<s>
In	O
the	O
mathematical	O
theory	O
of	O
probability	O
,	O
the	O
Indian	B-General_Concept
buffet	I-General_Concept
process	I-General_Concept
(	O
IBP	O
)	O
is	O
a	O
stochastic	O
process	O
defining	O
a	O
probability	O
distribution	O
over	O
sparse	B-Algorithm
binary	B-Algorithm
matrices	I-Algorithm
with	O
a	O
finite	O
number	O
of	O
rows	O
and	O
an	O
infinite	O
number	O
of	O
columns	O
.	O
</s>
<s>
Let	O
be	O
an	O
binary	B-Algorithm
matrix	I-Algorithm
indicating	O
the	O
presence	O
or	O
absence	O
of	O
a	O
latent	O
feature	O
.	O
</s>
<s>
where	O
is	O
the	O
number	O
of	O
non-zero	O
columns	O
in	O
,	O
is	O
the	O
number	O
of	O
ones	O
in	O
column	O
of	O
,	O
is	O
the	O
Nth	O
harmonic	O
number	O
,	O
and	O
is	O
the	O
number	O
of	O
occurrences	O
of	O
the	O
non-zero	O
binary	B-Data_Structure
vector	I-Data_Structure
among	O
the	O
columns	O
in	O
.	O
</s>
<s>
In	O
the	O
Indian	B-General_Concept
buffet	I-General_Concept
process	I-General_Concept
,	O
the	O
rows	O
of	O
correspond	O
to	O
customers	O
and	O
the	O
columns	O
correspond	O
to	O
dishes	O
in	O
an	O
infinitely	O
long	O
buffet	O
.	O
</s>
<s>
This	O
process	O
is	O
infinitely	O
exchangeable	O
for	O
an	O
equivalence	O
class	O
of	O
binary	B-Algorithm
matrices	I-Algorithm
defined	O
by	O
a	O
left-ordered	O
many-to-one	O
function	O
.	O
</s>
<s>
is	O
obtained	O
by	O
ordering	O
the	O
columns	O
of	O
the	O
binary	B-Algorithm
matrix	I-Algorithm
from	O
left	O
to	O
right	O
by	O
the	O
magnitude	O
of	O
the	O
binary	O
number	O
expressed	O
by	O
that	O
column	O
,	O
taking	O
the	O
first	O
row	O
as	O
the	O
most	O
significant	O
bit	O
.	O
</s>
