I'm working on a suggestion system. For a given input, the system outputs N suggestions.
We have collected data about what suggestions the users like. Example:
input1 - output11 output12 output13
input2 - output21
input3 - output31 output32
...
We now want to evaluate our system based on this data. The first metric is if these outputs are present in the suggestions of our system, that's easy.
But now, we would like to test how well positioned are these outputs in the suggestions. We would like to have the given outputs close to the first suggestions.
We would like a single score for the system or for each input.
Based on the previous data, here is what a score of 100% would be:
input1 - output11 output12 output13 other other other ...
input2 - output21 other other other other other ...
input3 - output31 output32 other other other other ...
...
(The order of output11 output12 output13 is not relevant. What is important is that ideally the three of them should be in the first three suggestions).
We could give a score to each position that is hold by a suggestion or count the displacement from the ideal position, but I don't see a good way to do this.
Is there an existing measure that could be used for that ?
You want something called the mean average precision (it's a metric from information retrieval).
Essentially, for each of the 'real' data points in your output list, you can compute the precision (#of correct entries above that point / #entries above that point). If you average this number across the positions of each of your real data points in the output list, you get a metric that does what you want.
Related
I have some features that are zero-centered values and supposed to represent change between a current value and previous value. Generally speaking i believe there should be some symmetry between these values. Ie. there should be roughly the same amount of positive values as negative values and roughly these values should operate on the same scale.
When i try to scale my samples using MaxAbsScaler, i notice that my negative values for this feature get almost completely drowned out by the positive values. And i don't really have any reason to believe my positive values should be that much larger than my negative values.
So what i've noticed is that fundamentally, the magnitude of percentage change values are not symmetrical in scale. For example if i have a value that goes from 50 to 200, that would result in a 300.0% change. If i have a value that goes from 200 to 50 that would result in a -75.0% change. I get there is a reason for this, but in terms of my feature, i don't see a reason why a change of 50 to 100 should be 3x+ more "important" than the same change in value but the opposite direction.
Given this information, i do not believe there would be any reason to want my model to treat a change of 200-50 as a "lesser" change than a change of 50-200. Since i am trying to represent the change of a value over time, i want to abstract this pattern so that my model can "visualize" the change of a value over time that same way a person would.
Right now i am solving this by using this formula
if curr > prev:
return curr / prev - 1
else:
return (prev / curr - 1) * -1
And this does seem to treat changes in value, similarly regardless of the direction. Ie from the example of above 50>200 = 300, 200>50 = -300. Is there a reason why i shouldn't be doing this? Does this accomplish my goal? Has anyone ran into similar dilemmas?
This is a discussion question and it's difficult to know the right answer to it without knowing the physical relevance of your feature. You are calculating a percentage change, and a percent change is dependent on the original value. I am not a big fan of a custom formula only to make percent change symmetric since it adds a layer of complexity when it is unnecessary in my opinion.
If you want change to be symmetric, you can try direct difference or factor change. There's nothing to suggest that difference or factor change are less correct than percent change. So, depending on the physical relevance of your feature, each of the following symmetric measures would be correct ways to measure change -
Difference change -> 50 to 200 yields 150, 200 to 50 yields -150
Factor change with logarithm -> 50 to 200 yields log(4), 200 to 50 yields log(1/4) = -log(4)
You're having trouble because you haven't brought the abstract questions into your paradigm.
"... my model can "visualize" ... same way a person would."
In this paradigm, you need a metric for "same way". There is no such empirical standard. You've dropped both of the simple standards -- relative error and absolute error -- and you posit some inherently "normal" standard that doesn't exist.
Yes, we run into these dilemmas: choosing a success metric. You've chosen a classic example from "How To Lie With Statistics"; depending on the choice of starting and finishing proportions and the error metric, you can "prove" all sorts of things.
This brings us to your central question:
Does this accomplish my goal?
We don't know. First of all, you haven't given us your actual goal. Rather, you've given us an indefinite description and a single example of two data points. Second, you're asking the wrong entity. Make your changes, run the model on your data set, and examine the properties of the resulting predictions. Do those properties satisfy your desired end result?
For instance, given your posted data points, (200, 50) and (50, 200), how would other examples fit in, such as (1, 4), (1000, 10), etc.? If you're simply training on the proportion of change over the full range of values involved in that transaction, your proposal is just what you need: use the higher value as the basis. Since you didn't post any representative data, we have no idea what sort of distribution you have.
I've been using Mathemathica in order to collect wind speed data in a certain location. Mathematica gives me a TimeSeries from which I would like to know what is the maximum value and the minimum one. I've used "FindPeaks" function, but as it is not a regularly sampled time series the function does not work. Is there a way to get the maximum value?
The following is the data:
data = WindSpeedData[{19.416258, -99.719266}, {DateObject[{2016, 1,
1}], DateObject[{2017, 1, 2}]}]
This
Normal[data]
will undo part of the layer of Timeseries that your actual wind speeds are wrapped up inside of.
In that you can see that what you probably want is part of the second item in each list, that appears to be the actual speed. So
Max[Map[#[[2, 1]] &, Normal[data]]]
will look at the beginning of the second part, which is your speed, and then try to find the maximum value.
For your example data that shows Max[29.0802, "NotAvailable"] and that 29.0802 is the maximum wind speed.
That trailing "NotAvailable" is still some part of their wrapping the actual data up inside layers. It is possible that there is one missing wind speed in there and Max doesn't know what to make of that.
Thanks #Bill,I used
Max[data]
It threw me ["Not available", 46.8 km/h]
I just used your code and gave me the same result but in different order [46.8 km/h, "Not available"]. I double checked the datum (46.8) by displaying the data in a grid. Thank you very much, I will use the normal function further on.
first time user of this forum - guidance on how to provide enough information is very appreciated. I am trying to replicate the presentation of data used in the Medical education field. This will help improve the quality of examiners' marking of trainees in a Clinical Exam. What I would like to communicate will be similar to what is already communicated in the College of General Practitioners regarding one of their own exams, please see www.gp10.com.au/slides/thursday/slide29.pdf to help understand what it is I want to present. I have access to Excel, SPSS and R, so any help with any of these would be great. However as a first attempt I have used SPSS and created 3 variables: dummy variable, a "station score" and a "global rating score"(GRS). The "station score"(ST) is a value between 0 and 10 (non-integers) and is on the y-axis similar to the pdf presentation of "Candidate Final Marks". The x-axis is the "global rating scale", an integer from 1 to 6 and is represented in the pdf as the "Overall Performance Scale". When I use SPSS's boxplot I get a boxplot as depicted.
.
What I would like to do is overlay a single examiners own scoring of X number of examinees. So for one examiner (examiner A) provided the following marks:
ST: 5.53,7.38,7.38,7.44,6.81
GRS: 3,4,4,5,3
(this is transposed into two columns).
Whether it be SPSS, Excel or R how would I be able to overlay the box and whisker plots with the individual data points provided by the one examiner? This would help show the degree to which the examiners' marking styles are in concordance with the expected distribution of ST scores across GRS. Any help greatly appreciated! I like Excel graphics but I have found it very difficult to work with when choosing the examiners' data as a separate series - somehow the examiners' GRS scores do not line up nicely on the x-axis. I am very new to R but am also very interested in R, and would expend time to get a good result in R if a good result is viable. I understand JMP may be preferable for this type of thing but access to this may not be possible.
I have a very small question which has been baffling me for a while. I have a dataset with interesting features, but some of them are dimensionless quantities (I've tried using z-scores) on them but they've made things worse. These are:
Timestamps (Like YYYYMMDDHHMMSSMis) I am getting the last 9 chars from this.
User IDs (Like in a Hash form) How do I extract meaning from them?
IP Addresses (You know what those are). I only extract the first 3 chars.
City (Has an ID like 1,15,72) How do I extract meaning from this?
Region (Same as city) Should I extract meaning from this or just leave it?
The rest of the things are prices, widths and heights which understand. Any help or insight would be much appreciated. Thank you.
Timestamps can be transformed into Unix Timestamps, which are reasonable natural numbers
User IF/Cities/Regions are nominal values, which has to be encoded somehow. The most common approach is to create as much "dummy" dimensions as the number of possible values. So if you have 100 ciries, than you create 100 dimensions and give "1" only on the one representing a particular city (and 0 on the others)
IPs should rather be removed, or transformed into some small group of them (based on the DNS-network identification and nominal to dummy transformation as above)
In mahout, I'm setting up a GenericUserBasedRecommender, pretty straight forward for now, typical settings.
In generating a "preference" value for an item, we have the following 5 data points:
Positive interest
User converted on item (highest possible sign of interest)
Normal like (user expressed interest, e.g. like buttons)
Indirect expression of interest (clicks, cursor movements, measuring "eyeballs")
Negative interest
Indifference (items the user ignored when active on other items, a vague expression of disinterest)
Active dislike (thumbs down, remove item from my view, etc)
Over what range I should express these different attributes, let's use a 1-100 scale for discussion?
Should I be keeping the 'Active dislike' and 'Indifference' clustered close together, for example, at 1 and 5 respectively, with all the likes clustered in the 90-100 range?
Should 'Indifference' and 'Indirect expressions of interest' by closer to the center? As in 'Indifference' in the 20-35 range and 'Indirect like' in the 60-70 range?
Should 'User conversion' blow the scale away and be heads and tails higher than the others? As in: 'User Conversion' # 100, 'Lesser likes' # ~65, 'Dislikes' clustered in the 1-10 range?
On the scale of 1-100 is 50 effectively "null", or equivalent to no data point at all?
I know the final answer lies in trial and error and in the meaning of our data, but as far as the algorithm goes, I'm trying to understand at what point I need to tip the scales between interest and disinterest for the algorithm to function properly.
The actual range does not matter, not for this implementation. 1-100 is OK, 0-1 is OK, etc. The relative values are all that really matters here.
These values are estimated by a simple (linearly) weighted average. Therefore the response ought to be "linear". It ought to match an intuition that if action X gets a score 2x higher than action Y, then X should be an indicator of twice as much interest in real life.
A decent place to start is to simply size them relative to their frequency. If click-to-conversion rate is 2%, you might make a click worth 2% of a conversion.
I would ignore the "Indifference" signal you propose. It is likely going to be too noisy to be of use.