I have a trading strategy on the foreign exchange market that I am attempting to improve upon.
I have a huge table (100k+ rows) that represent every possible trade in the market, the type of trade (buy or sell), the profit/loss after that trade closed, and 10 or so additional variables that represent various market measurements at the time of trade-opening.
I am trying to find out if any of these 10 variables are significantly related to the profits/losses.
For example, imagine that variable X ranges from 50 to -50.
The average value of X for a buy order is 25, and for a sell order is -25.
If most profitable buy orders have a value of X > 25, and most profitable sell orders have a value of X < -25 then I would consider the relationship of X-to-profit as significant.
I would like a good starting point for this. I have installed RapidMiner 5 in case someone can give me a specific recommendation for that.
A Decision Tree is perhaps the best place to begin.
The tree itself is a visual summary of feature importance ranking (or significant variables as phrased in the OP).
gives you a visual representation of the entire
classification/regression analysis (in the form of a binary tree),
which distinguishes it from any other analytical/statistical
technique that i am aware of;
decision tree algorithms require very little pre-processing on your data, no normalization, no rescaling, no conversion of discrete variables into integers (eg, Male/Female => 0/1); they can accept both categorical (discrete) and continuous variables, and many implementations can handle incomplete data (values missing from some of the rows in your data matrix); and
again, the tree itself is a visual summary of feature importance ranking
(ie, significant variables)--the most significant variable is the
root node, and is more significant than the two child nodes, which in
turn are more significant than their four combined children. "significance" here means the percent of variance explained (with respect to some response variable, aka 'target variable' or the thing
you are trying to predict). One proviso: from a visual inspection of
a decision tree you cannot distinguish variable significance from
among nodes of the same rank.
If you haven't used them before, here's how Decision Trees work: the algorithm will go through every variable (column) in your data and every value for each variable and split your data into two sub-sets based on each of those values. Which of these splits is actually chosen by the algorithm--i.e., what is the splitting criterion? The particular variable/value combination that "purifies" the data the most (i.e., maximizes the information gain) is chosen to split the data (that variable/value combination is usually indicated as the node's label). This simple heuristic is just performed recursively until the remaining data sub-sets are pure or further splitting doesn't increase the information gain.
What does this tell you about the "importance" of the variables in your data set? Well importance is indicated by proximity to the root node--i.e., hierarchical level or rank.
One suggestion: decision trees handle both categorical and discrete data usually without problem; however, in my experience, decision tree algorithms always perform better if the response variable (the variable you are trying to predict using all other variables) is discrete/categorical rather than continuous. It looks like yours is probably continuous, in which case in would consider discretizing it (unless doing so just causes the entire analysis to be meaningless). To do this, just bin your response variable values using parameters (bin size, bin number, and bin edges) meaningful w/r/t your problem domain--e.g., if your r/v is comprised of 'continuous values' from 1 to 100, you might sensibly bin them into 5 bins, 0-20, 21-40, 41-60, and so on.
For instance, from your Question, suppose one variable in your data is X and it has 5 values (10, 20, 25, 50, 100); suppose also that splitting your data on this variable with the third value (25) results in two nearly pure subsets--one low-value and one high-value. As long as this purity were higher than for the sub-sets obtained from splitting on the other values, the data would be split on that variable/value pair.
RapidMiner does indeed have a decision tree implementation, and it seems there are quite a few tutorials available on the Web (e.g., from YouTube, here and here). (Note, I have not used the decision tree module in R/M, nor have i used RapidMiner at all.)
The other set of techniques i would consider is usually grouped under the rubric Dimension Reduction. Feature Extraction and Feature Selection are two perhaps the most common terms after D/R. The most widely used is PCA, or principal-component analysis, which is based on an eigen-vector decomposition of the covariance matrix (derived from to your data matrix).
One direct result from this eigen-vector decomp is the fraction of variability in the data accounted for by each eigenvector. Just from this result, you can determine how many dimensions are required to explain, e.g., 95% of the variability in your data
If RapidMiner has PCA or another functionally similar dimension reduction technique, it's not obvious where to find it. I do know that RapidMiner has an R Extension, which of course let's you access R inside RapidMiner.R has plenty of PCA libraries (Packages). The ones i mention below are all available on CRAN, which means any of the PCA Packages there satisfy the minimum Package requirements for documentation and vignettes (code examples). I can recommend pcaPP (Robust PCA by Projection Pursuit).
In addition, i can recommend two excellent step-by-step tutorials on PCA. The first is from the NIST Engineering Statistics Handbook. The second is a tutorial for Independent Component Analysis (ICA) rather than PCA, but i mentioned it here because it's an excellent tutorial and the two techniques are used for the similar purposes.
Related
I am confused to get the context on biases in the following line (marked in bold):
Information gain ratio biases the decision tree against considering attributes with a large number of distinct values which might lead to overfitting.
Did you mean Information gain, as information gain is bias towards variables with large distinct values and information gain ratio is tries to solve this by taking into account the number of branches that would result before making the split, It corrects information gain by taking the intrinsic information of a split into account.
Answer for why information gain is biased towards variables with large distinct values
Please note that information gain (IG) is biased toward variables with large number of distinct values not variables that have observations with large values. Before describing the reason of this condition, lets review the definition of IG.
Information gain is the amount of information that's gained by knowing the value of the attribute, which is the entropy of the distribution before the split minus the entropy of the distribution after it. The largest information gain is equivalent to the smallest entropy.
In other words, a variable with the highest number of distinct values probability can divide data to smaller chunks. Also, we know that lower number of observations in each chunk reduces probability of variation occurrence.
Using ID variable in splitting data is a common example for this issue. Since each individual sample has their own distinct value, selecting ID features leads to many clusters with one sample and entropy of zero. Therefore, a decision tree that works with IG, selects the ID as the first separator attribute. Indeed, entropy will approach to zero by selecting the ID feature. However, we are not interested to such a feature. We are more interested to features that highly explain the variation of dependent variable.
Please refer to this discussion where this point was initially written.
The way I understand it, in creating a random forest, the algorithm bundles a bunch of randomly generated decision trees together, weighting them such that they fit the training data.
Is it reasonable to say that this average of forests could be simplified into a simple decision tree? And, if so - how can I access and present this tree?
What I'm looking to do here is extract the information in the tree to help identify both the leading attributes, their boundary values and placement in the tree. I'm assuming that such a tree would provide insight to a human (or computer heuristic) as to which attributes within a dataset provide the most insight into determining the target outcome.
This probably seems a naive question - and if so, please be patient, I'm new to this and want to get to a stage where I understand it sufficiently.
RandomForest uses bootstrap to create many training sets by sampling the data with replacement (bagging). Each bootstrapped set is very close to the original data, but slightly different, since it may have multiples of the some points and some other points in the original data will be missing. (This helps create a whole bunch of similar but different sets that as a whole represent the population your data came from, and allow better generalization)
Then it fits a DecisionTree to each set. However, what a regular DecisionTree does at each step, is to loop over each feature, find the best split for each feature, and in the end choose to do the split in the feature that produced the best one among all. In RandomForest, instead of looping over every feature to find the best split, you only try a random subsample at each step (default is sqrt(n_features)).
So, every tree in RandomForest is fit to a bootstrapped random training set. And at each branching step, it only looks at a subsample of features, so some of the branching will be good but not necessarily the ideal split. This means that each tree is a less than ideal fit to the original data. When you average the result of all these (sub-ideal) trees, though, you get a robust prediction. Regular DecisionTrees overfit the data, this two-way randomization (bagging and feature subsampling) allow them to generalize and a forest usually does a good job.
Here is the catch: While you can average out the output of each tree, you cannot really "average the trees" to get an "average tree". Since trees are a bunch of if-then statements that are chained, there is no way of taking these chains and coming up with a single chain that produces the result that's the same as averaged result from each chain. Each tree in the forest is different, even if same features show up, they show up in different places of the trees, which makes it impossible to combine. You cannot represent a RandomForest as a single tree.
There are two things you can do.
1) As RPresle mentioned, you can look at the .feature_importances_ attribute, which for each feature averages the splitting score from different trees. The idea is, while you can't get an average tree, you can quantify how much and how effectively each feature is used in the forest by averaging their score in each tree.
2) When I fit a RandomForest model and need to get some insight into what's happening, how the features are affecting the result, I also fit a single DecisionTree. Now, this model is usually not good at all by itself, it will easily be outperformed by the RandomForest and I wouldn't use it to predict anything, but by drawing and looking at the splits in this tree, combined with the .feature_importances_ of the forest, I usually get a pretty good idea of the big picture.
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 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.
A friend is using Factor Graphs to do text mining (identifying references to people in text), and it got me interested in this tool, but I'm having a hard time finding an intuitive explanation of what Factor Graphs are and how to use them.
Can anyone provide an explanation of Factor Graphs that isn't math heavy, and which focusses on practical applications rather than abstract theory?
They are used extensively for breaking down a problem into pieces. One very interesting application of factor graphs (and message passing on them) is the XBox Live TrueSkill algorithm. I wrote extensively about it on my blog where I tried to go for an introductory explanation rather than an overly academic one.
A factor graph is the graphical representation of the dependencies between variables and factors (parts of a formula) that are present in a particular kind of formula.
Suppose you have a function f(x_1,x_2,...,x_n) and you want to compute the marginalization of this function for some argument x_i, thus summing over all assignments to the remaining formula. Further f can be broken into factors, e.g.
f(x_1,x_2,...,x_n)=f_1(x_1,x_2)f_2(x_5,x_8,x_9)...f_k(x_1,x_10,x_11)
Then in order to compute the marginalization of f for some of the variables you can use a special algorithm called sum product (or message passing), that breaks the problem into smaller computations. For this algortithm, it is very important which variables appear as arguments to which factor. This information is captured by the factor graph.
A factor graph is a bipartite graph with both factor nodes and variable nodes. And there is an edge between a factor and a variable node if the variable appears as an argument of the factor. In our example there would be an edge between the factor f_2 and the variable x_5 but not between f_2 and x_1.
There is a great article: Factor graphs and the sum-product algorithm.
Factor graph is math model, and can be explained only with math equations. In nutshell it is way to explain complex relations between interest variables in your model. Example: A is temperature, B is pressure, components C,D,E are depends on B,A in some way, and component K is depends on B,A. And you want to predict value K based on A and B. So you know only visible states. Basic ML libraries don't allow to model such structure. Neural network do it better. And Factor Graph is exactly solve that problem.
Factor graph is an example of deep learning. When it is impossible to present model with features and output, Factor models allow to build hidden states, layers and complex structure of variables to fit real world behavior. Examples are Machine translation alignment, fingerprint recognition, co-reference etc.