https://xkcd.com/1399/
Probabilistic PCA
Autoencoders
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and Nonlinear Component Analysis
Autoencoders for image processing
Recommender systems
[PRML book]
Pre-read PCA – 12.1 This lecture:
12.2, 12.2.1, 12.4.2
Kernel week6
PCA 12.3 (read lectures)
Murphy’s PML book
Covariance matrix of (centered) data
variance projection
error formulation
Probabilistic PCA
x : D-dimensional vector
z : M-dimensional Gaussian D >= M
W: D-by-M matrix
latent variable
Likelihood a
nd posterior for x
also (2.113)-(2.117)
Woodbury / matrix inversion identity
Maximum likelihood for W, 𝝁, σ2
for probabilistic PCA
and Nonlinear Component Analysis
Probabilistic PCA
Autoencoders
Autoencoders for image processing
Recommender systems
Two-layer ass
neural nets
Linear autoencoder
Linear autoencoder
Easier to represent with
ore layers
“On the Expressive Power of Deep Architectures”, Bengio and Delalleau, 2011
Yao, A. (1985). Separating the polynomial-time hierarchy by oracles. In Proceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science, pages 1–10.
H ̊astad, J. (1986). Almost optimal lower bounds for small depth circuits. In Proceedings of the 18th annual ACM Symposium on Theory of Computing, pages 6–20, Berkeley, California.
Challenges
of “just ad
d more layers”
Cost function
of an autoencod
Glorot, Xavier, and . “Understanding the difficulty of training deep feedforward neural networks.” In AISTATS 2010 pp. 249-256.
and Nonlinear Component Analysis
Probabilistic PCA
Autoencoders
Autoencoders for image processing
Recommender systems
Xie, Junyuan, , and Enhong Chen. “Image
denoising and inpainting with deep neural
networks.”
Advances in neural information
processing systems
25 (2012): 341-349.
Xie, Junyuan, , and
Enhong Chen. “Image
denoising and inpainting with
deep neural networks.”
Advances in neural information
processing systems
25 (2012):
Resizing an
https://cimg.eu/greycstoration/demonstration.shtml
Image inpainting – undo
over image
Xie, Junyuan, , and Enhong Chen. “Image denoising and
inpainting with deep neural networks.”
Advances in neural
information processing systems
25 (2012): 341-349.
Image inpainting – free a bird
https://cimg.eu/greycstoration/demonstration.shtml
and nonlinea
Probabilistic PCA
Autoencoders
Applications in Image
processing
— denoising, upscaling, im
Recommender systems
Relational data and recom
Collaborative
Netflix prize dataset: 480K+
Newer public
MovieLens 1 M –
MovieLens 10 M
users, rating 17.8K movies, 100M ratings total
users, 3760 movies, 1M ratings
– ~70k users, 10K
~10M ratings
Matrix completion / matrix
prediction
Optimisation: alternating least squares, or stochastic
factorisation
gradient descent (SGD)
Autoencoders for
prediction
Loss function
recommendation
Sedhain et al, 2015]
https://cecs.anu.edu.au/events/event-series/anu-computing-leadership-seminar-series
Social recommendation
ocial Collaborative Filtering for Cold-start Recommendations. Sedhain,
uvash, Sanner, Scott, Braziunas, Darius, and Xie, Lexing, Recsys 2014
redit: for poster comic]
References
and Nonlinear Component Analysis
Probabilistic PCA
Autoencoders
Autoencoders for image processing
Recommender systems
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