Amortised learning by wake-sleep Li Kevin Wenliang, Ted Moskovitz, - - PowerPoint PPT Presentation

Amortised learning by wake-sleep

Li Kevin Wenliang, Ted Moskovitz, Heishiro Kanagawa, Maneesh Sahani Gatsby Unit, University College London

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• model s

model str tructur ucture giv gives es bett better er tr trained ained models models , approximate ximate biased… Intractable… simple le, direct! ect! consis isten tent! t! and ty and type pe of

• f Z

Z

Least square regression gives conditional expectation

How to estimate ?

• define

Algorithm:

• 1. 𝑨𝑜, 𝑦𝑜 ∼ 𝑞𝜄
• 2. find ො

𝑕 by regression

• 3. 𝑦𝑛 ∼ 𝒠
• 4. update 𝜄 by ො

𝑕(𝑦𝑛)

• then
• In practice, draws

and solve

}

sleep

}

wake Issues: is high dimensional

• computing

for all sleep samples can be slow

• define

How to estimate

• suppose we estimate with kernel ridge regression, then

more efficiently?

is an estimator of by kernel ridge regression Theorem: if and the kernel is rich, then is a consistent estimator of

auto-diff

Amortised learning by wake-sleep

• 1. 𝑨𝑜, 𝑦𝑜 ∼ 𝑞𝜄
• 2. kernel ridge regression
• 3. 𝑦𝑛 ∼ 𝒠
• 4. update 𝜄 by 𝑕 𝑦𝑛 = ∇𝜄 መ

𝑔

𝜄(𝑦𝑛) simple le, direct! ect! consis isten tent! t! ,

Assumptions:

• easy to sample from 𝑞𝜄
• ∇𝜄 log 𝑞𝜄(𝑦, 𝑨) exists
• true gradient is ℒ𝑞

2

Non-assumptions:

• posterior
• structure of 𝑞𝜄
• type of 𝑎

Experiments

• Log likelihood gradient estimation
• Non-Euclidean latent
• Dynamical models
• Image generation
• Non-negative matrix factorisation
• Hierarchical models
• Independent component analysis
• Neural processes

simple le, direct! ect! consis isten tent! t!

Experiment 1: gradient estimation

Experiment II: prior on the unit circle

𝑨 ∈

Experiment III: dynamical model

Experiment IV:sample quality

Experiment IV: downstream tasks

Thank you!

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