In this work, we deepen on the use of normalizing flows for causal reasoning. Specifically, we first leverage recent results on non-linear ICA to show that causal models are identifiable from observational data given a causal ordering, and thus can be recovered using autoregressive normalizing flows (NFs). Second, we analyze different design and learning choices for causal normalizing flows to capture the underlying causal data-generating process. Third, we describe how to implement the do-operator in causal NFs, and thus, how to answer interventional and counterfactual questions. Finally, in our experiments, we validate our design and training choices through a comprehensive ablation study; compare causal NFs to other approaches for approximating causal models; and empirically demonstrate that causal NFs can be used to address real-world problems, where the presence of mixed discrete-continuous data and partial knowledge on the causal graph is the norm. The code for this work can be found at https://github.com/psanch21/causal-flows.

Optimizing proper loss functions is popularly believed to yield predictors with good calibration properties; the intuition being that for such losses, the global optimum is to predict the ground-truth probabilities, which is indeed calibrated. However, typical machine learning models are trained to approximately minimize loss over restricted families of predictors, that are unlikely to contain the ground truth. Under what circumstances does optimizing proper loss over a restricted family yield calibrated models? What precise calibration guarantees does it give? In this work, we provide a rigorous answer to these questions. We replace the global optimality with a local optimality condition stipulating that the (proper) loss of the predictor cannot be reduced much by post-processing its predictions with a certain family of Lipschitz functions. We show that any predictor with this local optimality satisfies smooth calibration as defined in Kakade-Foster (2008), B{\l}asiok et al. (2023). Local optimality is plausibly satisfied by well-trained DNNs, which suggests an explanation for why they are calibrated from proper loss minimization alone. Finally, we show that the connection between local optimality and calibration error goes both ways: nearly calibrated predictors are also nearly locally optimal.

The notion of causality assumes a paramount position within the realm of human cognition. Over the past few decades, there has been significant advancement in the domain of causal effect estimation across various disciplines, including but not limited to computer science, medicine, economics, and industrial applications. Given the continued advancements in deep learning methodologies, there has been a notable surge in its utilization for the estimation of causal effects using counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective functions to estimate counterfactual data unbiasedly. Different from the existing surveys on causal models in machine learning, this review mainly focuses on the overview of the deep causal models, and its core contributions are as follows: 1) we cast insight on a comprehensive overview of deep causal models from both timeline of development and method classification perspectives; 2) we outline some typical applications of causal effect estimation to industry; 3) we also endeavor to present a detailed categorization and analysis on relevant datasets, source codes and experiments.

Gradient boosting performs exceptionally in most prediction problems and scales well to large datasets. In this paper we prove that a ``lassoed'' gradient boosted tree algorithm with early stopping achieves faster than $n^{-1/4}$ L2 convergence in the large nonparametric space of cadlag functions of bounded sectional variation. This rate is remarkable because it does not depend on the dimension, sparsity, or smoothness. We use simulation and real data to confirm our theory and demonstrate empirical performance and scalability on par with standard boosting. Our convergence proofs are based on a novel, general theorem on early stopping with empirical loss minimizers of nested Donsker classes.

Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in the presence of variations in the operating conditions, the model should be continuously refined to compensate for dynamics changes. In this paper, we present a self-supervised learning approach that actively models the dynamics of nonlinear robotic systems. We combine offline learning from past experience and online learning from current robot interaction with the unknown environment. These two ingredients enable a highly sample-efficient and adaptive learning process, capable of accurately inferring model dynamics in real-time even in operating regimes that greatly differ from the training distribution. Moreover, we design an uncertainty-aware model predictive controller that is heuristically conditioned to the aleatoric (data) uncertainty of the learned dynamics. This controller actively chooses the optimal control actions that (i) optimize the control performance and (ii) improve the efficiency of online learning sample collection. We demonstrate the effectiveness of our method through a series of challenging real-world experiments using a quadrotor system. Our approach showcases high resilience and generalization capabilities by consistently adapting to unseen flight conditions, while it significantly outperforms classical and adaptive control baselines.

The increasing use of stochastic models for describing complex phenomena warrants surrogate models that capture the reference model characteristics at a fraction of the computational cost, foregoing potentially expensive Monte Carlo simulation. The predominant approach of fitting a large neural network and then pruning it to a reduced size has commonly neglected shortcomings. The produced surrogate models often will not capture the sensitivities and uncertainties inherent in the original model. In particular, (higher-order) derivative information of such surrogates could differ drastically. Given a large enough network, we expect this derivative information to match. However, the pruned model will almost certainly not share this behavior. In this paper, we propose to find surrogate models by using sensitivity information throughout the learning and pruning process. We build on work using Interval Adjoint Significance Analysis for pruning and combine it with the recent advancements in Sobolev Training to accurately model the original sensitivity information in the pruned neural network based surrogate model. We experimentally underpin the method on an example of pricing a multidimensional Basket option modelled through a stochastic differential equation with Brownian motion. The proposed method is, however, not limited to the domain of quantitative finance, which was chosen as a case study for intuitive interpretations of the sensitivities. It serves as a foundation for building further surrogate modelling techniques considering sensitivity information.

Despite its exceptional soft tissue contrast, Magnetic Resonance Imaging (MRI) faces the challenge of long scanning times compared to other modalities like X-ray radiography. Shortening scanning times is crucial in clinical settings, as it increases patient comfort, decreases examination costs and improves throughput. Recent advances in compressed sensing (CS) and deep learning allow accelerated MRI acquisition by reconstructing high-quality images from undersampled data. While reconstruction algorithms have received most of the focus, designing acquisition trajectories to optimize reconstruction quality remains an open question. This thesis explores two approaches to address this gap in the context of Cartesian MRI. First, we propose two algorithms, lazy LBCS and stochastic LBCS, that significantly improve upon G\"ozc\"u et al.'s greedy learning-based CS (LBCS) approach. These algorithms scale to large, clinically relevant scenarios like multi-coil 3D MR and dynamic MRI, previously inaccessible to LBCS. Additionally, we demonstrate that generative adversarial networks (GANs) can serve as a natural criterion for adaptive sampling by leveraging variance in the measurement domain to guide acquisition. Second, we delve into the underlying structures or assumptions that enable mask design algorithms to perform well in practice. Our experiments reveal that state-of-the-art deep reinforcement learning (RL) approaches, while capable of adaptation and long-horizon planning, offer only marginal improvements over stochastic LBCS, which is neither adaptive nor does long-term planning. Altogether, our findings suggest that stochastic LBCS and similar methods represent promising alternatives to deep RL. They shine in particular by their scalability and computational efficiency and could be key in the deployment of optimized acquisition trajectories in Cartesian MRI.

In the field of surrogate modeling, polynomial chaos expansion (PCE) allows practitioners to construct inexpensive yet accurate surrogates to be used in place of the expensive forward model simulations. For black-box simulations, non-intrusive PCE allows the construction of these surrogates using a set of simulation response evaluations. In this context, the PCE coefficients can be obtained using linear regression, which is also known as point collocation or stochastic response surfaces. Regression exhibits better scalability and can handle noisy function evaluations in contrast to other non-intrusive approaches, such as projection. However, since over-sampling is generally advisable for the linear regression approach, the simulation requirements become prohibitive for expensive forward models. We propose to leverage transfer learning whereby knowledge gained through similar PCE surrogate construction tasks (source domains) is transferred to a new surrogate-construction task (target domain) which has a limited number of forward model simulations (training data). The proposed transfer learning strategy determines how much, if any, information to transfer using new techniques inspired by Bayesian modeling and data assimilation. The strategy is scrutinized using numerical investigations and applied to an engineering problem from the oil and gas industry.

We develop methods for estimating Fr\'echet bounds on (possibly high-dimensional) distribution classes in which some variables are continuous-valued. We establish the statistical correctness of the computed bounds under uncertainty in the marginal constraints and demonstrate the usefulness of our algorithms by evaluating the performance of machine learning (ML) models trained with programmatic weak supervision (PWS). PWS is a framework for principled learning from weak supervision inputs (e.g., crowdsourced labels, knowledge bases, pre-trained models on related tasks, etc), and it has achieved remarkable success in many areas of science and engineering. Unfortunately, it is generally difficult to validate the performance of ML models trained with PWS due to the absence of labeled data. Our algorithms address this issue by estimating sharp lower and upper bounds for performance metrics such as accuracy/recall/precision/F1 score.

Unmanned aerial vehicles (UAVs) in flying ad-hoc networks (FANETs) face security challenges due to the dynamic and distributed nature of these networks. This paper presents the Federated Learning-based Intrusion Detection System (FL-IDS), an innovative approach designed to improve FANET security. FL-IDS leverages federated learning to address privacy concerns of centralized intrusion detection systems. FL-IDS operates in a decentralized manner, enabling UAVs to collaboratively train a global intrusion detection model without sharing raw data. Local models are assigned to each UAV, using client-specific data, and only updated model weights are shared with a central server. This preserves privacy while utilizing collective intelligence for effective intrusion detection. Experimental results show FL-IDS's competitive performance with Central IDS (C-IDS) while mitigating privacy concerns. The Bias Towards Specific Clients (BTSC) method further enhances FL-IDS performance, surpassing C-IDS even at lower attacker ratios. A comparative analysis with traditional intrusion detection methods, including Local IDS (L-IDS), provides insights into FL-IDS's strengths. This study significantly contributes to FANET security by introducing a privacy-aware, decentralized intrusion detection approach tailored to the unique challenges of UAV networks.