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okay, let's dive into deep learning decal fall 2017 lecture 5: linear factor models. this is a foundational topic in understanding how to represent data in a lower-dimensional space while capturing the most important variations. we'll cover the theory, intuition, and a python code example to solidify your understanding.

*outline*

1. *introduction to linear factor models:*
what are factor models?
motivation: dimensionality reduction and latent variables.
linearity assumption.
examples of linear factor models: pca, factor analysis, ica.

2. *principal component analysis (pca):*
mathematical formulation.
objective: maximizing variance.
singular value decomposition (svd) and eigenvalue decomposition.
reconstruction error.
choosing the number of components.

3. *factor analysis:*
mathematical formulation.
introducing a noise/uniqueness term.
distinction from pca: common factors vs. principal components.
factor loadings and specific variances.
rotation of factors (orthogonal and oblique).
parameter estimation (expectation-maximization algorithm).

4. *independent component analysis (ica):*
motivation: blind source separation.
statistical independence vs. uncorrelation.
maximizing non-gaussianity (kurtosis, negentropy).
ica algorithms (e.g., fastica).

5. *code example (python with scikit-learn):*
generating sample data.
applying pca.
applying factor analysis.
applying ica.
visualizing results.

6. *discussion and extensions:*
limitations of linear models.
non-linear extensions (autoencoders, kernel pca).
applications in deep learning (initialization, regularization).
connections to other areas (recommendation systems, natural language processing).

*1. introduction to linear factor models*

*what are factor models?* fact ...

#DeepLearning #LinearFactorModels #windows
deep learning
linear factor models
lecture 5
fall 2017
machine learning
statistical modeling
dimensionality reduction
feature extraction
regression analysis
covariance structure
latent variables
regularization techniques
neural networks
unsupervised learning
predictive analytics