<s>
In	O
machine	O
learning	O
,	O
a	O
deep	B-Algorithm
belief	I-Algorithm
network	I-Algorithm
(	O
DBN	O
)	O
is	O
a	O
generative	O
graphical	O
model	O
,	O
or	O
alternatively	O
a	O
class	O
of	O
deep	B-Algorithm
neural	B-Architecture
network	I-Architecture
,	O
composed	O
of	O
multiple	O
layers	O
of	O
latent	O
variables	O
(	O
"	O
hidden	O
units	O
"	O
)	O
,	O
with	O
connections	O
between	O
the	O
layers	O
but	O
not	O
between	O
units	O
within	O
each	O
layer	O
.	O
</s>
<s>
When	O
trained	O
on	O
a	O
set	O
of	O
examples	O
without	B-General_Concept
supervision	I-General_Concept
,	O
a	O
DBN	O
can	O
learn	O
to	O
probabilistically	O
reconstruct	O
its	O
inputs	O
.	O
</s>
<s>
After	O
this	O
learning	O
step	O
,	O
a	O
DBN	O
can	O
be	O
further	O
trained	O
with	O
supervision	B-General_Concept
to	O
perform	O
classification	B-General_Concept
.	O
</s>
<s>
DBNs	O
can	O
be	O
viewed	O
as	O
a	O
composition	O
of	O
simple	O
,	O
unsupervised	O
networks	O
such	O
as	O
restricted	B-Algorithm
Boltzmann	I-Algorithm
machines	I-Algorithm
(	O
RBMs	O
)	O
or	O
autoencoders	B-Algorithm
,	O
where	O
each	O
sub-network	O
'	O
s	O
hidden	O
layer	O
serves	O
as	O
the	O
visible	O
layer	O
for	O
the	O
next	O
.	O
</s>
<s>
This	O
composition	O
leads	O
to	O
a	O
fast	O
,	O
layer-by-layer	O
unsupervised	O
training	O
procedure	O
,	O
where	O
contrastive	B-Algorithm
divergence	I-Algorithm
is	O
applied	O
to	O
each	O
sub-network	O
in	O
turn	O
,	O
starting	O
from	O
the	O
"	O
lowest	O
"	O
pair	O
of	O
layers	O
(	O
the	O
lowest	O
visible	O
layer	O
is	O
a	O
training	O
set	O
)	O
.	O
</s>
<s>
The	O
observation	O
that	O
DBNs	O
can	O
be	O
trained	O
greedily	B-Algorithm
,	O
one	O
layer	O
at	O
a	O
time	O
,	O
led	O
to	O
one	O
of	O
the	O
first	O
effective	O
deep	B-Algorithm
learning	I-Algorithm
algorithms	O
.	O
</s>
<s>
Overall	O
,	O
there	O
are	O
many	O
attractive	O
implementations	O
and	O
uses	O
of	O
DBNs	O
in	O
real-life	O
applications	O
and	O
scenarios	O
(	O
e.g.	O
,	O
electroencephalography	B-Application
,	O
drug	O
discovery	O
)	O
.	O
</s>
<s>
The	O
training	O
method	O
for	O
RBMs	O
proposed	O
by	O
Geoffrey	O
Hinton	O
for	O
use	O
with	O
training	O
"	O
Product	O
of	O
Expert	O
"	O
models	O
is	O
called	O
contrastive	B-Algorithm
divergence	I-Algorithm
(	O
CD	O
)	O
.	O
</s>
<s>
In	O
training	O
a	O
single	O
RBM	O
,	O
weight	O
updates	O
are	O
performed	O
with	O
gradient	B-Algorithm
descent	I-Algorithm
via	O
the	O
following	O
equation	O
:	O
</s>
<s>
The	O
issue	O
arises	O
in	O
sampling	O
because	O
this	O
requires	O
extended	O
alternating	O
Gibbs	B-Algorithm
sampling	I-Algorithm
.	O
</s>
<s>
CD	O
replaces	O
this	O
step	O
by	O
running	O
alternating	O
Gibbs	B-Algorithm
sampling	I-Algorithm
for	O
steps	O
(	O
values	O
of	O
perform	O
well	O
)	O
.	O
</s>
<s>
is	O
the	O
sigmoid	B-Algorithm
function	I-Algorithm
and	O
is	O
the	O
bias	O
of	O
.	O
</s>
