Supervised Learning for User Behavior over Time - statistics
I want to use machine learning to identify the signature of a user who converts to a subscriber of a website given their behavior over time.
Let's say my website has 6 different features which can be used before subscribing and users can convert to a subscriber at any time.
For a given user I have stats which represent the intensity on a continuous range of that user's interaction with features 1-6 on a daily basis so:
D1: f1,f2,f3,f4,f5,f6
D2: f1,f2,f3,f4,f5,f6
D3: f1,f2,f3,f4,f5,f6
D4: f1,f2,f3,f4,f5,f6
Let's say on day 5, the user converts.
What machine using algorithms would help me identify which are the most common patterns in feature usage which lead to a conversion?
(I know this is a super basic classification question, but I couldn't find a good example using longitudinal data, where input vectors are ordered by time like I have)
To develop the problem further, let's assume that each feature has 3 intensities at which the user can interact (H, M, L).
We can then represent each user as a string of states of interaction intensity. So, for a user:
LLLLMM LLMMHH LLHHHH
Would mean on day one they only interacted significantly with features 5 and 6, but by the third day they were interacting highly with features 3 through 6.
N-gram Style
I could make these states words and the lifetime of a user a sentence. (Would probably need to add a "conversion" word to the vocabulary as well)
If I ran these "sentences" through an n-gram model, I could get the likely future state of a user given his/her past few state which is somewhat interesting. But, what I really want to know the most common sets of n-grams that lead to the conversion word. Rather than feeding in an n-gram and getting the next predicted word, I want to give the predicted word and get back the 10 most common n-grams (from my data) which would be likely to lead to the word.
Amaç Herdağdelen suggests identifying n-grams to practical n and then counting how many n-gram states each user has. Then correlating with conversion data (I guess no conversion word in this example). My concern is that there would be too many n-grams to make this method practical. (if each state has 729 possibilities, and we're using trigrams, thats a lot of possible trigrams!)
Alternatively, could I just go thru the data logging the n-grams which led to the conversion word and then run some type of clustering on them to see what the common paths are to a conversion?
Survival Style
Suggested by Iterator, I understand the analogy to a survival problem, but the literature here seems to focus on predicting time to death as opposed to the common sequence of events which leads to death. Further, when looking up the Cox Proportional Hazard model, I found that it does not event accommodate variables which change over time (its good for differentiating between static attributes like gender and ethnicity)- so it seems very much geared toward a different question than mine.
Decision Tree Style
This seems promising though I can't completely wrap my mind around how to structure the data. Since the data is not flat, is the tree modeling the chance of moving from one state to another down the line and when it leads to conversion or not? This is very different than the decision tree data literature I've been able to find.
Also, need clarity on how to identify patterns which lead to conversion instead a models predicts likely hood of conversion after a given sequence.
Theoretically, hidden markov models may be a suitable solution to your problem. The features on your site would constitute the alphabet, and you can use the sequence of interactions as positive or negative instances depending on whether a user finally subscribed or not. I don't have a guess about what the number of hidden states should be, but finding a suitable value for that parameter is part of the problem, after all.
As a side note, positive instances are trivial to identify, but the fact that a user has not subscribed so far doesn't necessarily mean s/he won't. You might consider to limit your data to sufficiently old users.
I would also consider converting the data to fixed-length vectors and apply conceptually simpler models that could give you some intuition about what's going on. You could use n-grams (consecutive interaction sequences of length n).
As an example, assuming that the interaction sequence of a given user ise "f1,f3,f5", "f1,f3,f5" would constitute a 3-gram (trigram). Similarly, for the same user and the same interaction sequence you would have "f1,f3" and "f3,f5" as the 2-grams (bigrams). In order to represent each user as a vector, you would identify all n-grams up to a practical n, and count how many times the user employed a given n-gram. Each column in the vector would represent the number of times a given n-gram is observed for a given user.
Then -- probably with the help of some suitable normalization techniques such as pointwise mutual information or tf-idf -- you could look at the correlation between the n-grams and the final outcome to get a sense of what's going on, carry out feature selection to find the most prominent sequences that users are involved in, or apply classification methods such as nearest neighbor, support machine or naive Bayes to build a predictive model.
This is rather like a survival analysis problem: over time the user will convert or will may drop out of the population, or will continue to appear in the data and not (yet) fall into neither camp. For that, you may find the Cox proportional hazards model useful.
If you wish to pursue things from a different angle, namely one more from the graphical models perspective, then a Kalman Filter may be more appealing. It is a generalization of HMMs, suggested by #AmaçHerdağdelen, which work for continuous spaces.
For ease of implementation, I'd recommend the survival approach. It is the easiest to analyze, describe, and improve. After you have a firm handle on the data, feel free to drop in other methods.
Other than Markov chains, I would suggest decision trees or Bayesian networks. Both of these would give you a likely hood of a user converting after a sequence.
I forgot to mention this earlier. You may also want to take a look at the Google PageRank algorithm. It would help you account for the user completely disappearing [not subscribing]. The results of that would help you to encourage certain features to be used. [Because they're more likely to give you a sale]
I think Ngramm is most promising approach, because all sequnce in data mining are treated as elements depndent on few basic steps(HMM, CRF, ACRF, Markov Fields) So I will try to use classifier based on 1-grams and 2 -grams.
Related
Why word embedding technique works
I have look into some word embedding techniques, such as CBOW: from context to single word. Weight matrix produced used as embedding vector Skip gram: from word to context (from what I see, its acutally word to word, assingle prediction is enough). Again Weight matrix produced used as embedding Introduction to these tools would always quote "cosine similarity", which says words of similar meanning would convert to similar vector. But these methods all based on the 'context', account only for words around a target word. I should say they are 'syntagmatic' rather than 'paradigmatic'. So why the close in distance in a sentence indicate close in meaning? I can think of many counter example that frequently occurs "Have a good day". (good and day are vastly different, though close in distance). "toilet" "washroom" (two words of similar meaning, but a sentence contains one would unlikely to contain another) Any possible explanation?
This sort of "why" isn't a great fit for StackOverflow, but some thoughts:
The essence of word2vec & similar embedding models may be compression: the model is forced to predict neighbors using far less internal state than would be required to remember the entire training set. So it has to force similar words together, in similar areas of the parameter space, and force groups of words into various useful relative-relationships.
So, in your second example of 'toilet' and 'washroom', even though they rarely appear together, they do tend to appear around the same neighboring words. (They're synonyms in many usages.) The model tries to predict them both, to similar levels, when typical words surround them. And vice-versa: when they appear, the model should generally predict the same sorts of words nearby.
To achieve that, their vectors must be nudged quite close by the iterative training. The only way to get 'toilet' and 'washroom' to predict the same neighbors, through the shallow feed-forward network, is to corral their word-vectors to nearby places. (And further, to the extent they have slightly different shades of meaning – with 'toilet' more the device & 'washroom' more the room – they'll still skew slightly apart from each other towards neighbors that are more 'objects' vs 'places'.)
Similarly, words that are formally antonyms, but easily stand-in for each-other in similar contexts, like 'hot' and 'cold', will be somewhat close to each other at the end of training. (And, their various nearer-synonyms will be clustered around them, as they tend to be used to describe similar nearby paradigmatically-warmer or -colder words.)
On the other hand, your example "have a good day" probably doesn't have a giant influence on either 'good' or 'day'. Both words' more unique (and thus predictively-useful) senses are more associated with other words. The word 'good' alone can appear everywhere, so has weak relationships everywhere, but still a strong relationship to other synonyms/antonyms on an evaluative ("good or bad", "likable or unlikable", "preferred or disliked", etc) scale.
All those random/non-predictive instances tend to cancel-out as noise; the relationships that have some ability to predict nearby words, even slightly, eventually find some relative/nearby arrangement in the high-dimensional space, so as to help the model for some training examples.
Note that a word2vec model isn't necessarily an effective way to predict nearby words. It might never be good at that task. But the attempt to become good at neighboring-word prediction, with fewer free parameters than would allow a perfect-lookup against training data, forces the model to reflect underlying semantic or syntactic patterns in the data.
(Note also that some research shows that a larger window influences word-vectors to reflect more topical/domain similarity – "these words are used about the same things, in the broad discourse about X" – while a tiny window makes the word-vectors reflect a more syntactic/typical similarity - "these words are drop-in replacements for each other, fitting the same role in a sentence". See for example Levy/Goldberg "Dependency-Based Word Embeddings", around its Table 1.)
‘Embedding’ mean a semantic vector representation. e.g. how to represent words such that synonyms are nearer than antonyms or other unrelated words. Embeddings algorithms like Word2vec maps entities be it e-commerce items or words (say in English language), to N-dimensional vectors. Now since you have a mathematical representation of the entities in a Euclidean space, you can use associated semantics such as distance between vectors. e.g: For a given item say ‘Levis Jeans’ recommend the most related items which are often co-purchased with it. This can be easily done: search the nearest vectors to the vector of ‘Levis Jeans’, and recommend them. You will find that the nearest vectors correspond to items such as T-shirts etc., which are relevant to the Levis Jeans. Similarly it preserves distance/similarity between words e.g.: King - Queen = Man - Woman ! Yes, Word2vec captures such co-occurrance relationships, when mapping the items/words to vectors also called as ‘item/word embeddings’. This is not specifically targeted to sentence embeddings but nevertheless here you get some crucial insights extremely relevant to the core logic behind embedding generation. Read till the end.
Using Word2Vec for polysemy solving problems
I have some questions about Word2Vec: What determines the dimension of the result model vectors? What is elements of this vectors? Can I use Word2Vec for polysemy solving problems (state = administrative unit vs state = condition), if I already have texts for every meaning of words?
(1) You pick the desired dimensionality, as a meta-parameter of the model. Rigorous projects with enough time may try different sizes, to see what works best for their qualitative evaluations. (2) Individual dimensions/elements of each word-vector (floating-point numbers), in vanilla word2vec are not easily interpretable. It's only the arrangement of words as a whole that has usefulness – placing similar words near each other, and making relative directions (eg "towards 'queen' from 'king'") match human intuitions about categories/continuous-properties. And, because the algorithms use explicit randomization, and optimized multi-threaded operation introduces thread-scheduling randomness to the order-of-training-examples, even the exact same data can result in different (but equally good) vector-coordinates from run-to-run. (3) Basic word2vec doesn't have an easy fix, but there's a bunch of hints of polysemy in the vectors, and research work to do more to disambiguate contrasting senses. For example, generally more-polysemous word-tokens wind up with word-vectors that are some combination of their multiple senses, and (often) of a smaller-magnitude than less-polysemous words. This early paper used multiple representations per word to help discover polysemy. Similar later papers like this one use clustering-of-contexts to discover polysemous words then relabel them to give each sense its own vector. This paper manages an impressive job of detecting alternate senses via postprocessing of normal word2vec vectors.
Simple Binary Text Classification
I seek the most effective and simple way to classify 800k+ scholarly articles as either relevant (1) or irrelevant (0) in relation to a defined conceptual space (here: learning as it relates to work). Data is: title & abstract (mean=1300 characters) Any approaches may be used or even combined, including supervised machine learning and/or by establishing features that give rise to some threshold values for inclusion, among other. Approaches could draw on the key terms that describe the conceptual space, though simple frequency count alone is too unreliable. Potential avenues might involve latent semantic analysis, n-grams, .. Generating training data may be realistic for up to 1% of the corpus, though this already means manually coding 8,000 articles (1=relevant, 0=irrelevant), would that be enough? Specific ideas and some brief reasoning are much appreciated so I can make an informed decision on how to proceed. Many thanks!
Several Ideas: Run LDA and get document-topic and topic-word distributions say (20 topics depending on your dataset coverage of different topics). Assign the top r% of the documents with highest relevant topic as relevant and low nr% as non-relevant. Then train a classifier over those labelled documents. Just use bag of words and retrieve top r nearest negihbours to your query (your conceptual space) as relevant and borrom nr percent as not relevant and train a classifier over them. If you had the citations you could run label propagation over the network graph by labelling very few papers. Don't forget to make the title words different from your abstract words by changing the title words to title_word1 so that any classifier can put more weights on them. Cluster the articles into say 100 clusters and then choose then manually label those clusters. Choose 100 based on the coverage of different topics in your corpus. You can also use hierarchical clustering for this. If it is the case that the number of relevant documents is way less than non-relevant ones, then the best way to go is to find the nearest neighbours to your conceptual space (e.g. using information retrieval implemented in Lucene). Then you can manually go down in your ranked results until you feel the documents are not relevant anymore. Most of these methods are Bootstrapping or Weakly Supervised approaches for text classification, about which you can more literature.
Distance dependent Chinese Restaurant Process maybe
I'm new to machine learning and want to implement the distance dependent Chinese Restaurant process in MATLAB for the clustering of audio tracks. I'm looking to use the dd-CRP on 26 features. I'm guessing the process might go like this Read in 1st feature vector and assign it a "table" Read in 2nd feature vector and compare it to the 1st "table", maybe using the cosine angle(due to high dimension) of the two vectors and if it agrees within some defined theta, join that table, else start a new one. Read in next feature and repeat step 2 for the new feature vector for each existing table. While this is occurring, I will be keeping track of how many tables there are. I will be running the algorithm over say for example 16 audio tracks. The way the audio will be fed into the algorithm is the first feature vector will be from say the first frame from audio track 1, the second feature vector from form the first frame in track 2 etc. as I'm trying to find out which audio tracks like to cluster together most, but I don't want to define how many centroids there are. Obviously I'll have to keep track of which audio track is at which "table". Does this make sense?
This is not a Chinese Restaurant Process. This is a heuristic algorithm which has some similarity to a Chinese Restaurant Process. In a CRP everything is phrased in terms of priors over the assignments of items to clusters (the tables analogy), and these are combined with a likelihood function for each cluster (which formalises the similarity function you described). Inference is then done by Gibbs Sampling, which means non-deterministically sampling which cluster each track is assigned to in turn given all the other assignments. Variational methods for non-parametrics are still in a very preliminary state. Why do you want to use a CRP? Do you think you'll get something out of it beyond more conventional clustering methods? The bar to entry for the implementation and proper understanding of non-parametrics is pretty high, and they're often of little practical use at the moment because of the constraints on inference I mentioned.
You can use the X-means algorithm, which automatically determines the optimal number of centroids (and hence number of clusters) based on the Bayesian Information Criterion (or BIC). In short, the algorithm looks for how dense each cluster is, and how far is each cluster from the other.
I need a function that describes a set of sequences of zeros and ones?
I have multiple sets with a variable number of sequences. Each sequence is made of 64 numbers that are either 0 or 1 like so: Set A sequence 1: 0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0 sequence 2: 0,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0 sequence 3: 0,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0 ... Set B sequence1: 0,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1 sequence2: 0,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,0 ... I would like to find a mathematical function that describes all possible sequences in the set, maybe even predict more and that does not contain the sequences in the other sets. I need this because I am trying to recognize different gestures in a mobile app based on the cells in a grid that have been touched (1 touch/ 0 no touch). The sets represent each gesture and the sequences a limited sample of variations in each gesture. Ideally the function describing the sequences in a set would allow me to test user touches against it to determine which set/gesture is part of. I searched for a solution, either using Excel or Mathematica, but being very ignorant about both and mathematics in general I am looking for the direction of an expert. Suggestions for basic documentation on the subject is also welcome.
It looks as if you are trying to treat what is essentially 2D data in 1D. For example, let s1 represent the first sequence in set A in your question. Then the command ArrayPlot[Partition[s1, 8]] produces this picture: The other sequences in the same set produce similar plots. One of the sequences from the second set produces, in response to the same operations, the picture: I don't know what sort of mathematical function you would like to define to describe these pictures, but I'm not sure that you need to if your objective is to recognise user gestures. You could do something much simpler, such as calculate the 'average' picture for each of your gestures. One way to do this would be to calculate the average value for each of the 64 pixels in each of the pictures. Perhaps there are 6 sequences in your set A describing gesture A. Sum the sequences element-by-element. You will now have a sequence with values ranging from 0 to 6. Divide each element by 6. Now each element represents a sort of probability that a new gesture, one you are trying to recognise, will touch that pixel. Repeat this for all the sets of sequences representing your set of gestures. To recognise a user gesture, simply compute the difference between the sequence representing the gesture and each of the sequences representing the 'average' gestures. The smallest (absolute) difference will direct you to the gesture the user made. I don't expect that this will be entirely foolproof, it may well result in some user gestures being ambiguous or not recognisable, and you may want to try something more sophisticated. But I think this approach is simple and probably adequate to get you started.
In Mathematica the following expression will enumerate all the possible combinations of {0,1} of length 64.
Tuples[{1, 0}, {64}]
But there are 2^62 or 18446744073709551616 of them, so I'm not sure what use that will be to you.
Maybe you just wanted the unique sequences contained in each set, in that case all you need is the Mathematica Union[] function applied to the set. If you have a the sets grouped together in a list in Mathematica, say mySets, then you can apply the Union operator to every set in the list my using the map operator.
Union/#mySets
If you want to do some type of prediction a little more information might be useful.
Thanks you for the clarifications.
Machine Learning
The task you want to solve falls under the disciplines known by a variety of names, but probably most commonly as Machine Learning or Pattern Recognition and if you know which examples represent the same gestures, your case would be known as supervised learning.
Question: In your case do you know which gesture each example represents ?
You have a series of examples for which you know a label ( the form of gesture it is ) from which you want to train a model and use that model to label an unseen example to one of a finite set of classes. In your case, one of a number of gestures. This is typically known as classification.
Learning Resources
There is a very extensive background of research on this topic, but a popular introduction to the subject is machine learning by Christopher Bishop.
Stanford have a series of machine learning video lectures Standford ML available on the web.
Accuracy
You might want to consider how you will determine the accuracy of your system at predicting the type of gesture for an unseen example. Typically you train the model using some of your examples and then test its performance using examples the model has not seen. The two of the most common methods used to do this are 10 fold Cross Validation or repeated 50/50 holdout. Having a measure of accuracy enables you to compare one method against another to see which is superior.
Have you thought about what level of accuracy you require in your task, is 70% accuracy enough, 85%, 99% or better?
Machine learning methods are typically quite sensitive to the specific type of data you have and the amount of examples you have to train the system with, the more examples, generally the better the performance.
You could try the method suggested above and compare it against a variety of well proven methods, amongst which would be Random Forests, support vector machines and Neural Networks. All of which and many more are available to download in a variety of free toolboxes.
Toolboxes
Mathematica is a wonderful system, is infinitely flexible and my favourite environment, but out of the box it doesn't have a great deal of support for machine learning.
I suspect you will make a great deal of progress more quickly by using a custom toolbox designed for machine learning. Two of the most popular free toolboxes are WEKA and R both support more than 50 different methods for solving your task along with methods for measuring the accuracy of the solutions.
With just a little data reformatting, you can convert your gestures to a simple file format called ARFF, load them into WEKA or R and experiment with dozens of different algorithms to see how each performs on your data. The explorer tool in WEKA is definitely the easiest to use, requiring little more than a few mouse clicks and typing some parameters to get started.
Once you have an idea of how well the established methods perform on your data you have a good starting point to compare a customised approach against should they fail to meet your criteria.
Handwritten Digit Recognition
Your problem is similar to a very well researched machine learning problem known as hand written digit recognition. The methods that work well on this public data set of handwritten digits are likely to work well on your gestures.