<s>
IBM	B-General_Concept
alignment	I-General_Concept
models	I-General_Concept
are	O
a	O
sequence	O
of	O
increasingly	O
complex	O
models	O
used	O
in	O
statistical	B-General_Concept
machine	I-General_Concept
translation	I-General_Concept
to	O
train	O
a	O
translation	O
model	O
and	O
an	O
alignment	O
model	O
,	O
starting	O
with	O
lexical	O
translation	O
probabilities	O
and	O
moving	O
to	O
reordering	O
and	O
word	O
duplication	O
.	O
</s>
<s>
They	O
underpinned	O
the	O
majority	O
of	O
statistical	B-General_Concept
machine	I-General_Concept
translation	I-General_Concept
systems	O
for	O
almost	O
twenty	O
years	O
starting	O
in	O
the	O
early	O
1990s	O
,	O
until	O
neural	B-General_Concept
machine	I-General_Concept
translation	I-General_Concept
began	O
to	O
dominate	O
.	O
</s>
<s>
The	O
original	O
work	O
on	O
statistical	B-General_Concept
machine	I-General_Concept
translation	I-General_Concept
at	O
IBM	O
proposed	O
five	O
models	O
,	O
and	O
a	O
model	O
6	O
was	O
proposed	O
later	O
.	O
</s>
<s>
The	O
IBM	B-General_Concept
alignment	I-General_Concept
models	I-General_Concept
translation	O
as	O
a	O
conditional	O
probability	O
model	O
.	O
</s>
<s>
In	O
this	O
form	O
,	O
this	O
is	O
exactly	O
the	O
kind	O
of	O
problem	O
solved	O
by	O
expectation	B-Algorithm
–	I-Algorithm
maximization	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
In	O
short	O
,	O
the	O
EM	B-Algorithm
algorithm	I-Algorithm
goes	O
as	O
follows:INPUT	O
.	O
</s>
<s>
With	O
that	O
,	O
we	O
have	O
The	O
EM	B-Algorithm
algorithm	I-Algorithm
can	O
still	O
be	O
solved	O
in	O
closed-form	O
,	O
giving	O
the	O
following	O
algorithm:where	O
are	O
still	O
normalization	O
factors	O
.	O
</s>
