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arXiv 2021年

作者： Gong, Tieliang Dong, Yuxin Yu, Shujian Dong, Bo The School of Computer Science and Technology Xi'an Jiaotong University Shaanxi Provincial Key Laboratory of Big Data Knowledge Engineering Xi’an710049 China The Machine Learning Group UiT - The Arctic University of Norway Department of Computer Science Vrije University Amsterdam Amsterdam Netherlands

The recently developed matrix-based Rényi's αorder entropy enables measurement of information in data simply using the eigenspectrum of symmetric positive semi-definite (PSD) matrices in reproducing kernel Hilbert space, without estimation of the underlying data distribution. This intriguing property makes this new information measurement widely adopted in multiple statistical inference and learning tasks. However, the computation of such quantity involves the trace operator on a PSD matrix G to power α (i.e., tr(Gα)), with a normal complexity of nearly O(n3), which severely hampers its practical usage when the number of samples (i.e., n) is large. In this work, we present computationally efficient approximations to this new entropy functional that can reduce its complexity to even significantly less than O(n2). To this end, we leverage the recent progress on Randomized Numerical Linear Algebra, developing Taylor, Chebyshev and Lanczos approximations to tr(Gα) for arbitrary values of α by converting it into a matrix-vector multiplication problem. We also establish the connection between the matrix-based Rényi's entropy and PSD matrix approximation, which enables exploiting both clustering and block low-rank structure of G to further reduce the computational cost. We theoretically provide approximation accuracy guarantees and illustrate the properties for different approximations. Large-scale experimental evaluations on both synthetic and real-world data corroborate our theoretical findings, showing promising speedup with negligible loss in accuracy. Copyright © 2021, The Authors. All rights reserved.

关键词： Matrix algebra

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Uniform manifold approximation and projection (UMAP) and its variants: Tutorial and survey

arXiv

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arXiv 2021年

作者： Ghojogh, Benyamin Ghodsi, Ali Karray, Fakhri Crowley, Mark Department of Electrical and Computer Engineering Machine Learning Laboratory University of Waterloo WaterlooON Canada Department of Statistics and Actuarial Science David R. Cheriton School of Computer Science Data Analytics Laboratory University of Waterloo WaterlooON Canada Department of Electrical and Computer Engineering Centre for Pattern Analysis and Machine Intelligence University of Waterloo WaterlooON Canada

Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper on UMAP and its variants. We start with UMAP algorithm where we explain probabilities of neighborhood in the input and embedding spaces, optimization of cost function, training algorithm, derivation of gradients, and supervised and semisupervised embedding by UMAP. Then, we introduce the theory behind UMAP by algebraic topology and category theory. Then, we introduce UMAP as a neighbor embedding method and compare it with t-SNE and LargeVis algorithms. We discuss negative sampling and repulsive forces in UMAP's cost function. DensMAP is then explained for density-preserving embedding. We then introduce parametric UMAP for embedding by deep learning and progressive UMAP for streaming and out-of-sample data embedding. Copyright © 2021, The Authors. All rights reserved.

关键词： Embeddings

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Laplacian-Based Dimensionality Reduction Including Spectral Clustering, Laplacian Eigenmap, Locality Preserving Projection, Graph Embedding, and Diffusion Map: Tutorial and Survey

arXiv

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arXiv 2021年

This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matrix, definition of Laplacian matrix, and the interpretation of Laplacian. Then, we cover the cuts of graph and spectral clustering which applies clustering in a subspace of data. Different optimization variants of Laplacian eigenmap and its out-of-sample extension are explained. Thereafter, we introduce the locality preserving projection and its kernel variant as linear special cases of Laplacian eigenmap. Versions of graph embedding are then explained which are generalized versions of Laplacian eigenmap and locality preserving projection. Finally, diffusion map is introduced which is a method based on Laplacian of data and random walks on the data graph. Copyright © 2021, The Authors. All rights reserved.

关键词： Surveys

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Generative Adversarial Networks and adversarial autoencoders: Tutorial and survey

arXiv

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arXiv 2021年

This is a tutorial and survey paper on Generative Adversarial Network (GAN), adversarial autoencoders, and their variants. We start with explaining adversarial learning and the vanilla GAN. Then, we explain the conditional GAN and DCGAN. The mode collapse problem is introduced and various methods, including minibatch GAN, unrolled GAN, BourGAN, mixture GAN, D2GAN, and Wasserstein GAN, are introduced for resolving this problem. Then, maximum likelihood estimation in GAN are explained along with f-GAN, adversarial variational Bayes, and Bayesian GAN. Then, we cover feature matching in GAN, InfoGAN, GRAN, LSGAN, energy-based GAN, CatGAN, MMD GAN, LapGAN, progressive GAN, triple GAN, LAG, GMAN, AdaGAN, CoGAN, inverse GAN, BiGAN, ALI, SAGAN, Few-shot GAN, SinGAN, and interpolation and evaluation of GAN. Then, we introduce some applications of GAN such as image-to-image translation (including PatchGAN, CycleGAN, DeepFaceDrawing, simulated GAN, interactive GAN), text-to-image translation (including StackGAN), and mixing image characteristics (including FineGAN and MixNMatch). Finally, we explain the autoencoders based on adversarial learning including adversarial autoencoder, PixelGAN, and implicit autoencoder. Copyright © 2021, The Authors. All rights reserved.

关键词： Generative adversarial networks

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Restricted Boltzmann machine and Deep Belief Network: Tutorial and Survey

arXiv

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arXiv 2021年

This is a tutorial and survey paper on Boltzmann machine (BM), Restricted Boltzmann machine (RBM), and Deep Belief Network (DBN). We start with the required background on probabilistic graphical models, Markov random field, Gibbs sampling, statistical physics, Ising model, and the Hopfield network. Then, we introduce the structures of BM and RBM. The conditional distributions of visible and hidden variables, Gibbs sampling in RBM for generating variables, training BM and RBM by maximum likelihood estimation, and contrastive divergence are explained. Then, we discuss different possible discrete and continuous distributions for the variables. We introduce conditional RBM and how it is trained. Finally, we explain deep belief network as a stack of RBM models. This paper on Boltzmann machines can be useful in various fields including data science, statistics, neural computation, and statistical physics. Copyright © 2021, The Authors. All rights reserved.

关键词： Statistical Physics

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Florid – a Nationwide Identification Service for Plants from Photos and Habitat Information

SSRN

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SSRN 2024年

作者： Brun, Philipp de Witte, Lucienne Popp, Manuel Richard Zurell, Damaris Karger, Dirk Nikolaus Descombes, Patrice de Lutio, Riccardo Wegner, Jan Dirk Bornand, Christophe Eggenberg, Stefan Olevski, Tasko Zimmermann, Niklaus E. Swiss Federal Research Institute WSL Birmensdorf8903 Switzerland Musée et jardins botaniques cantonaux Lausanne1007 Switzerland Institute of Biochemistry and Biology University of Potsdam Potsdam14469 Germany EcoVision Lab Photogrammetry and Remote Sensing ETH Zurich Zürich8092 Switzerland Department of Mathematical Modeling and Machine Learning University of Zurich Zürich8057 Switzerland InfoFlora Switzerland Bern3013 Switzerland Swiss Data Science Center ETH Zurich Zürich8092 Switzerland University of Basel Switzerland

Citizen science has become key to biodiversity monitoring but critically depends on accurate quality control that is scalable and tailored to the focal region. We developed FlorID, a free-to-use identification service for all native and many non-native plants of Switzerland. FlorID can identify >3000 species, using vision transformers trained on 1.5M photos, and ecological predictions from multilayer perceptrons, trained on 6.7M occurrence observations and 20 high-resolution environmental variables. Embedded in a free-to-use application programming interface, FlorID can be accessed directly, via webservice, and via FlorApp smartphone application. If multiple images and spatiotemporal location are available, FlorID correctly identifies 93% of field observations and has a top-5 accuracy of 99%. Ecological predictions boost identification success especially for native species with distinct distributions. By evaluating information on appearance and fine-grained ecology, FlorID is a blueprint for similar solutions targeting different taxa or regions, and a basis for developments like automated community inventories. © 2024, The Authors. All rights reserved.

关键词： Blueprints

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Individual Fairness Through Reweighting and Tuning

arXiv

引用

arXiv 2024年

作者： Mahamadou, Abdoul Jalil Djiberou Goetz, Lea Altman, Russ Stanford Center for Biomedical Ethics Stanford University StanfordCA94305 United States Artificial Intelligence and Machine Learning GSK LondonN1C 4AG United Kingdom Department of Biomedical Data Science Stanford University StanfordCA94305 United States Department of Bioengineering Stanford University StanfordCA94305 United States Department of Genetics Stanford University StanfordCA94305 United States Department of Medicine Stanford University StanfordCA94305 United States

Inherent bias within society can be amplified and perpetuated by artificial intelligence (AI) systems. To address this issue, a wide range of solutions have been proposed to identify and mitigate bias and enforce fairness for individuals and groups. Recently, Graph Laplacian Regularizer (GLR), a regularization technique from the semi-supervised learning literature has been used as a substitute for the common Lipschitz condition to enhance individual fairness. Notable prior work has shown that enforcing individual fairness through a GLR can improve the transfer learning accuracy of AI models under covariate shifts. However, the prior work defines a GLR on the source and target data combined, implicitly assuming that the target data are available at train time, which might not hold in practice. In this work, we investigated whether defining a GLR independently on the train and target data could maintain similar accuracy. Furthermore, we introduced the Normalized Fairness Gain score (NFG) to measure individual fairness by measuring the amount of gained fairness when a GLR is used versus not. We evaluated the new and original methods under NFG, the Prediction Consistency (PC), and traditional classification metrics on the German Credit Approval dataset. The results showed that the two models achieved similar statistical mean performances over fivefold cross-validation. Furthermore, the proposed metric showed that PC scores can be misleading as the scores can be high and statistically similar to fairness-enhanced models while NFG scores are small. This work therefore provides new insights into when a GLR effectively enhances individual fairness and the pitfalls of PC. © 2024, CC BY.

关键词： Laplace transforms

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Johnson-lindenstrauss lemma, linear and nonlinear random projections, random fourier features, and random kitchen sinks: Tutorial and survey

arXiv

引用

arXiv 2021年

作者： Ghojogh, Benyamin Ghodsi, Ali Karray, Fakhri Crowley, Mark Department of Electrical and Computer Engineering Machine Learning Laboratory University of Waterloo WaterlooON Canada Department of Statistics and Actuarial Science & David R. Cheriton School of Computer Science Data Analytics Laboratory University of Waterloo WaterlooON Canada Department of Electrical and Computer Engineering Centre for Pattern Analysis and Machine Intelligence University of Waterloo WaterlooON Canada

This is a tutorial and survey paper on the Johnson-Lindenstrauss (JL) lemma and linear and nonlinear random projections. We start with linear random projection and then justify its correctness by JL lemma and its proof. Then, sparse random projections with `1 norm and interpolation norm are introduced. Two main applications of random projection, which are low-rank matrix approximation and approximate nearest neighbor search by random projection onto hypercube, are explained. Random Fourier Features (RFF) and Random Kitchen Sinks (RKS) are explained as methods for nonlinear random projection. Some other methods for nonlinear random projection, including extreme learning machine, randomly weighted neural networks, and ensemble of random projections, are also introduced. Copyright © 2021, The Authors. All rights reserved.

关键词： Surveys

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Sufficient dimension reduction for high-dimensional regression and low-dimensional embedding: tutorial and survey

arXiv

引用

arXiv 2021年

作者： Ghojogh, Benyamin Ghodsi, Ali Karray, Fakhri Crowley, Mark Department of Electrical and Computer Engineering Machine Learning Laboratory University of Waterloo WaterlooON Canada Department of Statistics and Actuarial Science & David R. Cheriton School of Computer Science Data Analytics Laboratory University of Waterloo WaterlooON Canada Department of Electrical and Computer Engineering Centre for Pattern Analysis and Machine Intelligence University of Waterloo WaterlooON Canada

This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality reduction. We start with introducing inverse regression methods including Sliced Inverse Regression (SIR), Sliced Average Variance Estimation (SAVE), contour regression, directional regression, Principal Fitted Components (PFC), Likelihood Acquired Direction (LAD), and graphical regression. Then, we introduce forward regression methods including Principal Hessian Directions (pHd), Minimum Average Variance Estimation (MAVE), Conditional Variance Estimation (CVE), and deep SDR methods. Finally, we explain Kernel Dimension Reduction (KDR) both for supervised and unsupervised learning. We also show that supervised KDR and supervised PCA are equivalent. Copyright © 2021, The Authors. All rights reserved.

关键词： Regression analysis

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Unified Framework for Spectral Dimensionality Reduction, Maximum Variance Unfolding, and Kernel learning By Semidefinite Programming: Tutorial and Survey

arXiv

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arXiv 2021年

This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first explain how the spectral dimensionality reduction methods can be unified as kernel Principal Component Analysis (PCA) with different kernels. This unification can be interpreted as eigenfunction learning or representation of kernel in terms of distance matrix. Then, since the spectral methods are unified as kernel PCA, we say let us learn the best kernel for unfolding the manifold of data to its maximum variance. We first briefly introduce kernel learning by SDP for the transduction task. Then, we explain MVU in detail. Various versions of supervised MVU using nearest neighbors graph, by class-wise unfolding, by Fisher criterion, and by colored MVU are explained. We also explain out-of-sample extension of MVU using eigenfunctions and kernel mapping. Finally, we introduce other variants of MVU including action respecting embedding, relaxed MVU, and landmark MVU for big data. Copyright © 2021, The Authors. All rights reserved.

关键词： Surveys

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