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Introduction to Deep Probabilistic Programming with Pyro

柯維然 Odie

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Outline

  1. Probabilistic Programming
  2. Pyro tutorial
  1. Realworld example

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Probabilistic Programming

Deep learning

Bayesian learning

Graphical model

Logic/Rule based

Domain knowledge

Handcrafted features

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Probabilistic Programming

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  • 3 AI paradigms
    • Symbolic: logic and reasoning
    • Bayesian: Inference and uncertainty
    • Connetion: learning from complicated data
  • Probabilistic Programming combine them !

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Intuition

  • Parameters
  • Latent variables

Program

Output / Sample

  • Input
  • Configuration

Program

Output

  • Parameters
  • Latent variables

Program

Data / Observation

Probabilistic Programming

Sampling

Inference

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Human-level concept learning through probabilistic program induction

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source

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Build, Compute, Critique, Repeat

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source

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Pyro

  • Pyro bulit on Pytorch and another version on JAX (NumPyro)
  • Support GPU and JIT mode
  • Flexible and minimal design
  • Focus on stochastic variational inference

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Temperature-Sensor Model

open in colab

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Sampling

  • Repeat testing can generate many sample

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Trace

model arguments

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Evaluation probability

  • Fix sampled value in model function
  • Return new trace

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Evidence Lower Bound

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  • Maximize the ELBO
  • Minimize KL

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Define the generative model

Define the guide model

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Monte Carlo ELBO

Define the generative model

Define the guide model

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Define model & guide

Obs is i.i.d !

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SVI

Pyro implement several ELBO object function , will have lower variance

Use navie ELBO or custom implementation

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Training & result

Posterior : temp ~ N(13,8661 , 0.1686)

Prior : temp ~ N(0 , 1)

Real data : temp ~ N(15 , 10)

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Take home …

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source

SVI

Model , Guide

Prior

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Gaussian Mixture Model

Z

X

locs

Scales

Weight

N

plate

K

open in colab

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Define model

Marginalized discrete RV in SVI

MLE

Gaussian component prior

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Define guide & training

Auto generate guide function for point estimation

Enumerate discrete RV

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Result

K=16

K=8

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Generate new data

K=16

K=8

Fix locs and scales from guide_trace , then resample x

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Latent Dirichlet Allocation

  • Elegant model
  • Need Gibbs sampling
  • Hard to scale up

open in colab

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Generate data

Sequential not vectorized

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Define model

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Define guide

mini batch training

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Topic result

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Variational Autoencoders

  • Pyro official tutorial

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Unsupervised object detection

open in colab

pos

B*H*W*N

logit

B*4*4*2

Yolo like model

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Unsupervised object detection

Model definition

differential image render

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Differential image render

Spatial transformer networks

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Transform pos and logit

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Result

use point estimation guide

use CNN guide and more object

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Research work

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Research work

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Conclusion

  • Probabilistic Programming Language is future of AI
  • Unsupervised learning , self-supervised learning , generative model , causal inference , uncertainty , bayesian neural networks ...
  • Challenge:
    • Discreate RV learning and inference (VI is not good for discreate RV)
    • New tools and algorithm combine AD system (Julia Gen)
    • Solve real world task

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Refernece & Resource

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Q&A

Thanks for listening

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