Slides of my presentation at the Machine Learning meets Fashion workshop of the KDD 2016 conference. https://kddfashion2016.mybluemix.net/

1. Detection of fashion trends
and seasonal cycles through
client feedback
KDD 2016 WORKSHOP: MACHINE LEARNING MEETS FASHION
Roberto Sanchis-Ojeda, Daragh Sibley, Paolo Massimi

2. Contents
1. Intro
2. The normal approximation
3. Generalized linear mixed effect models
4. Application to Stitch Fix’s style feedback data

7. Client Ci
Style Sj
Feedback Yij
Positive , Negative
1 , 0

8. 2. The normal
approximation

9. Simple mathematical law …
Sum of Bernoulli = Binomial
Positive response ratio
Sum of Bernoulli -> Gaussian
pi
= ∑j
Yij
/ N
Large N
N = 10 N = 100

10. … that can be very helpful …
p(time) = 0.7 - 0.2 * time p(time) = 0.5

11. … but certain assumptions break
Length of every time interval
● Poor temporal resolution
● p no longer constant
● Few interactions, normal
approximation breaks
● Slower computation
Large Small

12. 3. Generalized
linear mixed
effect models

13. Categorical aggregation
Bernoulli
Feedback Yij
0 or 1
Binomial
(N0
, N1
)
(34, 27)
logit(p) ~ time + style_color + style_group
Group by each feature to make sure that p is approximately constant within
Binomial draw. Now time can be aggregated to an arbitrarily small time scale

14. Statistical methods with Bernoulli variables
● Pros:
○ Simple, flexible
○ Well studied technique
● Cons:
○ Large dataset
○ Large number of features
○ Scalability problems
● Pros:
○ Smaller dataset
○ Faster computation
○ Natural regularization that
helps with non-uniform data
● Cons:
○ Requires a more complex
ETL and analysis process.
Logistic Regression Models Generalized Linear Mixed Models

15. Simulating linear fashion trends
1000
random
styles Si
in
inventory
Interacting
with a large
uniform set
of clients
3 interactions
per day for
two years with
probability pi
pi
= pi,o
+ mi
* time
pi,o
~ N(0.6, 0.1) mi
~ U(-0.1, 0.1)

16. A GLMM linear trend classifier
logit(p) ~ X + Z +
X and Z have an offset and time as features
There is a slope per style id, with 95% CI
Out of fashion
CI all negative
Trending
CI all positive

17. The results

18. The results
1
2
3

19. Simulating cyclical seasonal trends
1000
random
styles Si
in
inventory
Interacting
with a large
uniform set
of clients
3 interactions
per day for
two years with
probability pi
pi
= pi,o
+ Ai
* cos(2 (time - t0
))
pi,o
~ N(0.6, 0.1) Ai
~ U(0, 0.1) t0
~ U(0, 1)

20. The results

21. The results
1
2

22. 4. Application to
Stitch Fix’s style
feedback data

23. Discovering cyclical seasonal trends
Thousands
of real
styles Si
in
inventory
Interacting
with a large
uniform set
of clients
Use the style feedback as
a probe for seasonality

24. One great example of seasonal style
Jan Apr July Oct Dec

25. Conclusions
● Defining client feedback as a binary variable simplifies the
statistical analysis of trends
● The normal approximation is a useful tool but lacks the right
level of flexibility, and its assumptions are easily broken.
● Binomial data can be fit with generalized linear mixed effect
models, and the random effect coefficients can be used to
classify trends on styles.
● Our application to Stitch Fix data proves that the method
has real business applications.

27. Examples of binarized feedback
● Website feedback:
○ No Click on Picture = Negative = 0
○ Click on Picture = Positive = 1
● Style feedback:
○ (Hate it, Just ok) = Negative = 0
○ (Like it, Love it) = Positive = 1
● Numerical feedback 1, … , N:
○ 1, … , N/2 = Negative = 0
○ N/2, … , N = Positive = 1

28. Linearizing the cosine term
pi
= pi,o
+ Ai
* cos( 2 ( time - t0
) )
cos( - ) = cos( ) * cos( ) + sin( ) * sin( )
pi
= pi,o
+ Bi
* cos( 2 * time ) + Ci
* sin( 2 * time )

29. A GLMM seasonal trend classifier
logit(p) ~ X + Z +
X and Z have an offset and cosine
and sine of 2 by time as features
There are two temporal coefficients
per style id, with 95% CI
Non-seasonal
CI all comp. with 0 Any other case
Seasonal