PSY8219 : Week 12catlab.psy.vanderbilt.edu/.../Week12/Week12.pdf · Week12_GUI.m keeps GUI open...

PSY8219 : Week 12

Homework 10 Due Wednesday at 1pm

Homework 12 Due Wednesday November 28 at 1pm

Readings for Today

Attaway Chapter 13 (section on GUIs)

Readings for Next Week

None

Graphical User Interfaces (GUIs)

http://www.mathworks.com/help/pdf_doc/matlab/buildgui.pdf

GUIs in Matlab

let you get inputs from users or interact with graphical objects

Two ways to create GUIs: 1) GUIDE, the MATLAB Graphical User Interface Development Environment, provides interactive tools for creating GUIs 2) programming directly using GUI functions

GUIs in Matlab

GUIs are built within Matlab figures

fh=figure('Visible','off','Position',[11sxsy],...'Color','white','Name','AnexampleGUI');

size of figureinvisible while we create

figure handle

Formatting

You need to realize the internally Matlab has a hierarchical representation of figures.

root

figure

GUIobjects

axes

plotobjects

otherobjects

GUIs in Matlab

GUIs are built within Matlab figures

fh=figure('Visible','off','Position',[11sxsy],...'Color','white','Name','AnexampleGUI');

.

.

.

movegui(fh,'center');set(fh,'Visible','on');

move to the center of the screen

make the figure visible

GUIs in Matlab

uicontrol is one key routine for building GUIs

uicontrol(fh,'Style','text','Units','Normalized',... 'Position',[.05.80.2.1],'FontSize',18,...'String','SubjectName','BackgroundColor','white');

GUIs in Matlab



figure handle

GUIs in Matlab



what kind of GUI control

'text','sliders','radiobutton','popupmenu',etc.

GUIs in Matlab



use normalized (percent) units

GUIs in Matlab



where this text will go and how big it is 5% on x, 80% on y, 20% high, 10% wide

GUIs in Matlab



this is the value of the text to display

GUIs in Matlab


snameh=uicontrol(fh,'Style','edit',... 'Units','Normalized',... 'Position',[.30.83.4.1],'FontSize',18);

editable text box

GUIs in Matlab


snameh=uicontrol(fh,'Style','edit',... 'Units','Normalized',... 'Position',[.30.83.4.1],'FontSize',18);

control handle, important to read out value

GUIs in Matlab


snameh=uicontrol(fh,'Style','edit',... 'Units','Normalized',... 'Position',[.30.83.4.1],'FontSize',18);...sname=get(snameh,'String');

read out value typed in

GUIs in Matlab


llh=uicontrol(fh,'Style','slider',...'Units','Normalized','Position',[.42.24.50.2],... 'Min',minl,'Max',maxl,'Value',minl,...'SliderStep',[.1.2],'CallBack',@llcallback);

control handle, important to read out value

GUIs in Matlab



slider

GUIs in Matlab



min, max, and starting value

GUIs in Matlab



function called any time control element used

GUIs in Matlab



ll=round(get(llh,'Value'));

read out the number based on slider position

GUIs in Matlab

>>get(llh) BackgroundColor=[0.9294120.9294120.929412] Callback=[(1by1)function_handlearray] CData=[] Enable=on Extent=[000.006666670.008] FontAngle=normal FontName=Helvetica FontSize=[10] FontUnits=points FontWeight=normal ForegroundColor=[000]… Parent=[1] Selected=off SelectionHighlight=on Tag= Type=uicontrol UIContextMenu=[] UserData=[] Visible=on

justlikefigurehandlesyoucangetandsetparticularvalues

GUIs in Matlab

llh=uicontrol(fh,'Style','slider',...'Units','Normalized','Position',[.42.24.50.2],... 'Min',minl,'Max',maxl,'Value',minl,...'SliderStep',[.1.2],'CallBack',@llcallback);llth=uicontrol(fh,'Style','text',...'Units','Normalized','Position',[.30.35.08.1],... 'FontSize',18,'String',num2str(minl),...'BackgroundColor','white');

functionllcallback(source,eventdata) ll=get(llh,'Value'); set(llth,'String',num2str(round(ll)));end

slider

showvalueofslider

GUIs in Matlab


functionllcallback(source,eventdata) ll=get(llh,'Value'); set(llth,'String',num2str(round(ll)));end

getvalueofslider

GUIs in Matlab


functionllcallback(source,eventdata) ll=get(llh,'Value'); set(llth,'String',num2str(round(ll)));end updatetextdisplayofvalue

GUIs in Matlab

once created a GUI is a standalone object – you need to interrogate it explicitly via its handles, or let it impact your program via its callback functions

MainProgram GUI

usehandlestoaccessGUIdata

GUIcanchangeglobalvariables

GUIs in Matlab

Week12_GUI.m

keeps GUI open until all data entered and user presses OK

Week12_Figure.m

creates a GUI that is simply closed by clicking it closed in principle, you could essentially create something that acted like a full-blown program with menus and multiple windows all spawned by callback functions attached to GUI elements

Optimization and Curve Fitting

LinearRegressionModel

vs

NonlinearStatistical,Cognitive,NeuralModel

slopeandinterceptparametersarecalculatedusingclosed-formmathematicalexpressions

modelparameterscanbeestimatedusingavarietyofsearch/optimizationapproaches

Week12_Figure.m

imagine trying to fit data by adjusting all the parameters by hand

motion coherence

accu

racy

fittingapsychometricfunctiontoobserveddata

whatvaluesofα, β, γ, λ providethebestaccountoftheobserveddata?

P(correct | x) = γ + (1− λ − γ )F(x;α ,β )F(x;α ,β ) = 1− exp(−(x / β )α )

motion coherence

accu

racy

e.g.,whatvalueofcoherencegiveschanceperformance

fittingapsychometricfunctiontoobserveddata

motion coherence

accu

racy

luminance #1

luminance #2

motion coherence

luminance #1

luminance #2

isthesamepsychometricfunctionobservedwhenanothervariableismanipulated(ornot)?

isthethresholdsignificantlyhigherinoneconditionthantheother?

amount of learning (n)

resp

onse

tim

e

fitapowerlawfunctiontoalearningcurve

RT (n) = A + Bn−C

amount of learning (n)

resp

onse

tim

e

isapowerlaworanexponentiallawabetterfunction?

vs.RT (n) = A + Bn−C RT (n) = A + Be−C (n−1)

Zhang,W.,&Luck,S.J.(2008).Discretefixed-resolutionrepresentationsinvisualworkingmemory.Nature,453,233-235.

usedtocharacterizeVWMinagivencondition

probabilityanitemisstoredinVWM

fidelityofthememory

meancontentofthememory

Prob(x | µ,σ ,Pm ) = Pmecos(x−µ )/σ

2π I0 (1 /σ )+ (1− Pm )

12π

µ,σ ,Pm

StochasticAccumulationofEvidenceModels

perceptual processing

time

motorresponse

time

z

adrift

TR TM

Different kinds of models

• purely mathematical / statistical models – nonlinear regression

– power law of learning

– psychometric function

• hybrid mathematical / process model – mixture models of power law functions

– mixture model of VWM

• process / mechanistic model (cognitive or neural) – diffusion model of perceptual decision making

– temporal context model of memory

optimizationandparameterestimation

model


model

parameters


model

parameters

prediction


model

parameters

prediction data≡


model

parameters

prediction data≡

weneedtofindparametersthatcausethemodeltomakepredictionsthatmatchthedata


social,behavioral,orneuralprocess

parameters

unknownandunobservable observable

data



parameters data

modelofthatprocess

observableunknownandunobservable

hypothesized

perhapsoneofseveralcompetingmodelsbeingconsidered



parameters data

modelofthatprocess predictionparameters


hypothesized

generated



parameters data



hypothesized

generated

maximizethecorrespondence

minimizethediscrepancy



parameters data



hypothesized

byadjustingtheseparameters



generated



parameters data



hypothesized




generated

ifwe’veoptimizedcompetingmodels,wecanstatisticallydeterminewhethersomemodelspredictbetterthanothers



parameters data



hypothesized




generated

ifwe’veoptimizedcompetingmodels,wecanstatisticallydeterminewhethersomemodelspredictbetterthanothers



parameters data



hypothesized




generated

sometimes,parameterscanbesetbasedononesetofdataandused(withoutfitting)foranothersituation…

measuresofcorrespondenceordiscrepancy

Someexamples(oftencalled“objectivefunctions”)

Sum-of-SquaredError(SSE)

Correlation

χ2

Likelihood various

SSE = (obsi − prdi )2

i∑

r =(obsi − obs)(prdi − prd)

i∑(obsi − obs)

2

i∑ (prdi − prd)

2

i∑

χ 2 = (obsi − prdi )2

prdii∑

minimized

maximized

minimized

maximized

someobjectivefunctionsaremoreconducivetostatisticaltests

p

SSEwithonlyoneparameter,wewanttofindthevalueofparameterpthatmakestheSSEassmallaspossible–bestfittingvalueofp

optimal valueofp

smallestSSE

One-parameter model

p1

p2

SSE

valuesofp1andp2thatminimizeSSE

Two-parameter model

Three-parameter (or more) model

cannot visualize graphically, but the concept is the same …

what values of parameters minimize SSE (or maximize correlation, or maximize likelihood)

abriefsurveyofoptimizationmethods


BruteForce:GridSearch

tryeverycombinationofparametersandkeeptheonethatminimizes/maximizesyourobjectivefunction(e.g.,SSE)




basically,it'sthesameprogrammingyouwouldusetographthefunction,onlythatyou'realsotryingtofindthemin




parameter 1

para

met

er 2

likeanearlierhomeworkproblem




okayformodelswithdiscrete-valuedparameters…whentheyhavecontinuousvaluesitisimpossibletotryeverycombination

okayformodelswithacoupleofparameters…impossibleformodelswithdozensorhundredsofparameters



imaginewehaveamodelwith5parameters…

andforeachparameterwearegoingtoevaluate100valuesofit…

Howmanytotalevaluationsisthat?






1005or1010=10,000,000,000

Isthatalot?Wellitdepends.






1005or1010=10,000,000,000


Ifittakes1nanosecond(10-9seconds)perevaluation,thenitwouldtakeonly10secondstodoall1010evaluations…butthatwouldhavetobeaverysimplemodel






1005or1010=10,000,000,000


Ifittakes100seconds(102seconds)perevaluation,thenitwouldtakenearly32,000yearstodoalltheevaluations…

wearetestingsomeneuralmodelsthattakefarlongerthanthattorun






1005or1010=10,000,000,000


Ifittakes100seconds(102seconds)perevaluation,thenitwouldtakenearly32,000yearstodoalltheevaluations…evenifweranthison1000processors,itwouldtake32years


Calculus

formathematicallysimplemodelsandobjectivefunctions,youcansometimesoptimizeusingcalculus…


Calculus

SSE(p)

dSSE(p)dp

derivativeofafunctionisanotherfunctionthatspecifiestheslopeofthatfunction


Calculus

SSE(p)

dSSE(p)dp



Calculus

SSE(p)

dSSE(p)dp



Calculus

SSE(p)

dSSE(p)dp

minimizingormaximizingstartswithfindinganyplacesonthefunctionwherethederivativeiszero


Calculus

SSE(p)dSSE(p)dp

= 0 canoftenbedoneanalytically,solvingforvaluesofp


Calculus

p1

p2

SSE

∂SSE(p1)∂p1

= 0 ∂SSE(p2)∂p2

= 0and


Hill-climbingAlgorithms


SSE(p)



SSE(p)



SSE(p)



SSE(p)



SSE(p)



SSE(p)



SSE(p)



SSE(p)



SSE(p)



SSE(p)




Enrico Fermi and Nicholas Metropolis used one of the first digital computers, the Los Alamos Maniac, to determine which values of certain theoretical parameters (phase shifts) best fit experimental data (scattering cross sections). They varied one theoretical parameter at a time by steps of the same magnitude, and when no such increase or decrease in any one parameter further improved the fit to the experimental data, they halved the step size and repeated the process until the steps were deemed sufficiently small. Their simple procedure was slow but sure, and several of us used it on the Avidac computer at the Argonne National Laboratory for adjusting six theoretical parameters to fit the pion-proton scattering data we had gathered using the University of Chicago synchrocyclotron [7].

W. C. Davidon, Variable Metric Method for Minimization, Tech. Rep. 5990, Argonne National Laboratory, Argonne, IL, 1959.

these techniques only emerged 60 years ago (Calculus was invented 400 years ago)



Enrico Fermi and Nicholas Metropolis used one of the first digital computers, the Los Alamos Maniac, to determine which values of certain theoretical parameters (phase shifts) best fit experimental data (scattering cross sections). They varied one theoretical parameter at a time by steps of the same magnitude, and when no such increase or decrease in any one parameter further improved the fit to the experimental data, they halved the step size and repeated the process until the steps were deemed sufficiently small. Their simple procedure was slow but sure, and several of us used it on the Avidac computer at the Argonne National Laboratory for adjusting six theoretical parameters to fit the pion-proton scattering data we had gathered using the University of Chicago synchrocyclotron [7].

W. C. Davidon, Variable Metric Method for Minimization, Tech. Rep. 5990, Argonne National Laboratory, Argonne, IL, 1959.

these techniques only emerged 60 years ago (Calculus was invented 400 years ago)

p1

p2

SSE

howmanypointsdoyouneedtoevaluatewitheachstep?

2 parameters

21 3

4

567

8


SimpleHillClimbing

N parameters

5 parameters

10 parameters

3N-1 evaluations per step

242 evaluations per step

59049 evaluations per step

this ends up being inefficient because you can need to take 1000’s of steps

howmanypointsdoyouneedtoevaluatewitheachstep?


SimpleHillClimbing

Kolda, T.G., Lewis, R.M., & Torczon, V. (2003). Optimization by direct search: New perspectives on some classical and modern methods. SIAM Review, 45, 385-482.

Kelley, C.T. (1999). Iterative Methods for Optimization. SIAM. Chapters 6-8.


Moresophisticatedalgorithms

OptimizationToolboxhttp://www.mathworks.com/help/pdf_doc/optim/optim_tb.pdf

GlobalOptimizationToolboxhttp://www.mathworks.com/help/pdf_doc/gads/gads_tb.pdf

CurveFittingToolboxhttp://www.mathworks.com/help/pdf_doc/curvefit/curvefit.pdf

MATLAB:fminsearch(…)

http://en.wikipedia.org/wiki/Nelder-Mead_method

http://www.scholarpedia.org/article/Nelder-Mead_algorithm


Nelder-MeadeSimplex

[opt fit] = fminsearch(@myfun,p0)

params fit

change params to try to decrease fit

myfun()

p0=-2;[optfit]=fminsearch(@myfun1,p0);fprintf('p0=%5.2f\toptimalp=%5.2f\tf(p)=%6.3f\n',… p0,opt,fit);

functiony=myfun1(x) y=-humps(x); end

Week12_fmin.m

p0=[-20];[optfit]=fminsearch(@myfun2,p0);

functionz=myfun2(x,y) z=3*(1-x(:,1)).^2.*exp(-(x(:,1).^2)-(x(:,2)+1).^2)...-10*(x(:,1)/5-x(:,1).^3-x(:,2).^5).*... exp(-x(:,1).^2-x(:,2).^2)... -1/3*exp(-(x(:,1)+1).^2-x(:,2).^2);end

Week12_fmin2.m

p0=[1023];[optfit]=fminsearch(@myfun3,p0);

functionSSE=myfun3(p)%calculuatemodelpredictionsgivenparametervectorp

%thencalculateSSEcomparingpredictionstodata

%returnSSEasthevaluetominimizeend

thiscouldbeanonlinearfunctionifyouarecurvefittingorthiscouldbeaneuralorcognitivemodelifyouaretheorizing

p0=[351431];[optfit]=fminsearch(@myfun4,p0);

functionlnL=myfun4(p)%calculuatemodelpredictionsgivenparametervectorp

%thencalculatelnLcomparingpredictionstodata

%return-lnLasthevaluetominimizeend

maximizingissimply-minimizing

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