<s>
Multimodal	B-Algorithm
learning	I-Algorithm
attempts	O
to	O
model	O
the	O
combination	O
of	O
different	O
modalities	B-General_Concept
of	O
data	O
,	O
often	O
arising	O
in	O
real-world	O
applications	O
.	O
</s>
<s>
An	O
example	O
of	O
multi-modal	O
data	O
is	O
data	O
that	O
combines	O
text	O
(	O
typically	O
represented	O
as	O
discrete	O
word	O
count	O
vectors	O
)	O
with	O
imaging	O
data	O
consisting	O
of	O
pixel	B-Algorithm
intensities	O
and	O
annotation	O
tags	O
.	O
</s>
<s>
As	O
these	O
modalities	B-General_Concept
have	O
fundamentally	O
different	O
statistical	O
properties	O
,	O
combining	O
them	O
is	O
non-trivial	O
,	O
which	O
is	O
why	O
specialized	O
modelling	O
strategies	O
and	O
algorithms	O
are	O
required	O
.	O
</s>
<s>
However	O
,	O
data	O
usually	O
comes	O
with	O
different	O
modalities	B-General_Concept
(	O
it	O
is	O
the	O
degree	O
to	O
which	O
a	O
system	O
's	O
components	O
may	O
be	O
separated	O
or	O
combined	O
)	O
which	O
carry	O
different	O
information	O
.	O
</s>
<s>
Thus	O
,	O
in	O
cases	O
dealing	O
with	O
multi-modal	O
data	O
,	O
it	O
is	O
important	O
to	O
use	O
a	O
model	O
which	O
is	O
able	O
to	O
jointly	O
represent	O
the	O
information	O
such	O
that	O
the	O
model	O
can	O
capture	O
the	O
correlation	O
structure	O
between	O
different	O
modalities	B-General_Concept
.	O
</s>
<s>
Moreover	O
,	O
it	O
should	O
also	O
be	O
able	O
to	O
recover	O
missing	O
modalities	B-General_Concept
given	O
observed	O
ones	O
(	O
e.g.	O
</s>
<s>
The	O
Multimodal	O
Deep	O
Boltzmann	B-Algorithm
Machine	I-Algorithm
model	O
satisfies	O
the	O
above	O
purposes	O
.	O
</s>
<s>
A	O
Boltzmann	B-Algorithm
machine	I-Algorithm
is	O
a	O
type	O
of	O
stochastic	O
neural	O
network	O
invented	O
by	O
Geoffrey	O
Hinton	O
and	O
Terry	O
Sejnowski	O
in	O
1985	O
.	O
</s>
<s>
Boltzmann	B-Algorithm
machines	I-Algorithm
can	O
be	O
seen	O
as	O
the	O
stochastic	O
,	O
generative	O
counterpart	O
of	O
Hopfield	B-Algorithm
nets	I-Algorithm
.	O
</s>
<s>
The	O
units	O
in	O
Boltzmann	B-Algorithm
machines	I-Algorithm
are	O
divided	O
into	O
two	O
groups	O
:	O
visible	O
units	O
and	O
hidden	O
units	O
.	O
</s>
<s>
General	O
Boltzmann	B-Algorithm
machines	I-Algorithm
allow	O
connection	O
between	O
any	O
units	O
.	O
</s>
<s>
However	O
,	O
learning	O
is	O
impractical	O
using	O
general	O
Boltzmann	B-Algorithm
Machines	I-Algorithm
because	O
the	O
computational	O
time	O
is	O
exponential	O
to	O
the	O
size	O
of	O
the	O
machine	O
.	O
</s>
<s>
A	O
more	O
efficient	O
architecture	O
is	O
called	O
restricted	B-Algorithm
Boltzmann	I-Algorithm
machine	I-Algorithm
where	O
connection	O
is	O
only	O
allowed	O
between	O
hidden	O
unit	O
and	O
visible	O
unit	O
,	O
which	O
is	O
described	O
in	O
the	O
next	O
section	O
.	O
</s>
<s>
A	O
restricted	B-Algorithm
Boltzmann	I-Algorithm
machine	I-Algorithm
is	O
an	O
undirected	O
graphical	O
model	O
with	O
stochastic	O
visible	O
variable	O
and	O
stochastic	O
hidden	O
variables	O
.	O
</s>
<s>
Gaussian-Bernoulli	O
RBMs	O
are	O
a	O
variant	O
of	O
restricted	B-Algorithm
Boltzmann	I-Algorithm
machine	I-Algorithm
used	O
for	O
modeling	O
real-valued	O
vectors	O
such	O
as	O
pixel	B-Algorithm
intensities	O
.	O
</s>
<s>
The	O
joint	O
distribution	O
is	O
defined	O
the	O
same	O
as	O
the	O
one	O
in	O
restricted	B-Algorithm
Boltzmann	I-Algorithm
machine	I-Algorithm
.	O
</s>
<s>
The	O
Replicated	O
Softmax	O
Model	O
is	O
also	O
an	O
variant	O
of	O
restricted	B-Algorithm
Boltzmann	I-Algorithm
machine	I-Algorithm
and	O
commonly	O
used	O
to	O
model	O
word	O
count	O
vectors	O
in	O
a	O
document	O
.	O
</s>
<s>
In	O
a	O
typical	O
text	B-Algorithm
mining	I-Algorithm
problem	O
,	O
let	O
be	O
the	O
dictionary	O
size	O
,	O
and	O
be	O
the	O
number	O
of	O
words	O
in	O
the	O
document	O
.	O
</s>
<s>
A	O
deep	O
Boltzmann	B-Algorithm
machine	I-Algorithm
has	O
a	O
sequence	O
of	O
layers	O
of	O
hidden	O
units.There	O
are	O
only	O
connections	O
between	O
adjacent	O
hidden	O
layers	O
,	O
as	O
well	O
as	O
between	O
visible	O
units	O
and	O
hidden	O
units	O
in	O
the	O
first	O
hidden	O
layer	O
.	O
</s>
<s>
Multimodal	O
deep	O
Boltzmann	B-Algorithm
machine	I-Algorithm
uses	O
an	O
image-text	O
bi-modal	O
DBM	O
where	O
the	O
image	O
pathway	O
is	O
modeled	O
as	O
Gaussian-Bernoulli	O
DBM	O
and	O
text	O
pathway	O
as	O
Replicated	O
Softmax	O
DBM	O
,	O
and	O
each	O
DBM	O
has	O
two	O
hidden	O
layers	O
and	O
one	O
visible	O
layer	O
.	O
</s>
<s>
Multimodal	O
deep	O
Boltzmann	B-Algorithm
machines	I-Algorithm
are	O
successfully	O
used	O
in	O
classification	O
and	O
missing	O
data	O
retrieval	O
.	O
</s>
<s>
The	O
classification	O
accuracy	O
of	O
multimodal	O
deep	O
Boltzmann	B-Algorithm
machine	I-Algorithm
outperforms	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
,	O
latent	O
Dirichlet	O
allocation	O
and	O
deep	B-Algorithm
belief	I-Algorithm
network	I-Algorithm
,	O
when	O
models	O
are	O
tested	O
on	O
data	O
with	O
both	O
image-text	O
modalities	B-General_Concept
or	O
with	O
single	O
modality	B-General_Concept
.	O
</s>
<s>
Multimodal	O
deep	O
Boltzmann	B-Algorithm
machine	I-Algorithm
is	O
also	O
able	O
to	O
predict	O
missing	O
modalities	B-General_Concept
given	O
the	O
observed	O
ones	O
with	O
reasonably	O
good	O
precision	O
.	O
</s>
<s>
OpenAI	O
developed	O
CLIP	O
and	O
DALL-E	B-General_Concept
models	O
that	O
revolutionized	O
multimodality	O
.	O
</s>
<s>
Multimodal	B-Algorithm
deep	I-Algorithm
learning	I-Algorithm
is	O
used	O
for	O
cancer	O
screening	O
–	O
at	O
least	O
one	O
system	O
under	O
development	O
integrates	O
such	O
different	O
types	O
of	O
data	O
.	O
</s>
