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The power prior is a popular class of informative priors for incorporating information from historical data. It involves raising the likelihood for the historical data to a power, which acts as a discounting parameter. When the discounting parameter is modeled as random, the normalized power prior is recommended. Bayesian hierarchical modeling is a widely used method for synthesizing information from different sources, including historical data. In this work, we examine the analytical relationship between the normalized power prior (NPP) and Bayesian hierarchical models (BHM) for \emph{i.i.d.} normal data. We establish a direct relationship between the prior for the discounting parameter of the NPP and the prior for the variance parameter of the BHM. Such a relationship is first established for the case of a single historical dataset, and then extended to the case with multiple historical datasets with dataset-specific discounting parameters. For multiple historical datasets, we develop and establish theory for the BHM-matching NPP (BNPP) which establishes dependence between the dataset-specific discounting parameters leading to inferences that are identical to the BHM. Establishing this relationship not only justifies the NPP from the perspective of hierarchical modeling, but also provides insight on prior elicitation for the NPP. We present strategies on inducing priors on the discounting parameter based on hierarchical models, and investigate the borrowing properties of the BNPP.

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In the rapidly evolving field of autonomous driving, precise segmentation of LiDAR data is crucial for understanding complex 3D environments. Traditional approaches often rely on disparate, standalone codebases, hindering unified advancements and fair benchmarking across models. To address these challenges, we introduce MMDetection3D-lidarseg, a comprehensive toolbox designed for the efficient training and evaluation of state-of-the-art LiDAR segmentation models. We support a wide range of segmentation models and integrate advanced data augmentation techniques to enhance robustness and generalization. Additionally, the toolbox provides support for multiple leading sparse convolution backends, optimizing computational efficiency and performance. By fostering a unified framework, MMDetection3D-lidarseg streamlines development and benchmarking, setting new standards for research and application. Our extensive benchmark experiments on widely-used datasets demonstrate the effectiveness of the toolbox. The codebase and trained models have been publicly available, promoting further research and innovation in the field of LiDAR segmentation for autonomous driving.

Fairness is a critical objective in policy design and algorithmic decision-making. Identifying the causal pathways of unfairness requires knowledge of the underlying structural causal model, which may be incomplete or unavailable. This limits the practicality of causal fairness analysis in complex or low-knowledge domains. To mitigate this practicality gap, we advocate for developing efficient causal discovery methods for fairness applications. To this end, we introduce local discovery for direct discrimination (LD3): a polynomial-time algorithm that recovers structural evidence of direct discrimination. LD3 performs a linear number of conditional independence tests with respect to variable set size. Moreover, we propose a graphical criterion for identifying the weighted controlled direct effect (CDE), a qualitative measure of direct discrimination. We prove that this criterion is satisfied by the knowledge returned by LD3, increasing the accessibility of the weighted CDE as a causal fairness measure. Taking liver transplant allocation as a case study, we highlight the potential impact of LD3 for modeling fairness in complex decision systems. Results on real-world data demonstrate more plausible causal relations than baselines, which took 197x to 5870x longer to execute.

We consider limit probabilities of first order properties in random graphs with a given degree sequence. Under mild conditions on the degree sequence, we show that the closure set of limit probabilities is a finite union of closed intervals. Moreover, we characterize the degree sequences for which this closure set is the interval $[0,1]$, a property that is intimately related with the probability that the random graph is acyclic. As a side result, we compile a full description of the cycle distribution of random graphs and study their fragment (disjoint union of unicyclic components) in the subcritical regime. Finally, we amend the proof of the existence of limit probabilities for first order properties in random graphs with a given degree sequence; this result was already claimed by Lynch~[IEEE LICS 2003] but his proof contained some inaccuracies.

The former CMS Run 2 High Level Trigger (HLT) farm is one of the largest contributors to CMS compute resources, providing about 25k job slots for offline computing. This CPU farm was initially employed as an opportunistic resource, exploited during inter-fill periods, in the LHC Run 2. Since then, it has become a nearly transparent extension of the CMS capacity at CERN, being located on-site at the LHC interaction point 5 (P5), where the CMS detector is installed. This resource has been configured to support the execution of critical CMS tasks, such as prompt detector data reconstruction. It can therefore be used in combination with the dedicated Tier 0 capacity at CERN, in order to process and absorb peaks in the stream of data coming from the CMS detector. The initial configuration for this resource, based on statically configured VMs, provided the required level of functionality. However, regular operations of this cluster revealed certain limitations compared to the resource provisioning and use model employed in the case of WLCG sites. A new configuration, based on a vacuum-like model, has been implemented for this resource in order to solve the detected shortcomings. This paper reports about this redeployment work on the permanent cloud for an enhanced support to CMS offline computing, comparing the former and new models' respective functionalities, along with the commissioning effort for the new setup.

Deep neural networks for image super-resolution (ISR) have shown significant advantages over traditional approaches like the interpolation. However, they are often criticized as 'black boxes' compared to traditional approaches with solid mathematical foundations. In this paper, we attempt to interpret the behavior of deep neural networks in ISR using theories from the field of signal processing. First, we report an intriguing phenomenon, referred to as `the sinc phenomenon.' It occurs when an impulse input is fed to a neural network. Then, building on this observation, we propose a method named Hybrid Response Analysis (HyRA) to analyze the behavior of neural networks in ISR tasks. Specifically, HyRA decomposes a neural network into a parallel connection of a linear system and a non-linear system and demonstrates that the linear system functions as a low-pass filter while the non-linear system injects high-frequency information. Finally, to quantify the injected high-frequency information, we introduce a metric for image-to-image tasks called Frequency Spectrum Distribution Similarity (FSDS). FSDS reflects the distribution similarity of different frequency components and can capture nuances that traditional metrics may overlook. Code, videos and raw experimental results for this paper can be found in: //github.com/RisingEntropy/LPFInISR.

Machine learning models can be trained with formal privacy guarantees via differentially private optimizers such as DP-SGD. In this work, we study such privacy guarantees when the adversary only accesses the final model, i.e., intermediate model updates are not released. In the existing literature, this hidden state threat model exhibits a significant gap between the lower bound provided by empirical privacy auditing and the theoretical upper bound provided by privacy accounting. To challenge this gap, we propose to audit this threat model with adversaries that craft a gradient sequence to maximize the privacy loss of the final model without accessing intermediate models. We demonstrate experimentally how this approach consistently outperforms prior attempts at auditing the hidden state model. When the crafted gradient is inserted at every optimization step, our results imply that releasing only the final model does not amplify privacy, providing a novel negative result. On the other hand, when the crafted gradient is not inserted at every step, we show strong evidence that a privacy amplification phenomenon emerges in the general non-convex setting (albeit weaker than in convex regimes), suggesting that existing privacy upper bounds can be improved.

Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks but lack theoretical understanding with respect to their mean square error (MSE) optimality. This paper proposes a novel denoising strategy inspired by the structure of the MSE-optimal conditional mean estimator (CME). The resulting DM-based denoiser can be conveniently employed using a pre-trained DM, being particularly fast by truncating reverse diffusion steps and not requiring stochastic re-sampling. We present a comprehensive (non-)asymptotic optimality analysis of the proposed diffusion-based denoiser, demonstrating polynomial-time convergence to the CME under mild conditions. Our analysis also derives a novel Lipschitz constant that depends solely on the DM's hyperparameters. Further, we offer a new perspective on DMs, showing that they inherently combine an asymptotically optimal denoiser with a powerful generator, modifiable by switching re-sampling in the reverse process on or off. The theoretical findings are thoroughly validated with experiments based on various benchmark datasets.

Navigating efficiently across vortical flow fields presents a significant challenge in various robotic applications. The dynamic and unsteady nature of vortical flows often disturbs the control of underwater robots, complicating their operation in hydrodynamic environments. Conventional control methods, which depend on accurate modeling, fail in these settings due to the complexity of fluid-structure interactions (FSI) caused by unsteady hydrodynamics. This study proposes a deep reinforcement learning (DRL) algorithm, trained in a data-driven manner, to enable efficient navigation of a robotic fish swimming across vortical flows. Our proposed algorithm incorporates the LSTM architecture and uses several recent consecutive observations as the state to address the issue of partial observation, often due to sensor limitations. We present a numerical study of navigation within a Karman vortex street, created by placing a stationary cylinder in a uniform flow, utilizing the immersed boundary-lattice Boltzmann method (IB-LBM). The aim is to train the robotic fish to discover efficient navigation policies, enabling it to reach a designated target point across the Karman vortex street from various initial positions. After training, the fish demonstrates the ability to rapidly reach the target from different initial positions, showcasing the effectiveness and robustness of our proposed algorithm. Analysis of the results reveals that the robotic fish can leverage velocity gains and pressure differences induced by the vortices to reach the target, underscoring the potential of our proposed algorithm in enhancing navigation in complex hydrodynamic environments.

Runtime analysis has recently been applied to popular evolutionary multi-objective (EMO) algorithms like NSGA-II in order to establish a rigorous theoretical foundation. However, most analyses showed that these algorithms have the same performance guarantee as the simple (G)SEMO algorithm. To our knowledge, there are no runtime analyses showing an advantage of a popular EMO algorithm over the simple algorithm for deterministic problems. We propose such a problem and use it to showcase the superiority of popular EMO algorithms over (G)SEMO: OneTrapZeroTrap is a straightforward generalization of the well-known Trap function to two objectives. We prove that, while GSEMO requires at least $n^n$ expected fitness evaluations to optimise OneTrapZeroTrap, popular EMO algorithms NSGA-II, NSGA-III and SMS-EMOA, all enhanced with a mild diversity mechanism of avoiding genotype duplication, only require $O(n \log n)$ expected fitness evaluations. Our analysis reveals the importance of the key components in each of these sophisticated algorithms and contributes to a better understanding of their capabilities.

The number of artificial intelligence algorithms for learning causal models from data is growing rapidly. Most ``causal discovery'' or ``causal structure learning'' algorithms are primarily validated through simulation studies. However, no widely accepted simulation standards exist and publications often report conflicting performance statistics -- even when only considering publications that simulate data from linear models. In response, several manuscripts have criticized a popular simulation design for validating algorithms in the linear case. We propose a new simulation design for generating linear models for directed acyclic graphs (DAGs): the DAG-adaptation of the Onion (DaO) method. DaO simulations are fundamentally different from existing simulations because they prioritize the distribution of correlation matrices rather than the distribution of linear effects. Specifically, the DaO method uniformly samples the space of all correlation matrices consistent with (i.e. Markov to) a DAG. We also discuss how to sample DAGs and present methods for generating DAGs with scale-free in-degree or out-degree. We compare the DaO method against two alternative simulation designs and provide implementations of the DaO method in Python and R: //github.com/bja43/DaO_simulation. We advocate for others to adopt DaO simulations as a fair universal benchmark.

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