Simulation-based calibration checking (SBC) is a practical method to validate computationally-derived posterior distributions or their approximations. In this paper, we introduce a new variant of SBC to alleviate several known problems. Our variant allows the user to in principle detect any possible issue with the posterior, while previously reported implementations could never detect large classes of problems including when the posterior is equal to the prior. This is made possible by including additional data-dependent test quantities when running SBC. We argue and demonstrate that the joint likelihood of the data is an especially useful test quantity. Some other types of test quantities and their theoretical and practical benefits are also investigated. We provide theoretical analysis of SBC, thereby providing a more complete understanding of the underlying statistical mechanisms. We also bring attention to a relatively common mistake in the literature and clarify the difference between SBC and checks based on the data-averaged posterior. We support our recommendations with numerical case studies on a multivariate normal example and a case study in implementing an ordered simplex data type for use with Hamiltonian Monte Carlo. The SBC variant introduced in this paper is implemented in the $\mathtt{SBC}$ R package.
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Control barrier functions (CBF) have become popular as a safety filter to guarantee the safety of nonlinear dynamical systems for arbitrary inputs. However, it is difficult to construct functions that satisfy the CBF constraints for high relative degree systems with input constraints. To address these challenges, recent work has explored learning CBFs using neural networks via neural CBF (NCBF). However, such methods face difficulties when scaling to higher dimensional systems under input constraints. In this work, we first identify challenges that NCBFs face during training. Next, to address these challenges, we propose policy neural CBF (PNCBF), a method of constructing CBFs by learning the value function of a nominal policy, and show that the value function of the maximum-over-time cost is a CBF. We demonstrate the effectiveness of our method in simulation on a variety of systems ranging from toy linear systems to an F-16 jet with a 16-dimensional state space. Finally, we validate our approach on a two-agent quadcopter system on hardware under tight input constraints.
Full-spectrum out-of-distribution (F-OOD) detection aims to accurately recognize in-distribution (ID) samples while encountering semantic and covariate shifts simultaneously. However, existing out-of-distribution (OOD) detectors tend to overfit the covariance information and ignore intrinsic semantic correlation, inadequate for adapting to complex domain transformations. To address this issue, we propose a Likelihood-Aware Semantic Alignment (LSA) framework to promote the image-text correspondence into semantically high-likelihood regions. LSA consists of an offline Gaussian sampling strategy which efficiently samples semantic-relevant visual embeddings from the class-conditional Gaussian distribution, and a bidirectional prompt customization mechanism that adjusts both ID-related and negative context for discriminative ID/OOD boundary. Extensive experiments demonstrate the remarkable OOD detection performance of our proposed LSA especially on the intractable Near-OOD setting, surpassing existing methods by a margin of $15.26\%$ and $18.88\%$ on two F-OOD benchmarks, respectively.
Traditional partial differential equation (PDE) solvers can be computationally expensive, which motivates the development of faster methods, such as reduced-order-models (ROMs). We present GPLaSDI, a hybrid deep-learning and Bayesian ROM. GPLaSDI trains an autoencoder on full-order-model (FOM) data and simultaneously learns simpler equations governing the latent space. These equations are interpolated with Gaussian Processes, allowing for uncertainty quantification and active learning, even with limited access to the FOM solver. Our framework is able to achieve up to 100,000 times speed-up and less than 7% relative error on fluid mechanics problems.
Magnetic resonance imaging (MRI) is commonly used for brain tumor segmentation, which is critical for patient evaluation and treatment planning. To reduce the labor and expertise required for labeling, weakly-supervised semantic segmentation (WSSS) methods with class activation mapping (CAM) have been proposed. However, existing CAM methods suffer from low resolution due to strided convolution and pooling layers, resulting in inaccurate predictions. In this study, we propose a novel CAM method, Attentive Multiple-Exit CAM (AME-CAM), that extracts activation maps from multiple resolutions to hierarchically aggregate and improve prediction accuracy. We evaluate our method on the BraTS 2021 dataset and show that it outperforms state-of-the-art methods.
Molecular dynamics (MD) simulation is a widely used technique to simulate molecular systems, most commonly at the all-atom resolution where equations of motion are integrated with timesteps on the order of femtoseconds ($1\textrm{fs}=10^{-15}\textrm{s}$). MD is often used to compute equilibrium properties, which requires sampling from an equilibrium distribution such as the Boltzmann distribution. However, many important processes, such as binding and folding, occur over timescales of milliseconds or beyond, and cannot be efficiently sampled with conventional MD. Furthermore, new MD simulations need to be performed for each molecular system studied. We present Timewarp, an enhanced sampling method which uses a normalising flow as a proposal distribution in a Markov chain Monte Carlo method targeting the Boltzmann distribution. The flow is trained offline on MD trajectories and learns to make large steps in time, simulating the molecular dynamics of $10^{5} - 10^{6}\:\textrm{fs}$. Crucially, Timewarp is transferable between molecular systems: once trained, we show that it generalises to unseen small peptides (2-4 amino acids) at all-atom resolution, exploring their metastable states and providing wall-clock acceleration of sampling compared to standard MD. Our method constitutes an important step towards general, transferable algorithms for accelerating MD.
Modeling the ratio of two dependent components as a function of covariates is a frequently pursued objective in observational research. Despite the high relevance of this topic in medical studies, where biomarker ratios are often used as surrogate endpoints for specific diseases, existing models are based on oversimplified assumptions, assuming e.g.\@ independence or strictly positive associations between the components. In this paper, we close this gap in the literature and propose a regression model where the marginal distributions of the two components are linked by Frank copula. A key feature of our model is that it allows for both positive and negative correlations between the components, with one of the model parameters being directly interpretable in terms of Kendall's rank correlation coefficient. We study our method theoretically, evaluate finite sample properties in a simulation study and demonstrate its efficacy in an application to diagnosis of Alzheimer's disease via ratios of amyloid-beta and total tau protein biomarkers.
Human activity recognition (HAR) is a key challenge in pervasive computing and its solutions have been presented based on various disciplines. Specifically, for HAR in a smart space without privacy and accessibility issues, data streams generated by deployed pervasive sensors are leveraged. In this paper, we focus on a group activity by which a group of users perform a collaborative task without user identification and propose an efficient group activity recognition scheme which extracts causality patterns from pervasive sensor event sequences generated by a group of users to support as good recognition accuracy as the state-of-the-art graphical model. To filter out irrelevant noise events from a given data stream, a set of rules is leveraged to highlight causally related events. Then, a pattern-tree algorithm extracts frequent causal patterns by means of a growing tree structure. Based on the extracted patterns, a weighted sum-based pattern matching algorithm computes the likelihoods of stored group activities to the given test event sequence by means of matched event pattern counts for group activity recognition. We evaluate the proposed scheme using the data collected from our testbed and CASAS datasets where users perform their tasks on a daily basis and validate its effectiveness in a real environment. Experiment results show that the proposed scheme performs higher recognition accuracy and with a small amount of runtime overhead than the existing schemes.
Ontology matching (OM) enables semantic interoperability between different ontologies and resolves their conceptual heterogeneity by aligning related entities. OM systems currently have two prevailing design paradigms: conventional knowledge-based expert systems and newer machine learning-based predictive systems. While large language models (LLMs) and LLM-based agents have become revolutionary in data engineering and have been applied creatively in various domains, their potential for OM remains underexplored. This study introduces a novel agent-powered LLM-based design paradigm for OM systems. With thoughtful consideration of several specific challenges to leverage LLMs for OM, we propose a generic framework, namely Agent-OM, consisting of two Siamese agents for retrieval and matching, with a set of simple prompt-based OM tools. Our framework is implemented in a proof-of-concept system. Evaluations of three Ontology Alignment Evaluation Initiative (OAEI) tracks over state-of-the-art OM systems show that our system can achieve very close results to the best long-standing performance on simple OM tasks and significantly improve the performance on complex and few-shot OM tasks.
Many important tasks of large-scale recommender systems can be naturally cast as testing multiple linear forms for noisy matrix completion. These problems, however, present unique challenges because of the subtle bias-and-variance tradeoff of and an intricate dependence among the estimated entries induced by the low-rank structure. In this paper, we develop a general approach to overcome these difficulties by introducing new statistics for individual tests with sharp asymptotics both marginally and jointly, and utilizing them to control the false discovery rate (FDR) via a data splitting and symmetric aggregation scheme. We show that valid FDR control can be achieved with guaranteed power under nearly optimal sample size requirements using the proposed methodology. Extensive numerical simulations and real data examples are also presented to further illustrate its practical merits.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
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