I am reading about precision and recall in machine learning.
Question 1: When are precision and recall inversely related? That is, when does the situation occur where you can improve your precision but at the cost of lower recall, and vice versa? The Wikipedia article states:
Often, there is an inverse relationship between precision and recall,
where it is possible to increase one at the cost of reducing the
other. Brain surgery provides an obvious example of the tradeoff.
However, I have seen research experiment results where both precision and recall increase simultaneously (for example, as you use different or more features).
In what scenarios does the inverse relationship hold?
Question 2: I'm familiar with the precision and recall concept in two fields: information retrieval (e.g. "return 100 most relevant pages out of a 1MM page corpus") and binary classification (e.g. "classify each of these 100 patients as having the disease or not"). Are precision and recall inversely related in both or one of these fields?
The inverse relation only holds when you have some parameter in the system that you can vary in order to get more/less results. Then there's a straightforward relationship: you lower the threshold to get more results and among them some are TPs and some FPs. This, actually, doesn't always mean that precision or recall will rise and fall simultaneously - the real relationship can be mapped using the ROC curve. As for Q2, likewise, in both of these tasks precision and recall are not necessarily inversely related.
So, how do you increase recall or precision, not impacting the other simultaneously? Usually, by improving the algorithm or model. I.e. when you just change parameters of a given model, the inverse relationship will usually hold, although you should mind that it will also be usually non-linear. But if you, for example, add more descriptive features to the model, you can increase both metrics at once.
Regarding the first question, I interpret these concepts in terms of how restrictive your results must be.
If you're more restrictive, I mean, if you're more "demanding on the correctness" of the results, you want it to be more precise. For that, you might be willing to reject some correct results as long as everything you get is correct. Thus, you're raising your precision and lowering your recall. Conversely, if you do not mind getting some incorrect results as long as you get all the correct ones, you're raising your recall and lowering your precision.
On what concerns the second question, if I look at it from the point of view of the paragraphs above, I can say that yes, they are inversely related.
To the best of my knowledge, In order to be able to increase both, precision and recall, you'll need either, a better model (more suitable for your problem) or better data (or both, actually).
Related
i was reading about Classification Algorithm KNN and came across with one term Distance Sensitive Data. I was not able to Found what exactly is Distance Sensitive Data wha are it's classifications, How to say if our Data is Distance-Sensitive or Not?
Suppose that xi and xj are vectors of observed features in cases i and j. Then, as you probably know, kNN is based on distances ||xi-xj||, such as the Euclidean one.
Now if xi and xj contain just a single feature, individual's height in meters, we are fine, as there are no other "competing" features. Suppose that next we add annual salary in thousands. Consequently, we look at distances between vectors like (1.7, 50000) and (1.8, 100000).
Then, in the case of the Euclidean distance, clearly salary feature dominates height and it's almost like we are using the salary feature alone. That is,
||xi-xj||2 ≈ |50000-100000|.
However, if the two features actually have similar importance, then we are doing a poor job. It is even worse if salary is actually irrelevant and we should be using height alone. Interestingly, under weak conditions, our classifier still has nice properties such as universal consistency even in such bad situations. The problem is that in finite samples the performance is our classifier is very bad so that the convergence is very slow.
So, as to deal with that, one may want to consider different distances, such that do something about the scale. Commonly people standardize (set the mean to zero and variance to 1) each feature, but that's not a complete solution either. There are various proposals what could be done (see, e.g., here).
On the other hand, algorithms based on decision trees do not suffer from this. In those cases we just look for a point where to split the variable. For instance, if salary takes values in [0,100000] and the split is at 40000, then Salary/10 would be slit at 4000 so that the results would not change.
I am building an automatic translator in moses. To improve its performance, I use log-linear weight optimisation. This technique has a random component, which can affect slightly the final result (but I do not know exactly how much).
Suppose that the current performance of the model is 25 BLEU.
Suppose now I modify the language model (e.g. change the smoothing), and I get a performance of 26 BLEU.
My question is: how can I know if the improvement is because the modification, or is just noise from the random component?
This is pretty much what statistics is all about. You can basically do one of the two things (from the basic set of solutions, of course there are many more advanced):
try to measure/model/quantify the effect of randomness, if you know what is causing it, you might be able to actually compute how much it can affect your model. If analytical solution is not possible, you can always train 20 models with the same data/settings, gather results and estimate noise distribution. Once you have this you can perform statistical tests to check whether the improvement is statistically significant (for example by ANOVA tests).
simpler approach (but more expensive in terms of data/time) is to simply reduce the variance by averaging. In short - instead of training one model (or evaluating model once) which has this hard to determine noise component - do it many times, 10, 20, and average the results. This way you reduce the variance of the results in your analysis. This can (and should) be combined with the previous option - since now you have 20 results per run, thus you can again use statistical testes to see whether these are significantly different things.
I am trying to calculate precision, recall and f1-score for outlier detection (in my case attacks in a network) using a one-class SVM. I encounter a problem in doing that in a rigorous manner. I explain myself. Since precision is calculated like:
precision = true_positive /(true_positive + false_positive)
if I do my tests using a dataset that I already know that has a few number of attacks then the number of false_positive will be really big in comparison with the true_positive, therefore precision will be very low.
However, if I use a dataset that I already know that has lots of attacks, without changing my detection algorithm the number of true_positive will increase and then the precision will be higher.
I know that something must be wrong in the way that I calculate precision. What am I missing?
Thanks in advance!
if I do my tests using a dataset that I already know that has a few number of attacks then the number of false_positive will be really big in comparison with the true_positive, therefore precision will be very low.
That is (probably) expected behavior, because your data set is skewed. However, you should get a recall value that is acceptable.
However, if I use a dataset that I already know that has lots of attacks, without changing my detection algorithm the number of true_positive will increase and then the precision will be higher.
And in this case, I bet recall will be low.
Based on what you describe, there are a few issues and things you can do. I can address more specific issues if you add more information to your question:
Why are you using multiple test sets, all of which are unbalanced? You should use something that is balanced, or even better, use k-fold cross validation with your entire data set. Use it to find the best parameters for your model.
To decide if you have a good enough balance between precision and recall, consider using the F1 score.
Use a confusion matrix to decide if your measures are acceptable.
Plot learning curves to help avoid overfitting.
Say I'm evaluating some text classification research project using two approaches 'A' and 'B'. When using approach 'A', I get a x% increase in precision while with 'B', a x% increase in recall. How can I say A or B approach better?
It depends on your goal. If you need the first couple of returned classes to be correct then you should go for precision, if you want to focus on returning all relevant classes then try to increase recall.
If precision and recall both matter to you then an often used measure is the F1 score which combines precision and recall into a single measure.
I fully agree with what #Sicco wrote.
Also, I would recommend watching this video, it's from Machine Learning course at Coursera. From the video: in some cases you can manipulate precision and recall by changing threshold. If you're not sure what's more important for you just stick to F1.
So I guess this isn't technically a code question, but it's something that I'm sure will come up for other folks as well as myself while writing code, so hopefully it's still a good one to post on SO.
The Google has directed me to plenty of nice lengthy explanations of when to use one or the other as regards financial numbers, and things like that.
But my particular context doesn't fit in, and I'm wondering if anyone here has some insight. I need to take a whole bunch of individual users' votes on how "good" a particular item is. I.e., some number of users each give a particular item a score between 0 and 10, and I want to report on what the 'typical' score is. What would be the intuitive reasons to report the geometric and/or arithmetic mean as the typical response?
Or, for that matter, would I be better off reporting the median instead?
I imagine there's some psychology involved in what the "best" method might be...
Anyway, there you have it.
Thanks!
Generally speaking, the arithmetic mean will suffice. It is much less computationally intensive than the geometric mean (which involves taking an n-th root).
As for the psychology involved, the geometric mean is never greater than the arithmetic mean, so arithmetic is the best choice if you'd prefer higher scores in general.
The median is most useful when the data set is relatively small and the chance of a massive outlier relatively high. Depending on how much precision these votes can take, the median can sometimes end up being a bit arbitrary.
If you really really want the most accurate answer possible, you could go for calculating the arithmetic-geomtric mean. However, this involved calculating both arithmetic and geometric means repeatedly, so it is very computationally intensive in comparison.
you want the arithmetic mean. since you aren't measuring the average change in average or something.
Arithmetic mean is correct.
Your scale is artificial:
It is bounded, from 0 and 10
8.5 is intuitively between 8 and 9
But for other scales, you would need to consider the correct mean to use.
Some other examples
In counting money, it has been argued that wealth has logarithmic utility. So the median between Bill Gates' wealth and a bum in the inner city would be a moderately successful business person. (Arithmetic average would hive you Larry Page.)
In measuring sound level, decibels already normalizes the effect. So you can take arithmetic average of decibels.
But if you are measuring volume in watts, then use quadratic means (RMS).
The answer depends on the context and your purpose. Percent changes were mentioned as a good time to use geometric mean. I use geometric mean when calculating antennas and frequencies since the percentage change is more important than the average or middle of the frequency range or average size of the antenna is concerned. If you have wildly varying numbers, especially if most are similar but one or two are "flyers" (far from the range of the others) the geometric mean will "smooth" the results (not let the different ones exert a change in the results more than they should). This method is used to calculate bullet group sizes (the "flyer" was probably human error, not the equipment, so the average is ""unfair" in that case). Another variation similar to geometric mean is the root mean square method. First you take the square root of the numbers, take THAT mean, and then square your answer (this provides even more smoothing). This is often used in electrical calculations and most electical meters are calculated in "RMS" (root mean square), not average readings. Hope this helps a little. Here is a web site that explains it pretty well. standardwisdom.com