1) Canonical correlation analysis (CCA) is a statistical method that analyzes the correlation relationship between two sets of multidimensional variables.
2) CCA finds linear transformations of the two sets of variables so that their correlation is maximized. This can be formulated as a generalized eigenvalue problem.
3) The number of dimensions of the transformed variables is determined using Bartlett's test, which tests the eigenvalues against a chi-squared distribution.
1) Canonical correlation analysis (CCA) is a statistical method that analyzes the correlation relationship between two sets of multidimensional variables.
2) CCA finds linear transformations of the two sets of variables so that their correlation is maximized. This can be formulated as a generalized eigenvalue problem.
3) The number of dimensions of the transformed variables is determined using Bartlett's test, which tests the eigenvalues against a chi-squared distribution.
This document discusses various methods for calculating Wasserstein distance between probability distributions, including:
- Sliced Wasserstein distance, which projects distributions onto lower-dimensional spaces to enable efficient 1D optimal transport calculations.
- Max-sliced Wasserstein distance, which focuses sampling on the most informative projection directions.
- Generalized sliced Wasserstein distance, which uses more flexible projection functions than simple slicing, like the Radon transform.
- Augmented sliced Wasserstein distance, which applies a learned transformation to distributions before projecting, allowing more expressive matching between distributions.
These sliced/generalized Wasserstein distances have been used as loss functions for generative models with promising
MLP-Mixer: An all-MLP Architecture for Visionharmonylab
出典：Ilya Tolstikhin, Neil Houlsby, Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, Thomas Unterthiner, Jessica Yung, Andreas Steiner, Daniel Keysers, Jakob Uszkoreit, Mario Lucic, Alexey Dosovitskiy : Mlp-mixer: An all-mlp architecture for vision, Advances in Neural Information Processing Systems 34 (2021)
公開URL：https://arxiv.org/abs/2105.01601
概要：最近の画像処理分野ではCNNやVision Transformerのようなネットワークが人気です。この論文では、多層パーセプトロン（MLP）のみで作成したアーキテクチャ"MLP-Mixer"を提案します。MLP-Mixerは2種類のレイヤーを保持しており、チャネルとトークン（位置）をそれぞれ別のMLPで学習しています。このモデルは画像分類ベンチマークにおいて、事前学習と推論コストが最新モデルに匹敵するスコアを達成しました
This document discusses various methods for calculating Wasserstein distance between probability distributions, including:
- Sliced Wasserstein distance, which projects distributions onto lower-dimensional spaces to enable efficient 1D optimal transport calculations.
- Max-sliced Wasserstein distance, which focuses sampling on the most informative projection directions.
- Generalized sliced Wasserstein distance, which uses more flexible projection functions than simple slicing, like the Radon transform.
- Augmented sliced Wasserstein distance, which applies a learned transformation to distributions before projecting, allowing more expressive matching between distributions.
These sliced/generalized Wasserstein distances have been used as loss functions for generative models with promising
MLP-Mixer: An all-MLP Architecture for Visionharmonylab
出典：Ilya Tolstikhin, Neil Houlsby, Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, Thomas Unterthiner, Jessica Yung, Andreas Steiner, Daniel Keysers, Jakob Uszkoreit, Mario Lucic, Alexey Dosovitskiy : Mlp-mixer: An all-mlp architecture for vision, Advances in Neural Information Processing Systems 34 (2021)
公開URL：https://arxiv.org/abs/2105.01601
概要：最近の画像処理分野ではCNNやVision Transformerのようなネットワークが人気です。この論文では、多層パーセプトロン（MLP）のみで作成したアーキテクチャ"MLP-Mixer"を提案します。MLP-Mixerは2種類のレイヤーを保持しており、チャネルとトークン（位置）をそれぞれ別のMLPで学習しています。このモデルは画像分類ベンチマークにおいて、事前学習と推論コストが最新モデルに匹敵するスコアを達成しました
The document introduces R and provides URLs for R resources. It discusses R's use for data manipulation, statistical analysis, and data visualization. URLs listed include the main R project website, CRAN mirrors including one at Tsukuba University, Japanese wiki and tutorial pages for R, and suggestions to use Twitter and blogs to find additional R information online.
The document discusses probability distributions and their natural parameters. It provides examples of several common distributions including the Bernoulli, multinomial, Gaussian, and gamma distributions. For each distribution, it derives the natural parameter representation and shows how to write the distribution in the form p(x|η) = h(x)g(η)exp{η^T μ(x)}. Maximum likelihood estimation for these distributions is also briefly discussed.
非負値行列分解の確率的生成モデルと 多チャネル音源分離への応用 (Generative model in nonnegative matrix facto...Daichi Kitamura
北村大地, "非負値行列分解の確率的生成モデルと多チャネル音源分離への応用," 慶應義塾大学理工学部電子工学科湯川研究室 招待講演, Kanagawa, November, 2015.
Daichi Kitamura, "Generative model in nonnegative matrix factorization and its application to multichannel sound source separation," Keio University, Science and Technology, Department of Electronics and Electrical Engineeing, Yukawa Laboratory, Invited Talk, Kanagawa, November, 2015.
Understanding your data with Bayesian networks (in Python) by Bartek Wilczyns...PyData
This document discusses using Bayesian networks to model relationships in data. It introduces Bayesian networks as directed acyclic graphs that represent conditional dependencies between random variables. The document describes approaches for finding the optimal Bayesian network structure given data, including scoring functions and dealing with issues like cycles. It also introduces BNFinder, an open-source Python library for learning Bayesian networks from data that can handle both discrete and continuous variables efficiently in parallel. Examples are given demonstrating BNFinder's ability to learn predictive models from genomic and gene expression data.
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