Data size matters

Most research is evaluated on small to medium-sized collection of data instances which seems like a toy to real-world collections. This is especially true in fields like information retrieval where real data size (about size of the Web) is 1,000 to 100,000 times larger than most research data collections. In recommender systems, the recent release of Netflix Prize data (which is clearly much smaller than the actual Netflix data) has about 100 millions ratings. This is 100 times larger than the best data set known before.

What does it mean to research and industry? Since research is only the place where models and results are freely published so that everyone can study, there results must be considered with great care when applying for real-world problems.

• Computing power and programming. Much research today is done on single computers (may be information retrieval is the exception) and rapid development languages like Matlab, Python and Perl. When it comes to real-worlds, this assumption does not hold. It is likely that we will need clusters and low-level programming. This also puts more pressure on small research groups to upgrade their computers to match the state-of-the-art. For example, to freely do things with the Netflix data, we need somewhat 6GB RAM, which is clearly the top one at current time.
• Simplifying models. Previously, our group had been playing around with several polynomial time algorithms like the famous Inside-Outside for text parsing. This is theoretically interesting because it is at least tractable. It also works fine with small data set (e.g. 100-10000 sequences whose length is limited to the range 10-50). When facing real-world data, however, we cannot continue this line because it will take years to run a single experiment. My rule of thumb is anything that is not close to linear-time complexity has to be re-considered.
• Accepting approximation. The world is not perfect and it does not require perfect solutions anyway. Often exact computation is hard so approximation is the only way to go.
• Doing things on-the-fly. In news classification, it is not good to assume that news articles are static because they come in every single second with much shift in content and wordings. So, one clever solution is on-line learning where we just update the parameters as soon as a data instance (an article in this case) comes in. Previously, it is sometimes believed that on-line learning performs a little bit worse than batch-learning because on-line learning is considered as an approximation to batch-learning. However, when a lot of data is available from time to time, then how can we still say that after a certain point of time?
• Statistical change. This is a more fundamental problems. It will be very likely that large data collection will change the certain statistics. There are several reasons. First, in research collections, noise is usually less a problem, because the data is collected with care, or it is easier to remove noise, sometimes by hand. This is not true in real-world data where there is much noise, either from the nature of the data, or the collection procedure. Second, the change comes from the size of the data itself. With more data, there is more chance for extremal statistics to occur. If any method is sensitive to the outliers, it is more likely to fail. In addition, complex models generally require more data to estimate. For example, estimating n-gram language models with large n (n >= 4,5) is not reliable using small corpus.
• Over-fitting. Often, due to limited resources, research conclusions are drawn from very limited data with not enough variations. So models that perform well on limited training data and one or two domains will be likely to fail on the Web, where anything can happen. In statistical machine translation, Google has observed that many well-studied methods fail when more data is available.
• Simple statistics can do well. Google also observed in their translation experiments that it does not matter to strike for complex translation models. Simple unigrams are enough. More surprisingly, only first four characters are enough to represent a word! It seems that with enough data, simple models can be as powerful as complex models. Here, pure numerical statistics become very powerful, and it does not agree with common belief that complex, hand-crafted or semantics-driven models are better than simple counts. In my little study of Vietnamese text classification, even sub-syllable features like characters, vowels and consonants are indeed quite powerful although they are not comprehensive to readers. More general, in text classification, no linguistics-inspired document representations have proved to be widely effective.

As researchers have already warned, conclusions drawn from small data set must not be over-generalised.

Conditional random fields: Big innovation by many small improvements

The subject will be Conditional Random Fields (CRF), which cost me roughly 4 years of PhD. After 7 years since its first appearance in ICML 2001, there has been roughly 1,300 citations, according to Google Scholar. This is a very impressive figure so far. It is impressive because anyone can rightly criticise about CRF's novelty compared to its prior arts.

• From machine learning point of view, it is mostly Maximum Entropy, which was first introduced in 1957 by Jaynes, and had became popular since the work of IBM researchers in 1996. The most popular parameterisation is still log-linear, which has been known to physicists since the time of Gibbs. The famous Generalised Iterative Scaling method for optimising log-linear models was introduced in the 1970s.
• From graphical models point of view, it is just a conditional Markov random field (MRF), i.e., when conditioned on an observational data, we have a MRF of the output variables.
• From modelling point of view, it is just a correction of Maximum Entropy Markov Models (MEMM), introduced in 2000.

Then why is it so popular among researchers who value novelty above everything else? The answer is perhaps, because it works and it came at a right time. Let's see how:

• It was the right time in 2001. Statistical machine learning had reached the point of wide acceptance. At the same time, structural modelling had been widely recognised as indispensable in many domains. Graphical models had been come a mainstream in the AI research agenda. Computing power was strong enough to support large-scale real world applications.
• By 2003, it was discovered that a Limited memory Newton method known as L-BFGS works extremely well with CRFs. It helps to scale up to problems with several million parameters, the size unthinkable for statisticians and optimization hard-core guys. Of course, by 2002, it was known that a L-BFGS cousin, Conjugate Gradients outperform all previous known methods for log-linear models. L-BFGS and CGs are two major advances by the numerical optimisation community, and they have come to rescue.
• MRFs had been around for a long time, since the age of Ising models in physics early the 20th century, and the famous work of Besag in 1974 and the Browns in image modelling in 1984. However, MRFs are quite difficult to model because of its intractability in the joint form. By using the conditional forms, we do not need to model the messy observational data, rather we need only to deal with the output of interest. It makes thing significantly easier and more effective.
• The CRF works like magic because it overcome much inherent limits of the well-known HMM, and the related MEMM. It paves the way for domain experts to engineer features as they please - the things are not so easy in HMMs.

In short, CRFs are not a breakthrough that challenges the current belief. It is a right combination of several advances at the right time and makes incremental improvements in each aspect. As a net result, it became a winner and since then has triggered much interest in learning in structured output space.

Some of our related work (updated):

• Hierarchical semi-Markov conditional random fields for deep recursive sequential data, Truyen Tran, Dinh Phung, Hung Bui, Svetha Venkatesh,  Artificial Intelligence, Minor revision. (Extension of the NIPS'08 paper).
• Preference Relation-based Markov Random Fields in Recommender Systems, Shaowu Liu, Gang Li,Truyen Tran, Jiang Yuan, ACML'15, November 20-22, 2015, Hong Kong.
• Predicting delays in software projects using networked classification, Morakot Choetikertikul, Hoa Khanh Dam, Truyen Tran, Aditya Ghose, 30th IEEE/ACM International Conference on Automated Software Engineering, November 9–13, 2015 Lincoln, Nebraska, USA.
• Tree-based Iterated Local Search for Markov Random Fields with Applications in Image Analysis, Truyen Tran, Dinh Phung and Svetha Venkatesh, Journal of Heuristics, 2014, DOI:10.1007/s10732-014-9270-1 
• Ordinal random fields for recommender systems, Shaowu Liu, Truyen Tran, Gang Li, Yuan Jiang, ACML'14, Nha Trang, Vietnam, Nov 2014.
• MCMC for Hierarchical Semi-Markov Conditional Random Fields, Truyen Tran, Dinh Q. Phung, Svetha Venkatesh and Hung H. Bui. In NIPS'09 Workshop on Deep Learning for Speech Recognition and Related Applications. December, 2009, Whistler, BC, Canada.
• Hierarchical Semi-Markov Conditional Random Fields for Recursive Sequential Data, Truyen Tran, Dinh Q. Phung, Hung H. Bui, and Svetha Venkatesh. In Proc. of 21st Annual Conference on Neural Information Processing Systems, Dec 2008, Vancouver, Canada. [See technical report and thesis for more details and extensions.]
• Constrained Sequence Classification for Lexical Disambiguation, Truyen Tran, Dinh Q. Phung and Svetha Venkatesh. In Proc. of 10th Pacific Rim International Conference on Artificial Intelligence (PRICAI-08), 15-19 Dec 2008, Hanoi, Vietnam.
• Preference Networks: probabilistic models for recommendation systems, Truyen Tran, Dinh Q. Phung and Svetha Venkatesh, In Proc. of 6th Australasian Data Mining Conference: AusDM 2007, 3-4 Dec, Gold Coast, Australia. 
• AdaBoost.MRF: Boosted Markov random forests and application to multilevel activity recognition, Truyen Tran, Dinh Quoc Phung, Hung Hai Bui, and Svetha Venkatesh. In Proc. of  IEEE Conference on Computer Vision and Pattern Recognition, volume Volume 2, pages 1686-1693, New York, USA, June 2006.
• Boosted Markov networks for activity recognition, Truyen Tran, Hung Hai Bui and Svetha Venkatesh, In Proc. of International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP2005), 5-8 Dec, Melbourne, Australia.
• Human Activity Learning and Segmentation using Partially Hidden Discriminative Models, Truyen Tran, Hung Hai Bui and Svetha Venkatesh, HAREM 2005: Proceedings of the International Workshop on Human Activity Recognition.

Under/over-generating in learning structured output spaces

Consider learning the structured output spaces. By structured spaces, we roughly means that the space can only be jointly described by multiple variables. In other words, variables are not completely independent of each other. They can be conditionally independent given some other variables. From the graphical models perspective, those variables can be modelled as a graph whose edges depict direct dependency between variables.

While this is interesting because most real-world data can be described in this way, it is a hard problem as generally it is intractable to do any meaningful exact computation. Everything must be approximated.

In learning, we basically estimate some compact description of the structured space, whose size is exponentially many if we want to count every point in it. Since exact generation of the space is impossible, there are two ways to proceed: (1) under-generating where we limit to very small subspace so that we can deal with efficiently, and (2) over-generating where we try to describe a larger but much more relaxed space so many constraints are violated.

Examples of under-generating methods:

• Pseudo-likelihood of Besag: we exploit the conditional independence property to explore a subset of variables and their surrounding (also known as Markov blanket). The basic theory assures that if we have enough data, then there will be no difference between this localised estimation and the true global one.
• Re-ranking of Collin: the idea is that we should use some tractable and approximate methods to generate the most meaningful and tractable subspace, and then deal with the new subspace.

Examples of over-generating methods:

• Piecewise training of Sutton & McCallumn: the idea is that we can duplicate variables and break the structure into independent pieces. Since more variables are added, the new space is larger than the original one. In return we will have much more independence, which makes computation easy. This method may work fine if the independent pieces approximate the data well.
• Tree-superimposition of my own: we can always relax a graph by removing some edges until a spanning tree is left. Since spanning trees are tractable, they can be learned given the knowledge of all other trees accumulated so far.