propensity score matching for categorical - statistics

Can I do propensity score matching if my data are categorical? Let say my independent variable are: education (primary, secondary, college), has children (yes,no), wealth index (rich, middle, poor), accessibility (difficult, easy). Or can I make it dummy? But if yes, I think it's difficult to match the cases.
Thank you!

Propensity score matching doesn't depend on the variable type of the covariates. You can estimate a logistic regression model for the propensity score and then match on the predicted values for each unit. The whole point of propensity score matching is to reduce your covariate set to a single numerical summary: the propensity score. So it's not hard for a simple matching algorithm to match on the propensity score. Check out the MatchIt package in R if you want to perform propensity score matching. Note that like all statistical methods, not knowing what you're doing can make your results invalid, so try to consult with an expert as your proceed.

Related

Confusion matrix for LDA

I’m trying to check the performance of my LDA model using a confusion matrix but I have no clue what to do. I’m hoping someone can maybe just point my in the right direction.
So I ran an LDA model on a corpus filled with short documents. I then calculated the average vector of each document and then proceeded with calculating cosine similarities.
How would I now get a confusion matrix? Please note that I am very new to the world of NLP. If there is some other/better way of checking the performance of this model please let me know.
What is your model supposed to be doing? And how is it testable?
In your question you haven't described your testable assessment of the model the results of which would be represented in a confusion matrix.
A confusion matrix helps you represent and explore the different types of "accuracy" of a predictive system such as a classifier. It requires your system to make a choice (e.g. yes/no, or multi-label classifier) and you must use known test data to be able to score it against how the system should have chosen. Then you count these results in the matrix as one of the combination of possibilities, e.g. for binary choices there's two wrong and two correct.
For example, if your cosine similarities are trying to predict if a document is in the same "category" as another, and you do know the real answers, then you can score them all as to whether they were predicted correctly or wrongly.
The four possibilities for a binary choice are:
Positive prediction vs. positive actual = True Positive (correct)
Negative prediction vs. negative actual = True Negative (correct)
Positive prediction vs. negative actual = False Positive (wrong)
Negative prediction vs. positive actual = False Negative (wrong)
It's more complicated in a multi-label system as there are more combinations, but the correct/wrong outcome is similar.
About "accuracy".
There are many kinds of ways to measure how well the system performs, so it's worth reading up on this before choosing the way to score the system. The term "accuracy" means something specific in this field, and is sometimes confused with the general usage of the word.
How you would use a confusion matrix.
The confusion matrix sums (of total TP, FP, TN, FN) can fed into some simple equations which give you, these performance ratings (which are referred to by different names in different fields):
sensitivity, d' (dee-prime), recall, hit rate, or true positive rate (TPR)
specificity, selectivity or true negative rate (TNR)
precision or positive predictive value (PPV)
negative predictive value (NPV)
miss rate or false negative rate (FNR)
fall-out or false positive rate (FPR)
false discovery rate (FDR)
false omission rate (FOR)
Accuracy
F Score
So you can see that Accuracy is a specific thing, but it may not be what you think of when you say "accuracy"! The last two are more complex combinations of measure. The F Score is perhaps the most robust of these, as it's tuneable to represent your requirements by combining a mix of other metrics.
I found this wikipedia article most useful and helped understand why sometimes is best to choose one metric over the other for your application (e.g. whether missing trues is worse than missing falses). There are a group of linked articles on the same topic, from different perspectives e.g. this one about search.
This is a simpler reference I found myself returning to: http://www2.cs.uregina.ca/~dbd/cs831/notes/confusion_matrix/confusion_matrix.html
This is about sensitivity, more from a science statistical view with links to ROC charts which are related to confusion matrices, and also useful for visualising and assessing performance: https://en.wikipedia.org/wiki/Sensitivity_index
This article is more specific to using these in machine learning, and goes into more detail: https://www.cs.cornell.edu/courses/cs578/2003fa/performance_measures.pdf
So in summary confusion matrices are one of many tools to assess the performance of a system, but you need to define the right measure first.
Real world example
I worked through this process recently in a project I worked on where the point was to find all of few relevant documents from a large set (using cosine distances like yours). This was like a recommendation engine driven by manual labelling rather than an initial search query.
I drew up a list of goals with a stakeholder in their own terms from the project domain perspective, then tried to translate or map these goals into performance metrics and statistical terms. You can see it's not just a simple choice! The hugely imbalanced nature of our data set skewed the choice of metric as some assume balanced data or else they will give you misleading results.
Hopefully this example will help you move forward.

Bleu Score in Model Evaluation Metric

In many seq2seq implementations, I saw that they use accuracy metric in compiling the model and Bleu score only in predictions.
Why they don't use Bleu score in training to be more efficient? if I understand correctly!
Bilingual Evaluation Understudy Score was meant to replace humans, hence the word understudy comes in it's name.
Now, When you are training your data, you already have the targeted value and you can directly compare your generated output with it, but when you predict on a dataset, you don't have a way to measure if the sentence you translated into is correct. That is why you use Bleu, because no human can check after each machine translation if what you predicted is correct or not, and Bleu provides a sanity check.
P.S. Understudy means someone learning from a mentor to replace him if need be, Bleu "learns" from humans and then is able to score the translation.
For further reference check out https://www.youtube.com/watch?v=9ZvTxChwg9A&list=PL1w8k37X_6L_s4ncq-swTBvKDWnRSrinI&index=28
If any queries, comment below.

What's a good measure for classifying text documents?

I have written an application that measures text importance. It takes a text article, splits it into words, drops stopwords, performs stemming, and counts word-frequency and document-frequency. Word-frequency is a measure that counts how many times the given word appeared in all documents, and document-frequency is a measure that counts how many documents the given word appeared.
Here's an example with two text articles:
Article I) "A fox jumps over another fox."
Article II) "A hunter saw a fox."
Article I gets split into words (afters stemming and dropping stopwords):
["fox", "jump", "another", "fox"].
Article II gets split into words:
["hunter", "see", "fox"].
These two articles produce the following word-frequency and document-frequency counters:
fox (word-frequency: 3, document-frequency: 2)
jump (word-frequency: 1, document-frequency: 1)
another (word-frequency: 1, document-frequency: 1)
hunter (word-frequency: 1, document-frequency: 1)
see (word-frequency: 1, document-frequency: 1)
Given a new text article, how do I measure how similar this article is to previous articles?
I've read about df-idf measure but it doesn't apply here as I'm dropping stopwords, so words like "a" and "the" don't appear in the counters.
For example, I have a new text article that says "hunters love foxes", how do I come up with a measure that says this article is pretty similar to ones previously seen?
Another example, I have a new text article that says "deer are funny", then this one is a totally new article and similarity should be 0.
I imagine I somehow need to sum word-frequency and document-frequency counter values but what's a good formula to use?
A standard solution is to apply the Naive Bayes classifier which estimates the posterior probability of a class C given a document D, denoted as P(C=k|D) (for a binary classification problem, k=0 and 1).
This is estimated by computing the priors from a training set of class labeled documents, where given a document D we know its class C.
P(C|D) = P(D|C) * P(D) (1)
Naive Bayes assumes that terms are independent, in which case you can write P(D|C) as
P(D|C) = \prod_{t \in D} P(t|C) (2)
P(t|C) can simply be computed by counting how many times does a term occur in a given class, e.g. you expect that the word football will occur a large number of times in documents belonging to the class (category) sports.
When it comes to the other factor P(D), you can estimate it by counting how many labeled documents are given from each class, may be you have more sports articles than finance ones, which makes you believe that there is a higher likelihood of an unseen document to be classified into the sports category.
It is very easy to incorporate factors, such as term importance (idf), or term dependence into Equation (1). For idf, you add it as a term sampling event from the collection (irrespective of the class).
For term dependence, you have to plugin probabilities of the form P(u|C)*P(u|t), which means that you sample a different term u and change (transform) it to t.
Standard implementations of Naive Bayes classifier can be found in the Stanford NLP package, Weka and Scipy among many others.
It seems that you are trying to answer several related questions:
How to measure similarity between documents A and B? (Metric learning)
How to measure how unusual document C is, compared to some collection of documents? (Anomaly detection)
How to split a collection of documents into groups of similar ones? (Clustering)
How to predict to which class a document belongs? (Classification)
All of these problems are normally solved in 2 steps:
Extract the features: Document --> Representation (usually a numeric vector)
Apply the model: Representation --> Result (usually a single number)
There are lots of options for both feature engineering and modeling. Here are just a few.
Feature extraction
Bag of words: Document --> number of occurences of each individual word (that is, term frequencies). This is the basic option, but not the only one.
Bag of n-grams (on word-level or character-level): co-occurence of several tokens is taken into account.
Bag of words + grammatic features (e.g. POS tags)
Bag of word embeddings (learned by an external model, e.g. word2vec). You can use embedding as a sequence or take their weighted average.
Whatever you can invent (e.g. rules based on dictionary lookup)...
Features may be preprocessed in order to decrease relative amount of noise in them. Some options for preprocessing are:
dividing by IDF, if you don't have a hard list of stop words or believe that words might be more or less "stoppy"
normalizing each column (e.g. word count) to have zero mean and unit variance
taking logs of word counts to reduce noise
normalizing each row to have L2 norm equal to 1
You cannot know in advance which option(s) is(are) best for your specific application - you have to do experiments.
Now you can build the ML model. Each of 4 problems has its own good solutions.
For classification, the best studied problem, you can use multiple kinds of models, including Naive Bayes, k-nearest-neighbors, logistic regression, SVM, decision trees and neural networks. Again, you cannot know in advance which would perform best.
Most of these models can use almost any kind of features. However, KNN and kernel-based SVM require your features to have special structure: representations of documents of one class should be close to each other in sense of Euclidean distance metric. This sometimes can be achieved by simple linear and/or logarithmic normalization (see above). More difficult cases require non-linear transformations, which in principle may be learned by neural networks. Learning of these transformations is something people call metric learning, and in general it is an problem which is not yet solved.
The most conventional distance metric is indeed Euclidean. However, other distance metrics are possible (e.g. manhattan distance), or different approaches, not based on vector representations of texts. For example, you can try to calculate Levenstein distance between texts, based on count of number of operations needed to transform one text to another. Or you can calculate "word mover distance" - the sum of distances of word pairs with closest embeddings.
For clustering, basic options are K-means and DBScan. Both these models require your feature space have this Euclidean property.
For anomaly detection you can use density estimations, which are produced by various probabilistic algorithms: classification (e.g. naive Bayes or neural networks), clustering (e.g. mixture of gaussian models), or other unsupervised methods (e.g. probabilistic PCA). For texts, you can exploit the sequential language structure, estimating probabilitiy of each word conditional on the previous words (using n-grams or convolutional/recurrent neural nets) - this is called language models, and it is usually more efficient than bag-of-word assumption of Naive Bayes, which ignores word order. Several language models (one for each class) may be combined into one classifier.
Whatever problem you solve, it is strongly recommended to have a good test set with the known "ground truth": which documents are close to each other, or belong to the same class, or are (un)usual. With this set, you can evaluate different approaches to feature engineering and modelling, and choose the best one.
If you don't have resourses or willingness to do multiple experiments, I would recommend to choose one of the following approaches to evaluate similarity between texts:
word counts + idf normalization + L2 normalization (equivalent to the solution of #mcoav) + Euclidean distance
mean word2vec embedding over all words in text (the embedding dictionary may be googled up and downloaded) + Euclidean distance
Based on one of these representations, you can build models for the other problems - e.g. KNN for classifications or k-means for clustering.
I would suggest tf-idf and cosine similarity.
You can still use tf-idf if you drop out stop-words. It is even probable that whether you include stop-words or not would not make such a difference: the Inverse Document Frequency measure automatically downweighs stop-words since they are very frequent and appear in most documents.
If your new document is entirely made of unknown terms, the cosine similarity will be 0 with every known document.
When I search on df-idf I find nothing.
tf-idf with cosine similarity is very accepted and common practice
Filtering out stop words does not break it. For common words idf gives them low weight anyway.
tf-idf is used by Lucene.
Don't get why you want to reinvent the wheel here.
Don't get why you think the sum of df idf is a similarity measure.
For classification do you have some predefined classes and sample documents to learn from? If so can use Naive Bayes. With tf-idf.
If you don't have predefined classes you can use k means clustering. With tf-idf.
It depend a lot on your knowledge of the corpus and classification objective. In like litigation support documents produced to you, you have and no knowledge of. In Enron they used names of raptors for a lot of the bad stuff and no way you would know that up front. k means lets the documents find their own clusters.
Stemming does not always yield better classification. If you later want to highlight the hits it makes that very complex and the stem will not be the length of the word.
Have you evaluated sent2vec or doc2vec approaches? You can play around with the vectors to see how close the sentences are. Just an idea. Not a verified solution to your question.
While in English a word alone may be enough, it isn't the case in some other more complex languages.
A word has many meanings, and many different uses cases. One text can talk about the same things while using fews to none matching words.
You need to find the most important words in a text. Then you need to catch their possible synonyms.
For that, the following api can help. It is doable to create something similar with some dictionaries.
synonyms("complex")
function synonyms(me){
var url = 'https://api.datamuse.com/words?ml=' + me;
fetch(url).then(v => v.json()).then((function(v){
syn = JSON.stringify(v)
syn = JSON.parse(syn)
for(var k in syn){
document.body.innerHTML += "<span>"+syn[k].word+"</span> "
}
})
)
}
From there comparing arrays will give much more accuracy, much less false positive.
A sufficient solution, in a possibly similar task:
Use of a binary bag-of-word (BOW) approach for the vector representation (frequent words aren't higher weighted than seldom words), rather than a real TF approach
The embedding "word2vec" approach, is sensitive to sequence and distances effects. It might make - depending on your hyper-parameters - a difference between 'a hunter saw a fox' and 'a fox saw a jumping hunter' ... so you have to decide, if this means adding noise to your task - or, alternatively, to use it as an averaged vector only, over all of your text
Extract high within-sentence-correlation words ( e.g., by using variables- mean-normalized- cosine-similaritities )
Second Step: Use this list of high-correlated words, as a positive list, i.e. as new vocab for an new binary vectorizer
This isolated meaningful words for the 2nd step cosine comparisons - in my case, even for rather small amounts of training texts

Natural language query preprocessing

I am trying to implement a natural language query preprocessing module which would, given a query formulated in natural language, extract the keywords from that query and submit it to an Information Retrieval (IR) system.
At first, I thought about using some training set to compute tf-idf values of terms and use these values for estimating the importance of single words. But on second thought, this does not make any sense in this scenario - I only have a training collection but I dont have access to index the IR data. Would it be reasonable to only use the idf value for such estimation? Or maybe another weighting approach?
Could you suggest how to tackle this problem? Usually, the articles about NLP processing that I read address training and test data sets. But what if I only have the query and training data?
tf-idf (it's not capitalized, fyi) is a good choice of weight. Your intuition is correct here. However, you don't compute tf-idf on your training set alone. Why? You need to really understand what the tf and idf mean:
tf (term frequency) is a statistic that indicates whether a term appears in the document being evaluated. The simplest way to calculate it would simply be a boolean value, i.e. 1 if the term is in the document.
idf (inverse document frequency), on the other hand, measures how likely a term appears in a random document. It's most often calculated as the log of (N/number of document matches).
Now, tf is calculated for each of the document your IR system will be indexing over (if you don't have the access to do this, then you have a much bigger and insurmountable problem, since an IR without a source of truth is an oxymoron). Ideally, idf is calculated over your entire data set (i.e. all the documents you are indexing), but if this is prohibitively expensive, then you can random sample your population to create a smaller data set, or use a training set such as the Brown corpus.

Incrementally Trainable Entity Recognition Classifier

I'm doing some semantic-web/nlp research, and I have a set of sparse records, containing a mix of numeric and non-numeric data, representing entities labeled with various features extracted from simple English sentences.
e.g.
uid|features
87w39423|speaker=432, session=43242, sentence=34, obj_called=bob,favorite_color_is=blue
4535k3l535|speaker=512, session=2384, sentence=7, obj_called=tree,isa=plant,located_on=wilson_street
23432424|speaker=997, session=8945305, sentence=32, obj_called=salty,isa=cat,eats=mice
09834502|speaker=876, session=43242, sentence=56, obj_called=the monkey,ate=the banana
928374923|speaker=876, session=43242, sentence=57, obj_called=it,was=delicious
294234234|speaker=876, session=43243, sentence=58, obj_called=the monkey,ate=the banana
sd09f8098|speaker=876, session=43243, sentence=59, obj_called=it,was=hungry
...
A single entity may appear more than once (but with a different UID each time), and may have overlapping features with its other occurrences. A second data set represents which of the above UIDs are definitely the same.
e.g.
uid|sameas
87w39423|234k2j,234l24jlsd,dsdf9887s
4535k3l535|09d8fgdg0d9,l2jk34kl,sd9f08sf
23432424|io43po5,2l3jk42,sdf90s8df
09834502|294234234,sd09f8098
...
What algorithm(s) would I use to incrementally train a classifier that could take a set of features, and instantly recommend the N most similar UIDs and probability of whether or not those UIDs actually represent the same entity? Optionally, I'd also like to get a recommendation of missing features to populate and then re-classify to get a more certain matches.
I researched traditional approximate nearest neighbor algorithms. such as FLANN and ANN, and I don't think these would be appropriate since they're not trainable (in a supervised learning sense) nor are they typically designed for sparse non-numeric input.
As a very naive first-attempt, I was thinking about using a naive bayesian classifier, by converting each SameAs relation into a set of training samples. So, for each entity A with B sameas relations, I would iterate over each and train the classifier like:
classifier = Classifier()
for entity,sameas_entities in sameas_dataset:
entity_features = get_features(entity)
for other_entity in sameas_entities:
other_entity_features = get_features(other_entity)
classifier.train(cls=entity, ['left_'+f for f in entity_features] + ['right_'+f for f in other_entity_features])
classifier.train(cls=other_entity, ['left_'+f for f in other_entity_features] + ['right_'+f for f in entity_features])
And then use it like:
>>> print classifier.findSameAs(dict(speaker=997, session=8945305, sentence=32, obj_called='salty',isa='cat',eats='mice'), n=7)
[(1.0, '23432424'),(0.999, 'io43po5', (1.0, '2l3jk42'), (1.0, 'sdf90s8df'), (0.76, 'jerwljk'), (0.34, 'rlekwj32424'), (0.08, '09843jlk')]
>>> print classifier.findSameAs(dict(isa='cat',eats='mice'), n=7)
[(0.09, '23432424'), (0.06, 'jerwljk'), (0.03, 'rlekwj32424'), (0.001, '09843jlk')]
>>> print classifier.findMissingFeatures(dict(isa='cat',eats='mice'), n=4)
['obj_called','has_fur','has_claws','lives_at_zoo']
How viable is this approach? The initial batch training would be horribly slow, at least O(N^2), but incremental training support would allow updates to happen more quickly.
What are better approaches?
I think this is more of a clustering than a classification problem. Your entities are data points and the sameas data is a mapping of entities to clusters. In this case, clusters are the distinct 'things' your entities refer to.
You might want to take a look at semi-supervised clustering. A brief google search turned up the paper Active Semi-Supervision for Pairwise Constrained Clustering which gives pseudocode for an algorithm that is incremental/active and uses supervision in the sense that it takes training data indicating which entities are or are not in the same cluster. You could derive this easily from your sameas data, assuming that - for example - uids 87w39423 and 4535k3l535 are definitely distinct things.
However, to get this to work you need to come up with a distance metric based on the features in the data. You have a lot of options here, for example you could use a simple Hamming distance on the features, but the choice of metric function here is a little bit arbitrary. I'm not aware of any good ways of choosing the metric, but perhaps you have already looked into this when you were considering nearest neighbour algorithms.
You can come up with confidence scores using the distance metric from the centres of the clusters. If you want an actual probability of membership then you would want to use a probabilistic clustering model, like a Gaussian mixture model. There's quite a lot of software to do Gaussian mixture modelling, I don't know of any that is semi-supervised or incremental.
There may be other suitable approaches if the question you wanted to answer was something like "given an entity, which other entities are likely to refer to the same thing?", but I don't think that is what you are after.
You may want to take a look at this method:
"Large Scale Online Learning of Image Similarity Through Ranking" Gal Chechik, Varun Sharma, Uri Shalit and Samy Bengio, Journal of Machine Learning Research (2010).
[PDF] [Project homepage]
More thoughts:
What do you mean by 'entity'? Is entity the thing that is referred by 'obj_called'? Do you use the content of 'obj_called' to match different entities, e.g. 'John' is similar to 'John Doe'? Do you use proximity between sentences to indicate similar entities? What is the greater goal (task) of the mapping?

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