Probabilistic Graphical Models
10-708, Fall 2005
Your class project is an opportunity for you to explore an interesting multivariate analysis problem of your choice in the context of a real-world data set. Projects can be done by you as an individual, or in teams of two to three students. Each project will also be assigned a 708 instructor as a project consultant/mentor. They will consult with you on your ideas, but the final responsibility to define and execute an interesting piece of work is yours. Your project will be worth 30% of your final class grade, and will have two final deliverables:
2. a poster presenting your work for a special ML class poster session at the end of the semester, due Dec 2, worth 20% of the project grade.
In addition, you must turn in a midway progress report (5 pages maximum in NIPS format, including references) describing the results of your first experiments by Nov 14, worth 20% of the project grade. Note that, as with any conference, the page limits are strict! Papers over the limit will not be considered.
You must turn in a brief project proposal (1-page maximum) by Oct 19th.
You are encouraged to come up a topic directly related to your own current research project or research topics related to graphical models of your own interest that bears a non-trivial technical component (either theoretical or application-oriented), but the proposed work must be new and should not be copied from your previous published or unpublished work. For example, research on graphical models that you did this summer does not count as a class project.
You may use the list of available dataset provided bellow and pick a less adventurous project from the following list of potential project ideas. These data sets have been successfully used for machine learning in the past, and you can compare your results with those reported in the literature. Of course you can also choose to work on a new problem beyond our list used the provided dataset.
Project proposal format: Proposals should be one page maximum. Include the following information:
· Project title
· Project idea. This should be approximately two paragraphs.
· Software you will need to write.
· Papers to read. Include 1-3 relevant papers. You will probably want to read at least one of them before submitting your proposal
· Teammate(s): will you have teammate(s)? If so, whom? Maximum team size is three students.
· Nov 14 milestone: What will you complete by Nov 14? Experimental results of some kind are expected here.
· Ideally, you will want to pick a problem in a domain of your interest, e.g., natural language parsing, DNA sequence analysis, text information retrieval, network mining, reinforcement learning, sensor networks, etc., and formulate your problem using graphical models. You can then, for example, adapt and tailor standard inference/learning algorithms to your problem, and do a thorough performance analysis.
can also find some project ideas below.
This data set contains a time series of images of brain activation,
using fMRI, with one image every 500 msec. During this time, human subjects performed
of a sentence-picture comparison task (reading a sentence, observing a
and determining whether the sentence correctly described the picture).
the 40 trials lasts approximately 30 seconds. Each image contains
5,000 voxels (3D pixels), across a large
the brain. Data is available for 12 different human subjects.
Available software: we can provide Matlab software for reading the data, manipulating and visualizing it, and for training some types of classifiers (Gassian Naive Bayes, SVM).
Project A: Bayes network classifiers for fMRI
Project idea: Gaussian Naļve Bayes classifiers and SVMs have been used with this data to predict when the subject was reading a sentence versus perceiving a picture. Both of these classify 8-second windows of data into these two classes, achieving around 85% classification accuracy [Mitchell et al, 2004]. This project will explore going beyond the Gaussian Naļve Bayes classifier (which assumes voxel activities are conditionally independent), by training a Bayes network in particular a TAN tree [Friedman, et al., 1997]. Issues youll need to confront include which features to include (5000 voxels times 8 seconds of images is a lot of features) for classifier input, whether to train brain-specific or brain-independent classifiers, and a number of issues about efficient computation with this fairly large data set.
Papers to read: "Learning to Decode Cognitive States from Brain Images," Mitchell et al., 2004, "Bayesian Network Classifiers" Friedman et al., 1997.
The goal is to segment images in a meaningful way.
Project B: Region-Based Segmentation
Most segmentation algorithms have focused on segmentation based on edges or based on discontinuity of color and texture. The ground-truth in this dataset, however, allows supervised learning algorithms to segment the images based on statistics calculated over regions. One way to do this is to "oversegment" the image into superpixels (Felzenszwalb 2004, code available) and merge the superpixels into larger segments. Graphical models can be used to represent smoothness in clusters, by adding appropriate potentials between neighboring pixels. In this project, you can address, for example, learning of such potentials, and inference in models with very large tree-width.
Papers to read: Some segmentation papers from
This data set contains 1000 text articles posted to each of 20
online newgroups, for a total of 20,000
documentation and download, see this website.
This data is useful for a variety of text classification and/or
projects. The "label" of each article is which of the 20
newsgroups it belongs to. The newsgroups (labels) are
organized (e.g., "sports", "hockey").
Available software: The same website provides an implementation of a Naive Bayes classifier for this text data. The code is quite robust, and some documentation is available, but it is difficult code to modify.
EM text classification in the case where you
have labels for some documents, but not for others (see McCallum
and come up with your own suggestions)
Using this 54-node sensor network deployment, we collected temperature, humidity, and light data, along with the voltage level of the batteries at each node. The data was collected every 30 seconds, starting around 1am on February 28th 2004.
This is a real dataset, with lots of missing data, noise, and failed sensors giving outlier values, especially when battery levels are low.
· Learn graphical models representing the correlations between measurements at different nodes
· Develop new distributed algorithms for solving a learning task on this data
Optical character recognition, and the simpler digit recognition task, has been the focus of much ML research. We have two datasets on this topic. The first tackles the more general OCR task, on a small vocabulary of words: (Note that the first letter of each word was removed, since these were capital letters that would make the task harder for you.)
· Use an HMM to exploit correlations between neighboring letters in the general OCR case to improve accuracy. (Since ZIP codes don't have such constraints between neighboring digits, HMMs will probably not help in the digit case.)
This dataset has includes 45 years of daily precipitation data from
Northwest of the
· Weather prediction: Learn a probabilistic model to predict rain levels
· Sensor selection: Where should you place sensor to best predict rain
This dataset contains webpages from 4 universities, labeled with whether they are professor, student, project, or other pages.
· Learning classifiers to predict the type of webpage from the text
· Can you improve accuracy by exploiting correlations between pages that point to each other using graphical models?
Project K: Inference
(Variational Inference for Bayesian
networks) is an
alternative to BUGS in that it uses a deterministic mean field
VIBES is open source Java; there is also a Matlab
interface. The goal of this project is to compare speed vs
accuracy of the mean field and the Gibbs sampling methods on various
in Bayesian estimation. (For discrete random variables, e.g. Ising models, mean field is usually much faster,
belief propagation is even better, but for continuous (non Gaussian)
variables, it's not so clear.) See also Matt
for variational Bayes
Comparing approximate inference for Ising models:
Ising models are discrete-state 2D grid-structured MRFs with pairwise potentials. Many models (Bayes nets, Markov nets, factor graphs) can be converted into this form. Exact inference is intractable, so people have tried various approximations, such as mean field, loopy belief propagation (BP), generalized belief propagation, Gibbs sampling, Rao-Blackwellised MCMC, Swendsen-Wang, graph cuts, etc.
The goal of this project is to empirically compare these methods on some MRF models (using other people's code), and and to make a uniform matlab interface to all the functions (so they can be interchanged in a plug-n-play fashion). To test, you can use an MRF with random parameters, but it would be better to team up with someone who is trying to learn MRF parameters from real data (see below).
The C++ code (with a Matlab wrapper) for mean field, loopy BP, generalized BP, Gibbs sampling and Swendsen-Wang, which I've put here. Code for RB-MCMC can be obtained from Firas Hamze or Nando de Freitas. C++ graphcuts code is available (without matlab interface) here.
Some related papers you should read first:
Comparison of Graph Cuts with Belief Propagation for Stereo, using Identical MRF Parameters , ICCV 2003. (He has C code available.)
Tutorial on approximate inference, Frey and Jojic, PAMI 2004
Simple images, such
handwritten digits can be represented
by a grid of binary numbers, on which an Ising
can be defined. An IPF algorithm makes use of the junction tree
learn the model. In this project you are asked to plug in a mean field
generalized mean field methods for inference in the learning process,
compare the outcome with that of an IPF. See Yee
Whye Tehs paper
the IPF methods and description of the data and the problem. Since variational methods optimize a lower bound of
instead of the true likelihood, your results will reveal the
such approximation on learning and interesting theoretical insights.
Project L: MRF and vision:
Discriminative Fields for Modeling Spatial Dependencies in Natural Images is about applying 2D conditional random fields (CRFs) for classifying image regions as containing "man-made building" or not, on the basis of texture. The goal of this project is to reproduce the results in the NIPS 2003 paper. Useful links:
The goal of this project is to classify pixels in satellite image data into classes like field vs road vs forest, using MRFs/CRFs (see above), or some other technique. Some possibly useful links:
Project M: Object tracking and trajectory modeling using a non-linear dynamic model based on HMM or state-space model (e.g., input-output HMM, factorial HMM, switching SSM)
The goal of this project is to reproduce the results in the following paper: Transformed hidden Markov models: Estimating mixture models of images and inferring spatial transformations in video sequences (CVPR 2000). Note that Brendan Frey has Matlab code for transformation invariant EM on his home page. See also Real-time On-line Learning of Transformed Hidden Markov Models from Video, Nemanja Petrovic, Nebojsa Jojic, Brendan J. Frey, Thomas S, Huang, AIstats 2003, which is 10,000 times faster!
Genetic instability (this is an open research project, if you are interested, come to Eric Xing to discuss details):
Array CGH data are sequences of fluorescence measurements reflecting the DNA copy numbers along the chromosome. The measurements are continuous and can be highly distorted by noises in a complex, non-uniform fashion. Jane Fridlyand proposed a Hidden Markov Models Approach to the Analysis of Array CGH Data, where she implement an HMM model for estimating the CGH copy number. But this model is very restricted.
A switching Hidden Process Model assumes that the hybridization process on each chromosomal region with uniform copy number would ideally follow a standard copy-number-specific linear dynamic model (LDM) [West and Harrison, 1999]. To accommodate outliers and alternative hybridization and signaling dynamics, a mixture of LDMs can be used to model a hidden process that generates fluorescence signals from a chromosomal region with a speci_c copy number. For a chromosome with stochastic regional amplifications and deletions, a switching HPM assumes that another discrete hidden process is responsible to selecting the corresponding copy-number-specific HPM at each region to generate the signals. The switching HPM model is essentially a special dynamic Bayesian network that allows one to infer the temporalspatially-specific hidden dynamics underlying an observation stream and the ensuing segmentation of the stream. It is a generalization to Ghahramani's SSSM which can be understood as modeling each hidden process using a plain KF. In this project you are asked to formulate this model and implement a variational algorithm for inference with such model.
In the dataset
(log2.ratio.ex), there are two columns of numbers, corresponding to two
sources. Please read the original paper to get a more detailed
the data. You can choose the appropriate number of state you feel
after inspecting the plots of the points.
Project N: Learning POMDP structure so as to maximize utility
Hoey & Little (CVPR 04) show how to learn the state space, and parameters, of a POMDP so as to maximize utility in a visual face gesture recognition task. (This is similar to the concept of "utile distinctions" developed in Andrew McCallum's PhD thesis.) The goal of this project is to reproduce Hoey's work in a simpler (non-visual) domain, such as McCallum's driving task.
Project O: Learning partially observed MRFs: the Langevin algorithm
In the recently proposed exponential family harmonium model (Welling et. al., Xing et. al.), a constructive divergence (CD) algorithm was used to learn the parameters of the model (essentially a partially observed, two-layer MRF). In Xing et. al., a comparison to variational learning was performed. CD is essentially a gradient ascent algorithm of which the gradient is approximated by a few samples. The Langevin method adds a random perturbation to the gradient and can often help to get the learning process out of local optima. In this project you will implement the Langevin learning algorithm for Xings dual wing harmonium model, and test your algorithm on the data in my UAI paper. See Zoubin Ghahramanis paper of Bayesian learning of MRF for reference.
Project P: Context-specific independenceWe learned in class that CSI can speed-up inference. In this project, you can explore this further. For example, implement the recursive conditioning approach of Adnan Darwiche, and compare it to variable elimination and clique trees. When is recursive conditioning faster? Can you find practical BNs where the speed-up is considerable? Can you learn such BNs from data?
Project Q: More data
There are many other datasets out there. UC Irvine has a repository that could be useful for you project:
Sam Roweis also has a link to several datasets out there: