Regional disaster resilience quantifies the changing nature of physical risks to inform policy instruments ranging from local immediate recovery to international sustainable development. While many existing state-of-practice methods have greatly advanced the dynamic mapping of exposure and hazard, our understanding of large-scale physical vulnerability has remained static, costly, limited, region-specific, coarse-grained, overly aggregated, and inadequately calibrated. With the significant growth in the availability of time-series satellite imagery and derived products for exposure and hazard, we focus our work on the equally important yet challenging element of the risk equation: physical vulnerability. We leverage machine learning methods that flexibly capture spatial contextual relationships, limited temporal observations, and uncertainty in a unified probabilistic spatiotemporal inference framework. We therefore introduce Graph Variational State-Space Model (GraphVSSM), a novel modular spatiotemporal approach that uniquely integrates graph deep learning, state-space modeling, and variational inference using time-series data and prior expert belief systems in a weakly supervised or coarse-to-fine-grained manner. We present three major results: a city-wide demonstration in Quezon City, Philippines; an investigation of sudden changes in the cyclone-impacted coastal Khurushkul community (Bangladesh) and mudslide-affected Freetown (Sierra Leone); and an open geospatial dataset, METEOR 2.5D, that spatiotemporally enhances the existing global static dataset for UN Least Developed Countries (2020). Beyond advancing regional disaster resilience assessment and improving our understanding global disaster risk reduction progress, our method also offers a probabilistic deep learning approach, contributing to broader urban studies that require compositional data analysis in weak supervision.

Quantifying uncertainty in word embeddings is crucial for reliable inference from textual data. However, existing Bayesian methods such as Hamiltonian Monte Carlo (HMC) and mean-field variational inference (MFVI) are either computationally infeasible for large data or rely on restrictive assumptions. We propose a scalable Gibbs sampler using Polya-Gamma augmentation as well as Laplace approximation and compare them with MFVI and HMC for word embeddings. In addition, we address non-identifiability in word embeddings. Our Gibbs sampler and HMC correctly estimate uncertainties, while MFVI does not, and Laplace approximation only does so on large sample sizes, as expected. Applying the Gibbs sampler to the US Congress and the Movielens datasets, we demonstrate the feasibility on larger real data. Finally, as a result of having draws from the full posterior, we show that the posterior mean of word embeddings improves over maximum a posteriori (MAP) estimates in terms of hold-out likelihood, especially for smaller sampling sizes, further strengthening the need for posterior sampling of word embeddings.

Indian classical music relies on a sophisticated microtonal system of 22 shrutis (pitch intervals), which provides expressive nuance beyond the 12-tone equal temperament system. Existing symbolic music processing tools fail to account for these microtonal distinctions and culturally specific raga grammars that govern melodic movement. We present ShrutiSense, a comprehensive symbolic pitch processing system designed for Indian classical music, addressing two critical tasks: (1) correcting westernized or corrupted pitch sequences, and (2) completing melodic sequences with missing values. Our approach employs complementary models for different tasks: a Shruti-aware finite-state transducer (FST) that performs contextual corrections within the 22-shruti framework and a grammar-constrained Shruti hidden Markov model (GC-SHMM) that incorporates raga-specific transition rules for contextual completions. Comprehensive evaluation on simulated data across five ragas demonstrates that ShrutiSense (FST model) achieves 91.3% shruti classification accuracy for correction tasks, with example sequences showing 86.7-90.0% accuracy at corruption levels of 0.2 to 0.4. The system exhibits robust performance under pitch noise up to +/-50 cents, maintaining consistent accuracy across ragas (90.7-91.8%), thus preserving the cultural authenticity of Indian classical music expression.

The energy market has faced a significant structural change in the past decade. The global strife for decarbonization is encouraging the use of renewable energy sources, thus affecting the traditional supply-demand pattern, which were historically dominated by fossil fuels like coal, oil, and natural gas [18]. The growing integration of renewable energy sources into the power supply increases uncertainties in the electricity market due to intermittent nature of the sources such as wind or sunshine [57]. The volatility of the generation sources causes high price shocks and regime changes that is compromising to financial stability as well as investment strategies in the power market [58]. Particularly for countries such as Germany, where the larger percentage of electricity is produced by renewable energy sources [37], levels of sunlight and wind impact electricity generation and thus prices. This introduces, in addition to the physical problem of balancing the grid, non-stationarity to most price models, which further adds unreliability to the predictions. Accurate electricity price forecasting is crucial for efficient resource planning, financial risk management, and stabilization of the market, especially with increasing renewable energy penetration, which enables utilities, businesses, and governments to optimize planning and policy maximization while matching demand and supply. The building of an adequate prediction model, which is relatively straightforward and understandable but at the same time can reflect the market complexity and all influence factors engaged in it is not straightforward, and authors have utilized quite broadly three types of model for prediction: statistical/(probability-based) models [12], machine learning/deep learning models [42], and mixed models [30]. Precise forecasting allows the players in the market to make sound monetary policy.

Density operators, quantum generalizations of probability distributions, are gaining prominence in machine learning due to their foundational role in quantum computing. Generative modeling based on density operator models (\textbf{DOMs}) is an emerging field, but existing training algorithms -- such as those for the Quantum Boltzmann Machine -- do not scale to real-world data, such as the MNIST dataset. The Expectation-Maximization algorithm has played a fundamental role in enabling scalable training of probabilistic latent variable models on real-world datasets. \textit{In this paper, we develop an Expectation-Maximization framework to learn latent variable models defined through \textbf{DOMs} on classical hardware, with resources comparable to those used for probabilistic models, while scaling to real-world data.} However, designing such an algorithm is nontrivial due to the absence of a well-defined quantum analogue to conditional probability, which complicates the Expectation step. To overcome this, we reformulate the Expectation step as a quantum information projection (QIP) problem and show that the Petz Recovery Map provides a solution under sufficient conditions. Using this formulation, we introduce the Density Operator Expectation Maximization (DO-EM) algorithm -- an iterative Minorant-Maximization procedure that optimizes a quantum evidence lower bound. We show that the \textbf{DO-EM} algorithm ensures non-decreasing log-likelihood across iterations for a broad class of models. Finally, we present Quantum Interleaved Deep Boltzmann Machines (\textbf{QiDBMs}), a \textbf{DOM} that can be trained with the same resources as a DBM. When trained with \textbf{DO-EM} under Contrastive Divergence, a \textbf{QiDBM} outperforms larger classical DBMs in image generation on the MNIST dataset, achieving a 40--60\% reduction in the Fréchet Inception Distance.

Conditioning, the central operation in Bayesian statistics, is formalised by the notion of disintegration of measures. However, due to the implicit nature of their definition, constructing disintegrations is often difficult. A folklore result in machine learning conflates the construction of a disintegration with the restriction of probability density functions onto the subset of events that are consistent with a given observation. We provide a comprehensive set of mathematical tools which can be used to construct disintegrations and apply these to find densities of disintegrations on differentiable manifolds. Using our results, we provide a disturbingly simple example in which the restricted density and the disintegration density drastically disagree. Motivated by applications in approximate Bayesian inference and Bayesian inverse problems, we further study the modes of disintegrations. We show that the recently introduced notion of a "conditional mode" does not coincide in general with the modes of the conditional measure obtained through disintegration, but rather the modes of the restricted measure. We also discuss the implications of the discrepancy between the two measures in practice, advocating for the utility of both approaches depending on the modelling context.

We analyze the statistical problem of recovering an atomic signal, modeled as a discrete uniform distribution $μ$, from a binned Poisson convolution model. This question is motivated, among others, by super-resolution laser microscopy applications, where precise estimation of $μ$ provides insights into spatial formations of cellular protein assemblies. Our main results quantify the local minimax risk of estimating $μ$ for a broad class of smooth convolution kernels. This local perspective enables us to sharply quantify optimal estimation rates as a function of the clustering structure of the underlying signal. Moreover, our results are expressed under a multiscale loss function, which reveals that different parts of the underlying signal can be recovered at different rates depending on their local geometry. Overall, these results paint an optimistic perspective on the Poisson deconvolution problem, showing that accurate recovery is achievable under a much broader class of signals than suggested by existing global minimax analyses. Beyond Poisson deconvolution, our results also allow us to establish the local minimax rate of parameter estimation in Gaussian mixture models with uniform weights. We apply our methods to experimental super-resolution microscopy data to identify the location and configuration of individual DNA origamis. In addition, we complement our findings with numerical experiments on runtime and statistical recovery that showcase the practical performance of our estimators and their trade-offs.

Solving Markov Decision Processes (MDPs) remains a central challenge in sequential decision-making, especially when dealing with large state spaces and long-term optimization criteria. A key step in Bellman dynamic programming algorithms is the policy evaluation, which becomes computationally demanding in infinite-horizon settings such as average-reward or discounted-reward formulations. In the context of Markov chains, aggregation and disaggregation techniques have for a long time been used to reduce complexity by exploiting structural decompositions. In this work, we extend these principles to a structured class of MDPs. We define the Single-Input Superstate Decomposable Markov Decision Process (SISDMDP), which combines Chiu's single-input decomposition with Robertazzi's single-cycle recurrence property. When a policy induces this structure, the resulting transition graph can be decomposed into interacting components with centralized recurrence. We develop an exact and efficient policy evaluation method based on this structure. This yields a scalable solution applicable to both average and discounted reward MDPs.

Bayesian neural networks and deep ensemble methods have been proposed for uncertainty quantification; however, they are computationally intensive and require large storage. By utilizing a single deterministic model, we can solve the above issue. We propose an effective method based on feature space density to quantify uncertainty for distributional shifts and out-of-distribution (OOD) detection. Specifically, we leverage the information potential field derived from kernel density estimation to approximate the feature space density of the training set. By comparing this density with the feature space representation of test samples, we can effectively determine whether a distributional shift has occurred. Experiments were conducted on a 2D synthetic dataset (Two Moons and Three Spirals) as well as an OOD detection task (CIFAR-10 vs. SVHN). The results demonstrate that our method outperforms baseline models.

Hyperproperties for Time Window Temporal Logic (HyperTWTL) is a domain-specific formal specification language known for its effectiveness in compactly representing security, opacity, and concurrency properties for robotics applications. This paper focuses on HyperTWTL-constrained secure reinforcement learning (SecRL). Although temporal logic-constrained safe reinforcement learning (SRL) is an evolving research problem with several existing literature, there is a significant research gap in exploring security-aware reinforcement learning (RL) using hyperproperties. Given the dynamics of an agent as a Markov Decision Process (MDP) and opacity/security constraints formalized as HyperTWTL, we propose an approach for learning security-aware optimal policies using dynamic Boltzmann softmax RL while satisfying the HyperTWTL constraints. The effectiveness and scalability of our proposed approach are demonstrated using a pick-up and delivery robotic mission case study. We also compare our results with two other baseline RL algorithms, showing that our proposed method outperforms them.