Pierre Vermaak UCT. An attempt to automate the discovery of initial solution candidates. Example-based learning Why? ◦ Track record on difficult.

Pierre VermaakUCT

An attempt to automate the discovery of initial solution candidates.

Example-based learning Why?

◦ Track record on difficult problems◦ Very different to ∆2 – approaches ;

complimentary◦ Neat

In this talk, I’ll give a practical perspective

What is it?◦ Very broad field◦ Data mining◦ Machine learning

Well-known algorithms◦ Neural Networks◦ Tree inducers (J48, M5P)◦ Support Vector Machines◦ Nearest Neighbour

Same idea throughout ...

Attempt to map input to output◦ e.g. binary lens light curve -> model parameters

Uses example data set: “training set” ◦ e.g. many simulated curves and their model

parameters Adjusts learning model parameters to best

fit of training data: “training”◦ Usually some sort of iteration◦ Algorithm dependent

Evaluation◦ Usually performance measured on unseen data

set: “test set”.

Famous data set by Fisher. Want to classify irises into three categories

based on petal and sepal width and length. 150 examples

sepallength (cm) sepalwidth (cm) petallength (cm) petalwidth (cm) class5 2 3.5 1 Iris-versicolor6 2.2 4 1 Iris-versicolor6.2 2.2 4.5 1.5 Iris-versicolor6 2.2 5 1.5 Iris-virginica4.5 2.3 1.3 0.3 Iris-setosa

sepallength (cm) sepalwidth (cm) petallength (cm) petalwidth (cm) class5 2 3.5 1 Iris-versicolor6 2.2 4 1 Iris-versicolor6.2 2.2 4.5 1.5 Iris-versicolor6 2.2 5 1.5 Iris-virginica4.5 2.3 1.3 0.3 Iris-setosa

Data SnippetData Snippet

“OneR”◦ Deduces a rule based on one input column

(“attribute”)

ResultsResults

RuleRule

“Multi-layer Perceptron” ◦ simple Neural Network

ResultResult

NetworkNetwork

Neat examples ... Can it be used on the real problem? Issues

◦ Many ambiguities of binary model◦ No uniform input - not uniformly sampled◦ Noise◦ Complexity

Success/failure with a variety of approaches The approach I’d like to take DIY tools for the job

◦ Do try this at home.

“Raw” light curves are unsuitable Require uniform inputs for training

◦ And the same scheme needs to be applied to subsequent unseen curves

Interpolation – non-trivial◦ Which scheme? What biases are introduced?

Smoothing – non-trivial◦ Required for interpolation anyway◦ Also for derived features (extrema, slope)

Centering/Scaling – non-trivial◦ Algorithms performed much better with normalized light

curves◦ What to centre on? Peak? Which one?◦ What baseline? Real curves are truncated

How many example curves to use? Ranges of binary lens model parameters in

training set. Noise model for example curves. Choice of learning algorithm Pre-processing parameters etc.

Normalized Curves◦ Using truncation/centering/scaling and smoothing

Derived Features◦ Attempt to extract properties of a light curve◦ PCA◦ polynomial fits◦ extrema◦ etc.

Various schemes attempted Most successful

◦ Find time corresponding to peak brightness◦ Translate the curve in time to this this value◦ Discard all data fainter (by magnitude) than 20%

of the total magnitude range◦ Normalize the time axis (-0.5 to 05)

Required for interpolation of equally-spaced data points on the curve

Too much smoothing destroys features Too little smoothing turns noise into

features Final scheme was a fitted B-spline iteration.

◦ Fit a B-spline◦ Count extrema◦ Repeat until number of extrema in suitable range◦ Worked out to be surprisingly robust

Truncation◦ Slope-based ... Numerical derivatives too noisy◦ Fitting a simpler model (Gaussian, single-lens)◦ Brightness exceeds 3 standard deviations of wing

brightness Smoothing

◦ Moving window averaging – destroys small features

◦ Savitzky-Golay – only works on evenly-spaced points

Chebyshev PolynomialsChebyshev Polynomials

PCAPCA

Single lens fits Moments Derivatives Smoothed Curves Time and Magnitude of extrema

Features are then selected for usefulness using selection algos (brute-force, information-based, etc.)

Using simulated curvesUsing simulated curves

The pre-processed curves themselves performed slightly better than derived features.

A simple learning algorithm performed best (nearest neighbour)

It sort of works on real events, but not at Production strength and still with intervention.

Still required Genetic Algo fine-tuning. Not good at finding multiple solutions

Automation: Mimic a human expert Categorize curves instantly Use categorization to come up with joint

likelihood distribution in model parameter space.

I want multiple solutions and large regions of exclusion.

Still believe in feature selection Eliminate dodgy pre-processing

◦ Smoothing◦ Interpolation

Use fast fits of “basis” functions◦ Possibly use binary curves themselves for

comparison, but with a robust distance metric.◦ Use the quality of fits as main feature◦ Fit a single lens and characterize residuals

These algorithms are very powerful But no algorithm is any good against

impossible odds. So, alternative parameterizations, etc. are

extremely important to this approach, just like to traditional fitting.

Java◦ 60%-100% as fast as C++ nowadays◦ Cross-platform◦ Plugs into and out of everything (Python, legacy

COM, Matlab, etc.)◦ Oh, the tools! – Parallelisation, IDE’s, just

everything. “javalens” – my rather humble new Java code

◦ Asada’s method◦ Lots of abstraction, more like framework◦ Open Source◦ Search “javalens” on google code

R◦ Awesome, free and open source statistics environment◦ Can be called from Java

WEKA◦ Great data mining app, used extensively in my thesis◦ Dangerous! Can spend years playing with it.◦ Make sure you concentrate on the sensibility of your data◦ NOT the large variety of fitting algorithms

Netbeans◦ Just a great free, open source Java IDE◦ Code completion◦ Automatic refactoring tools

VI◦ No comment