Anchor PCA recovers a maximal invariant subspace for multi-domain data via PCA on a modified target matrix that trades off explained variance with domain agreement.
Distributional Principal Autoencoders
4 Pith papers cite this work, alongside 1 external citations. Polarity classification is still indexing.
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abstract
Dimension reduction techniques usually lose information in the sense that reconstructed data are not identical to the original data. However, we argue that it is possible to have reconstructed data identically distributed as the original data, irrespective of the retained dimension or the specific mapping. This can be achieved by learning a distributional model that matches the conditional distribution of data given its low-dimensional latent variables. Motivated by this, we propose Distributional Principal Autoencoder (DPA) that consists of an encoder that maps high-dimensional data to low-dimensional latent variables and a decoder that maps the latent variables back to the data space. For reducing the dimension, the DPA encoder aims to minimise the unexplained variability of the data with an adaptive choice of the latent dimension. For reconstructing data, the DPA decoder aims to match the conditional distribution of all data that are mapped to a certain latent value, thus ensuring that the reconstructed data retains the original data distribution. Our numerical results on climate data, single-cell data, and image benchmarks demonstrate the practical feasibility and success of the approach in reconstructing the original distribution of the data. DPA embeddings are shown to preserve meaningful structures of data such as the seasonal cycle for precipitations and cell types for gene expression.
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Distributional autoencoders trained on climate model simulations model full conditional distributions of European temperature fields to enable probabilistic storyline attribution, illustrated by higher intensities and probability ratios for a 2003-like heatwave in 2028 and 2053.
VECA learns effective visual representations using core-periphery attention where patches interact exclusively via a resolution-invariant set of learned core embeddings, achieving linear O(N) complexity while maintaining competitive performance.
DPA provides closed-form relation from level-set geometry to data score and proves extra latent components are conditionally independent, revealing intrinsic dimension.
citing papers explorer
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Anchor PCA
Anchor PCA recovers a maximal invariant subspace for multi-domain data via PCA on a modified target matrix that trades off explained variance with domain agreement.
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Probabilistic storyline attribution using machine learning
Distributional autoencoders trained on climate model simulations model full conditional distributions of European temperature fields to enable probabilistic storyline attribution, illustrated by higher intensities and probability ratios for a 2003-like heatwave in 2028 and 2053.
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Elastic Attention Cores for Scalable Vision Transformers
VECA learns effective visual representations using core-periphery attention where patches interact exclusively via a resolution-invariant set of learned core embeddings, achieving linear O(N) complexity while maintaining competitive performance.
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Distributional Autoencoders Know the Score
DPA provides closed-form relation from level-set geometry to data score and proves extra latent components are conditionally independent, revealing intrinsic dimension.