Big Data and Large Scale Inference: II. Amr Ahmed Research at Google

Amr Ahmed

Research at Google

Big Data and

Large Scale Inference: II

Wrapping  up    

•  Distributed  inference  in  latent  variable  models  

–  Star  Synchroniza:on  

–  Delta  aggrega:on  

Wrapping  up  …  

φ θ

z  

w  

α   Prior  over  topic  

mixtures  

Topic-­‐word   distribu:on  

Wrapping  up  …  

φ θ

z  

w   α  

•  Global  variables  

–  Φ:  Topic  distribu:on  over   words  

•  Local  variables  

–  θ:  topic  mixing  vector   –  Z:  topic  indicator  

Wrapping  up  …  

z  

w  

•  Collapse  global  variables  

–  Φ  

•  Collapse  local  variables  

–  θ  

•  Couples  all  Zs  

•  Run  collapsed  sampler  

P (z  

= k |w

= w, z

) / (n

+ ↵) n

+ n

+ W

P (z _di = k |w ^di = w, z _di ) / (n ^dk + ↵) n _kw +

n _k + W

Wrapping  up  …  

z  

w  

P (z

= k |w

= w, z

) / (n

+ ↵) n

+ n

+ W

P (z _di = k |w ^di = w, z _di ) / (n ^dk + ↵) n _kw + n _k + W

Global  counts   (global  state)   Local  counts  

(local  state)   Global  State  

n _kw

, n _k

Distributed  Inference:  LDA  

θ

z  

w   α  

φ

Distributed  Inference:  LDA  

θ

z  

w   θ

z  

w  

α  

φ

Distributed  Inference:  LDA  

z  

w   z  

w  

Global  State  

n _kw , n

_k

Distributed  Inference:  LDA  

z  

w   z  

w  

Global  State  

n _kw , n

_k

Global  replica   Global  replica  

General  Architecture  

•  Star  synchroniza:on  

–  Works  when  variables  depend  on  each  other  via   aggregates  

•  Counts,  sums,  etc.  

–  When  state  objects  form  an  Abelian  group  

State  1   u1   u2   u3   State  2  

State  1   u2   u1   u3   State  2  

Mul:lingual  LDA  

•  Each  topic  has  a  distribu:on  over  words  

•  Fits  parallel  documents  

–  Example:  Wikipedia    

What    Is  next?  

•  Can  we  fit  any  model  only  with  those   asynchronous  primi:ves?  

–  No  

•  We  need  synchronous  opera:ons  

–  Parameter  op:miza:on  

•  EM  style  algorithm      

–  Non-­‐collapsed  global  variables  

The  Need  for  Synchronous  Processing  

φ θ

z  

w  

α   Prior  over  topic  

mixtures  

Topic-­‐word   distribu:on        

   What  if  we  need  to  op:mize  over    α?  

The  Need  for  Synchronous  Processing  

φ θ

z  

w   α  

•  E-­‐Step  

–  Run  asynchronous   collapsed  sampler  as   before  

•  M-­‐step  

–  Reach  a  barrier  

–  Collect  values  needed  to   op:mize  α  

–  One  machine  op:mizes  α   –   Broadcast  value  back  

Distributed  Sampling  Cycle  

Sample  Z  

  Sample  Z   Sample  Z   Sample  Z  

Barrier  

Write  counts   to     memcached  

Write  counts   to     memcached  

Write  counts   to     memcached  

Write  counts   to     memcached  

Collect  counts  

and  sample  Ω   Do  nothing   Do  nothing   Do  nothing  

Barrier  

Read  Ω from  

memcached Read  Ω from  

memcached   Read  Ω from  

memcached   Read  Ω from  

memcached  

Op:mize  α  

Requires  a  reduc:on  step  

Asynchronous  

Synchronous  

Distributed  Sampling  Cycle  

Sample  Z   Sample  Z   Sample  Z   Sample  Z  

Barrier  

Write  counts   Write  counts   Write  counts   Write  counts  

Collect  counts  

and  op:mize   Do  nothing   Do  nothing   Do  nothing  

Barrier  

Read  α Read  α   Read   α   Read  α  

Up  next  

•  Applica:on  

–  Mul:-­‐domain  user  personaliza:on  

–  Non-­‐parametric  models:  DPs,  temporal  DPs,  etc   –   Temporal  Modeling  of  user  interests  

–  Mul:-­‐task  learning  and  computa:onal  adver:sing  

Modeling  User  Interests  

User-­‐1   User-­‐2  

Mul:-­‐domain  Personaliza:on  

Computa:onal  Adver:sing:  

 Mul:task  learning  

Mul:-­‐Domain  

Personaliza:on    

Problem  

Mul:-­‐domain  Personaliza:on  

•  Intui:on  

–  We  observe  user  interac:on  with  news  and  movies   –  Can  we  predict  his  music  taste?  

•  Interac:on  defini:on  

–  A  bag  of  words  describing  objects  user  interacts  with  

in  a  given  domain  

Example  

User  Meta   Profile  

User  Music  

Profile   User  News  

Profile  

Personalized News

Personalized

Music

Example  

User  Meta   Profile  

User  Music  

Profile   User  News  

Profile   User  Movie  

Profile  

The  Model  

↵ ✓ z w

N   User  u’s  interac:on  with  domain  d  

'

A  user’s  interac6on  with  a  domain  is  a  bag  of  words.  

A  topic  is  a  mixture  of  words.  

x

Each  user  has  a  meta-­‐profile:   x

2 R ^k

p

Each  domain  has  a  latent  matrix:   _d 2 R ^{k ⇥t}

User’s  prior  interest  in  a  domain  is  

= log(1 + exp(⇥ _d x _u ))

Slide  credit  Yucheng  Low  

The  Model  

User  Meta   Profile  

User  Music  

Profile   User  News  

Profile   User  Movie  

Profile  

x

2 R ^k

music

news

movie

lgt( _music x _u ) lgt( _news x _u ) lgt( _movie x _u )

lgt(x) = log(1 + exp(x))

Slide  credit  Yucheng  Low  

↵ ✓ w z

w 2 Wu,d

Music  

News  

Movies  

↵ ✓ w z

w 2 W^u,d

x ₁ x ₂ x ₃

1

2

3

Topic-­‐>word  table  

Topic-­‐>word  table  

Topic-­‐>word  table   Slide  credit  Yucheng  Low  

Inference  and  Learning  

↵ ✓ z w

N   User  u’s  interac:on  with  domain  p  

p

x

E-­‐Step:  sample  local  variables    

'

Collapse  and   synchronize   M-­‐Step  

Op:mize  via  barrier  

Distributed  Sampling  Cycle  

Sample  Z,  x  

For  users   Sample  Z,x  

For  users   Sample  Z,x  

For  users   Sample  Z,x  

For  users  

Barrier  

Write  counts   to     memcached  

Write  counts   to     memcached  

Write  counts   to     memcached  

Write  counts   to     memcached  

Collect  counts  

and  sample  Ω   Do  nothing   Do  nothing   Do  nothing  

Barrier  

Read  Ω from  

memcached Read  Ω from  

memcached   Read  Ω from  

memcached   Read  Ω from  

memcached  

Op:mize    λ  

Requires  a  reduc:on  step  

Distributed  Sampling  Cycle  

Sample  Z,  x  

For  users   Sample  Z,  x  

For  users   Sample  Z,  x  

For  users   Sample  Z,  x   For  users  

Barrier  

Write    

sta:s:cs   Write  

sta:s:cs   Write  

sta:s:cs   Write  

sta:s:cs  

Collect  and      

op:mize   Do  nothing   Do  nothing   Do  nothing  

Barrier  

Read Read   Read   Read  

Results  

•  2  domain  dataset.    

     Frontpage  and  News  clicks  of  5.6  million  users.  

     Frontpage/News:  Ar:cle  text  for  each  click.  

•   Measure  gain  rela:ve  to  independent  models  on  

each  domain  

Results  

Front Page News

0 5 10 15 20 25 30

% Gain in Cosine Similarity

25 Features

50 Features

Analysis  

sandra,  oscar,  oscars,  red,  carpet,  bullock,   golden,  gown,  bullocks,  nominee,  bestactress,   sparkles,  stunning,    

vienna,  bachelor,  jake,  pavelka,  giraldi,  finale,   show,  stars,  dancing,  love,  season,  :me,  abc,    

bacteria,  fight,  super,  struggling,  developed,   doctors,  resistant,  lethal,  virtually,  drugs,   an:bio:c,  compe:tors,  chad,    

film,  movie,  movies,  films,  director,  story,  

avatar,  james,  :me,  hollywood,  big,  make,  hes,   star,    

Celebrity  

Entertainment  

Science  

Science  Fic6on  

Non-­‐parametric  Mdoels  

Non-­‐parametric  Models  

•  How  many  clusters?  

•  How  many  topics?  

•  Dimensionality  of  the  model  grows  with  the  data  

•  Perfect  for  big  data  sedng  where  data  keeps  

arriving  and  we  want  to  refine  model  structure  

Parametric  Mixture  Models  

c

w

N

π

φ

Κ

φ

  φ

-­‐ For  Document  w_i    

-­‐   Sample  c_{i  ~}  Mul:(π)   -­‐   Sample  w_{i  ~}  Mult(φ_ci)  

w_i  

∝π₁   ∝ π_j   ∝ π_k  

Genera:ve  Process  

Infinite  Mixture  Models  

•  Allows  the  number  of  mixtures  to  grow  with  the  data  

•  They  are  called  non-­‐parametric  models  

–  Means  the  number  of  effec:ve  parameters  grow  with  data   –  S:ll  have  hyper-­‐parameters  that  control  the  rate  of  growth  

•   α:  how  fast  a  new  cluster/mixture  is  born?  

•  G

:    Prior  over  mixture  component  parameters  

•  We  can  arrive  at  them  from  many  angle  

–  Chinese  Restaurant  Process  Mixtures   –  S:ck  Breaking  construc:on  

–  Random  Measure  View  

Chinese  Restaurant  Process  Mixture  

-­‐ For  data  point  x_i    

-­‐   Choose  table  j  ∝  mj        and    Sample  x_{i  ~}  f(φ_j)   -­‐   Choose  a  new  table    K+1  ∝  α    

-­‐   Sample  φ_{K+1  ~}  G₀      and  Sample  x_{i  ~}  f(φ_K+1)   Genera:ve  Process  

φ

φ

  φ

α 6+

2 6+α

3 6+α

1

α α 6+

[Blackwell,  D.  and  MacQueen  1973]  

S:ck  Breaking  Construc:on  

c

x

π

φ

α

c

x

π

φ

Parametric  Mixture   Non-­‐  Parametric  Mixture  

X

k

⇡ _k

Mixture  distribu:on  =    

?  

[Sethuraman,  1994]  

S:ck  Breaking  Construc:on  

α

c

x

π

φ

X 1 k=1

⇡ _k

Mixture  distribu:on  =    

•  φ

   ~  G

is  called  atom  loca:on  

•  π

 is  called  atom  weight  

–  π    ~  GEM(α)  

π₁  

π₂  

π₃  

φ₁   φ₂   φ₃  

S:ck  Breaking  Construc:on  

α

c

x

π

φ

X 1 k=1

⇡ _k

Mixture  distribu:on  =    

•  φ

   ~  G

is  called  atom  loca:on  

•  π

 is  called  atom  weight  

–  π    ~  GEM(α)  

v

⇠ Beta(1, ↵)

⇡

= v

k 1

Y

i=1

(1 v

)

v

= ⇡

(1 v

) ^v

S:ck  Breaking  Construc:on  

α

c

x

π

φ

X 1 k=1

⇡ _k

Mixture  distribu:on  =    

•  φ

   ~  G

is  called  atom  loca:on  

•  π

 is  called  atom  weight  

–  π    ~  GEM(α)  

v

⇠ Beta(1, ↵)

⇡

= v

k 1

Y

i=1

(1 v

)

v

= ⇡

(1 v

) ^v

S:ck  Breaking  Construc:on  

α

c

x

π

φ

X 1 k=1

⇡ _k

Mixture  distribu:on  =    

•  φ

   ~  G

is  called  atom  loca:on  

•  π

 is  called  atom  weight  

–  π    ~  GEM(α)  

v

⇠ Beta(1, ↵)

⇡

= v

k 1

Y

i=1

(1 v

)

v

= ⇡

(1 v

)

(1 v

)(1 v

)

v

v

(1 v

)

Dirichlet  Process  Mixture  View  

•  G  is  always  discreet  (we  have  just  constructed  it)  

•  G  =    

•  G  is  a  random  measure,  why?  

G ⇠ DP (↵, G

)

✓

⇠ G x

⇠ f(✓

)

α

θ

x

G   G₀  

X1 k=1

⇡_{k k}

E[G] = G

V ar[G] = ↵

[Ferguson,  1973]  

Infinite  Mixture  Models  

•  Chinese  Restaurant  Process  

–  Useful  for  construc6ng  Gibbs  sampling  algorithms   [Neal  1998]  

•  S:ck-­‐breaking  construc:on  

–  Useful  for  deriving  Varia:onal  inference  algorithms.  

[Blei  and  Jordan  2004]  

•  DP  view  

–  Useful  for  conceptual  understanding  (esp.  later  in  the  

tutorial)    [Teh  et.  al.,  2006]    

Chinese  Restaurant  Process  Mixture  

-­‐ For  data  point  x_i    

-­‐   Choose  table  j  ∝  mj        and    Sample  x_{i  ~}  f(φ_j)   -­‐   Choose  a  new  table    K+1  ∝  α    

-­‐   Sample  φ_{K+1  ~}  G₀      and  Sample  x_{i  ~}  f(φ_K+1)   Genera:ve  Process  

φ

φ

  φ

α 6+

2 6+α

3 6+α

1

α α 6+

Inference  Via  Gibbs  Sampling  

•  Construct  a  Markov  chain  over  cluster  indicators   for  each  data  point  c _i   and  cluster  parameters  φ

P (c

|c

, ↵, G

) /

⇢ m

p(x

|

) for existing k

↵ R

p(x

| )p( |G

)d for a new cluster

P ( _k |c, G ⁰ ) / Y

c

=k

p(x _i | )P ( |G ⁰ )

Inference  Via  Collapsed  Gibbs  Sampling  

•  If  G ₀  is  conjugate  to  the  likelihood  func:on  p(.|φ)    then  we  can  integrate  it  out.  

P (c

|c

, ↵, G

) / 8 >

<

> :

m

p ⇣

x

|{x

}

⌘

for existing k

↵ R

p(x

| )p( |G

)d for a new cluster

Dynamic  Models  

Dynamic  Non-­‐Parametric  Models  

•  Evolve  atom  weights  

•  Evolve  atom  loca:ons  

•  Many  models  

–  What  assump:ons  they  are  making    

–  More  expressive  the  harder  the  inference   –  Examples  

•  RCRP  (Ahmed  and  Xing,  2008)  

•  Time-­‐Varying  Polya-­‐Urn  (Caron  et.  Al.  2007)  

•  Dependent  DPs  and  Ordered-­‐DPs  (Griffin  et.  Al.  2004)  

•  Normalized  Gamma  Processes  (Rao  and  Teh  2009)  

Recurrent  CRP  (RCRP)   [Ahmed  and  Xing  2008]  

•  Adapts  the  number  of  mixture  components  over  :me  

–  Mixture  components  can  die  out  

–  New  mixture  components  are  born  at  any  :me  

–  Retained  mixture  components  parameters  evolve  according  

to  a  Markovian  dynamics  

The  Recurrent  Chinese  Restaurant  Process  

φ

φ

  φ

Dish  eaten  at  table  3  at  :me  epoch  1  

OR  the  parameters  of  cluster  3  at  :me    epoch  1  

-­‐ Customers  at  :me  T=1  are  seated  as  before:  

-­‐   Choose  table  j  ∝  mj,1        and    Sample  x_{i  ~}  f(φ_j,1)   -­‐   Choose  a  new  table    K+1  ∝  α    

-­‐   Sample  φ_{K+1,1  ~}  G₀      and  Sample  x_{i  ~}  f(φ_K+1,1)   Genera:ve  Process  

φ

φ

  φ

T=2  

φ

φ

  φ

m'_1,1=2   m'_2,1=3   m'_3,1=1  

The  Recurrent  Chinese  Restaurant  Process  

φ

φ

  φ

T=2  

φ

φ

  φ

m'_1,1=2   m'_2,1=3   m'_3,1=1  

φ

φ

  φ

T=2  

φ

φ

  φ

α 6+

2 6+α

3 6+α

1

α α 6+

m'_1,1=2   m'_2,1=3   m'_3,1=1  

φ

φ

  φ

T=2  

φ

φ

  φ

α 6+

2

m'_1,1=2   m'_2,1=3   m'_3,1=1  

φ

φ

  φ

T=2  

φ

φ

  φ

Sample  φ_1,2  ~  P(.| φ_1,1)      

m'_1,1=2   m'_2,1=3   m'_3,1=1  

φ

φ

  φ

T=2  

φ

φ

  φ

α + +

+ 1 6

2

1 6+1+α

3 6+1+α

1

α α

+ 6+1

And  so  on  ……  

m'_1,1=2   m'_2,1=3   m'_3,1=1  

φ

φ

  φ

T=2  

φ

φ

  φ

At  the  end  of  epoch  2  

φ

Newly  born  cluster   Died  out  cluster  

m'_1,1=2   m'_2,1=3   m'_3,1=1  

φ

φ

  φ

T=2  

φ

φ

  φ

N_1,1=2   N_2,1=3   m'_3,1=1  

φ

T=3  

φ

φ

  φ

m'_4,2=1   m'_2,2=2  

m'_1,2=2  

Recurrent  Chinese  Restaurant  Process  

•  Can  be  extended  to  model  higher-­‐order   dependencies  

•  Can  decay  dependencies  over  :me  

–  Pseudo-­‐counts  for  table  k  at  :me  t  is  

History  size  

Decay  factory   Number  of  customers  sidng     at    table  K  at  :me  epoch  t-­‐h  

∑

=   -   -  

⎟

⎠

⎞

⎜

⎝

⎛

H  

h   k  t   h   h  

m

e

1   ,   ρ  

φ_2,1  

φ_1,1   φ_3,1  

T=1  

T=2  

φ

φ

  φ

m'_1,1=2   m'_2,1=3   m'_3,1=1  

φ

T=3  

φ

φ

  φ

∑

=  

-   -  

⎟

⎠

⎞

⎜

⎝

⎛

H  

h   k  t   h   h  

m

e

1   ,   ρ  

m'_2,3  

m'_2,3  =  

Tracking  Users  Interest  

Characterizing  User  Interests  

•  Short  term  vs  long-­‐term  

Jan   April   July   Oct  

Music  

Housing  

Furniture  

Buying  a  car  

Travel  plans  

Characterizing  User  Interests  

•  Short  term  vs  long-­‐term  

•  Latent  

Jan   April   July   Oct  

millage  

fast  

mortgage   Gaga  

seafood  

Barcelona  

used  

Problem  formula:on  

Input  

•  Queries  issued  by  the  user  or  tags  of  watched  content  

•  Snippet  of  page  examined  by  user  

•  Time  stamp  of  each  ac:on  (day  resolu:on)    

Output  

•     Users’  daily  distribu:on  over  interests  

•     Dynamic  interest  representa:on  

•     Online  and  scalable  inference  

•     Language  independent  

Flight   London   Hotel   weather    

School   Supplies   Loan   semester   classes  

registra:on   housing   rent  

Problem  formula:on  

Flight   London   Hotel   weather    

Travel  

Back   To  school  

finance   School  

Supplies   Loan   semester   classes  

registra:on   housing   rent   Input  

•  Queries  issued  by  the  user  or  tags  of  watched  content  

•  Snippet  of  page  examined  by  user  

•  Time  stamp  of  each  ac:on  (day  resolu:on)    

Output  

•     Users’  daily  distribu:on  over  interests  

•     Dynamic  interest  representa:on  

•     Online  and  scalable  inference  

•     Language  independent  

Problem  formula:on  

Flight   London   Hotel   weather    

Travel  

Back   To  school  

finance   School  

Supplies   Loan   semester   classes  

registra:on   housing   rent  

When  to  show  a  financing  ad?  

Problem  formula:on  

Flight   London   Hotel   weather    

Travel  

Back   To  school  

finance   School  

Supplies   Loan   semester   classes  

registra:on   housing   rent  

When  to  show  a  financing  ad?  

Problem  formula:on  

Flight   London   Hotel   weather    

Travel  

Back   To  school  

finance   School  

Supplies   Loan   semester   classes  

registra:on   housing   rent  

When  to  show  a  financing  ad?  

Problem  formula:on  

Flight   London   Hotel   weather    

Travel  

Back   To  school  

finance   School  

Supplies   Loan   semester   classes  

registra:on   housing   rent  

When  to  show  a  hotel  ad?  

Problem  formula:on  

Flight   London   Hotel   weather    

Travel  

Back   To  school  

finance   School  

Supplies   Loan   semester   classes  

registra:on   housing   rent  

When  to  show  a  hotel  ad?  

Problem  formula:on  

Flight   London   Hotel   weather    

Travel  

Back   To  school  

finance   School  

Supplies   Loan   semester   classes  

registra:on   housing   rent   Input  

•  Queries  issued  by  the  user  or  tags  of  watched  content  

•  Snippet  of  page  examined  by  user  

•  Time  stamp  of  each  ac:on  (day  resolu:on)    

Output  

•     Users’  daily  distribu:on  over  interests  

•     Dynamic  interest  representa:on  

•     Online  and  scalable  inference  

•     Language  independent  

Mixed-­‐Membership  Formula:on  

job     Career   Business   Assistant  

Hiring   Part-­‐:me   Recep:onist   Car    

Blue   Book   Kelley   Prices   Small   Speed  

large    

Bank   Online  

Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

Diet   Cars   Job   Finance  

Objects  

Mixtures   Degree  of   membership  

Job  Hiring       speed  price    part-­‐6me  Camry  

Career  opening     bonus  package  

card    diet  calories   loan  recipe  milk  

Weight  lb  kg    

In  Graphical  Nota:on  

In  Polya-­‐Urn  Representa:on  

•  Collapse  mul:nomial  variables:  

•  Fixed-­‐dimensional  Hierarchal  Polya-­‐Urn   representa:on  

–  Chinese  restaurant  franchise    

x  

x  

Food  Chicken  

job     Career   Business   Assistant   Hiring   Part-­‐:me  

Recep:o nist   Car    

Blue   Book   Kelley   Prices   Small   Speed   large  

Bank   Online   Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

Car  speed  offer   camry  accord  career  

Global  topics   trends

Topic    

word-­‐distribu:ons

User-­‐specific  topics  trends   (mixing-­‐vector)

User  interac:ons:  queries,  

keyword  from  pages  viewed

 Food  Chicken  

Car  speed  offer   camry  accord  career  

•   For  each  user  interac:on  

•     Choose  an  intent  from  local  distribu:on  

•  Sample  word  from  the  topic’s  word-­‐distribu:on    

• Choose  a  new  intent    ∝  λ    

•  Sample  a  new  intent  from  the  global  distribu:on  

•   Sample  word  from  the  new  topic  word-­‐

distribu:on     Genera:ve  Process  

………  

job     Career   Business   Assistant   Hiring   Part-­‐:me  

Recep:o nist   Car    

Blue   Book   Kelley   Prices   Small   Speed   large  

Bank   Online   Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

 Food  Chicken  

pizza  

Car  speed  offer   camry  accord  career  

•   For  each  user  interac:on  

•     Choose  an  intent  from  local  distribu:on  

•  Sample  word  from  the  topic’s  word-­‐distribu:on    

• Choose  a  new  intent    ∝  λ    

•  Sample  a  new  intent  from  the  global  distribu:on  

•   Sample  word  from  the  new  topic  word-­‐

distribu:on     Genera:ve  Process  

………  

job     Career   Business   Assistant   Hiring   Part-­‐:me  

Recep:o nist   Car    

Blue   Book   Kelley   Prices   Small   Speed   large  

Bank   Online   Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

 Food  Chicken  

pizza  

Car  speed  offer   camry  accord  career  

•   For  each  user  interac:on  

•     Choose  an  intent  from  local  distribu:on  

•  Sample  word  from  the  topic’s  word-­‐distribu:on    

• Choose  a  new  intent    ∝  λ    

•  Sample  a  new  intent  from  the  global  distribu:on  

•   Sample  word  from  the  new  topic  word-­‐

distribu:on     Genera:ve  Process  

………  

job     Career   Business   Assistant   Hiring   Part-­‐:me  

Recep:o nist   Car    

Blue   Book   Kelley   Prices   Small   Speed   large  

Bank   Online   Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

 Food  Chicken  

pizza    hiring  

Car  speed  offer   camry  accord  career  

•   For  each  user  interac:on  

•   Choose  an  intent  from  local  distribu:on  

•  Sample  word  from  the  topic’s  word-­‐distribu:on    

• Choose  a  new  intent    ∝  λ    

•  Sample  a  new  intent  from  the  global  distribu:on  

•   Sample  word  from  the  new  topic  word-­‐

distribu:on     Genera:ve  Process  

………  

job     Career   Business   Assistant   Hiring   Part-­‐:me  

Recep:o nist   Car    

Blue   Book   Kelley   Prices   Small   Speed   large  

Bank   Online   Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

 Food  Chicken  

pizza    millage  

Car  speed  offer   camry  accord  career  

•   For  each  user  interac:on  

•     Choose  an  intent  from  local  distribu:on  

•  Sample  word  from  topic’s  word-­‐distribu:on    

• Choose  a  new  intent    ∝  λ    

•  Sample  a  new  intent  from  the  global  distribu:on  

•   Sample  from  word  the  new  topic  word-­‐

distribu:on     Genera:ve  Process  

job     Career   Business   Assistant   Hiring   Part-­‐:me  

Recep:o nist   Car    

Blue   Book   Kelley   Prices   Small   Speed   large  

Bank   Online   Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

 Food  Chicken  

pizza    millage  

Car  speed  offer   camry  accord  career  

job     Career   Business   Assistant   Hiring   Part-­‐:me  

Recep:o nist   Car    

Blue   Book   Kelley   Prices   Small   Speed   large  

Bank   Online   Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

Problems

-­‐   Sta:c  Model  

-­‐   Does  not  evolve  user’s  interests  

-­‐   Does  not  evolve  the  global  trend  of  interests  

-­‐   Does  not  evolve  interest’s  distribu:on  over  terms    

 Food  Chicken  

pizza    millage  

Car  speed  offer   camry  accord  career  

job     Career   Business   Assistant   Hiring   Part-­‐:me  

Recep:o nist   Car    

Blue   Book   Kelley   Prices   Small   Speed   large  

Bank   Online   Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

At  6me  t   At  6me  t+1  

Build  a  dynamic  model   Connect  each  level    

using  a  RCRP  

At  6me  t   At  6me  t+1  

At  6me  t+2   At  6me  t+3  

User  1   process  

User  2   process  

User  3   process  

Global  

process   m   m'  

n   n'  

Which  :me  kernel  to    

use  at  each  level?  

Pseudo  counts

Decay  factor

 Food  Chicken  

pizza    millage  

Car  speed  offer   camry  accord  career  

At  6me  t  

Observa:on  1

-­‐ Popular  topics  at    :me  t  are  likely  to  be  popular  at  :me  t+1  

-  φ_k,t+1  is  likely  to  smoothly  evolve  from     φ_k,t    

At  6me  t+1  

job     Career   Business   Assistant   Hiring   Part-­‐:me  

Recep:o nist   Car    

Blue   Book   Kelley   Prices   Small   Speed   large  

Bank   Online   Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

 Food  Chicken  

pizza    millage  

Car  speed  offer   camry  accord  career  

At  6me  t   At  6me  t+1  

job     Career   Business   Assistant   Hiring   Part-­‐:me  

Recep:o nist   Car    

Blue   Book   Kelley   Prices   Small   Speed   large  

Bank   Online   Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

Observa:on  1

-­‐ Popular  topics  at    :me  t  are  likely  to  be  popular  at  :me  t+1  

-  φ_k,t+1  is  likely  to  smoothly  evolve  from     φ_k,t    

    Car   Al6ma   Accord   Book   Kelley   Prices   Small   Speed  

φk,t+1      ∼ Dir(β_k,t+1)   φ_k,t  

Car     Blue   Book   Kelley   Prices   Small   Speed   large  

Intui:on

Captures  current  trend  of   the  car  industry     (new  release  for  e.g.)  

~  

 Food  Chicken  

pizza    millage  

Car  speed  offer   camry  accord  career  

At  6me  t   At  6me  t+1  

Observa:on  2

-­‐   User  prior  at  :me  t+1  is  a  mixture  of  the  user  short  and   long  term  interest  

How  do  we  get  a  prior   that  captures  both  long  

and  short  term   interest?

job     Career   Business   Assistant   Hiring   Part-­‐:me  

Recep:o nist   Car    

Al:ma   Accord   Blue   Book   Kelley   Prices   Small   Speed  

Bank   Online   Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

All  

week  

job     Career   Business   Assistant  

Hiring   Part-­‐:me   Recep:onist   Car  

Blue   Book   Kelley   Prices   Small   Speed  

large  

Bank   Online  

Credit   Card   debt   porzolio  

Finance   Chase      

Recipe   Chocolate  

Pizza   Food   Chicken  

Milk   Bu{er   Powder  

month  

Time                  t                                  t+1                  

Food   Chicken   pizza  

recipe   job   hiring  

Part-­‐:me   Opening   salary  

food   chicken   Pizza   millage   Kelly  

recipe   cuisine  

Diet   Cars   Job   Finance  

Prior  for  user   ac:ons  at  :me  t   μ  

μ²   μ³  

Long-­‐term

short-­‐term