We develop a general framework for piecewise deterministic Markov process (PDMP) samplers that enables efficient Bayesian inference in non-linear inverse problems with expensive likelihoods. The key ingredient is a surrogate-assisted thinning scheme in which a surrogate model provides a proposal event rate and a robust correction mechanism enforces an upper bound on the true rate by dynamically adjusting an additive offset whenever violations are detected. This construction is agnostic to the choice of surrogate and PDMP, and we demonstrate it for the Zig-Zag sampler and the Bouncy particle sampler with constant, Laplace, and Gaussian process (GP) surrogates, including gradient-informed and adaptively refined GP variants. As a representative application, we consider Bayesian inference of a spatially varying Young's modulus in a one-dimensional linear elasticity problem. Across dimensions, PDMP samplers equipped with GP-based surrogates achieve substantially higher accuracy and effective sample size per forward model evaluation than Random Walk Metropolis algorithm and the No-U-Turn sampler. The Bouncy particle sampler exhibits the most favorable overall efficiency and scaling, illustrating the potential of the proposed PDMP framework beyond this particular setting.

Abstract-- Effective collective decision-making in swarm robotics often requires balancing exploration, communication and individual uncertainty estimation, especially in hazardous environments where direct measurements are limited or costly. We propose a decentralized Bayesian framework that enables a swarm of simple robots to identify the safer of two areas, each characterized by an unknown rate of hazardous events governed by a Poisson process. Robots employ a conjugate prior to gradually predict the times between events and derive confidence estimates to adapt their behavior . Our simulation results show that the robot swarm consistently chooses the correct area while reducing exposure to hazardous events by being sample-efficient. Compared to baseline heuristics, our proposed approach shows better performance in terms of safety and speed of convergence. The proposed scenario has potential to extend the current set of benchmarks in collective decision-making and our method has applications in adaptive risk-aware sampling and exploration in hazardous, dynamic environments. Collective decision-making under uncertainty is a fundamental challenge in multi-robot systems, including domains such as collective perception, environment classification, and spatial consensus [1]-[4]. Decentralized systems (e.g., robot swarms) operate under strict limitations on sensing, communication, and memory. Instead of sharing/storing complete observation histories, robots must maintain compact model representations of their knowledge. It is crucial to develop efficient strategies for collective decision-making, especially when observations are sparse, noisy [5], and gathered from stochastic processes [6]. This is typically characterized as a best-of-n problem [3], [7].

Motivation: Standard genome-wide association studies in cancer genomics rely on statistical significance with multiple testing correction, but systematically fail in underpowered cohorts. In TCGA breast cancer (n=967, 133 deaths), low event rates (13.8%) create severe power limitations, producing false negatives for known drivers and false positives for large passenger genes. Results: We developed a five-criteria computational framework integrating causal inference (inverse probability weighting, doubly robust estimation) with orthogonal biological validation (expression, mutation patterns, literature evidence). Applied to TCGA-BRCA mortality analysis, standard Cox+FDR detected zero genes at FDR<0.05, confirming complete failure in underpowered settings. Our framework correctly identified RYR2 -- a cardiac gene with no cancer function -- as a false positive despite nominal significance (p=0.024), while identifying KMT2C as a complex candidate requiring validation despite marginal significance (p=0.047, q=0.954). Power analysis revealed median power of 15.1% across genes, with KMT2C achieving only 29.8% power (HR=1.55), explaining borderline statistical significance despite strong biological evidence. The framework distinguished true signals from artifacts through mutation pattern analysis: RYR2 showed 29.8% silent mutations (passenger signature) with no hotspots, while KMT2C showed 6.7% silent mutations with 31.4% truncating variants (driver signature). This multi-evidence approach provides a template for analyzing underpowered cohorts, prioritizing biological interpretability over purely statistical significance. Availability: All code and analysis pipelines available at github.com/akarlaraytu/causal-inference-for-cancer-genomics

Bayesian inference is useful to obtain a predictive distribution with a small generalization error. However, since posterior distributions are rarely evaluated analytically, we employ the variational Bayesian inference or sampling method to approximate posterior distributions. When we obtain samples from a posterior distribution, Hamiltonian Monte Carlo (HMC) has been widely used for the continuous variable part and Markov chain Monte Carlo (MCMC) for the discrete variable part. Another sampling method, the bouncy particle sampler (BPS), has been proposed, which combines uniform linear motion and stochastic reflection to perform sampling. BPS was reported to have the advantage of being easier to set simulation parameters than HMC. To accelerate the convergence to a posterior distribution, we introduced parallel tempering (PT) to BPS, and then proposed an algorithm when the inverse temperature exchange rate is set to infinity. We performed numerical simulations and demonstrated its effectiveness for multimodal distribution.

The error-backpropagation (backprop) algorithm remains the most common solution to the credit assignment problem in artificial neural networks.

Area under the receiving operator characteristic curve (AUC) is commonly reported alongside binary prediction models. However, there are concerns that AUC might be a misleading measure of prediction performance in the rare event setting. This setting is common since many events of clinical importance are rare events. We conducted a simulation study to determine when or whether AUC is unstable in the rare event setting. Specifically, we aimed to determine whether the bias and variance of AUC are driven by the number of events or the event rate. We also investigated the behavior of other commonly used measures of prediction performance, including positive predictive value, accuracy, sensitivity, and specificity. Our results indicate that poor AUC behavior -- as measured by empirical bias, variability of cross-validated AUC estimates, and empirical coverage of confidence intervals -- is driven by the minimum class size, not event rate. Performance of sensitivity is driven by the number of events, while that of specificity is driven by the number of non-events. Other measures, including positive predictive value and accuracy, depend on the event rate even in large samples. AUC is reliable in the rare event setting provided that the total number of events is moderately large.

-- Egocentric gesture recognition is a pivotal technology for enhancing natural human-computer interaction, yet traditional RGB-based solutions suffer from motion blur and illumination variations in dynamic scenarios. While event cameras show distinct advantages in handling high dynamic range with ultra-low power consumption, existing RGB-based architectures face inherent limitations in processing asynchronous event streams due to their synchronous frame-based nature. Moreover, from an egocentric perspective, event cameras record data that includes events generated by both head movements and hand gestures, thereby increasing the complexity of gesture recognition. T o address this, we propose a novel network architecture specifically designed for event data processing, incorporating (1) a lightweight CNN with asymmetric depthwise convolutions to reduce parameters while preserving spatiotemporal features, (2) a plug-and-play state-space model as context block that decouples head movement noise from gesture dynamics, and (3) a parameter-free Bins-T emporal Shift Module (BSTM) that shifts features along bins and temporal dimensions to fuse sparse events efficiently. We further establish the EgoEvGesture dataset, the first large-scale dataset for egocentric gesture recognition using event cameras. Experimental results demonstrate that our method achieves 62.7% accuracy tested on unseen subjects with only 7M parameters, 3.1% higher than state-of-the-art approaches. Notable misclassifications in freestyle motions stem from high interpersonal variability and unseen test patterns differing from training data. Moreover, our approach achieved a remarkable accuracy of 97.0% on the DVS128 Gesture, demonstrating the effectiveness and generalization capability of our method on public datasets.