Deep Learning with H2O

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H2O.aiScalable In-Memory Machine Learning

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H20 Meetup, Mountain View, 3/20/14

Arno Candel

Who am I?

PhD in Computational Physics, 2005from ETH Zurich Switzerland

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6 years at SLAC - Accelerator Physics Modeling 2 years at Skytree, Inc - Machine Learning 3 months at 0xdata/H2O - Machine Learning

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10+ years in HPC, C++, MPI, Supercomputing

Arno Candel

OutlineIntro

Theory

Implementation

Results

MNIST handwritten digits classification

Live Demo

Prostate cancer classification and age regression

text classification

Distributed in-memory math platform ➔ GLM, GBM, RF, K-Means, PCA, Deep Learning

Easy to use SDK / API➔ Java, R, Scala, Python, JSON, Browser-based GUI

!Businesses can use ALL of their data (w or w/o Hadoop)

➔ Modeling without Sampling

Big Data + Better Algorithms ➔ Better Predictions

H2O Open Source in-memoryPrediction Engine for Big Data

About H20 (aka 0xdata)Pure Java, Apache v2 Open Source Join the www.h2o.ai/community!

H2O w or w/o Hadoop

H2OH2O H2O

HDFS HDFS HDFS

YARN Hadoop MR

R Java Scala JSON Python

Standalone Over YARN On MRv1

H2O Architecture

in-memory K-V store MapReduce

compression

Machine Learning

Algorithms

R EngineNano fast

Scoring Engine

Prediction Engine

memory manager

e.g. Deep Learning

Wikipedia:

Deep learning is a set of algorithms in machine learning that attempt to model high-level abstractions in data by

using architectures composed of multiple non-linear transformations.

!!!!!

Facebook DeepFace (LeCun): “Almost as good as humans at recognising faces” !

Google Brain (Andrew Ng, Jeff Dean & Geoffrey Hinton) !

FBI FACE: $1 billion face recognition project

What is Deep Learning?

Example: Input data

(facial image)

Prediction (person’s ID)

Deep Learning is trending

20132012

Google trends

2011

1970s multi-layer feed-forward Neural Network (supervised learning with back-propagation) !+ distributed processing for big data (H2O in-memory MapReduce paradigm on distributed data) !+ multi-threaded speedup (H2O Fork/Join worker threads update the model asynchronously) !+ smart algorithms for accuracy (weight initialization, adaptive learning, momentum, dropout, regularization)

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= Top-notch prediction engine!

Deep Learning in H2O

“fully connected” directed graph of neurons

age

income

employment

married

not married

Input layerHidden layer 1

Hidden layer 2

Output layer

3x4 4x3 3x2#connections

information flow

input/output neuronhidden neuron

4 3 2#neurons 3

Example Neural Network

age

income

employmentyj = tanh(sumi(xi*uij)+bj)

uij

xi

yj

per-class probabilities sum(pl) = 1

zk = tanh(sumj(yj*vjk)+ck)

vjk

zk pl

pl = softmax(sumk(zk*wkl)+dl)

wkl

softmax(xk) = exp(xk) / sumk(exp(xk))

“neurons activate each other via weighted sums”

Prediction: Forward Propagation

married

not married

activation function: tanh alternative:

x -> max(0,x) “rectifier”

pl is a non-linear function of xi: can approximate ANY function

with enough layers!

bj, ck, dl: bias values(indep. of inputs)

age

income

employment

xi

standardize input xi: mean = 0, stddev = 1 !

horizontalize categorical variables, e.g. {full-time, part-time, none, self-employed}

-> {0,1,0} = part-time, {0,0,0} = self-employed

Poor man’s initialization: random weights !

Better: Uniform distribution in+/- sqrt(6/(#units + #units_previous_layer))

Data preparation & InitializationNeural Networks are sensitive to numerical noise, operate best in the linear regime (not saturated)

married

not married

Mean Square Error = (0.2^2 + 0.2^2)/2 “penalize differences per-class” ! Cross-entropy = -log(0.8) “strongly penalize non-1-ness”

Stochastic Gradient Descent

SGD: improve weights and biases for EACH training row

married

not married

For each training row, we make a prediction and compare with the actual label (supervised training):

1

0

0.8

0.2

predicted actual

Objective: minimize prediction error (MSE or cross-entropy)

w <— w - rate * ∂E/∂w

1

Backward Propagation

!∂E/∂wi = ∂E/∂y * ∂y/∂net * ∂net/∂wi

= ∂(error(y))/∂y * ∂(activation(net))/∂net * xi

Backprop: Compute ∂E/∂wi via chain rule going backwards

wi

net = sumi(wi*xi) + b

xiE = error(y)

y = activation(net)

How to compute ∂E/∂wi for wi <— wi - rate * ∂E/∂wi ?

Naive: For every i, evaluate E twice at (w1,…,wi±∆,…,wN)… Slow!

H2O Deep Learning Architecture

K-V

K-V

HTTPD

HTTPD

nodes/JVMs: sync

threads: async

communication

w

w w

w w w w

w1 w3 w2w4

w2+w4w1+w3

w* = (w1+w2+w3+w4)/4

map: each node trains a copy of the weights

and biases with (some* or all of) its

local data with asynchronous F/J

threads

initial weights and biases w

updated weights and biases w*

H2O atomic in-memoryK-V store

reduce: average weights and biases from

all nodes

Keep iterating over the data (“epochs”), score from time to time

Query & display the model via

JSON, WWW

2

2 431

1

1

1

43 2

1 2

1

i

*mini-batch: number of total rows per iteration, can be less than 1 epoch

“Secret” Sauce to Higher Accuracy

Momentum training:keep changing weights and biases (even if there’s no error)

“find other local minima, and go faster along valleys”

Adaptive learning rate - ADADELTA (Google):automatically set learning rate for each neuron based on its training history, combines annealing and momentum features

Learning rate annealing: rate r = r0 / (1+ß*N), N = training samples

“dig deeper into local minimum”

Grid Search and Checkpointing: Run a grid search over multiple hyper-parameters,

then continue training the best model

L1/L2/Dropout/MaxSumWeights regularization: L1: penalizes non-zero weights, L2: penalizes large weights

Dropout: randomly ignore certain inputs “train exp. many models at once” MaxSumWeights: Reduce all incoming weights if the sum > max value

“regularization avoids overtraining and improves generalization error”

MNIST: digits classification

Train: 60,000 rows 784 integer columns 10 classes Test: 10,000 rows 784 integer columns 10 classes

MNIST: Digitized handwritten digits database (Yann LeCun) Data: 28x28=784 pixels with values in 0…255 (gray-scale) One of the most popular multi-class classification problems

Without distortions or convolutions (which help), the best-ever published error rate on test set: 0.83% (Microsoft)

most frequent mistakes: confuse 4 with 6 and 9, and 7 with 2

test set error: 1.5% after 40 epochs 1.02% after 400 epochs 0.95% after 4000 epochs

H2O Deep Learning on MNIST: 0.95% test set error (so far)

1 node

Prostate Cancer Dataset

Live Demo: Cancer Prediction

Interactive ROC curve with real-

time updates

Live Demo: Cancer Prediction

0% training error with only 322

model parameters in seconds!

Live Demo: Grid Search RegressionDoing a grid search to find good hyper-parameters

to predict AGE from other 7 features

Then continue training the best model 5 hidden 50 tanh layers, rho=0.99, epsilon = 1e-10

MSE < 1 for test set ages in 44…79

Regression: 1 linear output

neuron

Live Demo: ebay Text Classification

Users enter a description when selling an item Task: Predict the type of item Data prep: Binary word vector 0,0,1,0,0,0,0,0,1,0,0,0,1,…,0 H2O parses SVMLight sparse format: label 3:1 9:1 13:1 … !

“Small” sample dataset on jewelry and watches: Train: 578,361 rows 8,647 cols 467 classes Test: 64,263 rows 8,647 cols 143 classes !H2O compressed columnar in-memory store: Only needs 60MB to store 5 billion entries (never inflated)

Live Demo: ebay Text Classification

Work in progress, shown results are for illustration only! Default parameters, no tuning, 4 nodes (16-cores each)

Train: 578,361 rows 8,647 cols 467 classes Test: 64,263 rows 8,647 cols 143 classes

Tips for H2O Deep Learning!General: More layers: more complex functions (non-linearity) More neurons per layer: detect finer structure in data More regularization: less overfitting (better validation error) !Do a grid search to get a feel for convergence, then continue training. Try Tanh first. For Rectifier, try max_w2 = 50 and/or L1=1e-5. Try TanhDropout or RectifierDropout with test/validation set after finding good parameters for convergence on training set. Distributed: Smaller mini-batch: more comm., slower, but higher accuracy. With ADADELTA: Try epsilon = 1e-4,1e-6,1e-8,1e-10, rho = 0.9,0.95,0.99 Without ADADELTA: Try rate = 1e-4…1e-2, rate_annealing = 1e-5…1e-8 Try momentum_start = 0.5, momentum_stable = 0.99, momentum_ramp = 1/rate_annealing Try balance_classes = true for imbalanced classes. Try force_load_balance for small datasets.

SummaryH2O is a distributed in-memory math platform that allows fast prototyping in Java, R, Scala and Python. !H2o enables the development of enterprise-quality blazing fast machine learning applications. !H2O Deep Learning is distributed, easy to use, and early results compete with the world’s best. !Deep Learning makes better predictions! !Try it yourself and join our next meetup! git clone https://github.com/0xdata/h2o