Bayesian Deep Learning

Transcription

1 Bayesian Deep Learning Dealing with uncertainty and non-stationarity Dr. Thomas cki Director of Data Science, Quantopian

2 Disclaimer This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. ("Quantopian"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company. In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.

3 Quantopian > users (a s of Ap ril 1, 2017) Community, backtester + data, real-money trading competitions Select best trading strategies and invest tens of millions of dollars

4 Machine Learning in Algorith m ic Trading

5 Feature Extraction Hand-crafted alphas Non-linear, Linear risk hierarchical m odels risk E.g. factors PCA Deep Auto-Encoder Deep Learning Classifier Alphas are learned directly, E.g. instead SVM, of Random defined Forest by hand. Lo n g-sh ort-te rm -Mem ory (LSTM), 1D convolutional nets

6 However, certain problems in algorithm ic trading not we ll solve d by current deep learning research.

7 Non-Stationarity / Concept Drift Markets change Signals change / become obsolete Usual solution: Retrain model every t days, or, when change is detected. Unsatisfying: Old data could still be useful. Still assum es stationarity inside window.

8 Uncertainty Mod e ls will always p re d ict som e th in g, n o way of saying "I don't know". Unseen input can cause erratic behavior. Need uncertainty estimate of our predictions.

9 Solution: Combine with Bayesian Modeling Deep Learning Great performance Learn alphas directly from data Build better risk m odels Only point-estimates - No uncertainty in predictions Can't deal with non-stationarity Bayesian Modeling Principled uncertainty quantification Very flexible (can model nonstationarity) Bayesian Deep Learning

10 Bayesian Modeling: Coin flipping Model construction: How parameters relate to data Latent parameters (Posterior) (Prior) Likelihood of data, given parameters. Data (Heads / Tails) p(heads) Observe: HTTHTTT Inference: Bayes Formula most likely parameters given data

11 Probabilistic Programming Model construction: How was data generated Latent causes (Parameters) Distrib u tion of Data Observed Data Inference: Bayes Formula most likely parameters given data

12 Intuitive model specification syntax, for example, x ~ N(0,1) translates to x = Normal('x', 0, 1) Sampling algorithms (MCMC): Accurate approximation of posterior, but slow. Variational inference (BBVI): Less accurate approximation, but much faster. Uses Theano as computational backend: Computation optimization and dynamic C and GPU compilation Linear algebra operators Sim p le e xte n sib ility

13 Time for some code...

14 Resources Quantopian: Quant equtiy workflow: Quantopian implementation: arnin g-on-quantopian

15 Disclaimer This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. ("Quantopian"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company. In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.

16 Deep Learning: Pros and cons Deep Learning Bayesian Modeling Great performance Unified framework for model building, inference, Qu ite fle xib le prediction and decision making LSTMs, ConvNets, Neural Computers Scale s we ll Only point-estimates - No uncertainty in predictions Ove rfits e asily Can't deal with non-stationarity Baye sian : Prin cip le d uncertainty quantification of parameters and predictions Extre m e ly fle xib le (can m od e l n on -stationarity) Robust to overfitting Many conjugate / linear models Little ap p lication to ML Natural to try and combine these two: Bayesian Deep Learning

17 Random sample from input data

18 Random sample from output data Looks like a vanilla classification problem. However...

19 Probabilistic Programming 1. Build m odel, specify prior belief. 2. Observe data, update belief to posterior. 3. Canonical exam ple: Coin flipping Model: Random variable: p_heads = Beta(1, 1) Likelihood: Bernoulli(data p_heads) Inference: Infer posterior distribution P(p_heads data)