition. Expert systems have been proven to close this gap very efficiently. Furthermore, it is important to support understandability in HRI systems to establish trust in the system. To address the above-mentioned challenges in HRI we present an adaptable python library in which current state-of-the-art Models for context recognition can be integrated. For Context-Based Intention Recognition a two-layer Bayesian Network (BN) is used. The bayesian approach offers explainability and clarity in the creation of scenarios and is easily extendable with more modalities. Additionally, it can be used as an expert system if no data is available but can as well be fine-tuned when data becomes available.

Large skew-t factor copula models are attractive for the modeling of financial data because they allow for asymmetric and extreme tail dependence. We show that the copula implicit in the skew-t distribution of Azzalini and Capitanio (2003) allows for a higher level of pairwise asymmetric dependence than two popular alternative skew-t copulas. Estimation of this copula in high dimensions is challenging, and we propose a fast and accurate Bayesian variational inference (VI) approach to do so. The method uses a conditionally Gaussian generative representation of the skew-t distribution to define an augmented posterior that can be approximated accurately. A fast stochastic gradient ascent algorithm is used to solve the variational optimization. The new methodology is used to estimate copula models for intraday returns from 2017 to 2021 on 93 U.S. equities. The copula captures substantial heterogeneity in asymmetric dependence over equity pairs, in addition to the variability in pairwise correlations. We show that intraday predictive densities from the skew-t copula are more accurate than from some other copula models, while portfolio selection strategies based on the estimated pairwise tail dependencies improve performance relative to the benchmark index.

Spike trains data find a growing list of applications in computational neuroscience, imaging, streaming data and finance. Machine learning strategies for spike trains are based on various neural network and probabilistic models. The probabilistic approach is relying on parametric or nonparametric specifications of the underlying spike generation model. In this paper we consider the two-class statistical classification problem for a class of spike train data characterized by nonparametrically specified intensity functions. We derive the optimal Bayes rule and next form the plug-in nonparametric kernel classifier. Asymptotical properties of the rules are established including the limit with respect to the increasing recording time interval and the size of a training set. In particular the convergence of the kernel classifier to the Bayes rule is proved. The obtained results are supported by a finite sample simulation studies.

Multi-task learning is frequently used to model a set of related response variables from the same set of features, improving predictive performance and modeling accuracy relative to methods that handle each response variable separately. Despite the potential of multi-task learning to yield more powerful inference than single-task alternatives, prior work in this area has largely omitted uncertainty quantification. Our focus in this paper is a common multi-task problem in neuroimaging, where the goal is to understand the relationship between multiple cognitive task scores (or other subject-level assessments) and brain connectome data collected from imaging. We propose a framework for selective inference to address this problem, with the flexibility to: (i) jointly identify the relevant covariates for each task through a sparsity-inducing penalty, and (ii) conduct valid inference in a model based on the estimated sparsity structure. Our framework offers a new conditional procedure for inference, based on a refinement of the selection event that yields a tractable selection-adjusted likelihood. This gives an approximate system of estimating equations for maximum likelihood inference, solvable via a single convex optimization problem, and enables us to efficiently form confidence intervals with approximately the correct coverage. Applied to both simulated data and data from the Adolescent Brain Cognitive Development (ABCD) study, our selective inference methods yield tighter confidence intervals than commonly used alternatives, such as data splitting. We also demonstrate through simulations that multi-task learning with selective inference can more accurately recover true signals than single-task methods.

Thesis concerns the study and development of hierarchical representations for spatio-temporal visual attention modeling and understanding in video sequences. More specifically, we propose two computational models for visual attention. First, we present a generative probabilistic model for context-aware visual attention modeling and understanding. Secondly, we develop a deep network architecture for visual attention modeling, which first estimates top-down spatio-temporal visual attention, and ultimately serves for modeling attention in the temporal domain. The first part of the thesis introduces our first proposal: a generative probabilistic framework for spatio-temporal visual attention modeling and understanding.

Consider a setting where multiple parties holding sensitive data aim to collaboratively learn population level statistics, but pooling the sensitive data sets is not possible. We propose a framework in which each party shares a differentially private synthetic twin of their data. We study the feasibility of combining such synthetic twin data sets for collaborative learning on real-world health data from the UK Biobank. We discover that parties engaging in the collaborative learning via shared synthetic data obtain more accurate estimates of target statistics compared to using only their local data. This finding extends to the difficult case of small heterogeneous data sets. Furthermore, the more parties participate, the larger and more consistent the improvements become. Finally, we find that data sharing can especially help parties whose data contain underrepresented groups to perform better-adjusted analysis for said groups. Based on our results we conclude that sharing of synthetic twins is a viable method for enabling learning from sensitive data without violating privacy constraints even if individual data sets are small or do not represent the overall population well. The setting of distributed sensitive data is often a bottleneck in biomedical research, which our study shows can be alleviated with privacy-preserving collaborative learning methods.

We address the task of probabilistic anomaly attribution in the black-box regression setting, where the goal is to compute the probability distribution of the attribution score of each input variable, given an observed anomaly. The training dataset is assumed to be unavailable. This task differs from the standard XAI (explainable AI) scenario, since we wish to explain the anomalous deviation from a black-box prediction rather than the black-box model itself. We begin by showing that mainstream model-agnostic explanation methods, such as the Shapley values, are not suitable for this task because of their ``deviation-agnostic property.'' We then propose a novel framework for probabilistic anomaly attribution that allows us to not only compute attribution scores as the predictive mean but also quantify the uncertainty of those scores. This is done by considering a generative process for perturbations that counter-factually bring the observed anomalous observation back to normalcy. We introduce a variational Bayes algorithm for deriving the distributions of per variable attribution scores. To the best of our knowledge, this is the first probabilistic anomaly attribution framework that is free from being deviation-agnostic.

Differential privacy (DP) is by far the most widely accepted framework for mitigating privacy risks in machine learning. However, exactly how small the privacy parameter $\epsilon$ needs to be to protect against certain privacy risks in practice is still not well-understood. In this work, we study data reconstruction attacks for discrete data and analyze it under the framework of multiple hypothesis testing. We utilize different variants of the celebrated Fano's inequality to derive upper bounds on the inferential power of a data reconstruction adversary when the model is trained differentially privately. Importantly, we show that if the underlying private data takes values from a set of size $M$, then the target privacy parameter $\epsilon$ can be $O(\log M)$ before the adversary gains significant inferential power. Our analysis offers theoretical evidence for the empirical effectiveness of DP against data reconstruction attacks even at relatively large values of $\epsilon$.

Abstract-- Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem is usually difficult to solve and prone to local minima. However, recent advancements in computing hardware allow for parallel trajectory optimisation where multiple solutions are obtained simultaneously, each initialised from a different starting point. Unfortunately, without a strategy preventing two solutions to collapse on each other, naive parallel optimisation can suffer from mode collapse diminishing the efficiency of the approach and the likelihood of finding a global solution. In this paper we leverage on recent advances in the theory of rough paths to devise an algorithm for parallel trajectory optimisation that promotes diversity over the range of solutions, therefore avoiding mode collapses and achieving better global properties. These can be roughly divided into two main paradigms: sampling-based and trajectory optimisation algorithms. Sampling-based planning [2] is a class of planners with Trajectory optimisation is one of the key tools in robotic probabilistically complete and asymptotically optimal guarantees motion, used to find control signals or paths in obstaclecluttered [3]. These approaches decompose the planning problem environments that allow the robot to perform into a series of sequential decision-making problems with desired tasks. These trajectories can represent a variety of a tree-based [4] or graph-based [5], [6] approach.