Probabilistic Graphical Models (PGMs) encode conditional dependencies among random variables using a graph -nodes for variables, links for dependencies- and factorize the joint distribution into lower-dimensional components. This makes PGMs well-suited for analyzing complex systems and supporting decision-making. Recent advances in topological signal processing highlight the importance of variables defined on topological spaces in several application domains. In such cases, the underlying topology shapes statistical relationships, limiting the expressiveness of canonical PGMs. To overcome this limitation, we introduce Colored Markov Random Fields (CMRFs), which model both conditional and marginal dependencies among Gaussian edge variables on topological spaces, with a theoretical foundation in Hodge theory. CMRFs extend classical Gaussian Markov Random Fields by including link coloring: connectivity encodes conditional independence, while color encodes marginal independence. We quantify the benefits of CMRFs through a distributed estimation case study over a physical network, comparing it with baselines with different levels of topological prior.

We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a matrix product state (MPS). The density matrix of the ground truth state admits a tensor train ansatz as a result of the MPS assumption, and we estimate the tensor components of the ansatz through a series of observable estimations, thus outputting an approximation of the density matrix. The procedure is provably convergent with a sample complexity that scales quadratically in the system size. We conduct extensive numerical experiments to show that the procedure outputs an accurate approximation to the quantum state. For observable estimation tasks involving moderately large subsystems, we show that our procedure gives rise to a more accurate estimation than the classical shadow protocol. We also show that sketch tomography is more accurate in observable estimation than quantum states trained from the maximum likelihood estimation formulation.

High quality data is needed to unlock the full potential of AI for end users. However finding new sources of such data is getting harder: most publicly-available human generated data will soon have been used. Additionally, publicly available data often is not representative of users of a particular system -- for example, a research speech dataset of contractors interacting with an AI assistant will likely be more homogeneous, well articulated and self-censored than real world commands that end users will issue. Therefore unlocking high-quality data grounded in real user interactions is of vital interest. However, the direct use of user data comes with significant privacy risks. Differential Privacy (DP) is a well established framework for reasoning about and limiting information leakage, and is a gold standard for protecting user privacy. The focus of this work, \emph{Differentially Private Synthetic data}, refers to synthetic data that preserves the overall trends of source data,, while providing strong privacy guarantees to individuals that contributed to the source dataset. DP synthetic data can unlock the value of datasets that have previously been inaccessible due to privacy concerns and can replace the use of sensitive datasets that previously have only had rudimentary protections like ad-hoc rule-based anonymization. In this paper we explore the full suite of techniques surrounding DP synthetic data, the types of privacy protections they offer and the state-of-the-art for various modalities (image, tabular, text and decentralized). We outline all the components needed in a system that generates DP synthetic data, from sensitive data handling and preparation, to tracking the use and empirical privacy testing. We hope that work will result in increased adoption of DP synthetic data, spur additional research and increase trust in DP synthetic data approaches.

We introduce Density-Informed VAE (DiVAE), a lightweight, data-driven regularizer that aligns the VAE log-prior probability $\log p_Z(z)$ with a log-density estimated from data. Standard VAEs match latents to a simple prior, overlooking density structure in the data-space. DiVAE encourages the encoder to allocate posterior mass in proportion to data-space density and, when the prior is learnable, nudges the prior toward high-density regions. This is realized by adding a robust, precision-weighted penalty to the ELBO, incurring negligible computational overhead. On synthetic datasets, DiVAE (i) improves distributional alignment of latent log-densities to its ground truth counterpart, (ii) improves prior coverage, and (iii) yields better OOD uncertainty calibration. On MNIST, DiVAE improves alignment of the prior with external estimates of the density, providing better interpretability, and improves OOD detection for learnable priors.

Communication is one of the effective means to improve the learning of cooperative policy in multi-agent systems. However, in most real-world scenarios, lossy communication is a prevalent issue. Existing multi-agent reinforcement learning with communication, due to their limited scalability and robustness, struggles to apply to complex and dynamic real-world environments. To address these challenges, we propose a generalized communication-constrained model to uniformly characterize communication conditions across different scenarios. Based on this, we utilize it as a learning prior to distinguish between lossy and lossless messages for specific scenarios. Additionally, we decouple the impact of lossy and lossless messages on distributed decision-making, drawing on a dual mutual information estimatior, and introduce a communication-constrained multi-agent reinforcement learning framework, quantifying the impact of communication messages into the global reward. Finally, we validate the effectiveness of our approach across several communication-constrained benchmarks.

Crowdsourcing enables scalable autonomous driving map construction, but low-cost sensor noise hinders quality from improving with data volume. We propose CSMapping, a system that produces accurate semantic maps and topological road centerlines whose quality consistently increases with more crowdsourced data. For semantic mapping, we train a latent diffusion model on HD maps (optionally conditioned on SD maps) to learn a generative prior of real-world map structure, without requiring paired crowdsourced/HD-map supervision. This prior is incorporated via constrained MAP optimization in latent space, ensuring robustness to severe noise and plausible completion in unobserved areas. Initialization uses a robust vectorized mapping module followed by diffusion inversion; optimization employs efficient Gaussian-basis reparameterization, projected gradient descent zobracket multi-start, and latent-space factor-graph for global consistency. For topological mapping, we apply confidence-weighted k-medoids clustering and kinematic refinement to trajectories, yielding smooth, human-like centerlines robust to trajectory variation. Experiments on nuScenes, Argoverse 2, and a large proprietary dataset achieve state-of-the-art semantic and topological mapping performance, with thorough ablation and scalability studies.

Chronic diseases often progress differently across patients. Rather than randomly varying, there are typically a small number of subtypes for how a disease progresses across patients. To capture this structured heterogeneity, the Subtype and Stage Inference Event-Based Model (SuStaIn) estimates the number of subtypes, the order of disease progression for each subtype, and assigns each patient to a subtype from primarily cross-sectional data. It has been widely applied to uncover the subtypes of many diseases and inform our understanding of them. But how robust is its performance? In this paper, we develop a principled Bayesian subtype variant of the event-based model (BEBMS) and compare its performance to SuStaIn in a variety of synthetic data experiments with varied levels of model misspecification. BEBMS substantially outperforms SuStaIn across ordering, staging, and subtype assignment tasks. Further, we apply BEBMS and SuStaIn to a real-world Alzheimer's data set. We find BEBMS has results that are more consistent with the scientific consensus of Alzheimer's disease progression than SuStaIn.

Active inference proposes expected free energy as an objective for planning and decision-making to adequately balance exploitative and explorative drives in learning agents. The exploitative drive, or what an agent wants to achieve, is formalised as the Kullback-Leibler divergence between a variational probability distribution, updated at each inference step, and a preference probability distribution that indicates what states or observations are more likely for the agent, hence determining the agent's goal in a certain environment. In the literature, the questions of how the preference distribution should be specified and of how a certain specification impacts inference and learning in an active inference agent have been given hardly any attention. In this work, we consider four possible ways of defining the preference distribution, either providing the agents with hard or soft goals and either involving or not goal shaping (i.e., intermediate goals). We compare the performances of four agents, each given one of the possible preference distributions, in a grid world navigation task. Our results show that goal shaping enables the best performance overall (i.e., it promotes exploitation) while sacrificing learning about the environment's transition dynamics (i.e., it hampers exploration).

Network routing is a distributed decision problem which naturally admits numerical performance measures, such as the average time for a packet to travel from source to destination. OLPOMDP, a policy-gradient reinforcement learning algorithm, was successfully applied to simulated network routing under a number of network models. Multiple distributed agents (routers) learned co-operative behavior without explicit inter-agent communication, and they avoided behavior which was individually desirable, but detrimental to the group's overall performance. Furthermore, shaping the reward signal by explicitly penalizing certain patterns of sub-optimal behavior was found to dramatically improve the convergence rate.

This work introduces FiRE/FiRE.1, a novel sketching-based algorithm for anomaly detection to quickly identify rare cell sub-populations in large-scale single-cell RNA sequencing data. This method demonstrated superior performance against state-of-the-art techniques. Furthermore, the thesis proposes Enhash, a fast and resource-efficient ensemble learner that uses projection hashing to detect concept drift in streaming data, proving highly competitive in time and accuracy across various drift types.