In multivariate spline regression, the number and locations of knots influence the performance and interpretability significantly. However, due to non-differentiability and varying dimensions, there is no desirable frequentist method to make inference on knots. In this article, we propose a fully Bayesian approach for knot inference in multivariate spline regression. The existing Bayesian method often uses BIC to calculate the posterior, but BIC is too liberal and it will heavily overestimate the knot number when the candidate model space is large. We specify a new prior on the knot number to take into account the complexity of the model space and derive an analytic formula in the normal model. In the non-normal cases, we utilize the extended Bayesian information criterion to approximate the posterior density. The samples are simulated in the space with differing dimensions via reversible jump Markov chain Monte Carlo. We apply the proposed method in knot inference and manifold denoising. Experiments demonstrate the splendid capability of the algorithm, especially in function fitting with jumping discontinuity.
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Molecular discovery, when formulated as an optimization problem, presents significant computational challenges because optimization objectives can be non-differentiable. Evolutionary Algorithms (EAs), often used to optimize black-box objectives in molecular discovery, traverse chemical space by performing random mutations and crossovers, leading to a large number of expensive objective evaluations. In this work, we ameliorate this shortcoming by incorporating chemistry-aware Large Language Models (LLMs) into EAs. Namely, we redesign crossover and mutation operations in EAs using LLMs trained on large corpora of chemical information. We perform extensive empirical studies on both commercial and open-source models on multiple tasks involving property optimization, molecular rediscovery, and structure-based drug design, demonstrating that the joint usage of LLMs with EAs yields superior performance over all baseline models across single- and multi-objective settings. We demonstrate that our algorithm improves both the quality of the final solution and convergence speed, thereby reducing the number of required objective evaluations. Our code is available at //github.com/zoom-wang112358/MOLLEO
The performance of image super-resolution relies heavily on the accuracy of degradation information, especially under blind settings. Due to absence of true degradation models in real-world scenarios, previous methods learn distinct representations by distinguishing different degradations in a batch. However, the most significant degradation differences may provide shortcuts for the learning of representations such that subtle difference may be discarded. In this paper, we propose an alternative to learn degradation representations through reproducing degraded low-resolution (LR) images. By guiding the degrader to reconstruct input LR images, full degradation information can be encoded into the representations. In addition, we develop an energy distance loss to facilitate the learning of the degradation representations by introducing a bounded constraint. Experiments show that our representations can extract accurate and highly robust degradation information. Moreover, evaluations on both synthetic and real images demonstrate that our ReDSR achieves state-of-the-art performance for the blind SR tasks.
We consider the problem of performing Bayesian inference for logistic regression using appropriate extensions of the ensemble Kalman filter. Two interacting particle systems are proposed that sample from an approximate posterior and prove quantitative convergence rates of these interacting particle systems to their mean-field limit as the number of particles tends to infinity. Furthermore, we apply these techniques and examine their effectiveness as methods of Bayesian approximation for quantifying predictive uncertainty in neural networks.
Models for multiphysics problems often contain strong nonlinearities. Including fracture contact mechanics introduces discontinuities at the transition between open and closed or sliding and sticking fractures. The resulting system of equations is highly challenging to solve. The na\"ive choice of Newton's method frequently fails to converge, calling for more refined solution techniques such as line search methods. When dealing with strong nonlinearities and discontinuities, a global line search based on the magnitude of the residual of all equations is at best costly to evaluate and at worst fails to converge. We therefore suggest a cheap and reliable approach tailored to the discontinuities. Utilising adaptive variable scaling, the algorithm uses a line search to identify the transition between contact states. Then, a solution update weight is chosen to ensure that no fracture cells move too far beyond the transition. We demonstrate the algorithm on a series of test cases for poromechanics and thermoporomechanics in fractured porous media. We consider both single- and multifracture cases and study the importance of proper scaling of variables and equations.
Leveraging complementary relationships across modalities has recently drawn a lot of attention in multimodal emotion recognition. Most of the existing approaches explored cross-attention to capture the complementary relationships across the modalities. However, the modalities may also exhibit weak complementary relationships, which may deteriorate the cross-attended features, resulting in poor multimodal feature representations. To address this problem, we propose Inconsistency-Aware Cross-Attention (IACA), which can adaptively select the most relevant features on-the-fly based on the strong or weak complementary relationships across audio and visual modalities. Specifically, we design a two-stage gating mechanism that can adaptively select the appropriate relevant features to deal with weak complementary relationships. Extensive experiments are conducted on the challenging Aff-Wild2 dataset to show the robustness of the proposed model.
We consider the problem of selecting an optimal subset of information sources for a hypothesis testing/classification task where the goal is to identify the true state of the world from a finite set of hypotheses, based on finite observation samples from the sources. In order to characterize the learning performance, we propose a misclassification penalty framework, which enables nonuniform treatment of different misclassification errors. In a centralized Bayesian learning setting, we study two variants of the subset selection problem: (i) selecting a minimum cost information set to ensure that the maximum penalty of misclassifying the true hypothesis is below a desired bound and (ii) selecting an optimal information set under a limited budget to minimize the maximum penalty of misclassifying the true hypothesis. Under certain assumptions, we prove that the objective (or constraints) of these combinatorial optimization problems are weak (or approximate) submodular, and establish high-probability performance guarantees for greedy algorithms. Further, we propose an alternate metric for information set selection which is based on the total penalty of misclassification. We prove that this metric is submodular and establish near-optimal guarantees for the greedy algorithms for both the information set selection problems. Finally, we present numerical simulations to validate our theoretical results over several randomly generated instances.
High order accurate Hermite methods for the wave equation on curvilinear domains are presented. Boundaries are treated using centered compatibility conditions rather than more standard one-sided approximations. Both first-order-in-time (FOT) and second-order-in-time (SOT) Hermite schemes are developed. Hermite methods use the solution and multiple derivatives as unknowns and achieve space-time orders of accuracy $2m-1$ (FOT) and $2m$ (SOT) for methods using $(m+1)^d$ degree of freedom per node in $d$ dimensions. The compatibility boundary conditions (CBCs) are based on taking time derivatives of the boundary conditions and using the governing equations to replace the time derivatives with spatial derivatives. These resulting constraint equations augment the Hermite scheme on the boundary. The solvability of the equations resulting from the compatibility conditions are analyzed. Numerical examples demonstrate the accuracy and stability of the new schemes in two dimensions.
A community reveals the features and connections of its members that are different from those in other communities in a network. Detecting communities is of great significance in network analysis. Despite the classical spectral clustering and statistical inference methods, we notice a significant development of deep learning techniques for community detection in recent years with their advantages in handling high dimensional network data. Hence, a comprehensive overview of community detection's latest progress through deep learning is timely to both academics and practitioners. This survey devises and proposes a new taxonomy covering different categories of the state-of-the-art methods, including deep learning-based models upon deep neural networks, deep nonnegative matrix factorization and deep sparse filtering. The main category, i.e., deep neural networks, is further divided into convolutional networks, graph attention networks, generative adversarial networks and autoencoders. The survey also summarizes the popular benchmark data sets, model evaluation metrics, and open-source implementations to address experimentation settings. We then discuss the practical applications of community detection in various domains and point to implementation scenarios. Finally, we outline future directions by suggesting challenging topics in this fast-growing deep learning field.
The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
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