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Neuro-symbolic systems (NeSy), which claim to combine the best of both learning and reasoning capabilities of artificial intelligence, are missing a core property of reasoning systems: Declarativeness. The lack of declarativeness is caused by the functional nature of neural predicates inherited from neural networks. We propose and implement a general framework for fully declarative neural predicates, which hence extends to fully declarative NeSy frameworks. We first show that the declarative extension preserves the learning and reasoning capabilities while being able to answer arbitrary queries while only being trained on a single query type.

An essential problem in statistics and machine learning is the estimation of expectations involving PDFs with intractable normalizing constants. The self-normalized importance sampling (SNIS) estimator, which normalizes the IS weights, has become the standard approach due to its simplicity. However, the SNIS has been shown to exhibit high variance in challenging estimation problems, e.g, involving rare events or posterior predictive distributions in Bayesian statistics. Further, most of the state-of-the-art adaptive importance sampling (AIS) methods adapt the proposal as if the weights had not been normalized. In this paper, we propose a framework that considers the original task as estimation of a ratio of two integrals. In our new formulation, we obtain samples from a joint proposal distribution in an extended space, with two of its marginals playing the role of proposals used to estimate each integral. Importantly, the framework allows us to induce and control a dependency between both estimators. We propose a construction of the joint proposal that decomposes in two (multivariate) marginals and a coupling. This leads to a two-stage framework suitable to be integrated with existing or new AIS and/or variational inference (VI) algorithms. The marginals are adapted in the first stage, while the coupling can be chosen and adapted in the second stage. We show in several examples the benefits of the proposed methodology, including an application to Bayesian prediction with misspecified models.

The relevance of studies in queuing theory in social systems has inspired its adoption in other mainstream technologies with its application in distributed and communication systems becoming an intense research domain. Considerable work has been done regarding the application of the impatient queuing phenomenon in distributed computing to achieve optimal resource sharing and allocation for performance improvement. Generally, there are two types of common impatient queuing behaviour that have been well studied, namely balking and reneging, respectively. In this survey, we are interested in the third type of impatience: jockeying, a phenomenon that draws origins from impatient customers switching from one queue to another. This survey chronicles classical and latest efforts that labor to model and exploit the jockeying behaviour in queuing systems, with a special focus on those related to information and communication systems, especially in the context of Multi-Access Edge Computing. We comparatively summarize the reviewed literature regarding their methodologies, invoked models, and use cases.

Blocking, a special case of rerandomization, is routinely implemented in the design stage of randomized experiments to balance the baseline covariates. This study proposes a regression adjustment method based on the least absolute shrinkage and selection operator (Lasso) to efficiently estimate the average treatment effect in randomized block experiments with high-dimensional covariates. We derive the asymptotic properties of the proposed estimator and outline the conditions under which this estimator is more efficient than the unadjusted one. We provide a conservative variance estimator to facilitate valid inferences. Our framework allows one treated or control unit in some blocks and heterogeneous propensity scores across blocks, thus including paired experiments and finely stratified experiments as special cases. We further accommodate rerandomized experiments and a combination of blocking and rerandomization. Moreover, our analysis allows both the number of blocks and block sizes to tend to infinity, as well as heterogeneous treatment effects across blocks without assuming a true outcome data-generating model. Simulation studies and two real-data analyses demonstrate the advantages of the proposed method.

Weakly Supervised Semantic Segmentation (WSSS) employs weak supervision, such as image-level labels, to train the segmentation model. Despite the impressive achievement in recent WSSS methods, we identify that introducing weak labels with high mean Intersection of Union (mIoU) does not guarantee high segmentation performance. Existing studies have emphasized the importance of prioritizing precision and reducing noise to improve overall performance. In the same vein, we propose ORANDNet, an advanced ensemble approach tailored for WSSS. ORANDNet combines Class Activation Maps (CAMs) from two different classifiers to increase the precision of pseudo-masks (PMs). To further mitigate small noise in the PMs, we incorporate curriculum learning. This involves training the segmentation model initially with pairs of smaller-sized images and corresponding PMs, gradually transitioning to the original-sized pairs. By combining the original CAMs of ResNet-50 and ViT, we significantly improve the segmentation performance over the single-best model and the naive ensemble model, respectively. We further extend our ensemble method to CAMs from AMN (ResNet-like) and MCTformer (ViT-like) models, achieving performance benefits in advanced WSSS models. It highlights the potential of our ORANDNet as a final add-on module for WSSS models.

We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic array. Under the same umbrella, FFT-PIM allows computing the potential for 1D, 2D, and 3D periodicities for dynamic and static problems, including problems with and without a periodic phase shift. The computational complexity of the FFT-PIM is of $O(N \log N)$ for $N$ spatially coinciding sources and observer points. The FFT-PIM uses rapidly converging series representations of the Green's function serving as a kernel in the superposition sum. Based on these representations, the FFT-PIM splits the potential into its near-zone component, which includes a small number of images surrounding the unit cell of interest, and far-zone component, which includes the rest of an infinite number of images. The far-zone component is evaluated by projecting the non-uniform sources onto a sparse uniform grid, performing superposition sums on this sparse grid, and interpolating the potential from the uniform grid to the non-uniform observation points. The near-zone component is evaluated using an FFT-based method, which is adapted to efficiently handle non-uniform source-observer distributions within the periodic unit cell. The FFT-PIM can be used for a broad range of applications, such as periodic problems involving integral equations in computational electromagnetic and acoustic, micromagnetic solvers, and density functional theory solvers.

Agent-based models (ABM) provide an excellent framework for modeling outbreaks and interventions in epidemiology by explicitly accounting for diverse individual interactions and environments. However, these models are usually stochastic and highly parametrized, requiring precise calibration for predictive performance. When considering realistic numbers of agents and properly accounting for stochasticity, this high dimensional calibration can be computationally prohibitive. This paper presents a random forest based surrogate modeling technique to accelerate the evaluation of ABMs and demonstrates its use to calibrate an epidemiological ABM named CityCOVID via Markov chain Monte Carlo (MCMC). The technique is first outlined in the context of CityCOVID's quantities of interest, namely hospitalizations and deaths, by exploring dimensionality reduction via temporal decomposition with principal component analysis (PCA) and via sensitivity analysis. The calibration problem is then presented and samples are generated to best match COVID-19 hospitalization and death numbers in Chicago from March to June in 2020. These results are compared with previous approximate Bayesian calibration (IMABC) results and their predictive performance is analyzed showing improved performance with a reduction in computation.

This note discusses a simple modification of cross-conformal prediction inspired by recent work on e-values. The precursor of conformal prediction developed in the 1990s by Gammerman, Vapnik, and Vovk was also based on e-values and is called conformal e-prediction in this note. Replacing e-values by p-values led to conformal prediction, which has important advantages over conformal e-prediction without obvious disadvantages. The situation with cross-conformal prediction is, however, different: whereas for cross-conformal prediction validity is only an empirical fact (and can be broken with excessive randomization), this note draws the reader's attention to the obvious fact that cross-conformal e-prediction enjoys a guaranteed property of validity.

JAX is widely used in machine learning and scientific computing, the latter of which often relies on existing high-performance code that we would ideally like to incorporate into JAX. Reimplementing the existing code in JAX is often impractical and the existing interface in JAX for binding custom code either limits the user to a single Jacobian product or requires deep knowledge of JAX and its C++ backend for general Jacobian products. With JAXbind we drastically reduce the effort required to bind custom functions implemented in other programming languages with full support for Jacobian-vector products and vector-Jacobian products to JAX. Specifically, JAXbind provides an easy-to-use Python interface for defining custom, so-called JAX primitives. Via JAXbind, any function callable from Python can be exposed as a JAX primitive. JAXbind allows a user to interface the JAX function transformation engine with custom derivatives and batching rules, enabling all JAX transformations for the custom primitive.

Graph-centric artificial intelligence (graph AI) has achieved remarkable success in modeling interacting systems prevalent in nature, from dynamical systems in biology to particle physics. The increasing heterogeneity of data calls for graph neural architectures that can combine multiple inductive biases. However, combining data from various sources is challenging because appropriate inductive bias may vary by data modality. Multimodal learning methods fuse multiple data modalities while leveraging cross-modal dependencies to address this challenge. Here, we survey 140 studies in graph-centric AI and realize that diverse data types are increasingly brought together using graphs and fed into sophisticated multimodal models. These models stratify into image-, language-, and knowledge-grounded multimodal learning. We put forward an algorithmic blueprint for multimodal graph learning based on this categorization. The blueprint serves as a way to group state-of-the-art architectures that treat multimodal data by choosing appropriately four different components. This effort can pave the way for standardizing the design of sophisticated multimodal architectures for highly complex real-world problems.