17 Questions
What is the main purpose of using coherence measures in topic modeling?
To judge the relative quality of a fit
Why is the weighted geometric average not intuitively interpretable as probability?
Weighted geometric average is not intuitively interpretable as probability.
Explain the basic idea behind coherence measures in topic modeling.
In a coherent topic, the top words cooccur in the same documents.
What is the purpose of using a reference corpus like Wikipedia in coherence computation?
To compute coherence within the original corpus or a reference corpus such as Wikipedia.
Why is topic model evaluation considered difficult?
There is a disconnect between how topic models are evaluated and why we expect topic models to be useful.
What is the purpose of manual inspection of the most important words in each topic in topic modeling?
To evaluate the interpretability of topic models.
How is the evaluation of topic modeling often done in relation to perplexity and coherence?
Perplexity and coherence are common evaluation metrics used in topic modeling.
Explain the word intrusion task in the context of topic modeling evaluation.
It involves injecting an artificial word into the most important words of a topic to test if a user can identify it.
What are some caveats to using the likelihood of observing training data as a quality measure in probabilistic topic models?
Overfitting, model complexity, comparability, computational problems
What is the relationship between topic modeling and cluster analysis?
Topics in topic modeling are often comparable to cluster centers in cluster analysis.
What is the entropy of a sample and how is it related to cluster evaluation?
The entropy is the minimum average number of bits required to encode the values of a sample with an idealized compression technique. It relates to cluster evaluation through mutual information.
Why is evaluation a major challenge in topic modeling?
Subjective quality does not always agree with objective quality measures in evaluating topic models.
How does cross-entropy in probability relate to comparing two probability distributions?
Cross-entropy compares two probability distributions by quantifying the difference between them.
What does the Kullback-Leibler divergence measure in probability distributions?
The Kullback-Leibler divergence measures the excess entropy or difference between two probability distributions.
How does the interpretability of topic models relate to the ability to explain held out documents with existing clusters?
The interpretability is assessed based on how well the model can explain held out documents with high probability.
What is the geometric average in probability and how does it relate to encoding data?
The geometric average is the number of bits of 'information' in each object. It relates to encoding data by providing a measure of the average information content per object.
Why is it noted that in cross-entropy, we do not know the true probabilities?
In cross-entropy, we do not know the true probabilities because we compare two distributions without having access to the actual underlying probabilities.
Study Notes
Weighted Geometric Average
- Not suitable for interpreting probability
- Has been used to judge the relative quality of a fit
Coherence
- Measures the quality of a topic model
- Based on the idea that in a coherent topic, the top words co-occur in the same documents
- Computed within the original corpus or a reference corpus such as Wikipedia
- Several variants of this measure have been discussed in literature
Evaluation of Topic Models
- Difficult to evaluate due to disconnect between how topic models are evaluated and why they are expected to be useful
- Evaluation methods include:
- Manual inspection of top words in each topic
- Perplexity and coherence
- Secondary task evaluation (e.g., classification, IR)
- Ability to explain held-out documents with existing clusters
- Word intrusion task
- Topic intrusion task
Relation to Cluster Analysis
- Topics are comparable to cluster centers
- Documents may belong to multiple topics
- Algorithms share ideas, such as EM
- Algorithms contain special adaptations for text (e.g., sparsity, priors)
- Computationally expensive and scalable
- Evaluation is a major challenge, similar to clustering
- Subjective quality does not always agree with quality measures
Evaluation of Probabilistic Topic Models
- Compute probabilities for observing documents
- Training involves maximizing the likelihood of observing training data
- Challenges in using likelihood as a quality measure:
- Overfitting
- Model complexity
- Comparability issues
- Computational problems when approximating reference probabilities
Shannon Entropy
- Measures the minimum average number of bits required to encode values of an infinite sample
- Intuition: number of bits of "information" in each object
- Examples:
- Fair coin toss: 1 bit
- Fair dice: 3.32 bits
- Two dice: 5.64 bits
- Sum of two dice: 3.32 bits
- Uniform 2...12: 3.58 bits
Cross-Entropy
- Compares two probability distributions
- Intuition: encode data distributed as Q with the encoding scheme obtained by P
- Related to Kullback-Leibler divergence, which is the excess entropy
- Does not require knowledge of true probabilities
Explore different evaluation methods used in topic modeling, such as manual inspection of important words, perplexity, coherence, secondary task evaluation, and the word intrusion task. Understand how to assess the ability of topic models to explain held out documents and identify intruder words.
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