Variable Kernel Density Estimation in High-Dimensional Feature Spaces

Walt, Christiaan M Van der; Barnard, Etienne

doi:10.1609/aaai.v31i1.10885

Cited by 6 publications

(4 citation statements)

References 12 publications

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“…However, this is fundamentally different from statistical inference or variable importance estimation (Barber and Candès, 2015; Louppe et al, 2013; Nguyen et al, 2022). Recent extensions of permutation-based importance hold promise to provide statistical error control and effective variable-importance detection in the context of deep learning models and high-dimensional correlated inputs (Chamma et al, 2024a,b; Mi et al, 2021). The successful application of high-dimensional inference procedures will be an important opportunity for future work with the potential to add statistical rigor to the practical inference provided by the structural design choices of GREEN .…”

Section: Discussionmentioning

confidence: 99%

GREEN: a lightweight architecture using learnable wavelets and Riemannian geometry for biomarker exploration

Paillard,

Hipp,

Engemann

2024

Preprint

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Spectral analysis using wavelets has proven useful for analyzing electroencephalographic (EEG) signals and identifying biomarkers in a clinical context. Over the past decade, Riemannian geometry has crystalized as a theoretical framework providing robust methods for modeling biomedical outcomes and brain function from multi-channel EEG recordings. Combining both approaches yields applications with higher interpretability and efficiency. Yet these approaches rely on handcrafted rules and sequential optimization. On the contrary, the growing deep learning (DL) literature provides end-to-end trainable models for processing raw EEG. Despite state-of- the-art performance on various prediction tasks, clinical impact remains a challenge, which is at least in part due to their lack of interpretability and interoperability with established neuroscience concepts. In this work we introduce a new lightweight neural network for processing raw EEG data building on wavelet transforms and Riemannian geometry. The proposed architecture termed GREEN (Gabor Riemann EEGNet) is benchmarked on five different prediction tasks (age, sex, eyes-closed detection, dementia diagnosis, EEG pathology) from three different datasets (TUAB, CAUEEG, TDBRAIN) encompassing data from more than 5000 human participants. This new architecture significantly outperformed state-of-the-art non-deep models on several of the benchmarks and performed favorably compared to large DL models on the CAU bench- mark using orders of magnitude fewer parameters. Computational experiments revealed how GREEN facilitates learning sparse representations without compromising performance. We further demonstrate that the modularity of the GREEN architecture allows computing classical measures of phase synchrony, such as pairwise phase-locking values which are found to convey information relevant for predicting dementia diagnosis. Furthermore, the learned wavelets can easily be interpreted as bandpass filters, therefore making this architecture explainable by de- sign. We illustrate this with a classical example of the Berger effect i.e. modulation of 8-10Hz power when closing the eyes. By integrating domain-knowledge in architecture choices, the pro- posed model benefits from desirable complexity-performance trade-off and learns interpretable representations of EEG. The source code is made publicly available.

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Section: Discussionmentioning

confidence: 99%

GREEN: a lightweight architecture using learnable wavelets and Riemannian geometry for biomarker exploration

Paillard,

Hipp,

Engemann

2024

Preprint

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“…tight cluster, or intra‐cluster similarity). In our scenario, as data are drawn from a probability distribution, our analysis is driven by estimating, and visualizing, the density [vdWB17, BIW19] of objects in individual scenes (images). In this setting, we make fewer assumptions about our data compared to clustering [TWB06], while still prioritizing the density estimates we compute when deriving a low‐dimensional embedding of objects, akin to DR methods.…”

Section: Related Workmentioning

confidence: 99%

CUPID: Contextual Understanding of Prompt‐conditioned Image Distributions

Zhao,

Li,

Berger

2024

Computer Graphics Forum

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We present CUPID: a visualization method for the contextual understanding of prompt‐conditioned image distributions. CUPID targets the visual analysis of distributions produced by modern text‐to‐image generative models, wherein a user can specify a scene via natural language, and the model generates a set of images, each intended to satisfy the user's description. CUPID is designed to help understand the resulting distribution, using contextual cues to facilitate analysis: objects mentioned in the prompt, novel, synthesized objects not explicitly mentioned, and their potential relationships. Central to CUPID is a novel method for visualizing high‐dimensional distributions, wherein contextualized embeddings of objects, those found within images, are mapped to a low‐dimensional space via density‐based embeddings. We show how such embeddings allows one to discover salient styles of objects within a distribution, as well as identify anomalous, or rare, object styles. Moreover, we introduce conditional density embeddings, whereby conditioning on a given object allows one to compare object dependencies within the distribution. We employ CUPID for analyzing image distributions produced by large‐scale diffusion models, where our experimental results offer insights on language misunderstanding from such models and biases in object composition, while also providing an interface for discovery of typical, or rare, synthesized scenes.

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“…In spatial statistics, kernel density estimation (KDE) is a non-parametric method USED for estimating a probability density function of the probability variable [27]. KDE was applied as a continuous replacement for the discrete histogram of the spatial distribution of fatal road accidents.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…Namely, the Normal, the Epanechnikov, the Box, and the Triangle functions. Their form and efficiency are shown in Table 2 and Figure 1 [31,34].…”

Section: Theoretical Considerationsmentioning

confidence: 99%

Black-Spot Analysis in Hungary Based on Kernel Density Estimation

Baranyai

Sipos

2022

Sustainability

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Between 2010 and 2020 in the European Union, 30% of road accidents resulted in the death of a pedestrian or a cyclist. Accidents of unprotected pedestrians and cyclists are the reason why it is essential to introduce road safety measures. In our paper, we identify and rank black spots using an innovative reactive approach based on statistics. We elaborate on the mathematical methodological considerations through the processing of real-life empirical data in a Matlab environment. The applied black-spot analysis is based on a Kernel density estimate method, and the importance of the kernel functions and bandwidth are elaborated. Besides, special attention is devoted to the distorting effect of annual average daily traffic. The result of our research is a new methodology by which the real locations of the examined black spots can be determined. Furthermore, the boundaries of the critical sections and the extent of the formation of black spots can be determined by the introduced mathematical methods. With our innovative model, the black spots can be ranked, and the locations having the highest potential for improvement can be identified. Accordingly, optimal measures can be determined considering social-economic and sustainability aspects.

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Variable Kernel Density Estimation in High-Dimensional Feature Spaces

Cited by 6 publications

References 12 publications

GREEN: a lightweight architecture using learnable wavelets and Riemannian geometry for biomarker exploration

GREEN: a lightweight architecture using learnable wavelets and Riemannian geometry for biomarker exploration

CUPID: Contextual Understanding of Prompt‐conditioned Image Distributions

Black-Spot Analysis in Hungary Based on Kernel Density Estimation

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