Conditional quantile treatment effect (CQTE) can provide insight into the effect of a treatment beyond the conditional average treatment effect (CATE). This ability to provide information over multiple quantiles of the response makes CQTE especially valuable in cases where the effect of a treatment is not well-modelled by a location shift, even conditionally on the covariates. Nevertheless, the estimation of CQTE is challenging and often depends upon the smoothness of the individual quantiles as a function of the covariates rather than smoothness of the CQTE itself. This is in stark contrast to CATE where it is possible to obtain high-quality estimates which have less dependency upon the smoothness of the nuisance parameters when the CATE itself is smooth. Moreover, relative smoothness of the CQTE lacks the interpretability of smoothness of the CATE making it less clear whether it is a reasonable assumption to make. We combine the desirable properties of CATE and CQTE by considering a new estimand, the conditional quantile comparator (CQC). The CQC not only retains information about the whole treatment distribution, similar to CQTE, but also having more natural examples of smoothness and is able to leverage simplicity in an auxiliary estimand. We provide finite sample bounds on the error of our estimator, demonstrating its ability to exploit simplicity. We validate our theory in numerical simulations which show that our method produces more accurate estimates than baselines. Finally, we apply our methodology to a study on the effect of employment incentives on earnings across different age groups. We see that our method is able to reveal heterogeneity of the effect across different quantiles.

We conduct the convergence analysis of parameter estimation in the contaminated mixture of experts. This model is motivated from the prompt learning problem where ones utilize prompts, which can be formulated as experts, to fine-tune a large-scaled pre-trained model for learning downstream tasks. There are two fundamental challenges emerging from the analysis: (i) the proportion in the mixture of the pre-trained model and the prompt may converge to zero where the prompt vanishes during the training; (ii) the algebraic interaction among parameters of the pre-trained model and the prompt can occur via some partial differential equation and decelerate the prompt learning. In response, we introduce a distinguishability condition to control the previous parameter interaction. Additionally, we also consider various types of expert structures to understand their effects on the parameter estimation. In each scenario, we provide comprehensive convergence rates of parameter estimation along with the corresponding minimax lower bounds.

Transformers have demonstrated exceptional in-context learning capabilities, yet the theoretical understanding of the underlying mechanisms remain limited. A recent work (Elhage et al., 2021) identified a "rich" in-context mechanism known as induction head, contrasting with "lazy" $n$-gram models that overlook long-range dependencies. In this work, we provide both approximation and optimization analyses of how transformers implement induction heads. In the approximation analysis, we formalize both standard and generalized induction head mechanisms, and examine how transformers can efficiently implement them, with an emphasis on the distinct role of each transformer submodule. For the optimization analysis, we study the training dynamics on a synthetic mixed target, composed of a 4-gram and an in-context 2-gram component. This setting enables us to precisely characterize the entire training process and uncover an {\em abrupt transition} from lazy (4-gram) to rich (induction head) mechanisms as training progresses.

Graphs are a highly expressive abstraction for modeling entities and their relations, such as molecular structures, social networks, and traffic networks. Deep Graph Networks (DGNs) have emerged as a family of deep learning models that can effectively process and learn such structured information. However, learning effective information propagation patterns within DGNs remains a critical challenge that heavily influences the model capabilities, both in the static domain and in the temporal domain (where features and/or topology evolve). Given this challenge, this thesis investigates the dynamics of information propagation within DGNs for static and dynamic graphs, focusing on their design as dynamical systems. Throughout this work, we provide theoretical and empirical evidence to demonstrate the effectiveness of our proposed architectures in propagating and preserving long-term dependencies between nodes, and in learning complex spatio-temporal patterns from irregular and sparsely sampled dynamic graphs. In summary, this thesis provides a comprehensive exploration of the intersection between graphs, deep learning, and dynamical systems, offering insights and advancements for the field of graph representation learning and paving the way for more effective and versatile graph-based learning models.

This study employs explainable artificial intelligence (XAI) techniques to analyze the behavior of asphalt concrete with varying aggregate gradations, focusing on resilience modulus (MR) and dynamic stability (DS) as measured by wheel track tests. The research utilizes a deep learning model with a multi-layer perceptron architecture to predict MR and DS based on aggregate gradation parameters derived from Bailey's Method, including coarse aggregate ratio (CA), fine aggregate coarse ratio (FAc), and other mix design variables. The model's performance was validated using k-fold cross-validation, demonstrating superior accuracy compared to alternative machine learning approaches. SHAP (SHapley Additive exPlanations) values were applied to interpret the model's predictions, providing insights into the relative importance and impact of different gradation characteristics on asphalt concrete performance. Key findings include the identification of critical aggregate size thresholds, particularly the 0.6 mm sieve size, which significantly influences both MR and DS. The study revealed size-dependent performance of aggregates, with coarse aggregates primarily affecting rutting resistance and medium-fine aggregates influencing stiffness. The research also highlighted the importance of aggregate lithology in determining rutting resistance. To facilitate practical application, web-based interfaces were developed for predicting MR and DS, incorporating explainable features to enhance transparency and interpretation of results. This research contributes a data-driven approach to understanding the complex relationships between aggregate gradation and asphalt concrete performance, potentially informing more efficient and performance-oriented mix design processes in the future.

The Bayesian two-step change point detection method is popular for the Hawkes process due to its simplicity and intuitiveness. However, the non-conjugacy between the point process likelihood and the prior requires most existing Bayesian two-step change point detection methods to rely on non-conjugate inference methods. These methods lack analytical expressions, leading to low computational efficiency and impeding timely change point detection. To address this issue, this work employs data augmentation to propose a conjugate Bayesian two-step change point detection method for the Hawkes process, which proves to be more accurate and efficient. Extensive experiments on both synthetic and real data demonstrate the superior effectiveness and efficiency of our method compared to baseline methods. Additionally, we conduct ablation studies to explore the robustness of our method concerning various hyperparameters.

We propose a new way of building portfolios of cryptocurrencies that provide good diversification properties to investors. First, we seek to filter these digital assets by creating some clusters based on their path signature. The goal is to identify similar patterns in the behavior of these highly volatile assets. Once such clusters have been built, we propose "optimal" portfolios by comparing the performances of such portfolios to a universe of unfiltered digital assets. Our intuition is that clustering based on path signatures will make it easier to capture the main trends and features of a group of cryptocurrencies, and allow parsimonious portfolios that reduce excessive transaction fees. Empirically, our assumptions seem to be satisfied.

Novel optical imaging techniques, such as hyperspectral imaging (HSI) combined with machine learning-based (ML) analysis, have the potential to revolutionize clinical surgical imaging. However, these novel modalities face a shortage of large-scale, representative clinical data for training ML algorithms, while preclinical animal data is abundantly available through standardized experiments and allows for controlled induction of pathological tissue states, which is not ethically possible in patients. To leverage this situation, we propose a novel concept called "xeno-learning", a cross-species knowledge transfer paradigm inspired by xeno-transplantation, where organs from a donor species are transplanted into a recipient species. Using a total of 11,268 HSI images from humans as well as porcine and rat models, we show that although spectral signatures of organs differ across species, shared pathophysiological mechanisms manifest as comparable relative spectral changes across species. Such changes learnt in one species can thus be transferred to a new species via a novel "physiology-based data augmentation" method, enabling the large-scale secondary use of preclinical animal data for humans. The resulting ethical, monetary, and performance benefits of the proposed knowledge transfer paradigm promise a high impact of the methodology on future developments in the field.

In this paper, a multi-modal vehicle positioning framework that jointly localizes vehicles with channel state information (CSI) and images is designed. In particular, we consider an outdoor scenario where each vehicle can communicate with only one BS, and hence, it can upload its estimated CSI to only its associated BS. Each BS is equipped with a set of cameras, such that it can collect a small number of labeled CSI, a large number of unlabeled CSI, and the images taken by cameras. To exploit the unlabeled CSI data and position labels obtained from images, we design an meta-learning based hard expectation-maximization (EM) algorithm. Specifically, since we do not know the corresponding relationship between unlabeled CSI and the multiple vehicle locations in images, we formulate the calculation of the training objective as a minimum matching problem. To reduce the impact of label noises caused by incorrect matching between unlabeled CSI and vehicle locations obtained from images and achieve better convergence, we introduce a weighted loss function on the unlabeled datasets, and study the use of a meta-learning algorithm for computing the weighted loss. Subsequently, the model parameters are updated according to the weighted loss function of unlabeled CSI samples and their matched position labels obtained from images. Simulation results show that the proposed method can reduce the positioning error by up to 61% compared to a baseline that does not use images and uses only CSI fingerprint for vehicle positioning.

In recent years, the popularity of artificial intelligence has surged due to its widespread application in various fields. The financial sector has harnessed its advantages for multiple purposes, including the development of automated trading systems designed to interact autonomously with markets to pursue different aims. In this work, we focus on the possibility of recognizing and leveraging intraday price patterns in the Foreign Exchange market, known for its extensive liquidity and flexibility. Our approach involves the implementation of a Reinforcement Learning algorithm called Fitted Natural Actor-Critic. This algorithm allows the training of an agent capable of effectively trading by means of continuous actions, which enable the possibility of executing orders with variable trading sizes. This feature is instrumental to realistically model transaction costs, as they typically depend on the order size. Furthermore, it facilitates the integration of risk-averse approaches to induce the agent to adopt more conservative behavior. The proposed approaches have been empirically validated on EUR-USD historical data.