I have 4 sets of manually tagged data for 0 and 1, by 4 different people. I have to get the final labelled data in terms of 0 and 1 using the 4 sets of manually tagged data. I have calculated the degree of agreement between the users as
A-B : 0.3276,
A-C : 0.3263,
A-D : 0.4917,
B-C : 0.2896,
B-D : 0.4052,
C-D : 0.3540.
I do not know how to use this to calculate the final data as a single set.
Please help.
The Kappa coefficient works only for a pair of annotators. For more than two, you need to employ an extension of it. One popular way of doing so is to use this expansion proposed by Richard Light in 1971, or to use the average expected agreement for all annotator pairs, proposed by Davies and Fleiss in 1982. I am not aware of any readily available calculator that will compute these for you, so you may have to implement the code yourself.
There is this Wikipedia page on Fleiss' kappa, however, which you might find helpful.
These techniques can only be used for nominal variables. If your data is not on the nominal scale, use a different measure like the intraclass correlation coefficient.
Related
For big datasets with 2bil+ samples and approximately 100+ features per sample. Among these, 10% features you have are numerical/continuous variables and the rest of it are categorical variables (position, languages, url etc...).
Let's use some examples:
e.g: dummy categorical feature
feature: Position
real values: SUD | CENTRE | NORTH
encoded values: 1 | 2 | 3
...would have sense use reduction like SVD because distance beetween sud:north > sud:centre and, moreover, it's possible to encode (e.g OneHotEncoder, StringIndexer) this variable because of the small cardinality of it values-set.
e.g: real categorical feature
feature: url
real values: very high cardinality
encoded values: ?????
1) In MLlibthe 90% of the model works just with numerical values (a part of Frequent Itemset and DecisionTree techniques)
2) Features transformers/reductor/extractor as PCA or SVD are not good for these kind of data, and there is no implementation of (e.g) MCA
a) Which could be your approach to engage with this kind of data in spark, or using Mllib?
b) Do you have any suggestions to cope with this much categorical values?
c) After reading a lot in literature, and counting the implemented model in spark, my idea, about make inference on one of that features using the others (categorical), the models at point 1 could be the best coiche. What do you think about it?
(to standardize a classical use case you can imagine the problem of infer the gender of a person using visited url and other categorical features).
Given that I am a newbie in regards to MLlib, may I ask you to provide a concrete example?
Thanks in advance
Well, first I would say stackoverflow works in a different way, you should be the one providing a working example with the problem you are facing and we help you out using this example.
Anyways I got intrigued with the use of the categorical values like the one you show as position. If this is a categorical value as you mention with 3 levels SUD,CENTRE, NORTH, there is no distance between them if they are truly categorical. In this sense I would create dummy variables like:
SUD_Cat CENTRE_Cat NORTH_Cat
SUD 1 0 0
CENTRE 0 1 0
NORTH 0 0 1
This is a truly dummy representation of a categorical variable.
On the other hand if you want to take that distance into account then you have to create another feature which takes this distance into account explicitly, but that is not a dummy representation.
If the problem you are facing is that after you wrote your categorical features as dummy variables (note that now all of them are numerical) you have very many features and you want to reduce your feature's space, then is a different problem.
As a rule of thumbs I try to utilize the entire feature space first, now a plus since in spark computing power allows you to run modelling tasks with big datasets, if it is too big then I would go for dimensionality reduction techniques, PCA etc...
Let's say I have a user search query which looks like:
"the happy bunny"
I have already computed tf-idf and have something like this (following are made up example values) for each document in which I am searching (of coures the idf is always the same):
tf idf score
the 0.06 1 0.06 * 1 = 0.06
happy 0.002 20 0.002 * 20 = 0.04
bunny 0.0005 60 0.0005 * 60 = 0.03
I have two questions with what to do next.
Firstly, the still has the highest score, even though it is adjusted for rarity by idf, still it's not exactly important - do you think I should square the idf values to weight in terms of rare words, or would this give bad results? Otherwise I'm worried that the is getting equal importance to happy and bunny, and it should be obvious that bunny is the most important word in the search. As long as rare always equals important then it would be always a good idea to weight in terms of rarity, but if that is not always the case then doing so could really mess up the results.
Secondly and more importantly: what is the best/preferred method for combining the scores for each word together to give each document a single score that represents how well it reflects the entire search query? I was thinking of adding them, but it has become apparent that that is going to give higher priority to a document containing 10,000 happy but only 1 bunny instead of another document with 500 happy and 500 bunny (which would be a better match).
First, make sure that you are computing the correct TF-IDF values. As others have pointed they do not look right. TF is relative to specific documents, and we often do not need to compute them for queries (since raw term frequency is almost always 1 in queries). There are different types of TF functions to pick from (check the Wikipedia page on tf-idf, it has a good coverage). Log Normalisation is common and the most efficient scheme, since it saves an extra disk access to get the respective document's total frequency maxF that is needed for something like Double Normalisation. When you are dealing with large volumes of documents this can be expensive, especially if you can't bring these into memory. A bit of insight on inverted files can go a long way in understanding some of the underlying complexities. Log normalisation is efficient and is a non-linear function, therefore better than raw frequency.
Once you are certain on your weighting scheme, then you may want to consider a stop list to get rid of very common/noisy words. These do not contribute to the rank of documents. It is generally recommended to use a stop list of high frequency, very common words. Do a search and you will find many available, including the one that Lucene uses.
The remaining lies on your ranking strategy and that will depend on your implementation/model. The vector space model (VSM) is simple and readily available with libraries like Lucene, Lemur, etc. VSM computes the Dot product or scalar of the weights of common terms between the query and a document. Term weights are normalised via vector length normalisation (which solves your second question), and the result of applying the model is a value between 0 and 1. This is also justified/interpreted as the Cosine of the angle between two vectors in a planar graph, or the Euclidean distance divided by the Euclidean vector length of two vectors.
One of the earliest comprehensive studies on weighting schemes and ranking with VSM is an article by Salton (pdf) and is a good read if you are interested in Information Retrieval. A bit outdated perhaps (notice how log normalisation is not mentioned in the article).
Your best read I believe is the book Introduction to Information Retrieval by Christopher Manning. It will take you through everything that you need to know, from indexing to ranking schemes, etc. A bit lacking on ranking models (does not cover some of the more complex probabilistic approaches).
You should reconsider your TF and IDF values, they do not look correct. The TF value is usually just how often the word occurs, so if the word "the" appeared 20 times it's tf value would be 20. A word like "the" should have a very low IDF value (possibly around 4 decimal places, 0.000...).
You could use stop word removal if word like the are not necessary, they would be removed rather than just given a low score.
A vector space model could be used for this.
can you compute tf-idf for amalgamated terms? That is, you first generate a sentiment that considers each of its component as equal before treating the sentiment as a single term for which you now compute the tf-idf
I'm trying to find confidence intervals for the means of various variables in a database using SPSS, and I've run into a spot of trouble.
The data is weighted, because each of the people who was surveyed represents a different portion of the overall population. For example, one young man in our sample might represent 28000 young men in the general population. The problem is that SPSS seems to think that the young man's database entries each represent 28000 measurements when they actually just represent one, and this makes SPSS think we have much more data than we actually do. As a result SPSS is giving very very low standard error estimates and very very narrow confidence intervals.
I've tried fixing this by dividing every weight value by the mean weight. This gives plausible figures and an average weight of 1, but I'm not sure the resulting numbers are actually correct.
Is my approach sound? If not, what should I try?
I've been using the Explore command to find mean and standard error (among other things), in case it matters.
You do need to scale weights to the actual sample size, but only the procedures in the Complex Samples option are designed to account for sampling weights properly. The regular weight variable in Statistics is treated as a frequency weight.
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.
I have set of 200 data rows(implies a small set of data). I want to carry out some statistical analysis, but before that I want to exclude outliers.
What are the potential algos for the purpose? Accuracy is a matter of concern.
I am very new to Stats, so need help in very basic algos.
Overall, the thing that makes a question like this hard is that there is no rigorous definition of an outlier. I would actually recommend against using a certain number of standard deviations as the cutoff for the following reasons:
A few outliers can have a huge impact on your estimate of standard deviation, as standard deviation is not a robust statistic.
The interpretation of standard deviation depends hugely on the distribution of your data. If your data is normally distributed then 3 standard deviations is a lot, but if it's, for example, log-normally distributed, then 3 standard deviations is not a lot.
There are a few good ways to proceed:
Keep all the data, and just use robust statistics (median instead of mean, Wilcoxon test instead of T-test, etc.). Probably good if your dataset is large.
Trim or Winsorize your data. Trimming means removing the top and bottom x%. Winsorizing means setting the top and bottom x% to the xth and 1-xth percentile value respectively.
If you have a small dataset, you could just plot your data and examine it manually for implausible values.
If your data looks reasonably close to normally distributed (no heavy tails and roughly symmetric), then use the median absolute deviation instead of the standard deviation as your test statistic and filter to 3 or 4 median absolute deviations away from the median.
Start by plotting the leverage of the outliers and then go for some good ol' interocular trauma (aka look at the scatterplot).
Lots of statistical packages have outlier/residual diagnostics, but I prefer Cook's D. You can calculate it by hand if you'd like using this formula from mtsu.edu (original link is dead, this is sourced from archive.org).
You may have heard the expression 'six sigma'.
This refers to plus and minus 3 sigma (ie, standard deviations) around the mean.
Anything outside the 'six sigma' range could be treated as an outlier.
On reflection, I think 'six sigma' is too wide.
This article describes how it amounts to "3.4 defective parts per million opportunities."
It seems like a pretty stringent requirement for certification purposes. Only you can decide if it suits you.
Depending on your data and its meaning, you might want to look into RANSAC (random sample consensus). This is widely used in computer vision, and generally gives excellent results when trying to fit data with lots of outliers to a model.
And it's very simple to conceptualize and explain. On the other hand, it's non deterministic, which may cause problems depending on the application.
Compute the standard deviation on the set, and exclude everything outside of the first, second or third standard deviation.
Here is how I would go about it in SQL Server
The query below will get the average weight from a fictional Scale table holding a single weigh-in for each person while not permitting those who are overly fat or thin to throw off the more realistic average:
select w.Gender, Avg(w.Weight) as AvgWeight
from ScaleData w
join ( select d.Gender, Avg(d.Weight) as AvgWeight,
2*STDDEVP(d.Weight) StdDeviation
from ScaleData d
group by d.Gender
) d
on w.Gender = d.Gender
and w.Weight between d.AvgWeight-d.StdDeviation
and d.AvgWeight+d.StdDeviation
group by w.Gender
There may be a better way to go about this, but it works and works well. If you have come across another more efficient solution, I’d love to hear about it.
NOTE: the above removes the top and bottom 5% of outliers out of the picture for purpose of the Average. You can adjust the number of outliers removed by adjusting the 2* in the 2*STDDEVP as per: http://en.wikipedia.org/wiki/Standard_deviation
If you want to just analyse it, say you want to compute the correlation with another variable, its ok to exclude outliers. But if you want to model / predict, it is not always best to exclude them straightaway.
Try to treat it with methods such as capping or if you suspect the outliers contain information/pattern, then replace it with missing, and model/predict it. I have written some examples of how you can go about this here using R.