Presented at a meetup of ROS Japan user group. 25th Oct. 2017

1. Probabilistic programming in robotics
ROS Japan UG #13 移動ロボット勉強会
25th October 2017
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2. Confidential
センスタイムジャパンAbout me
• Name: Taku Yoshioka
• Interests: Bayesian inference, machine learning,
deep learning and robotics
• Robot and ROS: 6 months
• Affiliation: SenseTime Japan
§ Computer vision and deep learning
§ https://www.sensetime.jp
§ https://blog.sensetime.jp (lunch blog)
§ Kyoto, Tokyo
§ We are hiring!
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センスタイムジャパンAgenda
• Probabilistic programming (PP)
§ Bayesian neural network
§ What is PP
§ Recent advances in probabilistic inference
§ Why PP matters in robotics
• Example: SLAM with PyMC3
§ https://taku-
y.github.io/notebook/20170919/slam_advi.html
• Technical issues for real robotics application
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センスタイムジャパンBayesian neural network
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• Two-class classification model with PyMC3
• Left: posterior mean. Right: posterior standard
deviation (uncertainty)
§ http://docs.pymc.io/notebooks/bayesian_neural_ne
twork_advi.html

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センスタイムジャパンWhat is PP
• Programming of probabilistic models and
inference with high-level API:
§ Probability distribution, random variables (RVs)
§ MCMC (Gibbs, HMC), variational inference (VI)
§ GLM, mixture models, Gaussian processes
§ Stan, PyMC3, Edward
• Traditional application: bioinformatics, finance –
exploration of hypothesis (models)
• Advances in inference techniques – application
with large models (i.e., a large number of RVs)
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センスタイムジャパンRecent advances in probabilistic inference
• Traditional techniques
§ MCMC – slow for models with many RVs
§ VI for conjugate models – limitation on models,
derivation and implementation of inference
• Advanced techniques
§ VI with stochastic gradient [1] – arbitrary models
§ Automated inference (ADVI) [2] – without
derivation/implementation of inference
§ Auto-encoding VB (VAE) [3] – latent variables
§ Normalizing flows [4], GAN [5] – arbitrary posterior
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センスタイムジャパンWhy PP matters in robotics
• Why complex probabilistic models matter
§ Low-dimensional state representation
§ Incorporation of prior knowledge
§ Composition of multiple models
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Encoder (VAE) Decoder (VAE)RL
Deep predictive policy architecture for robot manipulation task [6]

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センスタイムジャパンExample: SLAM with PyMC3
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• Formulation
• Simulated data
• Motion model
• Observation model
• Inference
• Sampling from approximated posterior
• Result

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センスタイムジャパンFormulation
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: control signals (known)U = {ut}T
t=1
Z = {zt}T
t=1 : observations (known)
: car locations/directions (unknown)
M = {mi}I
i=1
: landmark locations (unknown)
• 2-D car, landmarks
S = {st}T
t=0
p(S, M|Z, U) / p(S, M, Z|U)
=
TY
t=1
p(zt|st, M)p(st|st 1, ut)p(s0)p(M)
Note: s_0 is fixed in the example.

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センスタイムジャパンFormulation
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センスタイムジャパンSimulated data
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• Green trace: prior of the car locations (known)
• Red dashed lines: observations of landmarks (known)
• Blue trace: true locations of the car (unknown)
• Stars: landmarks locations (unknown)
• Inference of unknown RVs from knowns

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センスタイムジャパンMotion model
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Adopted from [7]
• Gaussian fluctuation with a discrete time model:
p(st|st 1, ut) = N(f(st 1, ut), ⌃mot)

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センスタイムジャパンMotion model
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センスタイムジャパンObservation model
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• Range-bearing measurement
p(zt|st, M) =
Y
i2D(st)
N(h(mi|st), ⌃obs)
D(s) = {i|distance(mi, s) < threshold}
Adopted from [7]Note: D(s_t) is known here.

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センスタイムジャパンObservation model
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センスタイムジャパンInference
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• Mean-field approximation
• Maximization of variational objective (evidence
lower bound; ELBO [1][2][3][4])
q(·): Normal distribution
L(✓) = Eq [ln p(S, M, Z|U)] Eq [ln q(S, M)]
p(S, M|Z, U) ⇡ q(S, M) =
TY
t=1
q(st)
IY
i=1
q(mi)
: (variational) parameters of q(·)✓

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センスタイムジャパンSampling from approximated posterior
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• Drawing samples from q(S, M)

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センスタイムジャパンResult
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• Red trace: posterior mean of states
§ Improvements from prior (green trace)
• Diamonds: estimated locations of 4 landmarks

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センスタイムジャパンTechnical issues for real robot application
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• Computational efficiency in prediction
§ No control over computation on expression graph
with backend (Tensorflow, Theano) and Python
interpreter
§ Desired solution: zero-cost abstraction
• Optimization in real time
• Composition of multiple models
• Standard format (e.g., JSON) of probabilistic
models for reuse

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センスタイムジャパンReferences
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[1] Paisley, J., Blei, D. M., & Jordan, M. I. (2012, June). Variational
Bayesian inference with stochastic search. ICML 2012.
[2] Kucukelbir, A., Tran, D., Ranganath, R., Gelman, A., & Blei, D. M.
(2017). Automatic Differentiation Variational Inference. JMLR 2017.
[3] Kingma, D. P., & Welling, M. (2013). Auto-encoding variational
bayes. ICLR 2014.
[4] Rezende, D., & Mohamed, S. (2015). Variational Inference with
Normalizing Flows. ICML 2015.
[5] Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D.,
Ozair, S., & Bengio, Y. (2014). Generative adversarial nets. NIPS 2014.
[6] Ghadirzadeh, A., Maki, A., Kragic, D., & Björkman, M. (2017). Deep
Predictive Policy Training using Reinforcement Learning. IROS 2017.
[7] Tim Bailey (2009). Simultaneous Localisation and Mapping:
Probabilistic Formulation. Presentation slide at SLAM SUMMER SCHOOL
2009, organized by Australian Centre for Field Robotics