Randomized algorithm for Verification of Matrix Multiplication

Suppose you want to verify if AB = C and A is m by n and B is n by k then, the time taken for this is O(mnk + nk) = O(mnk)

What if you had a vector x, then ABx = Cx...  here x is a random vector.
x  is of dimensionality k by 1  and created by randomly sampling from a gaussian distribution.

Now the time taken to compute Bx is O(nk)  and is of dimentionaity n by 1 and time taken to compute ABx is O(mn). Similarly, time taken to compute Cx is O(mk)...

So the total time taken to verify is O(mn+nk+mk) and not O(mnk)

The hashing trick for a dynamically changing vocabulary

I recently learned about the "hashing" trick in Machine Learning. It is typically used to handle dynamically changing vocabulary in large-scale machine learning algorithms. With the hashing trick, we always have a "fixed" vocabulary. Only thing is what this vocabulary is, we dont know. The words are hashed into a M- length hash table, and no matter how many new words come in the hash contains all of these tables. Its amazing that Yahoo research is the company that came up with the idea and implemented a widely used open source software called the vowpal wabbit. Researchers who propose new online algorithms with a dynamically changing feature set implement their algorithm in vowpal Wabbit. I think there is also an effort to implement vowpal wabbit on top of hadoop.

It is indeed sad that a company like Yahoo which has been an innovator of so many cool ideas is under the weather. Hopefully Marissa Mayer will turn things around.

For more information on Vowpal Wabbit visit https://github.com/JohnLangford/vowpal_wabbit/wiki/Examples

PdfLatex wont render images in the pdf output

If you are writing a conference paper and using latex to create your paper, then this post might be useful to you.

Typically each document has a header of the following sort.

\documentclass[10pt,a4paper,draft]{article}

 If you have chosen the "draft" option as in "\documentclass[10pt,a4paper,draft]{article}", then a simple code as given below, will not work.

\begin{figure}[!t]
\centering
\includegraphics[width=3in]{fetch}
\caption{Pipeline: Fetch Instruction}
\label{fig:fetch}
\end{figure}

 The figure wont render in the output pdf if the "draft" option is selected in the \document command.

Make sure you say its final, or just leave that option alone, like this:  \documentclass[10pt,a4paper]{article}.

Measuring Query Difficulty

The trail of this reading began with Sonia Haiduc's paper "On the Effect of the Query in IR-based Concept Location". A lot of the paper is a review of the recent research focus in IR "predicting query difficulty". I was surprised to see that this paper was accepted. There were no results, not even an explanation of how evaluating query difficulty is different for concept location compared to traditional IR. Nevertheless, there was a good amount of literature review that guided me to several other interesting papers. There are "predictors" as well as "estimators" of query quality. Predictors usually examine the content of the query alone and generate a score that represents the query difficulty. The estimators use the ranked list to generate a score. The evaluation technique for all the algorithms in the umbrella of query difficulty prediction goes as follows:
The predictor or the estimator gives out score for each query that is expected to have correlation with the Average Precision for that query. The query quality score is correlated with the AP over all the queries in the entire test collection and in order to be doubly sure, a statistical significance test is conducted to illustrate that the two distributions originated from the same original system (demonstrate high p-value).

In order to get a better idea of how the specificities of the predictor or estimator algorithm goes I referred to the highly cited paper " Predicting Query Performance, SIGIR 2002". This paper is output of the Bruce Croft group and lives up to its reputation. The paper discuses an clarity based score, which measures the separateness of the query from the collection model. The following formula measures the divergence  = \sum_w p(w|q) log_2(p(w|q)/p(w|coll)). The numerator measures the entropy of the query while the denominator the divergence from the collection model. the p(w|q) is the query model. The experimentation is extensive spanning multiple test collections and setting up quantitative proof for all the thresholds they use in their experiments.
  
"Query Difficulty, Robustness, and Selective Application of Query Expansion" published in Advances in Information Retrieval in 2004, was one of the first to come up with a "use" of measuring query difficulty. They employed a number of retrieval models and test collections for their study. Not only did they correlate query difficulty with the P@10, AP and so on, they used the "relevance judgements"  also to understand its correlation with query difficulty.

There has been some work in the area of "traceability link recovery" for dealing with difficult queries. The method employed is simple. For queries that show poor performance, one uses an web based search to mine documents that could be used for query reformulation. I wonder if this comes under the umbrella of multi-modal retrieval.

I think it is worthwhile to spend some using these metrics on my own datasets and isolating "difficult" queries ahead of time to aid analysis.

Handling duplicates in ranking documents for Retrieval Algorithms

I never paid attention to the ranking step of a retrieval algorithm. All I had to do was sort the scores. These scores are computed by using a similarity (or divergence) function to compare a query with all the documents in the collection. What I had overlooked was the possibility of scores being equal. How do you rank documents with similar scores? Does it have a great impact on retrieval performance? Turns out, the answer to the second question is YES. To give a simple example, consider 6 documents with the following scores,

doc no   1      2      3       4    5        6
scores 0.87 0.97 0.97 0.85 0.49 0.87

Simple ranking would give out the following output

doc no   1      2      3    4    5   6
rank       3     1      2    5    6   4

If doc 3 is the relevant document,  it is still considered to be at rank 2 as opposed to rank 1(where it actually should be since it scores as much as doc2). The Precision goes from 1.00 to 0.5 just because of this sort of ranking.

This wikipedia article summarizes on ways to handle this. It seems like a trivial concept but it has tremendously improved bug localization results on my iBUGS dataset.

For 291 bugs, I compute the retrieval performance by using the "standard competition" ranking (1 2 2 4) and the retrieval performance shot up from 0.14 to 0.21 with a p-value of 0. Thus the improvement is statistically significant.

Quick Reference: cvs2cl

CVS is a primitive and unfriendly tool for version control (at least in my experience).

Gladly there is a tool called cvs2cl that makes it easier to manage the log files.

Here are the key concepts

1)Install cvs and cvs2cl (both available through sudo apt-get install commands)
2)Checkout the version you want into a directory
3) cd  
4) in this directory execute cvs2cl command

cvs2cl -T  gives out the changes in chronologically reverse order with locations where tags first appeared. But a word of caution, the tag here means, where a tag was first encountered as it appears in the logfile.

I tried
cvs2cl -T --chrono . But it gives out  inaccurate or even incorrect information here. Since, all it is doing is reversing the log file, and not really checking out information in reverse order

The option --xml outputs in xml format.

The overall command to track changes in trunk only with tag information when the tag first occurred (reverse chronological order) use this

cvs2cl --xml --no-wrap --summary --T -S -r --follow-only trunk

Each file in cvs is in a particular state, that is encoded in tag in the xml file. Meaning of file state is "Exp" most of the time and stands for experimental. Since we are tracking most of the files will be exp state, but in a release branch you might find "stab" for stable version of the file.

Hope this helps

Quick Reference: Student t's paired t-test for comparing retrieval algorithms

Given a set of queries Q of size n, two retrieval algorithms need to compared
calculate AP (Average precision) for each query using both the algorithms, call one AP1 and the second one AP2

To calculate if they are statistically significant, here are the steps

a) calculate D = AP1-AP2
b) t-score = mean(D)/(standard_deviation(D)/sqrt(n))
c) Feed it into a p-value calculator with df(degrees of freedom) = n-1 Click here

Pretty neat and quick