Tag Archives: recall

Substantial Reduction in Review Effort Required to Demonstrate Adequate Recall

Measuring the recall achieved to within +/- 5% to demonstrate that a production is defensible can require reviewing a substantial number of random documents.  For a case of modest size, the amount of review required to measure recall can be larger than the amount of review required to actually find the responsive documents with predictive coding.  This article describes a new method requiring much less document review to demonstrate that adequate recall has been achieved.  This is a brief overview of a more detailed paper I’ll be presenting at the DESI VII Workshop on June 12th.

The proportion of a population having some property can be estimated to within +/- 5% by measuring the proportion on a random sample of 400 documents (you’ll also see the number 385 being used, but using 400 will make it easier to follow the examples).  To measure recall we need to know what proportion of responsive documents are produced, so we need a sample of 400 random responsive documents.  Since we don’t know which documents in the population are responsive, we have to select documents randomly and review them until 400 responsive ones are found.  If prevalence is 10% (10% of the population is responsive), that means reviewing roughly 4,000 documents to find 400 that are relevant so that recall can be estimated.  If prevalence is 1%, it means reviewing roughly 40,000 random documents to measure recall.  This can be quite a burden.

multistage_acceptance_from_multistageOnce recall is measured, a decision must be made about whether it is high enough.  Suppose you decide that if at least 300 of the 400 random responsive documents were produced (75%) the production is acceptable.  For any actual level of recall, the probability of accepting the production can be computed (see figure to right).  The probability of accepting a production where the actual recall is less than 70% will be very low, and the probability of rejecting a production where the actual recall is greater than 80% will also be low — this comes from the fact that a sample of 400 responsive documents is sufficient to measure recall to within +/- 5%.

multistage_acceptance_procedureThe idea behind the new method is to achieve the same probability profile for accepting/rejecting a production using a multi-stage acceptance test.  The multi-stage test gives the possibility of stopping the process and declaring the production accepted/rejected long before reviewing 400 random responsive documents.  The procedure is shown in the flowchart to the right (click to enlarge).  A decision may be reached after reviewing enough documents to find just 25 random documents that are responsive.  If a decision isn’t made after reviewing 25 responsive documents, review continues until 50 responsive documents are found and another test is applied.  At worst, documents will be reviewed until 400 responsive documents are found (the same as the traditional direct recall estimation method).

multistage_barriers_85_recall_pathsThe figure to the right shows six examples of the multi-stage acceptance test being applied when the actual recall is 85%.  Since 85% is well above the 80% upper bound of the 75% +/- 5% range, we expect this production to virtually always be accepted.  The figure shows that acceptance can occur long before reviewing a full 400 random responsive documents.  The number of random responsive documents reviewed is shown on the vertical axis.  Toward the bottom of the graph the sample is very small and the percentage of the sample that has been produced may deviate greatly from the right answer of 85%.  As you go up the sample gets larger and the proportion of the sample that is produced is expected to get closer to 85%.  When a green decision boundary is touched, causing the production to be accepted as having sufficiently high recall, the color of the remainder of the path is changed to yellow — the yellow part represents the document review that is avoided by using the multi-stage acceptance method (since the traditional direct recall measurement would involve going all the way to 400 responsive documents).  As you can see, when the actual recall is 85% the number of random responsive documents that must be reviewed is often 50 or 100, not 400.

multistage_effort_for_multistageThe figure to the right shows the average number of documents that must be reviewed using the multi-stage acceptance procedure from the earlier flowchart.  The amount of review required can be much less than 400 random responsive documents.  In fact, the further above/below the 75% target (called the “splitting recall” in the paper) the actual recall is, the less document review is required (on average) to come to a conclusion about whether the production’s recall is high enough.  This creates an incentive for the producing party to aim for recall that is well above the minimum acceptable level since it will be rewarded with a reduced amount of document review to confirm the result is adequate.

It is important to note that the multi-stage procedure provides an accept/reject result, not a recall estimate.  If you follow the procedure until an accept/reject boundary is hit and then use the proportion of the sample that was produced as a recall estimate, that estimate will be biased (the use of “unbiased” in the paper title refers to the sampling being done on the full population, not on a subset [such as the discard set] that would cause a bias due to inconsistency in review of different subsets).

You may want to use a splitting recall other than 75% for the accept/reject decision — the full paper provides tables of values necessary for doing that.

Webinar: 10 Years Forward and Back: Automation in eDiscovery

George Socha, Doug Austin, David Horrigan, Bill Dimm, and Bill Speros will give presentations in this webinar on the history and future of ediscovery moderated by Mary Mack on December 1, 2016.  Bill Dimm will talk about the evolution of predictive coding technologies and our understanding of best practices, including recall estimation, the evil F1 score, research efforts, pre-culling, and the TAR 1.0, 2.0, and 3.0 workflows.  CLICK HERE FOR RECORDING OF WEBINAR, SLIDES, AND LINKS TO RELATED RESOURCES.

Gain Curves

You may already be familiar with the precision-recall curve, which describes the performance of a predictive coding system.  Unfortunately, the precision-recall curve doesn’t (normally) display any information about the cost of training the system, so it isn’t convenient when you want to compare the effectiveness of different training methodologies.  This article looks at the gain curve, which is better suited for that purpose.

The gain curve shows how the recall achieved depends on the number of documents reviewed (slight caveat to that at the end of the article).  Recall is the percentage of all relevant documents that have been found.  High recall is important for defensibility.  Here is an example of a gain curve (click to enlarge):

gain_curve_single

The first 12,000 documents reviewed in this example are randomly selected documents used to train the system.  Prevalence is very low in this case (0.32%), so finding relevant documents using random selection is hard.  The system needs to be exposed to a large enough number of relevant training documents for it to learn what they look like so it can make good predictions for the relevance of the remaining documents.

After the 12,000 training documents are reviewed the system orders the remaining documents to put the ones that are most likely to be relevant (based on patterns detected during training) at the top of the list.  To distinguish the training phase from the review phase I’ve shown the training phase as a solid line and review phase as a dashed line.  Review of the remaining documents starts at the top of the sorted list.  The gain curve is very steep at the beginning of the review phase because most of the documents being reviewed are relevant, so they have a big impact on recall.  As the review progresses the gain curve becomes less steep because you end up reviewing documents that are less likely to be relevant.  Review proceeds until a desired level of recall, such as 75% (the horizontal dotted line), is achieved.  The goal is to find the system and workflow that achieves the recall target at the lowest cost (i.e., the one that crosses the dotted line farthest to the left, with some caveats below).

What is the impact of using the same system with a larger or smaller number of randomly selected training documents?  This figure shows the gain curves for 9,000 and 15,000 training documents in addition to the 12,000 training document curve seen earlier:

gain_curve_multi

If the goal is to reach 75% recall, 12,000 is the most efficient option among the three considered because it crosses the horizontal dotted line with the least document review.  If the target was a lower level of recall, such as 70%, 9,000 training documents would be a better choice.  A larger number of training documents usually leads to better predictions (the gain curve stays steep longer during the review phase), but there is a point where the improvement in the predictions isn’t worth the cost of reviewing additional training documents.

The discussion above assumed that the cost of reviewing a document during the training phase is the same as the cost of reviewing a document during the review phase.  That will not be the case if expensive subject matter experts are used to review the training documents and low-cost contract reviewers are used for the review phase.  In that situation, the optimal result is less straightforward to identify from the gain curve.

In some situations it may be possible produce documents without reviewing them if there is no concern about disclosing privileged documents (because there are none or because they are expected to be easy to identify by looking at things like the sender/recipient email address) or non-relevant documents (because there is no concern about them containing trade secrets or evidence of bad acts not covered by the current litigation).  When it is okay to produce documents without reviewing them, the document review associated with the dashed part of the curve can be eliminated in whole or in part.  For example, documents predicted to be relevant with high confidence may be produced without review (unless they are identified as potential privileged), whereas documents with a lower likelihood of being relevant might be reviewed to avoid disclosing too many non-relevant documents.  Again, the gain curve would not show the optimal choice in a direct way–you would need to balance the potential harm (even if small) of producing non-relevant documents against the cost of additional training.

The predictive coding process described in this article, random training documents followed by review (with no additional learning by the algorithm), is sometimes known as Simple Passive Learning (SPL), which is one example of a TAR 1.0 workflow.  To determine the optimal point to switch from training to review with TAR 1.0, a random set of documents known as a control set is reviewed and used to monitor learning progress by comparing the predictions for the control set documents to their actual relevance tags.  Other workflows and analysis of their efficiency via gain curves will be the subject of my next article.

Using Extrapolated Precision for Performance Measurement

This is a brief overview of my paper “Information Retrieval Performance Measurement Using Extrapolated Precision,” which I’ll be presenting on June 8th at the DESI VI workshop at ICAIL 2015 (slides now available here).  The paper provides a novel method for extrapolating a precision-recall point to a different level of recall, and advocates making performance comparisons by extrapolating results for all systems to the same level of recall if the systems cannot be evaluated at exactly the same recall (e.g., some predictive coding systems produce a binary yes/no prediction instead of a relevance score, so the user cannot select the recall that will be achieved).

High recall (finding most of the relevant documents) is important in e-discovery for defensibility.  High precision is desirable to ensure that there aren’t a lot of non-relevant documents mixed in with the relevant ones (i.e., high precision reduces the cost of review for responsiveness and privilege).  Making judgments about the relative performance of two predictive coding systems knowing only a single precision-recall point for each system is problematic—if one system has higher recall but lower precision for a particular task, is it the better system for that task?

There are various performance measures like the F1 score that combine precision and recall into a single number to allow performance comparisons.  Unfortunately, such measures often assume a trade-off between precision and recall that is not appropriate for e-discovery (I’ve written about problems with the  F1 score before).  To understand the problem, it is useful to look at how F1 varies as a function of the recall where it is measured.  Here are two precision-recall curves, with the one on the left being for an easy categorization task and the one on the right being for a hard task, with the F1 score corresponding to each point on the precision-recall curve superimposed:

f1_compare2If we pick a single point from the precision-recall curve and compute the value of F1 for that point, the resulting F1 is very sensitive to the precision-recall point we choose.  F1 is maximized at 46% recall in the graph on the right, which means that the trade-off between precision and recall that F1 deems to be reasonable implies that it is not worthwhile to produce more than 46% of the relevant documents for that task because precision suffers too much when you push to higher recall.  That is simply not compatible with the needs of e-discovery.  In e-discovery, the trade-off  between precision (cost) and recall required should be dictated by proportionality, not by some performance measure that is oblivious to the value of the case.  Other problems with the F1 score are detailed in the paper.

The strong dependence that F1 has on recall as we move along the precision-recall curve means that it is easy to draw wrong conclusions about which system is performing better when performance is measured at different levels of recall.  This strong dependence on recall occurs because the contours of equal F1 are not shaped like precision-recall curves, so a precision-recall curve will cut across many contours.   In order to have the freedom to measure performance at recall levels that are relevant for e-discovery (e.g., 75% or higher) without drawing wrong conclusions about which system is performing best, the paper proposes a performance measure that has constant-performance contours that are shaped like precision-recall curves, so the performance measure depends much less on the recall level where the measurement is made than F1 does. In other words, the proposed performance measure aims to be sensitive to how well the system is working while being insensitive to the specific point on the precision-recall curve where the measurement is made.  This graph compares the constant-performance contours for F1 to the measure proposed in the paper:

f1_x_contours

Since the constant-performance contours are shaped like typical precision-recall curves, we can view this measure as being equivalent to extrapolating the precision-recall point to some other target recall level, like 75%, by simply finding an idealized precision-recall curve that passes through the point and moving along that curve to the target recall.  This figure illustrates extrapolation of precision measurements for three different systems at different recall levels to 75% recall for comparison:

x_extrapolate

Finally, here is what the performance measure looks like if we evaluate it for each point in the two precision-recall curves from the first figure:

x_compare2

The blue performance curves are much flatter than the red F1 curves from the first figure, so the value is much less sensitive to the recall level where it is measured.  As an added bonus, the measure is an extrapolated estimate of the precision that the system would achieve at 75% recall, so it is inversely proportional to the cost of the document review needed (excluding training and testing) to reach 75% recall.  For more details, read the paper or attend my talk at DESI VI.

Can You Really Compete in TREC Retroactively?

I recently encountered a marketing piece where a vendor claimed that their tests showed their predictive coding software demonstrated favorable performance compared to the software tested in the 2009 TREC Legal Track for Topic 207 (finding Enron emails about fantasy football).  I spent some time puzzling about how they could possibly have measured their performance when they didn’t actually participate in TREC 2009.

One might question how meaningful it is to compare to performance results from 2009 since the TREC participants have probably improved their software over the past six years.  Still, how could you do the comparison if you wanted to?  The stumbling block is that TREC did not produce a yes/no relevance determination for all of the Enron emails.  Rather, they did stratified sampling and estimated recall and prevalence for the participating teams by producing relevance determinations for just a few thousand emails.

Stratified sampling means that the documents are separated into mutually-exclusive buckets called “strata.”  To the degree that stratification manages to put similar things into the same stratum, it can produce better statistical estimates (smaller uncertainty for a given amount of document review).  The TREC Legal Track for 2009 created a stratum containing documents that all participants agreed were relevant.  It also created four strata containing documents that all but one participant predicted were relevant (there were four participants, so one stratum for each dissenting participant).  There were six strata where two participants agreed on relevance, and four strata where only one of the four participants predicted the documents were relevant.  Finally, there was one stratum containing documents that all participants predicted were non-relevant, which was called the “All-N” stratum.  So, for each stratum a particular participant either predicted that all of the documents were relevant or they predicted that all of the documents were non-relevant.  You can view details about the strata in table 21 on page 39 here.  Here is an example of what a stratification might look like for just two participants (the number of documents shown and percentage that are relevant may differ from the actual data):

stratification

A random subset of documents from each stratum was chosen and reviewed so that the percentage of the documents in the stratum that were relevant could be estimated.  Multiplying that percentage by the number of documents in the stratum gives an estimate for the number of relevant documents in the stratum.  Combining the results for the various strata allows precision and recall estimates to be computed for each participant.  How could this be done for a team that didn’t participate?  Before presenting some ideas, it will be useful to have some notation:

N[i] = number of documents in stratum i
n[i] = num docs in i that were assessed by TREC
n+[i] = num docs in i that TREC assessed as relevant
V[i] = num docs in i that vendor predicted were relevant
v[i] = num docs in i that vendor predicted were relevant and were assessed by TREC
v+[i] = num docs in i that vendor predicted were relevant and assessed as relevant by TREC

sampling

To make some of the discussion below more concrete, I’ll provide formulas for computing the number of true positives (TP), false positives (FP), and false negatives (FN).  The recall and precision can then be computed from:

R = TP / (TP + FN)
P = TP / (TP + FP)

Here are some ideas I came up with:

1) They could have checked to see which strata the documents they predicted to be relevant fell into and applied the percentages TREC computed to their data.  The problem is that since they probably didn’t identify all of the documents in a stratum as being relevant the percentage of documents that were estimated to be relevant for the stratum by TREC wouldn’t really be applicable.  If their system worked really well, they may have only predicted that the truly relevant documents from the stratum were relevant.  If their system worked badly, their system may have predicted that only the truly non-relevant documents from the stratum were relevant.  This approach could give estimates that are systematically too low or too high.  Here are the relevant formulas (summing over strata, i):

TP = Sum{ V[i] * n+[i] / n[i] }
FP = Sum{ V[i] * (1 – n+[i]/n[i]) }
FN = Sum{ (N[i] – V[i]) * n+[i] / n[i] }

2) Instead of using the percentages computed by TREC, they could have computed their own percentages by looking at only the documents in the stratum that they predicted were relevant and were reviewed by TREC to give a relevance determination.  This would eliminate the possible bias from approach (1), but it also means that the percentages would be computed from a smaller sample, so the uncertainty in the percentage that are relevant would be bigger.  The vendor didn’t provide confidence intervals for their results.  Here is how the computation would go:

TP = Sum{ V[i] * v+[i] / v[i] }
FP = Sum{ V[i] * (1 – v+[i]/v[i]) }
FN = Sum{ (N[i] – V[i]) * (n+[i] – v+[i]) / (n[i] – v[i]) }

It’s possible that for some strata there would be no overlap between the documents TREC assessed and the documents the vendor predicted to be relevant since TREC typically assessed only about 4% of each stratum for Topic 207 (except the All-N stratum, where they assessed only 0.46%).  This approach wouldn’t work for those strata since v[i] would be 0.  For strata where v[i] is 0, one might use approach (1) and hope it isn’t too wrong.

3) A more sophisticated tweak on (2) would be to use the ratio n+[i]/n[i] from (1) to generate a Bayesian prior probability distribution for the proportion of documents predicted by the vendor to be relevant that actually are relevant, and then use v+[i] and v[i] to compute a posterior distribution for that proportion and use the mean of that distribution instead of v+[i]/v[i] in the computation. The idea is to have a smooth interpolation between using n+[i]/n[i] and using v+[i]/v[i] as the proportion of documents estimated to be relevant, where the interpolation would be closer to v+[i]/v[i] if v[i] is large (i.e., if there is enough data for v+[i]/v[i] to be reasonably accurate).  The result would be sensitive to choices made in creating the Bayesian prior (i.e., how much variance to give the probability distribution), however.

4) They could have ignored all of the documents that weren’t reviewed in TREC (over 500,000 of them) and just performed their predictions and analysis on the 3,709 documents that had relevance assessments (training documents should come from the set TREC didn’t assess and should be reviewed by the vendor to simulate actual training at TREC being done by the participants).  It would be very important to weight the results to compensate for the fact that those 3,709 documents didn’t all have the same probability of being selected for review.  TREC oversampled the documents that were predicted to be relevant compared to the remainder (i.e., the number of documents sampled from a stratum was not simply proportional to the number of documents in the stratum), which allowed their stratification scheme to do a good job of comparing the participating teams to each other at the expense of having large uncertainty for some quantities like the total number of relevant documents.  The prevalence of relevant documents in the full population was 1.5%, but 9.0% of the documents having relevance assessments were relevant.  Without weighting the results to compensate for the uneven sampling, you would be throwing away over half a million non-relevant documents without giving the system being tested the opportunity to incorrectly predict that some of them are relevant, which would lead to an inflated precision estimate.  The expression “shooting fish in a barrel” comes to mind.  Weighting would be accomplished by dividing by the probability of the document having been chosen (after this article was published I learned that this is called the Horvitz-Thompson estimator, and it is what the TREC evaluation toolkit uses), which is just n[i]/N[i], so the computation would be:

TP = Sum{ (N[i]/n[i]) * v+[i] }
FP = Sum{ (N[i]/n[i]) * (v[i] – v+[i]) }
FN = Sum{ (N[i]/n[i]) * (n+[i] – v+[i]) }

Note that if N[i]/n[i] is equal to V[i]/v[i], which is expected to be approximately true since the subset of a stratum chosen for assessment by TREC is random, the result would be equal to that from (2).  If N[i]/n[i] is not equal to V[i]/v[i] for a stratum, we would have the disturbing result that the estimate for TP+FP for that stratum would not equal the number of documents the vendor predicted to be relevant for that stratum, V[i].

5) The vendor could have ignored the TREC relevance determinations, simply doing their own.  That would be highly biased in the vendor’s favor because there would be a level of consistency between relevance determinations for the training data and testing data that did not exist for TREC participants.  At TREC the participants made their own relevance determinations to train their systems and a separate set of Topic Authorities made the final relevance judgments that determined the performance numbers.  To the degree that participants came to different conclusions about relevance compared to the Topic Authorities, their performance numbers would suffer.  A more subtle problem with this approach is that the vendor’s interpretation of the relevance criteria would inevitably be somewhat different from that of TREC assessors (studies have shown poor agreement between different review teams), which could make the classification task either easier or harder for a computer.  As an extreme example, if the vendor took all documents containing the word “football” to be relevant and all other documents to be non-relevant, it would be very easy for a predictive coding system to identify that pattern and achieve good performance numbers.

Approaches (1)-(4) would all give the same results for the original TREC participants because for each stratum they would either have V[i]=0 (so v[i]=0 and v+[i]=0) or they would have V[i]=N[i] (so v[i]=n[i] and v+[i]=n+[i]).  The approaches differ in how they account for the vendor predicting that only a subset of a stratum is relevant.  None of the approaches described are great.  Is there a better approach that I missed? TREC designed their strata to make the best possible comparisons between the participants.  It’s hard to imagine how an analysis could be as accurate for a system that was not taken into account in the stratification process.  If a vendor is tempted to make such comparisons, they should at least disclose their methodology and provide confidence intervals on their results so prospective clients can determine whether the performance numbers are actually meaningful.

eRecall: No Free Lunch

There has been some debate recently about the value of the “eRecall” method compared to the “Direct Recall” method for estimating the recall achieved with technology-assisted review. This article shows why eRecall requires sampling and reviewing just as many documents as the direct method if you want to achieve the same level of certainty in the result.

Here is the equation:
eRecall = (TotalRelevant – RelevantDocsMissed) / TotalRelevant

Rearranging a little:
eRecall = 1 – RelevantDocsMissed / TotalRelevant
= 1 – FractionMissed * TotalDocumentsCulled / TotalRelevant

It requires estimation (via sampling) of two quantities: the total number of relevant documents, and the number of relevant documents that were culled by the TAR tool. If your approach to TAR involves using only random sampling for training, you may have a very good estimate of the prevalence of relevant documents in the full population by simply measuring it on your (potentially large) training set, so you multiply the prevalence by the total number of documents to get TotalRelevant. To estimate the number of relevant documents missed (culled by TAR), you would need to review a random sample of the culled documents to measure the percentage of them that were relevant, i.e. FractionMissed (commonly known as the false omission rate or elusion). How many?

To simplify the argument, let’s assume that the total number of relevant documents is known exactly, so there is no need to worry about the fact that the equation involves a non-linear combination of two uncertain quantities.  Also, we’ll assume that the prevalence is low, so the number of documents culled will be nearly equal to the total number of documents.  For example, if the prevalence is 1% we might end up culling about 95% to 98% of the documents.  With this approximation, we have:

eRecall = 1 – FractionMissed / Prevalence

It is the very small prevalence value in the denominator that is the killer–it amplifies the error bar on FractionMissed, which means we have to take a ton of samples when measuring FractionMissed to achieve a reasonable error bar on eRecall.

Let’s try some specific numbers.  Suppose the prevalence is 1% and the recall (that we’re trying to estimate) happens to be 75%.  Measuring FractionMissed should give a result of about 0.25% if we take a big enough sample to have a reasonably accurate result.  If we sampled 4,000 documents from the culled set and 10 of them were relevant (i.e., 0.25%), the 95% confidence interval for FractionMissed would be (using an exact confidence interval calculator to avoid getting bad results when working with extreme values, as I advocated in a previous article):

FractionMissed = 0.12% to 0.46% with 95% confidence (4,000 samples)

Plugging those values into the eRecall equation gives a recall estimate ranging from 54% to 88% with 95% confidence.  Not a very tight error bar!

If the number of samples was increased to 40,000 (with 100 being relevant, so 0.25% again), we would have:

FractionMissed = 0.20% to 0.30% with 95% confidence (40,000 samples)

Plugging that into the eRecall equation gives a recall estimate ranging from 70% to 80% with 95% confidence, so we have now reached the ±5% level that people often aim for.

For comparison, the Direct Recall method would involve pulling a sample of 40,000 documents from the whole document set to identify roughly 400 random relevant documents, and finding that roughly 300 of the 400 were correctly predicted by the TAR system (i.e., 75% recall).  Using the calculator with a sample size of 400 and 300 relevant (“relevant” for the calculator means correctly-identified for our purposes here) gives a recall range of 70.5% to 79.2%.

So, the number of samples required for eRecall is about the same as the Direct Recall method if you require a comparable amount of certainty in the result.  There’s no free lunch to be found here.

Fair Comparison of Predictive Coding Performance

Understandably, vendors of predictive coding software want to show off numbers indicating that their software works well.  It is important for users of such software to avoid drawing wrong conclusions from performance numbers.

Consider the two precision-recall curves below (if you need to brush up on the meaning of precision and recall, see my earlier article):precision_recall_for_diff_tasks

The one on the left is incredibly good, with 97% precision at 90% recall.  The one on the right is not nearly as impressive, with 17% precision at 70% recall, though you could still find 70% of the relevant documents with no additional training by reviewing only the highest-rated 4.7% of the document population (excluding the documents reviewed for training and testing).

Why are the two curves so different?  They come from the same algorithm applied to the same document population with the same features (words) analyzed and the exact same random sample of documents used for training.  The only difference is the categorization task being attempted, i.e. what type of document we consider to be relevant.  Both tasks have nearly the same prevalence of relevant documents (0.986% for the left and 1.131% for the right), but the task on the left is very easy and the one on the right is a lot harder.  So, when a vendor quotes performance numbers, you need to keep in mind that they are only meaningful for the specific document set and task that they came from.  Performance for a different task or document set may be very different.  Comparing a vendor’s performance numbers to those from another source computed for a different categorization task on a different document set would be comparing apples to oranges.

Fair comparison of different predictive coding approaches is difficult, and one must be careful not to extrapolate results from any study too far.  As an analogy, consider performing experiments to determine whether fertilizer X works better than fertilizer Y.  You might plant marigolds in each fertilizer, apply the same amount of water and sunlight, and measure plant growth.  In other words, keep everything the same except the fertilizer.  That would give a result that applies to marigolds with the specific amount of sunlight and water used.  Would the same result occur for carrots?  You might take several different types of plants and apply the same experiment to each to see if there is a consistent winner.  What if more water was used?  Maybe fertilizer X works better for modest watering (it absorbs and retains water better) and fertilizer Y works better for heavy watering.  You might want to present results for different amounts of water so people could choose the optimal fertilizer for the amount of rainfall in their locations.  Or, you might determine the optimal amount of water for each, and declare the fertilizer that gives the most growth with its optimal amount of water the winner, which is useful only if gardeners/farmers can adjust water delivery.  The number of experiments required to cover every possibility grows exponentially with the number of parameters that can be adjusted.

Predictive coding is more complicated because there are more interdependent parts that can be varied.  Comparing classification algorithms on one document set may give a result that doesn’t apply to others, so you might test on several document sets (some with long documents, some with short, some with high prevalence, some with low, etc.), much like testing fertilizer on several types of plants, but that still doesn’t guarantee that a consistent winner will perform best on some untested set of documents.  Does a different algorithm win if the amount of training data is higher/lower, similar to a different fertilizer winning if the amount of water is changed?  What if the nature of the training data (e.g., random sample vs. active learning) is changed?  The training approach can impact different classification algorithms differently (e.g., an active learning algorithm can be optimized for a specific classification algorithm), making the results from a study on one classification algorithm inapplicable to a different algorithm.  When comparing two classification algorithms where one is known to perform poorly for high-dimensional data, should you use feature selection techniques to reduce the dimensionality of the data for that algorithm under the theory that that is how it would be used in practice, but knowing that any poor performance may come from removing an important feature rather than from a failure of the classification algorithm itself?

What you definitely should not do is plant a cactus in fertilizer X and a sunflower in fertilizer Y and compare the growth rates to draw a conclusion about which fertilizer is better.  Likewise, you should not compare predictive coding performance numbers that came from different document sets or categorization tasks.