In this work, we propose a new approach to R-D estimation from the perspective of optimal transport.

Uncertainty quantification (UQ) over graphs arises in a number of safety-critical applications in network science. The Gaussian process (GP), as a classical Bayesian framework for UQ, has been developed to handle graph-structured data by devising topology-aware kernel functions. However, such GP-based approaches are limited not only by the prohibitive computational complexity, but also the strict modeling assumptions that might yield poor coverage, especially with labels arriving on the fly. To effect scalability, we devise a novel graph-aware parametric GP model by leveraging the random feature (RF)-based kernel approximation, which is amenable to efficient recursive Bayesian model updates. To further allow for adaptivity, an ensemble of graph-aware RF-based scalable GPs have been leveraged, with per-GP weight adapted to data arriving incrementally. To ensure valid coverage with robustness to model mis-specification, we wed the GP-based set predictors with the online conformal prediction framework, which post-processes the prediction sets using adaptive thresholds. Experimental results the proposed method yields improved coverage and efficient prediction sets over existing baselines by adaptively ensembling the GP models and setting the key threshold parameters in CP.

Mixtures of linear dynamical systems (MoLDS) provide a path to model time-series data that exhibit diverse temporal dynamics across trajectories. However, its application remains challenging in complex and noisy settings, limiting its effectiveness for neural data analysis. Tensor-based moment methods can provide global identifiability guarantees for MoLDS, but their performance degrades under noise and complexity. Commonly used expectation-maximization (EM) methods offer flexibility in fitting latent models but are highly sensitive to initialization and prone to poor local minima. Here, we propose a tensor-based method that provides identifiability guarantees for learning MoLDS, which is followed by EM updates to combine the strengths of both approaches. The novelty in our approach lies in the construction of moment tensors using the input-output data to recover globally consistent estimates of mixture weights and system parameters. These estimates can then be refined through a Kalman EM algorithm, with closed-form updates for all LDS parameters. We validate our framework on synthetic benchmarks and real-world datasets. On synthetic data, the proposed Tensor-EM method achieves more reliable recovery and improved robustness compared to either pure tensor or randomly initialized EM methods. We then analyze neural recordings from the primate somatosensory cortex while a non-human primate performs reaches in different directions. Our method successfully models and clusters different conditions as separate subsystems, consistent with supervised single-LDS fits for each condition. Finally, we apply this approach to another neural dataset where monkeys perform a sequential reaching task. These results demonstrate that MoLDS provides an effective framework for modeling complex neural data, and that Tensor-EM is a reliable approach to MoLDS learning for these applications.

Out-of-Distribution (OOD) detection is critical to AI reliability and safety, yet in many practical settings, only a limited amount of training data is available. Bayesian Neural Networks (BNNs) are a promising class of model on which to base OOD detection, because they explicitly represent epistemic (i.e. model) uncertainty. In the small training data regime, BNNs are especially valuable because they can incorporate prior model information. We introduce a new family of Bayesian posthoc OOD scores based on expected logit vectors, and compare 5 Bayesian and 4 deterministic posthoc OOD scores. Experiments on MNIST and CIFAR-10 In-Distributions, with 5000 training samples or less, show that the Bayesian methods outperform corresponding deterministic methods.

Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $\Vert \cdot \Vert_*$. However, despite the assortment of computational methods for such problems, there is a surprising lack of understanding of the underlying probability distributions being referred to. In this article, we study the distribution with density $f(X)\propto e^{-λ\Vert X\Vert_*}$, finding many of its fundamental attributes to be analytically tractable via differential geometry. We use these facts to design an improved MCMC algorithm for low rank Bayesian inference as well as to learn the penalty parameter $λ$, obviating the need for hyperparameter tuning when this is difficult or impossible. Finally, we deploy these to improve the accuracy and efficiency of low rank Bayesian matrix denoising and completion algorithms in numerical experiments.

We study meta-reinforcement learning in finite-horizon MDPs where related tasks share similar structures in their optimal action-value functions. Specifically, we posit a linear representation $Q^*_h(s,a)=Φ_h(s,a)\,θ^{(k)}_h$ and place a Gaussian meta-prior $ \mathcal{N}(θ^*_h,Σ^*_h)$ over the task-specific parameters $θ^{(k)}_h$. Building on randomized value functions, we propose two Thompson-style algorithms: (i) MTSRL, which learns only the prior mean and performs posterior sampling with the learned mean and known covariance; and (ii) $\text{MTSRL}^{+}$, which additionally estimates the covariance and employs prior widening to control finite-sample estimation error. Further, we develop a prior-alignment technique that couples the posterior under the learned prior with a meta-oracle that knows the true prior, yielding meta-regret guarantees: we match prior-independent Thompson sampling in the small-task regime and strictly improve with more tasks once the prior is learned. Concretely, for known covariance we obtain $\tilde{O}(H^{4}S^{3/2}\sqrt{ANK})$ meta-regret, and with learned covariance $\tilde{O}(H^{4}S^{3/2}\sqrt{AN^3K})$; both recover a better behavior than prior-independent after $K \gtrsim \tilde{O}(H^2)$ and $K \gtrsim \tilde{O}(N^2H^2)$, respectively. Simulations on a stateful recommendation environment (with feature and prior misspecification) show that after brief exploration, MTSRL/MTSRL\(^+\) track the meta-oracle and substantially outperform prior-independent RL and bandit-only meta-baselines. Our results give the first meta-regret guarantees for Thompson-style RL with learned Q-priors, and provide practical recipes (warm-start via RLSVI, OLS aggregation, covariance widening) for experiment-rich settings.

We propose a fully decentralized multi-agent world model that enables both symbol emergence for communication and coordinated behavior through temporal extension of collective predictive coding. Unlike previous research that focuses on either communication or coordination separately, our approach achieves both simultaneously. Our method integrates world models with communication channels, enabling agents to predict environmental dynamics, estimate states from partial observations, and share critical information through bidirectional message exchange with contrastive learning for message alignment. Using a two-agent trajectory drawing task, we demonstrate that our communication-based approach outperforms non-communicative models when agents have divergent perceptual capabilities, achieving the second-best coordination after centralized models. Importantly, our decentralized approach with constraints preventing direct access to other agents' internal states facilitates the emergence of more meaningful symbol systems that accurately reflect environmental states. These findings demonstrate the effectiveness of decentralized communication for supporting coordination while developing shared representations of the environment.

Single nucleotide polymorphism (SNP) datasets are fundamental to genetic studies but pose significant privacy risks when shared. The correlation of SNPs with each other makes strong adversarial attacks such as masked-value reconstruction, kin, and membership inference attacks possible. Existing privacy-preserving approaches either apply differential privacy to statistical summaries of these datasets or offer complex methods that require post-processing and the usage of a publicly available dataset to suppress or selectively share SNPs. In this study, we introduce an innovative framework for generating synthetic SNP sequence datasets using samples derived from time-inhomogeneous hidden Markov models (TIHMMs). To preserve the privacy of the training data, we ensure that each SNP sequence contributes only a bounded influence during training, enabling strong differential privacy guarantees. Crucially, by operating on full SNP sequences and bounding their gradient contributions, our method directly addresses the privacy risks introduced by their inherent correlations. Through experiments conducted on the real-world 1000 Genomes dataset, we demonstrate the efficacy of our method using privacy budgets of $\varepsilon \in [1, 10]$ at $δ=10^{-4}$. Notably, by allowing the transition models of the HMM to be dependent on the location in the sequence, we significantly enhance performance, enabling the synthetic datasets to closely replicate the statistical properties of non-private datasets. This framework facilitates the private sharing of genomic data while offering researchers exceptional flexibility and utility.

Masked diffusion models (MDMs) have recently emerged as a novel framework for language modeling. MDMs generate sentences by iteratively denoising masked sequences, filling in [MASK] tokens step by step. Although MDMs support any-order sampling, performance is highly sensitive to the choice of which position to unmask next. Prior work typically relies on rule-based schedules (e.g., max-confidence, max-margin), which provide ad hoc improvements. In contrast, we replace these heuristics with a learned scheduler. Specifically, we cast denoising as a KL-regularized Markov decision process (MDP) with an explicit reference policy and optimize a regularized objective that admits policy improvement and convergence guarantees under standard assumptions. We prove that the optimized policy under this framework generates samples that more closely match the data distribution than heuristic schedules. Empirically, across four benchmarks, our learned policy consistently outperforms max-confidence: for example, on SUDOKU, where unmasking order is critical, it yields a 20.1% gain over random and a 11.2% gain over max-confidence.

The Internet of Things (IoT) has revolutionized various applications including agriculture, but it still faces challenges in data collection and understanding. This paper proposes a real-time framework with three additional semantic layers to help IoT devices and sensors comprehend data meaning and source. The framework consists of six layers: perception, semantic annotation, interoperability, transportation, semantic reasoning, and application, suitable for dynamic environments. Sensors collect data in the form of voltage, which is then processed by microprocessors or microcontrollers in the semantic annotation and preprocessing layer. Metadata is added to the raw data, including the purpose, ID number, and application. Two semantic algorithms are proposed in the semantic interoperability and ontologies layer: the interoperability semantic algorithm for standardizing file types and the synonym identification algorithm for identifying synonyms. In the transportation layer, raw data and metadata are sent to other IoT devices or cloud computing platforms using techniques like WiFi, Zigbee networks, Bluetooth, and mobile communication networks. A semantic reasoning layer is proposed to infer new knowledge from the existing data, using fuzzy logic, Dempster-Shafer theory, and Bayesian networks. A Graphical User Interface (GUI) is proposed in the application layer to help users communicate with and monitor IoT sensors, devices, and new knowledge inferred. This framework provides a robust solution for managing IoT data, ensuring semantic completeness, and enabling real-time knowledge inference. The integration of uncertainty reasoning methods and semantic interoperability techniques makes this framework a valuable tool for advancing IoT applications in general and in agriculture in particular.