The application of Shapley values to high-dimensional, time-series-like data is computationally challenging - and sometimes impossible. For $N$ inputs the problem is $2^N$ hard. In image processing, clusters of pixels, referred to as superpixels, are used to streamline computations. This research presents an efficient solution for time-seres-like data that adapts the idea of superpixels for Shapley value computation. Motivated by a forensic DNA classification example, the method is applied to multivariate time-series-like data whose features have been classified by a convolutional neural network (CNN). In DNA processing, it is important to identify alleles from the background noise created by DNA extraction and processing. A single DNA profile has $31,200$ scan points to classify, and the classification decisions must be defensible in a court of law. This means that classification is routinely performed by human readers - a monumental and time consuming process. The application of a CNN with fast computation of meaningful Shapley values provides a potential alternative to the classification. This research demonstrates the realistic, accurate and fast computation of Shapley values for this massive task
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Processing 是一門開源編程語言和與之配套的集成開發環境（IDE）的名稱。Processing 在電子藝術和視覺設計社區被用來教授編程基礎，并運用于大量的新媒體和互動藝術作品中。
The purpose of this paper is to employ the language of Cartan moving frames to study the geometry of the data manifolds and its Riemannian structure, via the data information metric and its curvature at data points. Using this framework and through experiments, explanations on the response of a neural network are given by pointing out the output classes that are easily reachable from a given input. This emphasizes how the proposed mathematical relationship between the output of the network and the geometry of its inputs can be exploited as an explainable artificial intelligence tool.
Within the field of hierarchical modelling, little attention is paid to micro-macro models: those in which group-level outcomes are dependent on covariates measured at the level of individuals within groups. Although such models are perhaps underrepresented in the literature, they have applications in economics, epidemiology, and the social sciences. Despite the strong mathematical similarities between micro-macro and measurement error models, few efforts have been made to apply the much better-developed methodology of the latter to the former. Here, we present a new empirical Bayesian technique for micro-macro data, called FRODO (Functional Regression On Densities of Observations). The method jointly infers group-specific densities for multilevel covariates and uses them as functional predictors in a functional linear regression, resulting in a model that is analogous to a generalized additive model (GAM). In doing so, it achieves a level of generality comparable to more sophisticated methods developed for errors-in-variables models, while further leveraging the larger group sizes characteristic of multilevel data to provide richer information about the within-group covariate distributions. After explaining the hierarchical structure of FRODO, its power and versatility are demonstrated on several simulated datasets, showcasing its ability to accommodate a wide variety of covariate distributions and regression models.
We discover a novel connection between two classical mathematical notions, Eulerian orientations and Hadamard codes by studying the counting problem of Eulerian orientations (\#EO) with local constraint functions imposed on vertices. We present two special classes of constraint functions and a chain reaction algorithm, and show that the \#EO problem defined by each class alone is polynomial-time solvable by the algorithm. These tractable classes of functions are defined inductively, and quite remarkably the base level of these classes is characterized perfectly by the well-known Hadamard code. Thus, we establish a novel connection between counting Eulerian orientations and coding theory. We also prove a \#P-hardness result for the \#EO problem when constraint functions from the two tractable classes appear together.
While overparameterization is known to benefit generalization, its impact on Out-Of-Distribution (OOD) detection is less understood. This paper investigates the influence of model complexity in OOD detection. We propose an expected OOD risk metric to evaluate classifiers confidence on both training and OOD samples. Leveraging Random Matrix Theory, we derive bounds for the expected OOD risk of binary least-squares classifiers applied to Gaussian data. We show that the OOD risk depicts an infinite peak, when the number of parameters is equal to the number of samples, which we associate with the double descent phenomenon. Our experimental study on different OOD detection methods across multiple neural architectures extends our theoretical insights and highlights a double descent curve. Our observations suggest that overparameterization does not necessarily lead to better OOD detection. Using the Neural Collapse framework, we provide insights to better understand this behavior. To facilitate reproducibility, our code will be made publicly available upon publication.
In real-world data, information is stored in extremely large feature vectors. These variables are typically correlated due to complex interactions involving many features simultaneously. Such correlations qualitatively correspond to semantic roles and are naturally recognized by both the human brain and artificial neural networks. This recognition enables, for instance, the prediction of missing parts of an image or text based on their context. We present a method to detect these correlations in high-dimensional data represented as binary numbers. We estimate the binary intrinsic dimension of a dataset, which quantifies the minimum number of independent coordinates needed to describe the data, and is therefore a proxy of semantic complexity. The proposed algorithm is largely insensitive to the so-called curse of dimensionality, and can therefore be used in big data analysis. We test this approach identifying phase transitions in model magnetic systems and we then apply it to the detection of semantic correlations of images and text inside deep neural networks.
Mobile devices and the Internet of Things (IoT) devices nowadays generate a large amount of heterogeneous spatial-temporal data. It remains a challenging problem to model the spatial-temporal dynamics under privacy concern. Federated learning (FL) has been proposed as a framework to enable model training across distributed devices without sharing original data which reduce privacy concern. Personalized federated learning (PFL) methods further address data heterogenous problem. However, these methods don't consider natural spatial relations among nodes. For the sake of modeling spatial relations, Graph Neural Netowork (GNN) based FL approach have been proposed. But dynamic spatial-temporal relations among edge nodes are not taken into account. Several approaches model spatial-temporal dynamics in a centralized environment, while less effort has been made under federated setting. To overcome these challeges, we propose a novel Federated Adaptive Spatial-Temporal Attention (FedASTA) framework to model the dynamic spatial-temporal relations. On the client node, FedASTA extracts temporal relations and trend patterns from the decomposed terms of original time series. Then, on the server node, FedASTA utilize trend patterns from clients to construct adaptive temporal-spatial aware graph which captures dynamic correlation between clients. Besides, we design a masked spatial attention module with both static graph and constructed adaptive graph to model spatial dependencies among clients. Extensive experiments on five real-world public traffic flow datasets demonstrate that our method achieves state-of-art performance in federated scenario. In addition, the experiments made in centralized setting show the effectiveness of our novel adaptive graph construction approach compared with other popular dynamic spatial-temporal aware methods.
Parameter inference for linear and non-Gaussian state space models is challenging because the likelihood function contains an intractable integral over the latent state variables. While Markov chain Monte Carlo (MCMC) methods provide exact samples from the posterior distribution as the number of samples go to infinity, they tend to have high computational cost, particularly for observations of a long time series. Variational Bayes (VB) methods are a useful alternative when inference with MCMC methods is computationally expensive. VB methods approximate the posterior density of the parameters by a simple and tractable distribution found through optimisation. In this paper, we propose a novel sequential variational Bayes approach that makes use of the Whittle likelihood for computationally efficient parameter inference in this class of state space models. Our algorithm, which we call Recursive Variational Gaussian Approximation with the Whittle Likelihood (R-VGA-Whittle), updates the variational parameters by processing data in the frequency domain. At each iteration, R-VGA-Whittle requires the gradient and Hessian of the Whittle log-likelihood, which are available in closed form for a wide class of models. Through several examples using a linear Gaussian state space model and a univariate/bivariate non-Gaussian stochastic volatility model, we show that R-VGA-Whittle provides good approximations to posterior distributions of the parameters and is very computationally efficient when compared to asymptotically exact methods such as Hamiltonian Monte Carlo.
Many models require integrals of high-dimensional functions: for instance, to obtain marginal likelihoods. Such integrals may be intractable, or too expensive to compute numerically. Instead, we can use the Laplace approximation (LA). The LA is exact if the function is proportional to a normal density; its effectiveness therefore depends on the function's true shape. Here, we propose the use of the probabilistic numerical framework to develop a diagnostic for the LA and its underlying shape assumptions, modelling the function and its integral as a Gaussian process and devising a "test" by conditioning on a finite number of function values. The test is decidedly non-asymptotic and is not intended as a full substitute for numerical integration - rather, it is simply intended to test the feasibility of the assumptions underpinning the LA with as minimal computation. We discuss approaches to optimize and design the test, apply it to known sample functions, and highlight the challenges of high dimensions.
Modelling multivariate spatio-temporal data with complex dependency structures is a challenging task but can be simplified by assuming that the original variables are generated from independent latent components. If these components are found, they can be modelled univariately. Blind source separation aims to recover the latent components by estimating the unmixing transformation based on the observed data only. The current methods for spatio-temporal blind source separation are restricted to linear unmixing, and nonlinear variants have not been implemented. In this paper, we extend identifiable variational autoencoder to the nonlinear nonstationary spatio-temporal blind source separation setting and demonstrate its performance using comprehensive simulation studies. Additionally, we introduce two alternative methods for the latent dimension estimation, which is a crucial task in order to obtain the correct latent representation. Finally, we illustrate the proposed methods using a meteorological application, where we estimate the latent dimension and the latent components, interpret the components, and show how nonstationarity can be accounted and prediction accuracy can be improved by using the proposed nonlinear blind source separation method as a preprocessing method.
Invasive brain-computer interfaces with Electrocorticography (ECoG) have shown promise for high-performance speech decoding in medical applications, but less damaging methods like intracranial stereo-electroencephalography (sEEG) remain underexplored. With rapid advances in representation learning, leveraging abundant recordings to enhance speech decoding is increasingly attractive. However, popular methods often pre-train temporal models based on brain-level tokens, overlooking that brain activities in different regions are highly desynchronized during tasks. Alternatively, they pre-train spatial-temporal models based on channel-level tokens but fail to evaluate them on challenging tasks like speech decoding, which requires intricate processing in specific language-related areas. To address this issue, we collected a well-annotated Chinese word-reading sEEG dataset targeting language-related brain networks from 12 subjects. Using this benchmark, we developed the Du-IN model, which extracts contextual embeddings based on region-level tokens through discrete codex-guided mask modeling. Our model achieves state-of-the-art performance on the 61-word classification task, surpassing all baselines. Model comparisons and ablation studies reveal that our design choices, including (i) temporal modeling based on region-level tokens by utilizing 1D depthwise convolution to fuse channels in the ventral sensorimotor cortex (vSMC) and superior temporal gyrus (STG) and (ii) self-supervision through discrete codex-guided mask modeling, significantly contribute to this performance. Overall, our approach -- inspired by neuroscience findings and capitalizing on region-level representations from specific brain regions -- is suitable for invasive brain modeling and represents a promising neuro-inspired AI approach in brain-computer interfaces.
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