Detection of fashion trends and seasonal cycles through client feedback

KDD 2016 WORKSHOP: MACHINE LEARNING MEETS FASHION

Roberto Sanchis-Ojeda, Daragh Sibley, Paolo Massimi

Contents

1. Intro2. The normal approximation3. Generalized linear mixed effect models4. Application to Stitch Fix’s style feedback data

Client Ci

Style Sj

Feedback Yij

Positive , Negative

1 , 0

2. The normal approximation

Simple mathematical law …

Sum of Bernoulli = Binomial

Positive response ratio

Sum of Bernoulli -> Gaussian

pi = ∑j Yij / N

Large N

N = 10 N = 100

… that can be very helpful …

p(time) = 0.7 - 0.2 * time p(time) = 0.5

… but certain assumptions breakLength of every time interval

● Poor temporal resolution

● p no longer constant

● Few interactions, normal approximation breaks

● Slower computation

Large Small

3. Generalized linear mixed effect models

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

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

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)

A GLMM linear trend classifier

logit(p) ~ X + Z +

X and Z have an offset and time as featuresThere is a slope per style id, with 95% CI

Out of fashion

CI all negative

Trending

CI all positive

The results

The results

1

2

3

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)

The results

The results

1

2

4. Application to Stitch Fix’s style feedback data

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

One great example of seasonal style

Jan Apr July Oct Dec

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.

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

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 )

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