Data Management and Machine Learning

Victor, Hogwild, Felix, Tuffy: Chris Re has been doing some very interesting work at the intersection of databases and machine learning at the University of Wisconsin. Victor proposes to support many kinds of learning tasks that can be solved using Stochastic Gradient Descent (SGD) in a traditional relational database. Victor provides a python interface to design your learning task and it is executed using the UDF mechanism available in the database. They show that it is not particularly hard to solve a variety of statistical problems with this infrastructure. As expected linear models, such as logistic regression can easily be implemented. The examples go on to show conditional random fields, min-cut, and factored models.

Felix is a relational optimizer for statistical inference. In particular, if you want to solve a Markov Logic Network based on data sitting in some database (say postgres), Felix is your guy. Check out this example. In a VLDB paper this year they describe a system called Tuffy -- one of the components that Felix uses. I haven't had to play with  Bayesian Networks or Graphical Models since my machine learning course back in grad school, so I can more easily see the applicability of regression and factored models compared with MLNs :-) Any pointers to applications where MLNs have been used successfully to solve big-data learning tasks will be much appreciated.

A recent paper (HOGWILD) points out some very interesting results on parallelizing SGD algorithms. SGD is an incredibly convenient way to deal with large data sets while trying to learn statistical models. A particularly thorny issue of parallelizing an SGD algorithm is one of concurrent updates to a shared model from different threads. While standard techniques of locking and synchronization can be used to make sure updates to the model follow some serial order, they often end up being the critical performance bottleneck.

In HOGWILD, the authors show that for optimization problems where the model is sparse, that is concurrent updates have a low probability of causing conflicting updates, it is reasonable to proceed with the updates without locking or synchronization. While this might cause some threads (or processes) to occasionally over-write each other's work, the convergence rate is still close to optimal. On several machine learning tasks, such as matrix factorization and learning sparse SVMs -- they show that HOGWILD is at least as as good and often substantially faster than known serial methods and previous parallel techniques. This is a really cool result, and I've used it in a different context in my current research with impressive results! I'll describe that work in the coming weeks...

Parallel Stochastic Gradient Descent

I've been learning about stochastic gradient descent (SGD) and why people seem to be excited about it in the context of building models over large datasets. Rainer Gemulla, Peter Haas, Erik Nijcamp, and Yannis Sismanis published a really cool paper at KDD this year that was my introduction to the problem.

At a high level. SGD is simply an optimization technique that can be used to minimize some objective function (such as a loss function). The main difference from traditional "batch" gradient descent is that SGD samples from the data at each step. That is, the model can be updated after evaluating the gradient of the loss function for a sample of the input data -- a sample that can be as small as a single point! SGD can achieve incredibly fast performance on a variety of machine learning tasks -- and often converges to a good solution much faster than conventional batch gradient descent. On large data sets, the performance difference could be an order of magnitude or more. There are, of course, lots of caveats about data size, learning rates, sampling techniques, and convergence rates, when it comes to SGD.

The KDD paper focuses on matrix factorization -- a technique that has received a lot of interest in the context of the "Netflix Problem". Given a sparse C by I matrix M of C customers and I  items (say movies), where each entry in the matrix contains a rating, the problem is one of finding factors of the matrix A , B such that the matrix M' = A x B matches the existing values in M, and offers a prediction for the missing values in M. There are many techniques for solving this problem. However, as the matrix M gets larger, and you have billions of ratings from millions of customers, the problem becomes too big to solve on a single machine.

Rainer's KDD paper shows how you can use a distributed version of SGD to solve this problem using a cluster of machines. The central idea in the paper is a clever partitioning of the matrix so that each node in the cluster can work on a partition of the data and update the model (the factors A and B) without fine grained coordination with other nodes in the cluster. The bulk of the paper deals with proving why their partitioning strategy is statistically sound. The paper describes an implementation of this using R and Snowfall for small clusters. They also describe an implementation of this algorithm using Hadoop. The details of the implementation are tricky and complicated -- you need to achieve a certain partitioning of the data,  there are certain communication patterns on the model that are not a natural fit for Hadoop resulting in some inelegant MapReduce code, and a certain amount of additional coordination is required for efficient performance. However, the results are impressive -- the Distributed SGD algorithm converges to a good solution faster and scales way better than alternative techniques.

As one can imagine, Netflix isn't the only company that needs to solve large recommendation problems. There are many large content publishers, marketplaces, and retailers working hard on good solutions to this problem. What's more, the ability to factorize large matrices is good not just for content recommendation. It can be used as a building block for clustering algorithms, topic detection, and even risk analytics. Neat stuff. This should enable some interesting new recommendation-style applications and provide alternate/faster implementations for existing ones.