GRAMMATICAL EVOLUTION FOR THE PREDICTION OF
HYPOGLYCEMIA IN DIABETES
G amá icas E olu i as pa a la p edicción de hipoglucemias en
diabe es
MARINA DE LA CRUZ LÓPEZ
T abajo Fin de G ado en Ingenie ía In o má ica
Facul ad de In o má ica, Uni e sidad
Complu ense de Mad id
Mayo de 2022
di igido po
Ca los Ce igón Rückaue
Depa amen o Ingenie ía del So wa e e In eligencia A i icial
Facul ad de In o má ica
Uni e sidad Complu ense de Mad id
Resumen
Los pacien es con diabe es deben con ola co ec amen e su ni el de azúca en sang e
pa a e i a complicaciones. Una de es as complicaciones es la hipoglucemia o ni el bajo de
azúca en sang e, que ocu e cuando la concen ación de glucosa en la sang e cae po debajo
de cie o umb al. Un episodio de hipoglucemia debe co egi se an es de que se uel a dañino
y puede se una si uación muy angus iosa pa a el pacien e.
El obje i o p incipal de es e es udio es p og ama los algo i mos de G amá icas E olu-
i as Es uc u adas y G amá icas E olu i as Es uc u adas Dinámicas, y u iliza los pa a
gene a modelos de p edicción de episodios hipoglucémicos en pacien es con diabe es.
Los algo i mos se u iliza án pa a ob ene un modelo de caja blanca o mado po sen en-
cias i - hen-else que, dados unos da os de en ada, compues os po el ni el de la glucosa en
sang e y las lec u as de da os de eje cicio de los pacien es de las 2 ho as an e io es, op imiza
una elación lógica en e es as a iables. La ó mula esul an e se usa pa a de e mina si el
pacien e a a ene un episodio de hipoglucemia en un plazo de 30, 60, 90 y 120 minu os.
Palab as cla e
Diabe es, G amá icas E olu i a, Algo i mos Gené icos, Ap endizaje Au omá ico, P edic-
ción de Glucosa, G amá icas E olu i as Es uc u adas, G amá icas E olu i as Es uc u adas
Dinámicas
Abs ac
Diabe ic pa ien s ha e o manage hei blood suga co ec ly o p e en complica ions.
One such complica ion is hypoglycemia o low blood suga , which occu s when he blood
glucose concen a ion goes below a ce ain h eshold. A hypoglycemic episode needs o be
ec i ied be o e i becomes ha m ul and can be a e y dis essing si ua ion o he pa ien .
The main goal o his s udy is o p og am S uc u ed G amma ical E olu ion and Dy-
namic S uc u ed G amma ical E olu ion algo i hms and use hem o gene a e models o
he p edic ion o hypoglycemic episodes in pa ien s wi h diabe es.
The algo i hms will be used o ob ain a whi e-box model made up o i - hen-else s a e-
men s ha gi en some inpu da a, comp ised o he blood glucose and exe cise eadings o
he pa ien s om he p e ious 2 hou s, op imizes a logical ela ion be ween hese a iables.
The esul ing o mula will be able o de e mine i he pa ien is going o ha e a hypoglycemic
episode in a 30, 60, 90 and 120 minu es p edic ion ho izon.
Keywo ds
Diabe es, G amma ical E olu ion, Gene ic Algo i hms, Machine Lea ning, Glucose P e-
dic ion, S uc u ed G amma ical E olu ion, Dynamic S uc u ed G amma ical E olu ion.
Con en s
Index i
Acknowledgmen s iii
1 In oduc ion 1
1.1 In oduc ion.................................... 1
1.2 Hypoglycemia................................... 2
1.3 Objec i e ..................................... 3
2 Rela ed Wo k 5
2.1 In oduc ion.................................... 5
2.2 Symbolic P edic ion using Gene ic p og amming . . . . . . . . . . . . . . . . 6
2.2.1 S uc u ed G amma ical E olu ion . . . . . . . . . . . . . . . . . . . 6
2.3 Classi ica ion ................................... 7
2.3.1 Va iables and p edic ion ho izon . . . . . . . . . . . . . . . . . . . . . 7
2.3.2 Machine lea ning algo i hms . . . . . . . . . . . . . . . . . . . . . . . 7
3 Me hodology 10
3.1 G amma icalE olu ion.............................. 10
3.2 S uc u ed G amma ical E olu ion . . . . . . . . . . . . . . . . . . . . . . . 11
3.2.1 S a ic S uc u ed G amma ical E olu ion . . . . . . . . . . . . . . . . 14
3.2.2 Dynamic S uc u ed G amma ical E olu ion . . . . . . . . . . . . . . 16
3.2.3 Dep h ................................... 21
3.3 Ope a o s ..................................... 22
3.3.1 Mu a ionope a o ............................ 22
3.3.2 C osso e ope a o ............................ 23
3.4 G amma ..................................... 27
3.5 Fi nessFunc ion ................................. 30
3.5.1 Mul i-classRecall............................. 30
3.5.2 F1measu e ................................. 31
3.5.3 Weigh edAccu acy............................ 31
3.6 E olu iona yAlgo i hm ............................. 32
4 Da a 33
4.1 In oduc ion.................................... 33
4.2 Desc ip ion .................................... 33
4.2.1 Classi yingda a.............................. 36
4.3 Da aP ep ocessing................................ 37
i
4.3.1 Co ela ions................................ 38
4.3.2 Classbalancing.............................. 43
5 Resul s 45
5.1 Expe imen alSe -up ............................... 45
5.1.1 Gene al and Indi idual Models . . . . . . . . . . . . . . . . . . . . . 47
5.2 2Classes...................................... 48
5.2.1 30Minu es ................................ 49
5.2.2 60Minu es ................................ 53
5.2.3 90Minu es ................................ 57
5.2.4 120Minu es................................ 61
5.2.5 Resul s o 2classes............................ 65
5.2.6 Used a iables............................... 66
5.3 3Classes...................................... 71
5.3.1 120minu es................................ 72
5.3.2 Resul s o 3 Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.3.3 Used a iables............................... 78
5.4 Fu u eWo k.................................... 80
5.5 Di usion...................................... 81
Bibliog aphy 85
A JECO and Panc eas Model Tools 86
ii

Acknowledgmen s
Fi s ly, I would like o hank my amily o suppo ing me du ing hese pas yea s,
my classma es and iends who ha e s udied alongside me and all he eache s ha ha e
been a pa o my educa ion. An special hanks o Ca los Ce igón Rückaue and J. Ignacio
Hidalgo o aiding and men o ing me h ough he c ea ion o his p ojec . I am also hank ul
o Jo ge Al a ado o compiling he da a and o all he pa ien s whose da a was used o
pe o m his s udy.
A inal hanks o he Facul y o Compu e Science o he UCM ha has made all o his
possible, and o he Adap i e and Bioinspi ed Sys em G oup o gi ing me he oppo uni y
o add o his g ea p ojec .
iii
Chap e 1
In oduc ion
1.1 In oduc ion
Diabe es is an illness cha ac e ized by high blood suga le els, hese le els a e caused by
insulin abso p ion de iciency ha makes he body unable o keep he blood glucose le els
wi hin a no mal ange. This can be a esul o ei he he body no p oducing enough insulin
o he cells no being able o use i p ope ly. The e a e wo main ypes o diabe es.
•Type 1 diabe es, he panc eas is no able o p oduce enough insulin o con ol blood
suga le els as a esul o he loss o he be a cells o he panc eas ha p oduce i ,
mos commonly due o an au oimmune esponse om he body. Type 1 pa ien s need
o injec insulin o keep hei no mal blood suga le el.
•Type 2 diabe es, is gene ally caused by a high insulin esis ance ha o ces he pan-
c eas o make mo e insulin han no mal o main ain heal hy blood glucose le els, as a
esul o his he panc eas migh e en ually s op gene a ing enough insulin and end in
a s a e simila o ha o ype 1 diabe es, al hough i s de elopmen akes longe and
can be s opped o e e sed in some cases h ough a li es yle change ea ly on in he
illness de elopmen . In his case, depending on he e olu ion o he illness he e a e
di e en ea men op ions.
Keeping blood suga le els wi hin a ce ain ange is impe a i e o main ain heal h and
1
p e en complica ions ha can esul om a bad blood glucose managemen , he e o e i ’s
impe a i e o a pe son wi h diabe es o ha e good con ol a all imes.
Fo ou s udy, we will be cen e ing ou sel es in Type 1 insulin dependan pa ien s as, by
he na u e o he insulin injec ions, and o he ac o s, hey ha e mo e blood suga a iabili y
and will be a isk o su e some o he s a es desc ibed husly.
1.2 Hypoglycemia
Hypoglycemia, o low blood suga , is a s a e ha can happen mos commonly in people wi h
diabe es. I is due o an excess in he ac i e insulin ha esul s in oo much o he blood
suga being abso bed. I is conside ed hypoglycemia once he blood suga le el is less han 70
millig ams pe decili e (mg/dL), o 3.9 millimoles pe li e (mmol/L). The body has glucose
homeos asis mechanisms ha p e en hypoglycemia om occu ing in mos cases, howe e
people wi h diabe es ha e a sub-op imal glucagon esponse4and o he coun e - egula o y
ho mones o insulin, making i easie o en e a hypoglycemic s a e. Ha ing blood suga
le el below a ce ain h eshold can se iously a ec b ain unc ions and p oduces a ne ous
esponse in he body, some o i s symp oms include, swea ing, dizziness, hunge , shakiness
o embling. I no ea ed i can de elop in o se e e hypoglycemia and esul in he pe son
passing ou , o e en dea h in ex eme cases.
Hypoglycemic episodes should be p e en ed o a ious easons:
•The ange o alues conside ed is ela i ely small and he e o e he ea lie a po en ial
hypoglycemia is caugh he easie i is o p e en i om de eloping u he .
•Ha ing a lo o hypoglycemic episodes makes he body ge used o hem so he symp-
oms ha cha ac e ize hem become less appa en , his makes he pe son less likely
o ecognize hem ea ly on wi hou measu ing hei blood suga .
•An episode migh lead o an o e -compensa ion and esul in hype glycemia o high
blood suga la e on.
2
The main issue ega ding being able o p e en hypoglycemia e en s is ha an excess in
he insulin injec ed is no always easy o ealize, because i depends on he body’s insulin
sensi i i y, which can a y du ing he day depending on di e en ac o s.
One o he causes o a ia ion in insulin sensi i i y is he p ac ice o exe cise, which
enhances i . I inc eases he abili y o he body o abso b glucose and ans o m i in o
ene gy wi h less amoun o insulin. This can be e y help ul o a pe son wi h diabe es, and
as such, i is ecommended o pe o m egula exe cise o s abilize glucose alues. The less
insulin a pe son has o injec o ob ain he same esul , he mo e s able hei blood glucose
will be, and i also p e en s hype glycemia episodes o high blood suga .
Howe e , inc easing insulin sensi i i y means ha he pe son may be a isk o hypo-
glycemic episodes om pas insulin injec ions and u u e ones i hey a e no calib a ed
co ec ly in acco dance wi h he amoun o exe cise pe o med. This inc eased isk is one
o he easons why people wi h diabe es a e o en sca ed o pe o m exe cise, e en hough
he posi i es hea ily ou weigh he nega i es. Since he symp oms o hypoglycemia a e so
no iceable, he hough o en e ing in o a hypoglycemic s a e can cause a psychological e-
ac ion in he pe son ha makes hem a aid o pe o ming ac i i ies ha migh cause a
hypoglycemic s a e, e en i his is coun e ac i e o hei well-being.
Fo his s udy, we will use exe cise (o ac i eness) da a and glucose alues o p edic
u u e hypoglycemia episodes a di e en ime ho izons.
1.3 Objec i e
In o de o p edic u u e hypoglycemic e en s, we will use S uc u ed G amma ical E olu-
ion, bo h he o iginal SGE and Dynamic SGE, o ob ain a whi e-box model composed o
i - hen-else s a emen s ha pe o m a classi ica ion o u u e hypoglycemia episodes. These
i - hen-else s a emen s will ha e a se ies o inpu a iables whose alues de e mine wha
class we ob ain as a esul . The a iables conside ed will be he glucose eadings o he
las wo hou s in i e-minu e in e als, ob ained by means o a con inuous glucose moni o
3
Chap e 3
Me hodology
In his chap e , we will explain how he classi ica ion me hod we ha e de eloped wo ks.
We will explain he implemen a ion o bo h S uc u ed G amma ical E olu ion ypes and
o he ope a o s needed o use hem in an e olu iona y algo i hm. Ope a o s ha a e no
discussed in his sec ion, such as selec ion, ha e no been implemen ed speci ically o SGE
and o pe o m he es s we ha e used he ones al eady a ailable in he JECO lib a y.
3.1 G amma ical E olu ion
G amma ical E olu ion (GE) is a a ia ion o Gene ic P og amming (GP) ha uses a g am-
ma o gene a e he pheno ype om he geno ype o he indi iduals. The geno ype is made
up o a lis o numbe s, each one o which will gene a e a p oduc ion om a ule made up
o e minal and/o non- e minal symbols o he g amma .
The indi idual pheno ype will be o med by he e minals o he g amma and ha e he
s uc u e de ined by i .
The lis ha con o ms he geno ype is o ixed leng h, de e mined by he use . I we
inish decoding he lis and ou indi idual’s pheno ype is s ill incomple e, we can go back
o he s a o he lis and epea he p ocess o an namoun o imes, called w aps, which
a e also de ined by he use . I a e his ou indi idual is s ill incomple e we s op, gi e i a
bad i ness, and do no compu e i , he indi idual is conside ed in alid.
Each numbe on he lis s could gene a e any o he p oduc ions o ming he pheno ype
10

un il he e a e no mo e possible expansions, and i has been comple ely c ea ed, o be able o
gene alize his p ocess he numbe in he lis go om 0 o a codon uppe bound, o example,
256, and he modulus o he o al amoun o p oduc ions o one ule is he ope a ion used
o decode he esul when gene a ing he pheno ype.
This ype o e olu ion has a couple o issues. On one hand, since each allele depends
on he p e ious one a small change in one can comple ely change he inal esul , making
mu a ion and c osso e a po en ially des uc i e p ocess. On he o he , as we use a modulus
ope a o o de e mine he nex ule we could po en ially change an allele, bu he esul
gene a ed migh be he same one, i depends g ea ly on he numbe o p oduc ions a ule
has, he e o e mu a ing ce ain alleles migh e u n he same esul . Bo h hese issues ha e
an impac on he o e all e olu ion o he esul and a e wha he S uc u ed G amma ical
E olu ion is ying o imp o e.
Howe e , he abili y o change he p oblem by changing he g amma a he han edi ing
he code is a g ea ea u e o G amma ical E olu ion (GE) because i makes i e y lexible
as i can wo k wi h any p oblem o which we ha e a G amma c ea ed, wi hou needing o
pe o m any changes o he implemen a ion. Wi h di e en g amma iles we can change
he way ou indi iduals will be s uc u ed, he inpu a iables we wan o conside , and how
complex we wan he inal solu ions o be.
3.2 S uc u ed G amma ical E olu ion
Al hough GE has been success ully applied o di e en p oblems, i p esen s some d awbacks
de i ed om he p ocess o decoding he solu ions. In o de o pa ially sol e hese conce ns,
Lou enço e al. p oposed S uc u ed G amma ical E olu ion17.
In compa ison o G amma ical E olu ion, whe e indi iduals a e made up o a lis o num-
be s o a se leng h and each numbe is used o gene a e he nex symbol o he pheno ype,
in S uc u ed G amma ical E olu ion, indi iduals a e made up o a lis o lis s.
Each in e nal lis ep esen s a non- e minal o he g amma and he numbe s con ained
11
a e he possible expansions o his ule o a ce ain indi idual in ou popula ion, he e o e
each in e nal lis ’s leng h can be a mos he maximum numbe o e e ences o ha ule.
Each o he numbe s con ained in he in e nal lis ep esen s a p oduc ion o he ule in
ques ion, he e o e he numbe s can go om 0 o Cn−1wi h Cnequal o he maximum
amoun o p oduc ions o a non- e minal, as shown in Figu e 3.1.
Figu e 3.1:Possible alleles o each ule
When decoding an indi idual we will ha e a lis o indexes, ins ead o jus one as we had
in G amma ical E olu ion (GE). E e y ime we ha e o decode a non- e minal, we will go
o he lis o p oduc ions o his non- e minal and ge he nex elemen o he lis we ha e
no consumed up o ha poin , gi en o us by he index alue o ha lis o non- e minals,
as shown in Figu e 3.2.
Wi h his, he decoding p ocess will be: I he nex symbol is a e minal, we add i o ou
pheno ype and con inue wi h he nex elemen . I he nex symbol is a non- e minal hen
12
we ge he co esponding p oduc ion based on wha he indi idual’s geno ype s a es and
epea he p ocess o all he symbols o he p oduc ion un il we don’ ha e mo e symbols.
Figu e 3.2:Geno ype o pheno ype
13
3.2.1 S a ic S uc u ed G amma ical E olu ion
The o iginal e sion o S uc u ed G amma ical E olu ion uses s a ic in e nal lis s, whose
leng hs will no a y du ing he e olu ion, o ep esen he di e en ules. We ha e called
he o iginal e sion S a ic S uc u ed G amma ical E olu ion o S a ic SGE o di e en ia e
i om he dynamic e sion and highligh i s main di e ence.
To ensu e he p econdi ion o ha ing s a ic lis s each in e nal lis is gene a ed comple ely
o i s maximum possible leng h, and he maximum numbe o e e ences o each non-
e minal elemen o he g amma , e en i said expansions a e no being used by an indi idual.
In Figu e 3.3 can be seen an example o his p ocess, o each non- e minal o he
g amma we need o compu e he uppe bound o imes ha a ce ain ule can be called
om ano he one. The i s ule will always be called once, as is i he en y poin o he
pheno ype cons uc ion.
This mechanism o coun ing e e ences o ces us o elimina e ecu sion om he g amma
ile since ha ing ecu sion in ou g amma means ha he e could exis an in ini e numbe
o e e ences o he ecu si e ule. We ha e pe o med his by se ing a maximum ecu si e
dep h, de ined by he use , and ans o ming he ecu si e ule in o a se o ules ha mimic
he ecu sion up o he se dep h, wi h dep h = 0 equi alen o elimina ing he ecu si e
p oduc ion and only keeping he non- ecu si e ones.
<exp > ::= <exp > <op> <exp >
As an example, o dep h 3 his ule will be ans o med in o:
<exp > ::= <exp 0> <op> <exp 0> | < e m> <op> < e m>
<exp 0> ::= <exp 1> <op> <exp 1> | < e m> <op> < e m>
<exp 1> ::= <exp 2> <op> <exp 2> | < e m> <op> < e m>
<exp 2> ::= < e m> <op> < e m>
14
Figu e 3.3:Coun ing he maximum amoun o e e ences o a non- e minal
We change he o iginal ecu si e ule o call o he newly c ea ed non- ecu si e ules,
each dep h numbe calls o he nex one. The inal one will elimina e all he ecu si e
p oduc ions and only keep he ones ha ha e non- ecu si e symbols, he newly made ules
will be added o he loaded g amma and a e wa d, he e e ences a e coun ed.
Conside a ions o S a ic SGE
In s a ic SGE he indi idual’s geno ype will be e y long since we ha e o gene a e he
uppe bound o possible alleles gene a ed. As a esul , he mo e ecu si e dep h is added
by he use he longe he indi idual, as we will ha e o add as many ex a lis s as non-
e minals gene a ed h ough he dep h, each one wi h a leas 1 elemen . This will a ec
15

he pe o mance o he e olu ion o e hem, making S a ic SGE slowe han he dynamic
e sion.
Gene a ing non- ecu si e ules in his ashion will change he s uc u e o he inal in-
di idual in compa ison o he Dynamic e sion, his a ec s bo h mu a ion and c osso e ,
making hem no equi alen . In he case o c osso e , i inc emen s he numbe o elemen s
ha can be in e changed be ween he indi iduals and also allows a mo e speci ic exchange,
al hough he e is a highe chance ha he non- e minal lis exchanged won’ be used o
gene a e he pheno ype. In he case o he mu a ion i only a ec s i we a e pe o ming a
mu a ion on he le el o he lis s and no he alleles, because we ha e mo e lis s we can
mu a e (because we ha e mo e non- e minals) we will mu a e mo e alleles pe indi idual.
3.2.2 Dynamic S uc u ed G amma ical E olu ion
The o iginal S uc u ed G amma ical E olu ion o S a ic SGE is able o sol e he main
issues wi h G amma ical E olu ion, al hough i adds a new one due o he need o g amma
p epossessing and dele ing ecu sion. Making ou solu ions o be o he maximum leng h
ensu es ha we will ne e go o e he se bound, howe e , his leng h will be unnecessa y
in mos cases, as mos solu ions will no need he maximum leng h. Pai ed wi h ecu sion,
i becomes e y unscalable. As a esul , a dynamic app oach o he lis gene a ion was
implemen ed called Dynamic S uc u ed G amma ical E olu ion ha would ix his issue
by making he geno ype able o g ow dynamically.
In Dynamic SGE he lis s a e gene a ed dynamically, meaning, when he indi iduals a e
gene a ed we gene a e he lis s up o wha is needed o comple e he indi idual’s pheno ype
(all he gene a ed indi iduals mus be alid om c ea ion). This adds a le el o complexi y
in compa ison o he S a ic e sion as an indi idual migh become in alid a e we ha e
pe o med c osso e and mu a ion o e hem. To a oid gene a ing in alid indi iduals when
he pheno ype is being compu ed we can add ex a alleles o a ce ain non- e minal lis as
needed o comple e he indi idual pheno ype and be able o calcula e i s i ness.
16
Figu e 3.4:Geno ype o pheno ype in DSGE when indi idual is in alid
As seen in Fig. 3.4, he indi idual a e c osso e and mu a ion is in alid, he e o e
when gene a ing he pheno ype as we ge o he second < op > ob ained om expanding
< e m > he e is no possible elemen o expand, we will ha e o gene a e a andom allele,
in he example case, we gene a e allele 1 and append i o he end o he lis o < op >.
17
The same hing happens in he nex non- e minal < a > o which we also don’ ha e an
expansion, we gene a e a new alue and append i . A he end o he geno ype o pheno ype
con e sion, he indi idual has changed o become alid. The index compu ing emains he
same as in S a ic SGE.
As wi h he s a ic e sion ecu sion poses an issue since we could po en ially c ea e an
indi idual ha ne e comple es i sel , o s op his om happening and om ha ing indi id-
uals ha a e ex emely big, we add a maximum dep h. In he o iginal implemen a ion,16,
he maximum dep h was implemen ed h ough maximum ee dep h, which limi ed how long
an indi idual can be. I was en o ced only when gene a ing ex a alleles in he pheno ype
c ea ion, i he dep h o he ee became bigge o equal o he numbe se by he use he
algo i hm could only gene a e non- ecu si e expansions and no ecu si e ones. Using his
implemen a ion a b anch o he ee migh become longe han he maximum ee dep h,
since we ha e o gene a e alid indi iduals, howe e , as a esul o no gene a ing ecu si e
ules he maximum leng h is s ill limi ed.
In Fig. 3.5 he e is a g aphical ep esen a ion o how he maximum dep h is en o ced in
he o iginal implemen a ion. We ha e changed he g amma so ha he < exp > ule is
now ecu si e. When we each he second < exp > p oduc ion, we don’ ha e any mo e
alleles, so we need o dynamically gene a e hem o comple e he indi idual. Since he
cu en dep h o his b anch is equal o he maximum dep h se , we only ha e one op ion
in he possible p oduc ions we can gene a e: < e m > as i is he only non- ecu si e
p oduc ion o he ule.
The ac ha a b anch can become longe han he maximum dep h makes his imple-
men a ion dependen on he g amma s uc u e, i he ecu si e ules appea u he down
in he g amma ee i will ha e less p obabili y o pe o ming ecu sion han up he g am-
ma ee. Due o his, we ha e chosen o p og am ano he implemen a ion ha makes i
equi alen o he s a ic SGE.
In his al e na e implemen a ion, we ha e changed he maximum ee dep h by a ecu -
18
Figu e 3.5:Geno ype o pheno ype in DSGE showing limi ed ecu si e dep h
si e dep h jus as wha we had in he S a ic e sion, each ecu si e ule can be expanded
n imes, comple ely independen o he non- ecu si e ules and he es o he g amma
s uc u e.
Ano he change we ha e added is an op ion o mo e bloa ing con ol o he indi iduals.
19
we each a e minal, o we don’ change any mo e lis s. This p ocess is shown in Fig. 3.9
I wo ks a bi be e han he Uni o m c osso e in some cases, especially o he s a ic
lis s uc u ed g amma ical e olu ion, whe e adding ecu sion gene a es new ules o he
g amma . When pe o ming a andom in e change o lis s, he child en will look less han
he pa en s he mo e dep h added in c ea ion, because mo e in e media e non- e minals can
be exchanged. I main ains he s uc u e o he pa en s be e in he child en, adding less
a ia ion o he o sp ing.
Figu e 3.9:T ee C osso e Diag am
26

3.4 G amma
As we ha e s a ed be o e, he geno ype o pheno ype con e sion is pe o med by means o
a g amma ile ha de e mines he s uc u e o he pheno ype o he indi idual. In SGE,
compa ed o no mal GE, he g amma s uc u e also a ec s he indi idual in e nally.
The g amma will be he one ha s a es he s uc u e o ou indi iduals in e ms o
he numbe o lis s, which co esponds o he numbe o ules o he g amma , and he
maximum leng h ha each lis can ha e, which co esponds o he numbe o e e ences
made o a ce ain ule o non- e minal expansion. The classi ica ion will also be pe o med
h ough he g amma ile in he geno ype o pheno ype con e sion, i will allow us o change
he numbe o classes jus by edi ing he g amma ile.
Fo ou p oblem, he g amma will be used o ans o m he lis o lis s in o a sequence
o i - hen-else s a emen s ha e u n a class. The classes ha e o also be de ined in he inpu
da a o compa e he esul om he i - hen-else o he ac ual alue o he inpu example.
The i - hen-else s a emen s use he inpu da a and some cons an s o c ea e condi ions,
i all he condi ions a e me hen we conside ha he example belongs o ha speci ic
class. Since we a e e u ning he s a emen s as ou models, he condi ions can be s udied
o obse e wha inpu pa ame e s he model has conside ed o e o he s. This whi e-box
app oach makes i so ha we can gi e a medical explana ion o he esul s, o disca d a
model ha we conside is no co ec using knowledge om he p oblem speci ica ion.
We ha e es ed wo di e en ypes o g amma s depending on he numbe o classes
we ha e o classi y, one o 2 classes 3.10 and ano he o 3 classes 3.11, hei s uc u e is
he same and hei only di e ence is he ule < ype > ha gene a es a cons uc ion o 2
classes o one o 3 classes.
In e ms o he s uc u e o he condi ions ha hey can gene a e hey a e as ollows:
The < ype > ule is he en ance o he p og am and he one ha will wield he inal
esul , i gene a es < binexp > ules ha c ea e he logical condi ions. The < binexp >
27
Figu e 3.10:Example G amma 2 Classes
Figu e 3.11:Example G amma 3 Classes
28
ule is a ecu si e ule ha c ea es a sequence o condi ions used by "&&" o "||" logical
ope a o s. The in e nal condi ions a e s a emen s ha can be e alua ed and compa ed wi h
each o he using he ela ional ope a o s "<", ">", "≥", "≤". The le -hand side o he
s a emen s has he < exp > ecu si e ule ha gene a es a ma hema ical ope a ion made
up o he inpu a iables, ha in ou g amma appea as he "ge Va iable(x,k)" unc ion,
and cons an s ha a e gene a ed wi h he < numbe > ule. The igh -hand side is he
< mix > ule ha can ei he gene a e a < exp > o a < numbe >.
Recu sion appea s in wo di e en places in ou g amma , so he max dep h we se
o each ype o algo i hm will con ol he numbe o condi ions ha a e gene a ed by he
indi idual, by he < binexp > ule, and he leng h o he condi ions, om he < exp >
ule.
The inpu a iables, de ined by he "ge Va iable(x,k)" unc ion, ep esen each ype o
a iable "x", o each example "k" in ou inpu o aining o es .
We will explain he inpu da a s uc u e in he Da a sec ion, bu in gene al e ms, he
a iables a e de ined as such:
•Glucose alues o he wo hou s be o e he ime o p edic ion (x∈(0,25]).
•Hea a e alues o he pa ien o he wo hou s be o e he ime o p edic ion
(x∈(25,50]).
•Amoun o s eps pe o med by he pa ien on he wo hou s be o e he ime o p edic-
ion (x∈(50,75]).
•Amoun o calo ies bu ned by he pa ien in he wo hou s be o e he ime o p edic ion
(x∈(75,100]).
As can be obse ed in ig 3.10 and ig 3.11 we ha e no aken in o accoun e e y single
possible inpu o gene a e he models, we ha e handpicked a subse o hem o cons uc
he solu ions, howe e , he a ailable inpu s ha could be used by he g amma a e he ones
desc ibed abo e. This selec ion will be discussed in Chap e 4.
29
3.5 Fi ness Func ion
As wi h any e olu iona y algo i hm, we need o es ablish a i ness unc ion ha will de e -
mine how good an indi idual is. Since we a e conside ing a classi ica ion p oblem, we can
es di e en classi ica ion me ics and compa e hei ou pu wi h he esul s ob ained om
he es .
In ou p oblem, he main me ic we a e going o conside when es ing whe he a solu ion
is good o no is he sensi i i y (o ecall) o each class. This e e s o he numbe o elemen s
ha ha e been classi ied as one class and ac ually belong o his class. This me ic is he
mos impo an as we wan o be able o ecognize all ins ances o a po en ial Hypoglycemia
o e all he cases, mo e han we wan ha he ones ha we ha e classi ied o be co ec .
In bina y classi ica ion we alk abou sensi i i y (o ecall) and speci ici y since we only
conside posi i es o nega i es, hese e e o he pe cen ages o ue-posi i es and ue-
nega i es o e he o al numbe o posi i es o nega i es in ou da a.
In mul i-class classi ica ion, we can jus look a he sensi i i y o each class, which would
be equi alen .
All he i ness unc ions conside ed will e u n a alue be ween 0 and 1 whe e he highe
he esul he be e he classi ica ion. Since we a e minimizing in ou e olu iona y algo-
i hm, we will use 1−F i nessF unc ion in all cases so ha he esul ha ge s close o 0
is he bes esul o e all.
3.5.1 Mul i-class Recall
This i ness unc ion calcula es he sensi i i y o each class and makes he ha monic mean
o all he classes. In bina y classi ica ion, i would be equi alen o making 2*(sensi i -
i y*speci ici y)/(sensi i i y+speci ici y). By pe o ming he ha monic mean o he ecalls,
we make su e ha no one class has a much highe ecall han he o he s.
30
Mul i −classRecall =numClasses
PnumClases
i=1
1
Recalli
(3.1)
Recall =T ueP osi i es
To alP osi i es (3.2)
I s main ad an age is ha i can wo k wi h unbalanced da a se s because i doesn’
ma e how many examples we ha e o one class, each class coun s he same as he es .
3.5.2 F1measu e
This is a classi ica ion me ic ha makes he ha monic mean o he p ecision and ecall o
he class 0.
F1measu e =2∗Recall ∗P ecision
Recall +P ecision (3.3)
whe e P ecision co esponds o he ac ion o elemen s ha we a e classi ying co ec ly
in he Hypoglycemia class om he he o al amoun we ha e classi ied in his class and
Recall o he ac ion o elemen s ha we a e classi ying co ec ly om he o al amoun o
elemen s in he Hypoglycemia class.
In a mul i-class p oblem, we will calcula e he F1measu e measu e o each class and
e u n he a e age (mac o-a e age).
3.5.3 Weigh ed Accu acy
This is a i ness o mula p oposed in3 o E olu iona y algo i hms in he con ex o classi i-
ca ion. I combines he F1measu e wi h accu acy in a 50% spli .
I s main d awback is ha because i uses accu acy, we won’ be able o use i wi h
unbalanced classes.
31

WA = 0.5∗Accu acy + 0.5∗F1measu e (3.4)
I gi es good esul s, be e han when we a e only conside ing he F1-measu e s an-
dalone, which is why we ha e used i o pe o m he es s.
3.6 E olu iona y Algo i hm
Finally, we ha e implemen ed an e olu iona y algo i hm ha pe o ms he p ocess o selec-
ion, c osso e , and mu a ion, o each gene a ion. These a e made sequen ially and a e he
s anda d p ocess o a gene al gene ic algo i hm. We selec 2 indi iduals using he selec ion
me hod chosen, we pe o m c osso e , hen mu a ion, and hen we add hem o he lis
o child en. The wo main di e ences be ween ou algo i hm and a gene al e olu iona y
algo i hm is he eplacemen policy and he egene a ion o he popula ion.
In e ms o eplacemen , o each gene a ion, we will ge he bes indi iduals be ween
he pa en s and child en, and hose a e he ones ha will compose he popula ion o he
nex gene a ion. This makes he e olu ion a e y eli is p ocess and migh end up in he
popula ion con e ging oo quickly and no e ol ing u he han a local op imum, in o de
o pallia e his om happening we ha e added a egene a ion o a sec ion o he popula ion.
I he popula ion i ness e e con e ges o a numbe a pe cen age o he popula ion, se by
he use , will be egene a ed om sc a ch o add new genes o he e olu ion and hope ully
make he p oblem ge o e he local op imum.
32
Chap e 4
Da a
4.1 In oduc ion
As s a ed be o e he goal o ou sys em is o be able o p edic hypoglycemic episodes a
a ce ain ime, ou da a will only include glucose eadings, numbe o s eps, hea a e,
and calo ies bu ned o e he p e ious wo hou s om he ime o p edic ion measu ed
in 5-minu e in e als. The glucose eadings ha e been ob ained by means o a Con inuous
Glucose Moni o (CGM) F eeS yleLib e, and he es o he da a is ob ained h ough a
sma wa ch Fi bi Ionic, making all he necessa y da a o ou model ob ainable wi hou
needing use inpu .
4.2 Desc ip ion
The da a used in his s udy has been ob ained om 11 pa ien s wi h ype 1 diabe es, whose
desc ip ions appea in 4.1. We will es ic he da a o a maximum o 2 weeks wo h o
obse a ions pe pa ien .
F om he 11 pa ien s, we ha e 4 males and 7 emales, whose ages ange om 20 yea s
old o 56. They ollow 2 di e en ea men me hods, 3 pa ien s con ol hei blood suga
h ough mul iple doses o insulin and he o he 8 do i by means o an insulin pump ha
adminis e s a con inuous subcu aneous s eam o insulin. Thei HBA1c alues ep esen he
a e age alue o blood suga in he pas 8 o 12 weeks and a e used as a ep esen a ion o
33
he glycemic his o y25. The pa ien ’s alues go om 6.4% o 8.5%, which is ans o med
o a e age glucose mg/dl would be om 137 mg/dL o 197 mg/dL on a e age. In gene al,
a heal hy ange o a pe son wi h diabe es should be 7% o less, howe e , i ’s impo an
o keep in mind ha his is an a e age and a low alue does no necessa ily mean a good
con ol, a pe son wi h a low o high HBA1c can s ill ha e equen hypoglycemias and high
glucose a iabili y. In e ms o hei BMI 7 pa ien s a e wi hin he no mal ange (18.5-24.9),
3 a e in he o e weigh ca ego y (25-29.9) and one is in he obese ange (30 o highe ), his
is impo an o ake in o accoun in e ms o hei blood glucose con ol because an excess
in weigh gain dec eases insulin sensi i i y and makes glucose con ol ha de . Finally, we
can obse e ha all pa ien s ha e been diabe ic o mo e han 8 yea s wi h he maximum
being 36 yea s, his implies ha hei le o e insulin p oduc ion is p obably negligible.
ID Gende Age IMC HBA1c T ea men Yea s
DMT1
HUPA001 F 56.3 22.76 8.2 ISCI 15.46
HUPA002 M 48.6 23.82 7.1 ISCI 36.47
HUPA003 F 43.4 18.72 7.3 ISCI 12.45
HUPA004 M 41.2 27.16 7.8 ISCI 8.5
HUPA005 F 20.9 22.57 6.9 ISCI 39.5
HUPA007 M 37.6 30.64 6.6 ISCI 10.1
HUPA011 F 35.0 23.92 7.8 ISCI 27.3
HUPA014 F 50.0 25.39 8.5 MDI 12.9
HUPA015 F 43.1 22.33 6.4 MDI 11.2
HUPA016 F 29.9 26.33 6.5 ISCI 20.1
HUPA027 M 26.4 22.21 7.0 MDI 23.7
Table 4.1:Cha ac e is ics o he pa icipan s: ID, Gende (M=Male; F=Female), Age,
BMI, HbA1c, T ea men (MDI: Mul iples doses o insulin; ISCI. In usion Subcu aneal con-
inuous o Insulin)Yea s o e olu ion o DMT1.
The inpu da a ob ained om he pa ien s is s uc u ed as ollows: Each ow con ains
101 columns, he i s one is he glucose alue a he ime ho izon H∈ {30,60,90,120}
ollowed by he glucose eadings om he p e ious 2 hou s, hen he hea a e, ollowed by
he s eps and ending in he calo ies bu ned. Each one o hese ypes has 25 eadings, whe e
34
he i s alue is always eading a ime and he nex alues a e he eadings om -120
o -5 in 5-minu e in e als o each ype o da a.
In his way, o each da a poin we can access o all he a ailable in o ma ion by looking
a he column alues. We will ha e as many ows as da a poin s o each pa ien .
Figu e 4.1:O iginal Da a o +30
Figu e 4.2:Edi ed Da a
In Fig. 4.1 we can obse e a agmen o he o iginal da a s uc u e ha we hen p ocess
so ha ou algo i hm can wo k wi h i , i includes he alues om -120 o +30 as in his
example his is he alue o p edic ion, sepa a ed in 5-minu e in e als, he i s column is
he ime a which he da a is aken. I allows o a Wha -I scena io, whe e we can use he
o +30 da a as i we knew i , bu we will no be using i .
In Fig. 4.2 we see he inal da a s uc u e ha is sen o he algo i hm, he i s column
35
Fig. 4.6
Figu e 4.6:Co ela ions o he 7 Hea a e alues conside ed
S eps
This is he inpu a iable wi h he leas amoun o co ela ion be ween i sel , which makes
sense as he numbe o s eps aken om one 5-minu e in e al o ano he can a y a lo . Fo
ou p oblem we a e in e es ed in i desc ibing ’ac i eness’ since he mos common exe cise
people do in hei daily li e is walking o unning we ha e aken i in o accoun . Fo he
a iables used we ha e chosen S eps ( ), S eps ( -15), S eps ( -30), S eps ( -45), S eps ( -60),
S eps ( -75), S eps ( -90), S eps ( -105), S eps ( -120), ha co espond o he amoun o
s eps aken a ins an , ime o p edic ion, minus kminu es. Thei co ela ion alues can
be seen in Fig. 4.7
Calo ies bu ned
The co ela ion o he numbe o calo ies bu ned in 5-minu e in e als is lowe han he Glu-
cose o Hea a e, bu highe han he co ela ion o e he numbe o s eps. This a iable
ep esen s a so o combina ion o he p e ious wo, alongside a basal alue ha is cons an .
42

Figu e 4.7:Co ela ions o he 9 S eps alues conside ed
Al hough he speci ic o mula used o compu e he alue depends on he Sma wa ch used.
The a iables included a e Calo ies ( ), Calo ies ( -20), Calo ies ( -40), Calo ies ( -60), Calo-
ies ( -80), Calo ies ( -100), and Calo ies ( -115), o a o al o 7 a iables, ha co espond
o he numbe o calo ies bu ned a ins an , ime o p edic ion, minus kminu es. Thei
co ela ions can be seen in Fig. 4.8
4.3.2 Class balancing
A e pe o ming he classi ica ion, we will ob ain a da a se whe e he classes a e e y
unbalanced, since he ecommended pe cen age o hypoglycemia alues is unde 4% o he
o al alues. To help he algo i hm lea n p ope ly and quicke , we should pe o m class
balancing, so ha he e a e app oxima ely he same amoun o examples in each class.
Fo balancing he di e en classes we can ei he do unde -sampling; whe e we ge all he
examples o he class wi h ewe ins ances and a andom sample o he o he classes so ha
he amoun o ins ances o each class is app oxima ely he same, o o e sampling; whe e we
gene a e ex a samples o he classes wi h he leas amoun o ins ances syn he ically.
43
Figu e 4.8:Co ela ions o he 7 bu ned calo ies alues conside ed
Fo ob aining he esul s shown in he nex chap e we ha e chosen o pe o m an unde -
sampling o he da a, as in e ms o pe o mance i is he cheapes op ion and he esul s
ob ained om p e ious es s don’ show a huge ad an age in pe o ming an o e sampling
o he da a. The balancing will only be pe o med o e he aining se .
Fo he 3.1 unc ion discussed p e iously he da a doesn’ need o be balanced o wo k,
howe e , i is ecommended since he inal esul s a e be e wi h balanced aining da a.
44
Chap e 5
Resul s
In his chap e , we will show and explain some esul s ob ained using he me hodology
commen ed p e iously wi h he da a o he pa ien s discussed. The da a has been di ided
in o aining and es wi h 70% and 30% o he o al da a espec i ely, main aining he
o iginal da a dis ibu ion o he classes. The i ness unc ion we ha e used o pe o m
he p edic ion, om he ones desc ibed, is he Weigh ed Accu acy, al hough any o hem
could be used. As a esul o his decision he aining da a mus be balanced o ob ain
good esul s, in gene al e en i we use he Recall i ness unc ion, which can deal wi h an
unbalanced da a se , we will ob ain he bes esul s a e pe o ming he da a balancing.
The da a balancing chosen was andom unde -balancing.
The es da a will main ain he o iginal dis ibu ion o he classes. This ensu es ha he
da a we a e es ing o e is he same da a ha will be encoun e ed in a eal-li e scena io.
5.1 Expe imen al Se -up
To ob ain he esul s om he e olu iona y algo i hm, we ha e se i s pa ame e s as such
o all he es s:
S a ic S uc u ed G amma ical E olu ion
•Replacemen policy: Bes indi iduals om pa en s and child en wi h a 10% egene -
a ion pe cen age
45
•100 popula ion size
•500 gene a ions o +30 and +60 and 800 gene a ions o +90 and +120
•Recu si e Dep h: 3
•Tou namen selec ion ope a o wi h p essu e 2
•T ee c osso e ope a o
–70% c osso e p obabili y
–60% in e change p obabili y
•Basic mu a ion o all alleles
–5% p obabili y
Dynamic S uc u ed G amma ical E olu ion
•Replacemen policy: Bes indi iduals om pa en s and child en wi h a 10% egene -
a ion pe cen age
•100 popula ion size
•500 gene a ions o +30 and +60 and 800 gene a ions o +90 and +120
•Maximum T ee Dep h and Ini ial Maximum T ee Dep h: 7
•Ini ial Minimum Recu si e Dep h: 0
•Tou namen selec ion ope a o wi h p essu e 2
•Uni o m c osso e ope a o
–70% c osso e p obabili y
–20% in e change p obabili y
46
•Basic mu a ion o all alleles
–5% p obabili y
We ha e se he pa ame e s o be equi alen o bo h algo i hm ypes, he wo main
di e ences a e he dep hs: whe ein he S uc u ed G amma ical E olu ion as we ha e wo
ecu si e ules we se dep h 3 o each o hem and in Dynamic G amma ical E olu ion we
se maximum ee dep h o 7 ha conside s bo h ecu si e ules plus he ini ial ule. And
he c osso e ope a o , whe e we es ed he ee c osso e o he S a ic SGE, since i wo ks
be e because we ha e mo e ules and he Uni o m c osso e o he Dynamic SGE.
Fo each se o da a, we ha e execu ed 30 imes he algo i hm and ob ained he mean,
median, and s anda d de ia ion o he bes esul o each execu ion. Wi h he bes elemen
o hose 30 gene a ions, we ob ain he ecall alue on he Tes da a-se which will ep esen
how well he model is able o classi y he da a o each class.
5.1.1 Gene al and Indi idual Models
Fo each o he 11 pa ien s, we a e able o gene a e an indi idual model, ha only uses
hei da a o aining, bu i can also be use ul o c ea e a gene al model, ha has been
ained wi h he da a o all he pa ien s and es his model on each pa ien . E en hough
an indi idual app oach will gi e us be e esul s in almos all cases, using a gene al model
can be use ul i we wan o p edic a pa ien ha we don’ ha e a lo o da a on, o a all.
How well his model wo ks will g ea ly depend on he speci ic pa ien and whe he he da a
om o he pa ien s can be gene alized o hem o no .
We will no make such dis inc ions in his s udy, howe e , we will obse e ha some
pa ien s consis en ly gi e wo se esul s in he gene al models han o he s, whose sco e is
highe .
47

5.2 2 Classes
The da a will only be di ided in o wo classes, Hypoglycemia (Hypo) = 0 and Non-hypoglycemia
(No Hypo) = 1, o each p edic ion ho izon we will ob ain how well he algo i hm classi ies
he di e en inpu pa ame e s and compa e he ecall o he gene al and indi idual models.
The g amma used will be he one shown p e iously in Fig. 3.10.
This p ocess is epea ed o he 4 p edic ion ho izons, [30, 60, 90, 120] minu es. Fo
each p edic ion ho izon, we ge he Mean, Median, S d. De . and bes i ness o he 30
execu ions, his in o ma ion is shown in he ables; +30: Tab. 5.1 , +60: Tab. 5.4 , +90:
Tab. 5.7 and +120: Tab. 5.10. Fo he model wi h he smalles i ness alue o he 30
execu ions (bo h indi idual and gene al) we ob ain he Recall o he classes, his is shown
in he ables; +30: Tab. 5.2 , +60. Tab. 5.5 , +90: Tab. 5.8 , +120: Tab. 5.11.
Fo each p edic ion ho izon, we ha e also es ed o he machine lea ning algo i hms om
SkLea n o compa e how he bes -ob ained model a es in compa ison wi h o he Machine
Lea ning algo i hms, his can be seen in; +30: Tab. 5.3 , +60: Tab. 5.6, +90: Tab. 5.9
and +120: Tab. 5.12. The numbe shown is he a e age Recall o each class o all he
pa ien s by pe o ming he aining and es o e he da a om all he pa ien s since we
jus wan ed a gene al iew o he compa ison.
48
5.2.1 30 Minu es
Table 5.1:S a is ics: Mean, Median, S anda d de ia ion and Bes Fi ness o all he models
we ha e ained
Pa ien Algo i hm Type Mean Median S d. De . Bes Fi ness
HUPA001 S a ic 0.0197 0.0227 0.0091 0.0
HUPA001 Dynamic 0.0186 0.0227 0.009 0.0
HUPA002 S a ic 0.101 0.1031 0.0085 0.0791
HUPA002 Dynamic 0.1004 0.1002 0.0077 0.0839
HUPA003 S a ic 0.0833 0.0829 0.0053 0.0733
HUPA003 Dynamic 0.0832 0.0838 0.0059 0.0684
HUPA004 S a ic 0.0443 0.0472 0.0081 0.0304
HUPA004 Dynamic 0.0459 0.0493 0.0086 0.0279
HUPA005 S a ic 0.0732 0.0759 0.01 0.0522
HUPA005 Dynamic 0.069 0.0642 0.0085 0.0578
HUPA007 S a ic 0.0559 0.0612 0.0118 0.0324
HUPA007 Dynamic 0.053 0.0566 0.0122 0.0302
HUPA011 S a ic 0.0709 0.0703 0.0103 0.0510
HUPA011 Dynamic 0.0693 0.0694 0.0097 0.0510
HUPA014 S a ic 0.0556 0.0567 0.0086 0.0343
HUPA014 Dynamic 0.0507 0.0517 0.0098 0.0303
HUPA015 S a ic 0.0664 0.0721 0.0134 0.0321
HUPA015 Dynamic 0.0643 0.0679 0.0129 0.0413
HUPA016 S a ic 0.096 0.0976 0.008 0.0739
HUPA016 Dynamic 0.0931 0.0933 0.0098 0.0769
HUPA027 S a ic 0.0776 0.0787 0.0032 0.0694
HUPA027 Dynamic 0.0764 0.0761 0.0034 0.0674
All S a ic 0.0975 0.0984 0.008 0.0820
All Dynamic 0.0945 0.0930 0.0083 0.0791
P11_s a ic P11_dynamic P14_s a ic P14_dynamic P15_s a ic P15_dynamic P16_s a ic P16_dynamic P27_s a ic P27_dynamic All_s a ic All_dynamic
0.04
0.06
0.08
0.10
0.12
Figu e 5.1:Box plo o he i ness +30
49
P11_s a ic P11_dynamic P14_s a ic P14_dynamic P15_s a ic P15_dynamic P16_s a ic P16_dynamic P27_s a ic P27_dynamic All_s a ic All_dynamic
0.04
0.06
0.08
0.10
0.12
Figu e 5.2:Box plo o he i ness +30
Table 5.2:Compa ison o he ecall o he Indi idual and Gene al model o each pa ien
in + 30 minu es
Pa ien Algo i hm Indi idual Models Gene al Models
Recall Hypo Recall No Hypo Recall Hypo Recall No Hypo
HUPA001 S a ic 0.9412 0.9504 0.8824 0.9488
HUPA001 Dynamic 1.0 0.9289 0.9412 0.8329
HUPA002 S a ic 0.88 0.9266 0.9511 0.8435
HUPA002 Dynamic 0.8756 0.9169 0.9556 0.8698
HUPA003 S a ic 0.9125 0.9107 0.9250 0.8896
HUPA003 Dynamic 0.9375 0.8935 0.9500 0.9002
HUPA004 S a ic 0.9785 0.966 1.0 0.959
HUPA004 Dynamic 1.0 0.9426 0.9785 0.966
HUPA005 S a ic 0.9706 0.865 0.7353 0.9109
HUPA005 Dynamic 0.9706 0.865 0.7647 0.9298
HUPA007 S a ic 0.9394 0.9513 0.9899 0.9217
HUPA007 Dynamic 0.9394 0.9351 0.9697 0.9255
HUPA011 S a ic 0.9677 0.848 0.9677 0.9263
HUPA011 Dynamic 0.9677 0.9317 0.9677 0.8903
HUPA014 S a ic 1.0 0.9222 0.9787 0.957
HUPA014 Dynamic 0.9574 0.9597 0.9362 0.9689
HUPA015 S a ic 0.9535 0.9392 0.9767 0.9309
HUPA015 Dynamic 0.9535 0.9373 0.9535 0.9244
HUPA016 S a ic 0.9711 0.8906 0.9075 0.903
HUPA016 Dynamic 0.9306 0.8999 0.9480 0.9133
HUPA027 S a ic 0.9510 0.9194 0.9301 0.9044
HUPA027 Dynamic 0.9650 0.8969 0.9161 0.9203
50
Figu e 5.3:A e age ecall o he bes solu ion o all pa ien s in +30
Figu e 5.4:E olu ion o he a e age popula ion i ness in +30
As can be seen in Fig. 5.3 he a e age ecall o bo h classes o all pa ien s is be ween
90% and 95%, and bo h he gene al and indi idual models yield simila esul s on a e age.
Indi idually, he only pa ien ha sees a big d op in he Recall alues is HUPA005, whe e
using da a om he o he pa ien s does no seem o be e ec i e o he p edic ion.
51
P11_s a ic P11_dynamic P14_s a ic P14_dynamic P15_s a ic P15_dynamic P16_s a ic P16_dynamic P27_s a ic P27_dynamic All_s a ic All_dynamic
0.075
0.100
0.125
0.150
0.175
0.200
0.225
0.250
Figu e 5.10:Box plo o he i ness +90
Table 5.8:Compa ison o he ecall o he Indi idual and Gene al model o each pa ien
in + 90 minu es
Pa ien Algo i hm Indi idual Models Gene al Models
Recall Hypo Recall No Hypo Recall Hypo Recall No Hypo
HUPA001 S a ic 0.9375 0.8702 0.8750 0.8494
HUPA001 Dynamic 0.875 0.8309 0.8750 0.7877
HUPA002 S a ic 0.8739 0.6741 0.9009 0.6699
HUPA002 Dynamic 0.8604 0.7337 0.9054 0.6699
HUPA003 S a ic 0.825 0.8508 0.7875 0.7247
HUPA003 Dynamic 0.7875 0.8422 0.8250 0.7113
HUPA004 S a ic 0.8387 0.9353 0.8495 0.8776
HUPA004 Dynamic 0.8495 0.9106 0.9032 0.8341
HUPA005 S a ic 0.7647 0.7669 0.5882 0.7696
HUPA005 Dynamic 0.8235 0.6784 0.5294 0.7660
HUPA007 S a ic 0.8081 0.7969 0.7879 0.7711
HUPA007 Dynamic 0.8687 0.7778 0.8687 0.7366
HUPA011 S a ic 0.9677 0.7211 0.7419 0.8114
HUPA011 Dynamic 0.9032 0.7987 0.6452 0.7861
HUPA014 S a ic 0.8936 0.8431 0.8511 0.8385
HUPA014 Dynamic 0.8723 0.8450 0.7234 0.8523
HUPA015 S a ic 0.9024 0.7011 0.7805 0.7915
HUPA015 Dynamic 0.9268 0.7814 0.7805 0.7934
HUPA016 S a ic 0.8035 0.7772 0.8613 0.6974
HUPA016 Dynamic 0.8555 0.7119 0.7977 0.7161
HUPA027 S a ic 0.8844 0.7865 0.9184 0.7103
HUPA027 Dynamic 0.8980 0.8109 0.9048 0.7093
58

Figu e 5.11:A e age ecall o he bes solu ion o all pa ien s in +90
Figu e 5.12:E olu ion o he a e age popula ion i ness in +90
Fo +90 we can obse e ha once mo e he gene al model has less a e age Recall o
bo h classes han he indi idual model, his is mo e no iceable han o +60, bu he
di e ence is s ill no s a is ically signi ican . The a e age Recall alues a e be ween 80%
and 90% as shown in Fig. 5.11. Lowe han be o e bu a signi ican pe cen age.
59
Compa ison wi h o he Machine Lea ning algo i hms
Table 5.9:Compa ison o he a e age Recall o ou algo i hm wi h o he ML algo i hms
o +90
Algo i hm Recall Hypo Recall No Hypo
G adien
boos ing 0.8209 0.8218
G adien
boos ing wi h
C oss al
0.8036 0.8202
Logis ic
Reg ession 0.8260 0.7541
Random o es
classi ie 0.9633 0.8544
Random o es
Reg eso 0.9562 0.8491
Gaussian Nai e
Bayes 0.7924 0.5963
Be noulli Nai e
Bayes 0.5857 0.5312
Decision T ee
Classi ie
(6 dep h)
0.7924 0.8013
Ada Boos
Classi ie 0.9186 0.8051
Bagging
Classi ie 0.9532 0.8446
Ex a T ees
Classi ie 0.9593 0.8807
SGDClassi ie 0.6998 0.8275
MLPClassi ie 0.8769 0.7055
Dynamic SGE 0.8654 0.7928
S a ic SGE 0.8630 0.7930
60
5.2.4 120 Minu es
Table 5.10:S a is ics: Mean, Median, S anda d de ia ion and Bes Fi ness o all he
models we ha e ained
Pa ien Algo i hm Type Mean Median S d. De . Bes Fi ness
HUPA001 S a ic 0.0788 0.0737 0.0261 0.0252
HUPA001 Dynamic 0.0774 0.0801 0.0325 0.0125
HUPA002 S a ic 0.2455 0.2446 0.0080 0.2264
HUPA002 Dynamic 0.2416 0.2393 0.0085 0.2274
HUPA003 S a ic 0.1942 0.1956 0.0167 0.1535
HUPA003 Dynamic 0.1925 0.1888 0.0136 0.1646
HUPA004 S a ic 0.1845 0.1841 0.0159 0.1553
HUPA004 Dynamic 0.1882 0.1844 0.0156 0.1541
HUPA005 S a ic 0.2006 0.1974 0.0186 0.1611
HUPA005 Dynamic 0.1972 0.1916 0.0153 0.1588
HUPA007 S a ic 0.2456 0.2535 0.0218 0.1951
HUPA007 Dynamic 0.2339 0.2358 0.0194 0.1875
HUPA011 S a ic 0.1414 0.1363 0.0190 0.1127
HUPA011 Dynamic 0.1374 0.1363 0.0148 0.1102
HUPA014 S a ic 0.1991 0.1938 0.0176 0.1639
HUPA014 Dynamic 0.1967 0.1930 0.0193 0.1632
HUPA015 S a ic 0.2078 0.2070 0.0220 0.1549
HUPA015 Dynamic 0.2021 0.2041 0.0238 0.1542
HUPA016 S a ic 0.2395 0.2378 0.0121 0.2170
HUPA016 Dynamic 0.2424 0.2398 0.0161 0.2160
HUPA027 S a ic 0.2209 0.2219 0.0117 0.2021
HUPA027 Dynamic 0.2206 0.2192 0.0085 0.2072
All S a ic 0.2840 0.2833 0.0100 0.2662
All Dynamic 0.2829 0.2820 0.0072 0.2678
P11_s a ic P11_dynamic P14_s a ic P14_dynamic P15_s a ic P15_dynamic P16_s a ic P16_dynamic P27_s a ic P27_dynamic All_s a ic All_dynamic
0.125
0.150
0.175
0.200
0.225
0.250
0.275
0.300
Figu e 5.13:Box plo o he i ness +120
61
P11_s a ic P11_dynamic P14_s a ic P14_dynamic P15_s a ic P15_dynamic P16_s a ic P16_dynamic P27_s a ic P27_dynamic All_s a ic All_dynamic
0.125
0.150
0.175
0.200
0.225
0.250
0.275
0.300
Figu e 5.14:Box plo o he i ness +120
Table 5.11:Compa ison o he ecall o he Indi idual and Gene al model o each pa ien
in + 120 minu es
Pa ien Algo i hm Indi idual Models Gene al Models
Recall Hypo Recall No Hypo Recall Hypo Recall No Hypo
HUPA001 S a ic 0.75 0.749 0.8125 0.6512
HUPA001 Dynamic 0.8125 0.7498 0.7500 0.7057
HUPA002 S a ic 0.8364 0.6893 0.8273 0.6574
HUPA002 Dynamic 0.7955 0.7060 0.8364 0.6630
HUPA003 S a ic 0.7875 0.7907 0.6625 0.6220
HUPA003 Dynamic 0.7625 0.8457 0.6625 0.7059
HUPA004 S a ic 0.8280 0.8196 0.7849 0.8160
HUPA004 Dynamic 0.8602 0.8443 0.7527 0.8408
HUPA005 S a ic 0.7647 0.7167 0.8235 0.5439
HUPA005 Dynamic 0.7059 0.7964 0.6176 0.6742
HUPA007 S a ic 0.7374 0.7553 0.6465 0.8052
HUPA007 Dynamic 0.6566 0.8666 0.6970 0.7850
HUPA011 S a ic 0.8387 0.8083 0.7742 0.7269
HUPA011 Dynamic 0.8710 0.7577 0.7097 0.7568
HUPA014 S a ic 0.8511 0.7711 0.6170 0.7381
HUPA014 Dynamic 0.8511 0.7693 0.6154 0.7426
HUPA015 S a ic 0.8974 0.6384 0.6154 0.7177
HUPA015 Dynamic 0.7949 0.6190 0.3846 0.7196
HUPA016 S a ic 0.7977 0.7095 0.8844 0.5902
HUPA016 Dynamic 0.8439 0.6784 0.7746 0.6992
HUPA027 S a ic 0.8725 0.7125 0.8859 0.6437
HUPA027 Dynamic 0.8188 0.7804 0.8255 0.7257
62
Figu e 5.15:A e age ecall o he bes solu ion o all pa ien s in +120
Figu e 5.16:E olu ion o he a e age popula ion i ness in +30
In +120 is whe e we obse e he algo i hm e u ning he wo s esul s, i is he ha des
ime ame o p edic as we don’ ha e any da a o he p e ious 2 hou s. The compa ison
be ween he indi idual and gene al model show he bigges di e ence. The a e age Recall
ob ained o his p edic ion is be ween 70% and 80% as shown in Fig. 5.15.
63

Compa ison wi h o he Machine Lea ning algo i hms
Table 5.12:Compa ison o he a e age Recall o ou algo i hm wi h o he ML algo i hms
o +120
Algo i hm Recall Hypo Recall No Hypo
G adien
boos ing 0.7573 0.7995
G adien
boos ing wi h
C oss al
0.7390 0.7940
Logis ic
Reg ession 0.7889 0.6984
Random o es
classi ie 0.9347 0.8575
Random o es
Reg eso 0.9317 0.8503
Gaussian Nai e
Bayes 0.7624 0.5600
Be noulli Nai e
Bayes 0.5857 0.5312
Decision T ee
Classi ie
(6 dep h)
0.7533 0.7520
Ada Boos
Classi ie 0.9133 0.7756
Bagging
Classi ie 0.9317 0.8056
Ex a T ees
Classi ie 0.9531 0.8811
SGDClassi ie 0.7900 0.5823
MLPClassi ie 0.9255 0.4865
Dynamic SGE 0.7975 0.7648
S a ic SGE 0.8149 0.7418
64
5.2.5 Resul s o 2 classes
As can be seen in he BoxPlo s included o +30: Fig. 5.1, Fig, 5.2, +60: Fig. 5.5,
Fig. 5.6, +90: Fig. 5.9, Fig. 5.10 and +120: Fig. 5.13, Fig. 5.14, he e seems o
be no s a is ical di e ence be ween he pe o mance o he S a ic o o iginal SGE and he
Dynamic SGE, howe e he Dynamic SGE ge s sligh ly be e a e age esul s o almos all
pa ien s. The ecall esul s o e he es da ase a e also e y simila wi h bo h e sions o
he algo i hm, he sligh di e ence be ween bo h shows no s a is ical signi icance.
In e ms o he gene al model, we can obse e ha i wo ks ela i ely well o all pa ien s
wi h he excep ion o HUPA005, whe e i gi es lowe esul s han i s indi idual model, his
end is also seen in HUPA014 and HUPA015 when conside ing bigge p edic ion ho izons
( +90 and +120). Howe e , he esul s ob ained in he o he pa ien s show ha a gene al
model can be possible when a speci ic subse o pa ien s is conside ed.
In compa ison wi h he o he ML lea ning algo i hms conside ed ou algo i hms do no
do as well as some o hem, especially Ada Boos , Bagging Classi ie , Random Fo es , and
Ex a T ees Classi ie . All o hem gi e excellen esul s o he ecall, especially in he
Hypoglycemia class o all he ime ames conside ed, whe e bo h ou algo i hms s a o
lose Recall pe cen age in bigge p edic ion ho izons. The main ad an age o ou algo i hm
is ha he inal model is an exp ession ha can be easily unde s ood, s udied, and manually
edi ed by an expe a e ob aining i .
The esul s ob ained will ha e a s uc u e simila o he ollowing one, wi h di e en
cons an s, a iables and ela ional/logical ope a o s:
i (((ge Va iable(1,k)<=103.465)||(((ge Va iable(47,k)-(ge Va iable(28,k)*
ge Va iable(43,k)/ge Va iable(31,k)))>=(ge Va iable(1,k)/6.184))&&
(((3.956/(ge Va iable(21,k)+94.433))*406.226)<=ge Va iable(35,k)))))
{ esul =0:}else{ esul =1:}
Which is equi alen o his exp ession wi h he ac ual names o he a iables:
65
i ((( Glucose( ) <=103.465)||((HR( -20) -(HR( -115) * HR
( -40)/HR( -100)))>=(Glucose( )/6.184))&&
(((3.956/(Gluc( -25) +94.433))*406.226)<=HR( -80)))))
{ esul =0:}else{ esul =1:}
5.2.6 Used a iables
The used a iables depend on he solu ion, he ime ame we a e conside ing o he p e-
dic ion, and he pa ien , howe e , we can s udy in wide e ms wha a iables a e mos used
by he bes solu ions o each un. In he able below 5.13 and in Fig. 5.17 we ha e all he
a iables o de ed by hei numbe and wi h he co esponding name o + [30,60,90,120],
whe e he o al numbe is he o al amoun o solu ions ob ained, and we only coun one
appea ance pe solu ion. Fi s ly, we a e di ing be ween he S a ic o o iginal SGE and he
Dynamic SGE. Clea ly, by a , he a iable ha he solu ions use mos is Glucose ( ), his
makes sense as is i he mos ecen glucose alue be o e he p edic ion, he o he a iables
a , Hea Ra e ( ), Cal ( ), and S eps ( ) a e also used in a highe p opo ion han o he
a iables in hei espec i e ypes, al hough he di e ence is much smalle han o he
Glucose ( ).
In bo h algo i hms, he second and hi d mos used a iables, appea ing in mo e han
30% o he solu ions, a e Hea Ra e ( ) and Calo ies Bu ned ( ) espec i ely. A e his he
o de o he a iables changes sligh ly o bo h algo i hms, howe e , he ac ual pe cen ages
a e no oo di e en as hey a e all be ween 20% and 30%. The wo less used a iables in
bo h algo i hms a e Glucose ( -10) and S eps ( -60) bu in a di e en o de o each one.
The glucose alue migh be a esul o duplica ed in o ma ion as we ha e added he newe
alues, bu he algo i hms don’ seem o use hem a lo in he solu ions.
In gene al, besides he Glucose( ) all he o he a iables a e used be ween 18.7%, 19.7%,
and 31%, 33% o each algo i hm.
We canno see a big di e ence be ween he a iables used in bo h algo i hms, so we
66
a e doing o choose one, DSGE, and obse e he a iable dis ibu ion o he di e en
p edic ion ho izons, Tab. 5.14 and Fig. 5.18. In his case, mo e a ia ion in he a iables
use is no iceable, especially o +120 whe e he amoun o ins ances o Glucose ( ) is a lo
less han in he o he p edic ion ho izons. None heless, Glucose ( ) is s ill, by a , he mos
used a iable, and he es ollow a simila end o wha we explained p e iously.
67
Table 5.17:Recall o he Gene al model o each pa ien
Pa ien Algo i hm Recall
Hypo
Recall L
No-Hypo
Recall H
No-Hypo
Recall Hypo
+ L No-Hypo
Recall
No-Hypo
HUPA001 S a ic 0.0 0.4151 0.6759 0.6250 0.9498
HUPA001 Dynamic 0.3125 0.2453 0.7781 0.5625 0.9012
HUPA002 S a ic 0.6364 0.5054 0.4898 0.9546 0.8306
HUPA002 Dynamic 0.6455 0.4511 0.5289 0.9591 0.8417
HUPA003 S a ic 0.5125 0.4516 0.5578 0.8417 0.8417
HUPA003 Dynamic 0.3250 0.4452 0.5805 0.8000 0.8605
HUPA004 S a ic 0.5591 0.2955 0.7612 0.8279 0.9105
HUPA004 Dynamic 0.6452 0.2500 0.7886 0.7850 0.9017
HUPA005 S a ic 0.4412 0.3786 0.6497 0.6765 0.9052
HUPA005 Dynamic 0.2353 0.5049 0.6966 0.6765 0.9411
HUPA007 S a ic 0.3535 0.6486 0.7014 0.7070 0.8958
HUPA007 Dynamic 0.5354 0.4595 0.7368 0.7071 0.8861
HUPA011 S a ic 0.1613 0.6064 0.6492 0.7742 0.9427
HUPA011 Dynamic 0.3226 0.5000 0.7075 0.7742 0.9032
HUPA014 S a ic 0.4894 0.2368 0.7914 0.6596 0.8952
HUPA014 Dynamic 0.1489 0.2632 0.8143 0.4892 0.9191
HUPA015 S a ic 0.0513 0.4333 0.6358 0.7436 0.9195
HUPA015 Dynamic 0.4103 0.2444 0.6710 0.7180 0.9104
HUPA016 S a ic 0.6763 0.3377 0.6000 0.8902 0.7283
HUPA016 Dynamic 0.5318 0.5390 0.6160 0.8671 0.8740
HUPA027 S a ic 0.6174 0.5444 0.5573 0.9597 0.8853
HUPA027 Dynamic 0.5436 0.7000 0.5823 0.9462 0.9206
74

Figu e 5.21:E olu ion o he a e age popula ion i ness in +120
Figu e 5.22:Boxplo s o he Recall o he bes execu ion in +120 o 3 Clases and 2 Clases
75
Compa ison wi h o he Machine Lea ning algo i hms
Table 5.18:Compa ison o he ecall be ween di e en ML algo i hms
Algo i hm Recall Low
No-Hypo
Recall High
No-Hypo
Recall High
No-Hypo
Recall Hypo +
Low No-Hypo
Recall
No-Hypo
G adien
boos ing 0.6676 0.5538 0.6770 0.8718 0.8797
G adien
boos ing wi h
C oss al
0.6676 0.5538 0.6770 0.8718 0.8797
Logis ic
Reg ession 0.6727 0.2313 0.6693 0.8357 0.7979
Random o es
classi ie 0.9378 0.8266 0.7371 0.9704 0.8967
Random o es
Reg eso 0.8012 0.9535 0.4518 0.9999 0.9936
Gaussian Nai e
Bayes 0.7054 0.1965 0.5004 0.8491 0.7097
Be noulli Nai e
Bayes 0.5657 0.2943 0.2710 0.7505 0.5121
Decision T ee
Classi ie
(6 dep h)
0.5076 0.5854 0.5587 0.9194 0.8572
Ada Boos
Classi ie 0.8888 0.7703 0.6184 0.9468 0.8451
Bagging
Classi ie 0.9296 0.8175 0.7212 0.9596 0.8914
Ex a T ees
Classi ie 0.9551 0.8349 0.7615 0.9551 0.9055
SGD Classi ie 0.6564 0.1426 0.7058 0.7746 0.7942
MLP Classi ie 0.7940 0.1393 0.6249 0.8327 0.6859
Dynamic SGE 0.5097 0.4701 0.6926 0.8318 0.8996
S a ic SGE 0.5321 0.4677 0.6512 0.8522 0.8902
76
5.3.2 Resul s o 3 Classes
F om his expe imen al example, we don’ eally ob ain much be e esul s han in he
case o he 2 classes. The indi idual class Recalls a e much lowe since pe o ming a 3-class
classi ica ion is ha de han when we jus ha e 2 classes, he in e media e class is making i
ha de o p edic he hypoglycemia s a e, as shown in Tab. 5.16 and Tab. 5.17. In e ms
o he columns o "Recall Hypo + L No-Hypo" and "Recall No-Hypo" we can see a sligh
imp o emen in compa ison o he Hypoglycemia p edic ion o he 2 classes. Howe e , we
a e s ill making an e oneous p edic ion since "Recall Hypo + L No-Hypo" co esponds o
he addi ion o he Hypoglycemic alues co ec ly classi ied and inco ec ly classi ied in o he
second class, and "Recall No-Hypo" he Non-Hypoglycemic alues o e 90 mg/dl classi ied
co ec ly and inco ec ly in o he second class. This compa ison is shown in Fig. 5.22 whe e
we can obse e he a e age Recall alues o 3 Classes, conside ing hese p e iously desc ibed
columns, and 2 Classes o +120. The a e age Recall o he usion o he classes ises o a
alue be ween 80% and 90%.
I we compa e ou p edic ion wi h o he ML algo i hms we ob ain simila esul s han
o he 2 classes, he ensemble me hods (Ada Boos , Bagging Classi ie , Random Fo es , and
Ex a T ees Classi ie ) ob ain be e esul s on he Recall, and ou algo i hms gi e simila
esul s o Logis ic Reg ession o G adien Boos ing.
The solu ions ob ained ha e his o m:
i ((((ge Va iable(35,k)*ge Va iable(61,k)*ge Va iable(58,k)-ge Va iable(31,k
))<=(324.978-ge Va iable(76,k)*96.752))&&((ge Va iable(28,k)+ge Va iable(47,k)
-ge Va iable(22,k))>(ge Va iable(73,k)-2.471))))
{ esul =0:}
else{
i (((ge Va iable(1,k)*ge Va iable(89,k))<805.928-(ge Va iable(89,k)+
ge Va iable(70,k)))){ esul =1:}
else{ esul =2:}}
77
Tha wi h he a iables names ansla ed would be:
i ((((HR ( -80) * S eps( -75) * S eps( -100) - HR ( -100)
)<=(324.978- Cal ( ) *96.752))&&(( HR ( -115) )+ HR( -20) - Gluc ( -25) )
>(S eps ( -15) -2.471))))
{ esul =0:}
else{
i ((( Gluc( ) * Cal ( -60) )<805.928-( Cal ( -60) +S eps( -30) ))){ esul =1:}
else{ esul =2:}}
5.3.3 Used a iables
The pe cen age o he a iables being used by bo h algo i hms is s ill e y simila o he
wo o hem as can be seen in he able 5.19 and in Fig. 5.23. The alue wi h he highes
pe cen age is Glucose ( ) and he o he a iables ha e a used pe cen age o a ound 30% o
40%. The less-used a iable in bo h algo i hms is Glucose ( -20) wi h a pe cen age o 23.6%
and 25.7% espec i ely.
I we compa e i o he esul s ob ained o +120 o jus wo classes we can see some
di e ences in some a iables, such as S eps ( -90) o HR ( -115) ha a e used much mo e
o en in he 3 class e sion. I can also be seen ha he a e age o he pe cen ages a e a
bi highe in he 3 class solu ions, which is p obably due o he ac ha he solu ions a e
much longe han o wo classes so mo e a iables can be used pe solu ion.
78
Table 5.19:Pe cen age o a iable in ol emen in he inal solu ions o all execu ions o
30 uns
Va iable Name S a ic
+120
Dynamic
+120
ge Va iable(1,k) Gluc ( ) 0.8273 0.7939
ge Va iable(6,k) Gluc ( -100) 0.3909 0.4182
ge Va iable(11,k) Gluc ( -75) 0.3455 0.3364
ge Va iable(16,k) Gluc ( -50) 0.2848 0.3242
ge Va iable(21,k) Gluc ( -25) 0.3091 0.2818
ge Va iable(22,k) Gluc ( -20) 0.2364 0.2576
ge Va iable(23,k) Gluc ( -15) 0.3000 0.2576
ge Va iable(24,k) Gluc ( -10) 0.3030 0.3030
ge Va iable(25,k) Gluc ( -5) 0.4364 0.4121
ge Va iable(26,k) HR ( ) 0.3667 0.3758
ge Va iable(28,k) HR ( -115) 0.3939 0.4121
ge Va iable(31,k) HR ( -100) 0.4030 0.3515
ge Va iable(35,k) HR ( -80) 0.3576 0.3303
ge Va iable(39,k) HR ( -60) 0.3152 0.2939
ge Va iable(43,k) HR ( -40) 0.3061 0.2788
ge Va iable(47,k) HR ( -20) 0.3364 0.3000
ge Va iable(51,k) S eps ( ) 0.4212 0.3848
ge Va iable(52,k) S eps ( -120) 0.3485 0.3030
ge Va iable(55,k) S eps ( -105) 0.3424 0.2939
ge Va iable(58,k) S eps ( -90) 0.3364 0.3576
ge Va iable(61,k) S eps ( -75) 0.2667 0.3121
ge Va iable(64,k) S eps ( -60) 0.3818 0.3485
ge Va iable(67,k) S eps ( -45) 0.3242 0.2939
ge Va iable(70,k) S eps ( -30) 0.2727 0.3091
ge Va iable(73,k) S eps ( -15) 0.3576 0.3273
ge Va iable(76,k) Cal ( ) 0.4212 0.3788
ge Va iable(78,k) Cal ( -115) 0.3242 0.3545
ge Va iable(81,k) Cal ( -100) 0.3879 0.3182
ge Va iable(85,k) Cal ( -80) 0.3394 0.2970
ge Va iable(89,k) Cal ( -60) 0.3333 0.3212
ge Va iable(93,k) Cal ( -40) 0.3576 0.3515
ge Va iable(97,k) Cal ( -20) 0.3424 0.3152
79

Figu e 5.23:Va iable dis ibu ion o +120 o SGE and DSGE
5.4 Fu u e Wo k
This s udy can be expanded o y o p edic o he s a es, no only hypoglycemia, such as
hype glycemia. This would be pe o med by using o he da a elemen s such as ca bohy-
d a es, insulin, s ess da a, e c. Addi ionally, di e en class di isions can be made depending
on wha each pa ien needs, o example, some pa ien s don’ co ec hei glucose alue
un il i d ops o 65 mg/dl, o hey choose o co ec i when i eaches highe alues.
The algo i hms de eloped should be es ed on mo e pa ien s o e a longe pe iod o ime,
o he p ojec we ha e only included da a o 11 o he 38 pa ien s we cu en ly ha e a ou
disposal, in he nea u u e we will make a s udy ha includes all o he pa ien s. We should
also s udy wha condi ions can be me o c ea e a gene al model wi h wha ype o pa ien s.
In ou s udy we ha e used he da a o all he pa ien s o es all o hem, howe e , i can
be seen in he esul s ha some pa ien s wo k be e wi h some da a o e o he s. I we can
di ide he da a in o di e en subse s we could p edic o a pa ien ha we don’ ha e da a
on, i we choose a subse o o he pa ien ’s da a ha a e simila o he new pa ien . This
gene a es a gene al model ha uses da a ha does no belong o a pa ien bu which would
80
yield good esul s because hei da a a ia ion is mo e simila .
5.5 Di usion
Conside ing he impac ha he p ojec could ha e, we ha e decided o publish he JECO
lib a y and Panc easModelTools on he Gi Hub pla o m, bo h p ojec s a e unde he Adap-
i e and Bioinspi ed Sys em G oup.
The wo k o de eloping his p ojec has allowed us o c ea e a pape wi h he i le
"E ol ing Classi ica ion Rules o P edic ing Hypoglycemia E en s" and accep ed o he
2022 IEEE Wo ld Cong ess on Compu a ional In elligence.
81
Bibliog aphy
[1] P edic ing and P e en ing Noc u nal Hypoglycemia in Type 1 Diabe es Using Big
Da a Analy ics and Decision Theo e ic Analysis. Diabe es echnology & he apeu ics,
22(11):801–811, no 2020.
[2] A hu Be achi, Cla a Viñals, Ly ia Biagi, I an Con e as, Josep Vehí, Ignacio Conge ,
and Ma ga Giménez. P edic ion o noc u nal hypoglycemia in adul s wi h ype 1 dia-
be es unde mul iple daily injec ions using con inuous glucose moni o ing and physical
ac i i y moni o . Senso s, 20(6), 2020.
[3] U esh Bhowan, Mengjie Zhang, and Ma k Johns on. Gene ic p og amming o clas-
si ica ion wi h unbalanced da a. In Anna Isabel Espa cia-Alcáza , Anikó Eká , Sa a
Sil a, S ephen Dignum, and A. Şima Uya , edi o s, Gene ic P og amming, pages 1–13,
Be lin, Heidelbe g, 2010. Sp inge Be lin Heidelbe g.
[4] Mads Bisgaa d Beng sen and Niels Mølle . Mini- e iew: Glucagon esponses in ype 1
diabe es – a ma e o complexi y. Physiological Repo s, 9(16):e15009, 2021.
[5] Ca los Ce igón, J. Manuel Velasco, Cla a Bu gos-Simón, Ra ael J. Villanue a, and
J. Ignacio Hidalgo. P obabilis ic i ing o glucose models wi h eal-coded gene ic al-
go i hms. pages 736–743, 2021.
[6] Philip E. C ye , S ephen N. Da is, and Ha y Shamoon. Hypoglycemia in Diabe es .
Diabe es Ca e, 26(6):1902–1912, 06 2003.
[7] Da pi Da e, Daniel J. DeSal o, Balak ishna Ha idas, Si ipoom McKay, Akhil Shenoy,
Ches e J. Koh, Ma k Lawley, and Madha E agun la. Fea u e-based machine lea ning
model o eal- ime hypoglycemia p edic ion. Jou nal o Diabe es Science and Technol-
ogy, 15(4):842–855, 2021. PMID: 32476492.
82
[8] I anoe De Falco, An onio Della Cioppa, Tomas Kou ny, Michal K cma, Umbe o
Sca u i, and E nes o Ta an ino. Gene ic p og amming-based induc ion o a glucose-
dynamics model o elemedicine. Jou nal o Ne wo k and Compu e Applica ions,
119:1–13, 2018.
[9] Ampa o Güemes, Giacomo Cappon, Be na d He nandez, Monika Reddy, Nick Oli e ,
Pan elis Geo giou, and Pau He e o. P edic ing quali y o o e nigh glycaemic con ol
in ype 1 diabe es using bina y classi ie s. IEEE Jou nal o Biomedical and Heal h
In o ma ics, 24(5):1439–1446, 2020.
[10] J. Ignacio Hidalgo, J. Manuel Colmena , Gab iel K onbe ge , S ephan M. Winkle ,
Osca Ga nica, and Juan Lancha es. Da a based p edic ion o blood glucose concen-
a ions using e olu iona y me hods. Jou nal o Medical Sys ems, 41, 2017.
[11] J. Ignacio Hidalgo, J. Manuel Colmena , José L. Risco-Ma in, Al edo Cues a-In an e,
Es he Maqueda, Ma a Bo ella, and José An onio Rubio. Modeling glycemia in humans
by means o g amma ical e olu ion. Applied So Compu ing, (20):40–53, 2014.
[12] J. Ignacio Hidalgo, J. Manuel Colmena , J. Manuel Velasco, Gab iel K onbe ge ,
S ephan M. Winkle , Osca Ga nica, and Juan Lancha es. Iden i ica ion o Models o
Glucose Blood Values in Diabe ics by G amma ical E olu ion, pages 367–393. Sp inge
In e na ional Publishing, Cham, 2018.
[13] J. Ignacio Hidalgo, Es he Maqueda, Jose L. Risco-Ma an, Al edo Cues a-In an e,
J. Manuel Colmena , and Ja ie Nobel. glucmodel: A moni o ing and modeling sys em
o ch onic diseases applied o diabe es. Jou nal o Biomedical In o ma ics, 48:183 –
192, 2014.
[14] Jose Ignacio Hidalgo, Jose Manuel Velasco, Juan Lancha es, Se gio Con ado , and Osca
Ga nica. An analysis o solu ions based on Gene ic P og amming o sol e p oblems o
83