Introduction to tidylda
Note: for code examples, see README.md
Introduction to the tidylda package
tidylda implements Latent Dirichlet Allocation using
style conventions from the tidyverse and tidymodels.
tidylda’s Gibbs sampler is written in C++ for performance
and offers several novel features. It also has methods for sampling from
the posterior of a trained model, for more traditional Bayesian
analyses.
tidylda’s Gibbs sampler has several unique features, described below.
Non-uniform initialization: Most LDA Gibbs samplers initialize by assigning words to topics and topics to documents (i.e., construct the Cd and Cv matrices) by sampling from a uniform distribution. This ensures initialization without incorporating any prior information. tidylda incorporates the priors in its initialization. It begins by drawing P(topic|document) and P(word|topic) from Dirichlet distributions with parameters α and η, respectively. Then tidylda uses the above probabilities to construct P(topic|word, document) and makes a single run of the Gibbs sampler to initialize Cd and Cv. This non-uniform initialization powers transfer learning with LDA (tLDA), described elsewhere, by starting a Gibbs run near where the previous run left off. For initial models, it uses the user’s prior information to tune where sampling starts.
Flexible priors: tidylda has multiple options for setting LDA priors. Users may set scalar values for α and η to construct symmetric priors. Users may also choose to construct vector priors for both α and η for a full specification of LDA. Additionally, tidylda allows users to set a matrix prior for η, enabled by its implementation of tLDA. This lets users to set priors over word-topic relationships informed by expert input. The best practices for encoding expert input in this manner are not yet well studied. Nevertheless, this capability makes tidylda unique among LDA implementations.
Burn in iterations and posterior averaging: Most LDA
Gibbs samplers construct posterior estimates of Θ and B from Cd and
Cv’s
values of the final iteration of sampling, effectively using a single
sample. This is inconsistent with best practices from Bayesian
statistics, which is to average over many samples from a stable
posterior. tidylda enables averaging across multiple samples of
the posterior with the burnin argument. When
burnin is set to a positive integer, tidylda
averages the posterior across all iterations larger than
burnin. For example, if iterations is 200 and
burnin is 150, tidylda will return a posterior
estimate that is an average of the last 50 sampling iterations. This
ensures that posterior estimates are more likely to be representative
than any single sample.
Transfer learning with tLDA: Finally, tidylda’s Gibbs sampler enables transfer learning with tLDA. The full specification of tLDA and details on its implementation in tidylda are described briefly in the tLDA vignette and more thoroughly in forthcoming research.
Tidy Methods
tidylda’s construction follows Conventions of R Modeling
Packages [@tidymodelsbook]. In
particular, it contains methods for print,
summary, glance, tidy, and
augment, consistent with other “tidy” packages. These
methods are briefly described below.
print,summary, andglancereturn various summaries of the contents of atidyldaobject, into which an LDA model trained with tidylda is stored.tidyreturns the contents of Θ, B, or Λ (stored astheta,beta, andlambdarespectively), as specified by the user, formatted as a tidytibble, instead of a numeric matrix.augmentappends model outputs to observational-level data. Taking the cue from tidytext, “observational-level” data is one row per word per document. Therefore, the key statistic used byaugmentis P(topic|word, document). tidylda calculates this as Λ × P(word|document), where $P(\text{word}|\text{document}_d) = \frac{\boldsymbol{x}_d}{\sum_{v=1}^V x_{d,v}}$.
Other Notable Features
tidylda has three evaluation metrics for topic models, two
goodness-of-fit measures—R2 as implemented from mvrsquared
and the log likelihood of the model given the data—and one coherence
measure—probabilistic coherence. A flag set during model fitting with
calc_r2 = TRUE1 will return a model with an R2 statistic. Similarly,
the log likelihood of the model, given the data, is calculated at each
Gibbs iteration if the user selects calc_likelihood = TRUE
during model fitting.
The coherence measure is called probabilistic coherence. (See vignette on probabilistic coherence.) Probabilistic coherence is bound between -1 and 1. Values near zero indicate that the top words in a topic are statistically independent from each other. Positive values indicate that the top words in a topic are positively correlated in a statistically-dependent manner. Negative values indicate that the words in a topic are negatively correlated with each other in a statistically-dependent manner. (In practice, negative values tend to be very near zero.)
tidylda enables traditional Bayesian uncertainty
quantification by sampling from the posterior. The posterior
distribution for θd is
Dirichlet(Cdd + α)
and the posterior distribution for βk is
Dirichlet(Cvk + η)
(or Dirichlet(Cvk + ηk)
for tLDA). tidylda enables a posterior method for
tidylda objects, allowing users to sample from the
posterior to quantify uncertainty for estimates of estimated
parameters.
tidylda uses one of two calculations for predicting topic distributions (i.e., $\hat{\boldsymbol\theta}_d$) for new documents. The first, and default, is to run the Gibbs sampler, constructing a new Cd for the new documents but without updating topic-word distributions in B. The second uses a dot product as described in Appendix 1. tidylda actually uses the dot product prediction combined with the non-uniform initialization—described above—to initialize Cd when predicting using the Gibbs sampler.
Discussion
While many other topic modeling packages exist, tidylda is very user friendly and brings novel features. Its user friendliness comes from compatibility with the tidyverse. And tidylda includes tLDA and other methods contained in the previous chapters of this dissertation. It also has methods for sampling from the posterior of a trained model, for more traditional Bayesian analyses. tidylda’s Gibbs sampler is written in C++ for performance.
Installation
You can install the development version from GitHub with:
Example
##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack### Initial set up ---
# load some documents
docs <- nih_sample
# tokenize using tidytext's unnest_tokens
tidy_docs <- docs |>
select(APPLICATION_ID, ABSTRACT_TEXT) |>
unnest_tokens(output = word,
input = ABSTRACT_TEXT,
stopwords = stop_words$word,
token = "ngrams",
n_min = 1, n = 2) |>
count(APPLICATION_ID, word) |>
filter(n>1) #Filtering for words/bigrams per document, rather than per corpus
tidy_docs <- tidy_docs |> # filter words that are just numbers
filter(! stringr::str_detect(tidy_docs$word, "^[0-9]+$"))
# append observation level data
colnames(tidy_docs)[1:2] <- c("document", "term")
# turn a tidy tbl into a sparse dgCMatrix
# note tidylda has support for several document term matrix formats
d <- tidy_docs |>
cast_sparse(document, term, n)
# let's split the documents into two groups to demonstrate predictions and updates
d1 <- d[1:50, ]
d2 <- d[51:nrow(d), ]
# make sure we have different vocabulary for each data set to simulate the "real world"
# where you get new tokens coming in over time
d1 <- d1[, colSums(d1) > 0]
d2 <- d2[, colSums(d2) > 0]
### fit an intial model and inspect it ----
set.seed(123)
lda <- tidylda(
data = d1,
k = 10,
iterations = 200,
burnin = 175,
alpha = 0.1, # also accepts vector inputs
eta = 0.05, # also accepts vector or matrix inputs
optimize_alpha = FALSE, # experimental
calc_likelihood = TRUE,
calc_r2 = TRUE, # see https://arxiv.org/abs/1911.11061
return_data = FALSE
)
# did the model converge?
# there are actual test stats for this, but should look like "yes"
qplot(x = iteration, y = log_likelihood, data = lda$log_likelihood, geom = "line") +
ggtitle("Checking model convergence")## Warning: `qplot()` was deprecated in ggplot2 3.4.0.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
## # A tibble: 1 × 5
## num_topics num_documents num_tokens iterations burnin
## <int> <int> <int> <dbl> <dbl>
## 1 10 50 1524 200 175## A Latent Dirichlet Allocation Model of 10 topics, 50 documents, and 1524 tokens:
## tidylda(data = d1, k = 10, iterations = 200, burnin = 175, alpha = 0.1,
## eta = 0.05, optimize_alpha = FALSE, calc_likelihood = TRUE,
## calc_r2 = TRUE, return_data = FALSE)
##
## The model's R-squared is 0.2692
## The 5 most prevalent topics are:
## # A tibble: 10 × 4
## topic prevalence coherence top_terms
## <dbl> <dbl> <dbl> <chr>
## 1 4 11.6 0.134 cdk5, natural, determine, calpain, adaptive, ...
## 2 6 11.3 0.0745 diabetes, specific, cells, numeracy, lung, ...
## 3 7 10.9 0.0685 cancer, sleep, imaging, cells, rb, ...
## 4 9 10.7 0.189 core, research, data, ppg, imaging, ...
## 5 3 10.6 0.347 cns, infection, cell, cells, brain, ...
## # ℹ 5 more rows
##
## The 5 most coherent topics are:
## # A tibble: 10 × 4
## topic prevalence coherence top_terms
## <dbl> <dbl> <dbl> <chr>
## 1 8 7.28 0.567 cmybp, function, injury, fragment, 29 kda, ...
## 2 3 10.6 0.347 cns, infection, cell, cells, brain, ...
## 3 10 10.0 0.309 sud, plasticity, risk, factors, risk factors, ...
## 4 1 7.17 0.259 stiffening, wall, pd, effects, nmdar, ...
## 5 5 10.1 0.201 dcis, v4, activity, cancer, genetic, ...
## # ℹ 5 more rows## # A tibble: 10 × 4
## topic prevalence coherence top_terms
## <dbl> <dbl> <dbl> <chr>
## 1 1 7.17 0.259 stiffening, wall, pd, effects, nmdar, ...
## 2 2 10.3 0.173 mitochondrial, research, disparities, redox, stud…
## 3 3 10.6 0.347 cns, infection, cell, cells, brain, ...
## 4 4 11.6 0.134 cdk5, natural, determine, calpain, adaptive, ...
## 5 5 10.1 0.201 dcis, v4, activity, cancer, genetic, ...
## 6 6 11.3 0.0745 diabetes, specific, cells, numeracy, lung, ...
## 7 7 10.9 0.0685 cancer, sleep, imaging, cells, rb, ...
## 8 8 7.28 0.567 cmybp, function, injury, fragment, 29 kda, ...
## 9 9 10.7 0.189 core, research, data, ppg, imaging, ...
## 10 10 10.0 0.309 sud, plasticity, risk, factors, risk factors, ...## # A tibble: 500 × 3
## document topic theta
## <chr> <dbl> <dbl>
## 1 8574224 1 0.00238
## 2 8574224 2 0.00238
## 3 8574224 3 0.00238
## 4 8574224 4 0.00238
## 5 8574224 5 0.00238
## 6 8574224 6 0.00238
## 7 8574224 7 0.00238
## 8 8574224 8 0.00238
## 9 8574224 9 0.00333
## 10 8574224 10 0.978
## # ℹ 490 more rows## # A tibble: 15,240 × 3
## topic token beta
## <dbl> <chr> <dbl>
## 1 1 adolescence 0.0000979
## 2 1 age 0.0000979
## 3 1 application 0.0000979
## 4 1 depressive 0.0000979
## 5 1 disorder 0.0000979
## 6 1 emotionality 0.0000979
## 7 1 information 0.0000979
## 8 1 mdd 0.0000979
## 9 1 onset 0.00394
## 10 1 onset mdd 0.0000979
## # ℹ 15,230 more rows## # A tibble: 15,240 × 3
## topic token lambda
## <dbl> <chr> <dbl>
## 1 1 adolescence 0.00737
## 2 1 age 0.00875
## 3 1 application 0.00738
## 4 1 depressive 0.0193
## 5 1 disorder 0.0193
## 6 1 emotionality 0.0193
## 7 1 information 0.00641
## 8 1 mdd 0.0107
## 9 1 onset 0.301
## 10 1 onset mdd 0.0193
## # ℹ 15,230 more rows## Joining with `by = join_by(document, term, n)`## # A tibble: 4,566 × 4
## document term n topic
## <chr> <chr> <int> <int>
## 1 8574224 adolescence 1 10
## 2 8646901 adolescence 1 10
## 3 8689019 adolescence 1 10
## 4 8705323 adolescence 1 10
## 5 8574224 age 1 10
## 6 8705323 age 1 10
## 7 8757072 age 1 10
## 8 8823186 age 1 10
## 9 8574224 application 1 2
## 10 8605875 application 1 2
## # ℹ 4,556 more rows### predictions on held out data ---
# two methods: gibbs is cleaner and more technically correct in the bayesian sense
p_gibbs <- predict(lda, new_data = d2[1, ], iterations = 100, burnin = 75)
# dot is faster, less prone to error (e.g. underflow), noisier, and frequentist
p_dot <- predict(lda, new_data = d2[1, ], method = "dot")
# pull both together into a plot to compare
tibble(topic = 1:ncol(p_gibbs), gibbs = p_gibbs[1,], dot = p_dot[1, ]) |>
pivot_longer(cols = gibbs:dot, names_to = "type") |>
ggplot() +
geom_bar(mapping = aes(x = topic, y = value, group = type, fill = type),
stat = "identity", position="dodge") +
scale_x_continuous(breaks = 1:10, labels = 1:10) +
ggtitle("Gibbs predictions vs. dot product predictions")
### Augment as an implicit prediction using the 'dot' method ----
# Aggregating over terms results in a distribution of topics over documents
# roughly equivalent to using the "dot" method of predictions.
augment_predict <-
augment(lda, tidy_docs, "prob") |>
group_by(document) |>
select(-c(document, term)) |>
summarise_all(function(x) sum(x, na.rm = T))## Joining with `by = join_by(document, term, n)`## Adding missing grouping variables: `document`# reformat for easy plotting
augment_predict <-
as_tibble(t(augment_predict[, -c(1,2)]), .name_repair = "minimal")
colnames(augment_predict) <- unique(tidy_docs$document)
augment_predict$topic <- 1:nrow(augment_predict) |> as.factor()
compare_mat <-
augment_predict |>
select(
topic,
augment = matches(rownames(d2)[1])
) |>
mutate(
augment = augment / sum(augment), # normalize to sum to 1
dot = p_dot[1, ]
) |>
pivot_longer(cols = c(augment, dot))
ggplot(compare_mat) +
geom_bar(aes(y = value, x = topic, group = name, fill = name),
stat = "identity", position = "dodge") +
labs(title = "Prediction using 'augment' vs 'predict(..., method = \"dot\")'")
# Not shown: aggregating over documents results in recovering the "tidy" lambda.
### updating the model ----
# now that you have new documents, maybe you want to fold them into the model?
lda2 <- refit(
object = lda,
new_data = d, # save me the trouble of manually-combining these by just using d
iterations = 200,
burnin = 175,
calc_likelihood = TRUE,
calc_r2 = TRUE
)
# we can do similar analyses
# did the model converge?
qplot(x = iteration, y = log_likelihood, data = lda2$log_likelihood, geom = "line") +
ggtitle("Checking model convergence")
## # A tibble: 1 × 5
## num_topics num_documents num_tokens iterations burnin
## <int> <int> <int> <dbl> <dbl>
## 1 10 99 2962 200 175## A Latent Dirichlet Allocation Model of 10 topics, 99 documents, and 2962 tokens:
## refit.tidylda(object = lda, new_data = d, iterations = 200, burnin = 175,
## calc_likelihood = TRUE, calc_r2 = TRUE)
##
## The model's R-squared is 0.1417
## The 5 most prevalent topics are:
## # A tibble: 10 × 4
## topic prevalence coherence top_terms
## <dbl> <dbl> <dbl> <chr>
## 1 9 14.4 0.0431 research, core, data, hiv, center, ...
## 2 6 12.4 0.0781 cells, cell, lung, diabetes, specific, ...
## 3 2 12.3 0.0785 research, program, mitochondrial, health, cancer, …
## 4 3 11.7 0.210 infection, cns, cell, cells, brain, ...
## 5 7 10.0 0.102 cancer, tumor, sleep, imaging, cells, ...
## # ℹ 5 more rows
##
## The 5 most coherent topics are:
## # A tibble: 10 × 4
## topic prevalence coherence top_terms
## <dbl> <dbl> <dbl> <chr>
## 1 8 7.19 0.575 cmybp, injury, function, fragment, 29 kda, ...
## 2 3 11.7 0.210 infection, cns, cell, cells, brain, ...
## 3 10 6.93 0.152 risk, factors, sud, plasticity, risk factors, ...
## 4 1 7.46 0.120 muscle, wall, stiffening, pd, study, ...
## 5 7 10.0 0.102 cancer, tumor, sleep, imaging, cells, ...
## # ℹ 5 more rows## A Latent Dirichlet Allocation Model of 10 topics, 50 documents, and 1524 tokens:
## tidylda(data = d1, k = 10, iterations = 200, burnin = 175, alpha = 0.1,
## eta = 0.05, optimize_alpha = FALSE, calc_likelihood = TRUE,
## calc_r2 = TRUE, return_data = FALSE)
##
## The model's R-squared is 0.2692
## The 5 most prevalent topics are:
## # A tibble: 10 × 4
## topic prevalence coherence top_terms
## <dbl> <dbl> <dbl> <chr>
## 1 4 11.6 0.134 cdk5, natural, determine, calpain, adaptive, ...
## 2 6 11.3 0.0745 diabetes, specific, cells, numeracy, lung, ...
## 3 7 10.9 0.0685 cancer, sleep, imaging, cells, rb, ...
## 4 9 10.7 0.189 core, research, data, ppg, imaging, ...
## 5 3 10.6 0.347 cns, infection, cell, cells, brain, ...
## # ℹ 5 more rows
##
## The 5 most coherent topics are:
## # A tibble: 10 × 4
## topic prevalence coherence top_terms
## <dbl> <dbl> <dbl> <chr>
## 1 8 7.28 0.567 cmybp, function, injury, fragment, 29 kda, ...
## 2 3 10.6 0.347 cns, infection, cell, cells, brain, ...
## 3 10 10.0 0.309 sud, plasticity, risk, factors, risk factors, ...
## 4 1 7.17 0.259 stiffening, wall, pd, effects, nmdar, ...
## 5 5 10.1 0.201 dcis, v4, activity, cancer, genetic, ...
## # ℹ 5 more rowsI plan to have more analyses and a fuller accounting of the options of the various functions when I write the vignettes.
See the “Issues” tab on GitHub to see planned features as well as bug fixes.
If you have any suggestions for additional functionality, changes to functionality, changes to arguments or other aspects of the API please let me know by opening an issue on GitHub or sending me an email: jones.thos.w at gmail.com.
Users can calculate R2 after a model is fit by using the mvrsquared package or calling
tidylda:::calc_lda_rsquared.calc_lda_rsquaredis an internal function to tidylda, requiring the package name followed by three colons, as is R’s standard.↩︎