Differential privacy is a well-established framework for safeguarding sensitive information in data. While extensively applied across various domains, its application to network data -- particularly at the node level -- remains underexplored. Existing methods for node-level privacy either focus exclusively on query-based approaches, which restrict output to pre-specified network statistics, or fail to preserve key structural properties of the network. In this work, we propose GRAND (Graph Release with Assured Node Differential privacy), which is, to the best of our knowledge, the first network release mechanism that releases entire networks while ensuring node-level differential privacy and preserving structural properties. Under a broad class of latent space models, we show that the released network asymptotically follows the same distribution as the original network. The effectiveness of the approach is evaluated through extensive experiments on both synthetic and real-world datasets.

We consider a Bayesian diffusion control problem of expected terminal utility maximization. The controller imposes a prior distribution on the unknown drift of an underlying diffusion. The Bayesian optimal control, tracking the posterior distribution of the unknown drift, can be characterized explicitly. However, in practice, the prior will generally be incorrectly specified, and the degree of model misspecification can have a significant impact on policy performance. To mitigate this and reduce overpessimism, we introduce a distributionally robust Bayesian control (DRBC) formulation in which the controller plays a game against an adversary who selects a prior in divergence neighborhood of a baseline prior. The adversarial approach has been studied in economics and efficient algorithms have been proposed in static optimization settings. We develop a strong duality result for our DRBC formulation. Combining these results together with tools from stochastic analysis, we are able to derive a loss that can be efficiently trained (as we demonstrate in our numerical experiments) using a suitable neural network architecture. As a result, we obtain an effective algorithm for computing the DRBC optimal strategy. The methodology for computing the DRBC optimal strategy is greatly simplified, as we show, in the important case in which the adversary chooses a prior from a Kullback-Leibler distributional uncertainty set.

Optimizing high-dimensional black-box functions under black-box constraints is a pervasive task in a wide range of scientific and engineering problems. These problems are typically harder than unconstrained problems due to hard-to-find feasible regions. While Bayesian optimization (BO) methods have been developed to solve such problems, they often struggle with the curse of dimensionality. Recently, generative model-based approaches have emerged as a promising alternative for constrained optimization. However, they suffer from poor scalability and are vulnerable to mode collapse, particularly when the target distribution is highly multi-modal. In this paper, we propose a new framework to overcome these challenges. Our method iterates through two stages. First, we train flow-based models to capture the data distribution and surrogate models that predict both function values and constraint violations with uncertainty quantification. Second, we cast the candidate selection problem as a posterior inference problem to effectively search for promising candidates that have high objective values while not violating the constraints. During posterior inference, we find that the posterior distribution is highly multi-modal and has a large plateau due to constraints, especially when constraint feedback is given as binary indicators of feasibility. To mitigate this issue, we amortize the sampling from the posterior distribution in the latent space of flow-based models, which is much smoother than that in the data space. We empirically demonstrate that our method achieves superior performance on various synthetic and real-world constrained black-box optimization tasks. Our code is publicly available \href{https://github.com/umkiyoung/CiBO}{here}.

Feature importance quantification faces a fundamental challenge: when predictors are correlated, standard methods systematically underestimate their contributions. We prove that major existing approaches target identical population functionals under squared-error loss, revealing why they share this correlation-induced bias. To address this limitation, we introduce \emph{Disentangled Feature Importance (DFI)}, a nonparametric generalization of the classical $R^2$ decomposition via optimal transport. DFI transforms correlated features into independent latent variables using a transport map, eliminating correlation distortion. Importance is computed in this disentangled space and attributed back through the transport map's sensitivity. DFI provides a principled decomposition of importance scores that sum to the total predictive variability for latent additive models and to interaction-weighted functional ANOVA variances more generally, under arbitrary feature dependencies. We develop a comprehensive semiparametric theory for DFI. For general transport maps, we establish root-$n$ consistency and asymptotic normality of importance estimators in the latent space, which extends to the original feature space for the Bures-Wasserstein map. Notably, our estimators achieve second-order estimation error, which vanishes if both regression function and transport map estimation errors are $o_{\mathbb{P}}(n^{-1/4})$. By design, DFI avoids the computational burden of repeated submodel refitting and the challenges of conditional covariate distribution estimation, thereby achieving computational efficiency.

This thesis contributes to the theoretical understanding of local update algorithms, especially Local SGD, in distributed and federated optimization under realistic models of data heterogeneity. A central focus is on the bounded second-order heterogeneity assumption, which is shown to be both necessary and sufficient for local updates to outperform centralized or mini-batch methods in convex and non-convex settings. The thesis establishes tight upper and lower bounds in several regimes for various local update algorithms and characterizes the min-max complexity of multiple problem classes. At its core is a fine-grained consensus-error-based analysis framework that yields sharper finite-time convergence bounds under third-order smoothness and relaxed heterogeneity assumptions. The thesis also extends to online federated learning, providing fundamental regret bounds under both first-order and bandit feedback. Together, these results clarify when and why local updates offer provable advantages, and the thesis serves as a self-contained guide for analyzing Local SGD in heterogeneous environments.

Graphs are a powerful data structure for representing relational data and are widely used to describe complex real-world systems. Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) can both leverage graph-structured data, but their inherent functioning is different. The question is how do they compare in capturing the information contained in networked datasets? We address this objective by solving a link prediction task and we conduct three main experiments, on both synthetic and real networks: one focuses on how PGMs and GNNs handle input features, while the other two investigate their robustness to noisy features and increasing heterophily of the graph. PGMs do not necessarily require features on nodes, while GNNs cannot exploit the network edges alone, and the choice of input features matters. We find that GNNs are outperformed by PGMs when input features are low-dimensional or noisy, mimicking many real scenarios where node attributes might be scalar or noisy. Then, we find that PGMs are more robust than GNNs when the heterophily of the graph is increased. Finally, to assess performance beyond prediction tasks, we also compare the two frameworks in terms of their computational complexity and interpretability.

Learning the underlying dynamics from data with deep neural networks has shown remarkable potential in modeling various complex physical dynamics. However, current approaches are constrained in their ability to make reliable predictions in a specific domain and struggle with generalizing to unseen systems that are governed by the same general dynamics but differ in environmental characteristics. In this work, we formulate a parameter-efficient method, Fourier Neural Simulator for Dynamical Adaptation (FNSDA), that can readily generalize to new dynamics via adaptation in the Fourier space. Specifically, FNSDA identifies the shareable dynamics based on the known environments using an automatic partition in Fourier modes and learns to adjust the modes specific for each new environment by conditioning on low-dimensional latent systematic parameters for efficient generalization. We evaluate our approach on four representative families of dynamic systems, and the results show that FNSDA can achieve superior or competitive generalization performance compared to existing methods with a significantly reduced parameter cost. Our code is available at https://github.com/WonderSeven/FNSDA.

Due to its invariance to rigid transformations such as rotations and reflections, Procrustes-Wasserstein (PW) was introduced in the literature as an optimal transport (OT) distance, alternative to Wasserstein and more suited to tasks such as the alignment and comparison of point clouds. Having that application in mind, we carefully build a space of discrete probability measures and show that over that space PW actually is a distance. Algorithms to solve the PW problems already exist, however we extend the PW framework by discussing and testing several initialization strategies. We then introduce the notion of PW barycenter and detail an algorithm to estimate it from the data. The result is a new method to compute representative shapes from a collection of point clouds. We benchmark our method against existing OT approaches, demonstrating superior performance in scenarios requiring precise alignment and shape preservation. We finally show the usefulness of the PW barycenters in an archaeological context. Our results highlight the potential of PW in boosting 2D and 3D point cloud analysis for machine learning and computational geometry applications.

Accurately predicting potato sprouting before the emergence of any visual signs is critical for effective storage management, as sprouting degrades both the commercial and nutritional value of tubers. Effective forecasting allows for the precise application of anti-sprouting chemicals (ASCs), minimizing waste and reducing costs. This need has become even more pressing following the ban on Isopropyl N-(3-chlorophenyl) carbamate (CIPC) or Chlorpropham due to health and environmental concerns, which has led to the adoption of significantly more expensive alternative ASCs. Existing approaches primarily rely on visual identification, which only detects sprouting after morphological changes have occurred, limiting their effectiveness for proactive management. A reliable early prediction method is therefore essential to enable timely intervention and improve the efficiency of post-harvest storage strategies, where early refers to detecting sprouting before any visible signs appear. In this work, we address the problem of early prediction of potato sprouting. To this end, we propose a novel machine learning (ML)-based approach that enables early prediction of potato sprouting using electrophysiological signals recorded from tubers using proprietary sensors. Our approach preprocesses the recorded signals, extracts relevant features from the wavelet domain, and trains supervised ML models for early sprouting detection. Additionally, we incorporate uncertainty quantification techniques to enhance predictions. Experimental results demonstrate promising performance in the early detection of potato sprouting by accurately predicting the exact day of sprouting for a subset of potatoes and while showing acceptable average error across all potatoes. Despite promising results, further refinements are necessary to minimize prediction errors, particularly in reducing the maximum observed deviations.

In this study, we propose, evaluate and compare three quantum inspired data encoding strategies, Instance Level Strategy (ILS), Global Discrete Strategy (GDS) and Class Conditional Value Strategy (CCVS), for transforming classical data into quantum data for use in pure classical machine learning models. The primary objective is to reduce high encoding time while ensuring correct encoding values and analyzing their impact on classification performance. The Instance Level Strategy treats each row of dataset independently; mimics local quantum states. Global Discrete Value Based encoding strategy maps all unique feature values across the full dataset to quantum states uniformly. In contrast, the Class conditional Value based encoding strategy encodes unique values separately for each class, preserving class dependent information. We apply these encoding strategies to a classification task and assess their impact on en-coding efficiency, correctness, model accuracy, and computational cost. By analyzing the trade offs between encoding time, precision, and predictive performance, this study provides insights into optimizing quantum inspired data transformations for classical machine learning workflows.