Interactive & Dynamic Statistical Web Graphics

• Why interactive & dynamic graphics? They help us:
  • Find high-dimensional, abstract relationships in data that may otherwise go unnoticed
  • Diagnose models by plotting them in the data space (Wickham, Cook, & Hofmann 2015)
  • Explore and understand complicated statistical model fit(s)
  • Communicate/share our work with others in a compelling way
• Why web-based?
  • simple to share, portable (web browser)
  • encourages composability
  • guide your audience by providing links to interesting selections/states

• Topic models are a collection of statistical models with the common goal of finding hidden structure in a collection of text documents.
• Basic example: Given a document discussing 'sports', you're more likely to see the word 'baseball' in that document compared to a document discussing 'music' (and vice-versa for 'guitar').
• Documents usually don't have a clear "topic", but we can develop models with latent RV to "discover topics".
• Latent Dirichlet Allocation (LDA) is a topic model which allows documents to be mixtures of topics (Blei, Ng, Jordan; 2003).

The Generative Model

1. Choose # of topics K. Let V be # of unique words (vocabulary).
2. For each document d∈{1,...,D}, draw Θd∼Dir(α) where Θd=(θ1,...,θK)>0 and ∑Ki=1θi=1
3. For each topic k∈{1,...,K}, draw Φk∼Dir(β) where Φk=(ϕ1,...,ϕV)>0 and ∑Ki=1ϕi=1
4. Let Nd be # of words in doc d and n∈{1,…,Nd}. For each word wd,n:
   • Draw a (latent) topic, zd,n∼Mult(1,Θd)
   • Draw a word given topic, wd,n∼Mult(1,Φzd,n)

Model fitting

• Griffiths & Steyvers (2004) derive a collapsed Gibbs sampler. Implemented in R packages LDAtools (Shirley & Sievert, 2013) and lda (Chang, 2015).
• Wide array of fitting algorithms available in topicmodels (Grun & Hornik, 2011) and mallet (Mimno, 2013).

• In the digital humanities (& elsewhere), LDA is often used to "discover topics" in a large collection of text documents.
• How are researchers supposed to interpret topics? We can't possibly examine each pmf.
• "Overview first, then zoom & filter, then detail on demand" (Schneiderman, 1996)

• Numerous interactive systems allow users to select a topic z, then list top ~30 words based on p(w|z) (Gardner et al., 2010; Chaney and Blei, 2012; Snyder et al., 2013).
• But, words likely to occur overall are also likely to occur for a given topic!
• Taddy (2011) proposed to rank terms by lift=p(w|z)/p(w)
• But if p(w) is small, lift is large!
• Bischof and Airoldi (2012) propose a new model to directly estimate an average frequency and exclusivity to a given topic.
• Sievert & Shirley (2014) propose choosing 0<λ<1, for: relevance(λ)=λ∗p(w|z)+(1−λ)∗lift

• We expect the optimal value of λ to vary across data.
• LDAvis allows users to interactively alter rankings by changing λ

• People who use LDA and want a tool for interpreting topics.
• Combined LDAvis and pyLDAvis currently have 356 stars on GitHub (a measure of popularity).
• I know a number of consultants, industry workers, and educators using it for exploration, presentation, and teaching. Here are a few videos.
• Dr. Grant Arndt in the Department of Anthropology at Iowa State University (and his research assistant) are using it as a research aid.

Why is this important?

• We're helping analysts to gain insight from sophisticated statistical models, communicate their results, and teach others.

• Producing interactive and dynamic web graphics from "scratch" is time-consuming, but very powerful, and flexible.
• How do we best enable statisticians to create their own interactive dynamic web graphics?
• I've worked on two R packages in this direction: animint and plotly.
• Both can translate ggplot2 (Wickham, 2009) graphics to a web-based format (SVG/canvas) with some basic interactivity.
• ggplot2 is wildly successful thanks to its implementation of a "Grammar of Graphics" (Wilkinson, 1999).
• animint extends this grammar in a novel direction to enable a constrained form of "linked views" (Hocking et. al., 2015).

library(ggplot2)
p <- qplot(data = iris, x = Sepal.Width, y = Sepal.Length, color = Species)
p

library(plotly)
ggplotly(p)

library(animint)
structure(list(plot = p), class = "animint")