Slides & Talks
Relational Learning as Collective Matrix Factorization
Machine Learning Lunch, CMU (Feb 08)
We present a unified view of matrix factorization models,
including singular value decompositions, non-negative matrix
factorization, probabilistic latent semantic indexing, and
generalizations of these models to exponential families and
non-regular Bregman divergences. One can model relational data as a
set of matrices, where each matrix represents the value of a relation
between two entity-types. Instead of a single matrix, relational data
is represented as a set of matrices with shared dimensions and tied
low-rank representation. Our example domain is augmented collaborative
filtering, where both user ratings and side information about items
are available. To predict the value of a relation, we extend Bregman
matrix factorization to a set of related matrices. Using an
alternating minimization scheme, we show the existence of a practical
Newton step. The use of stochastic second-order methods for large
matrices is also covered.
[Video]
[Slides]
Finding Optimal Bayesian Networks by Dynamic Programming
KDD Project Talk, CMU (Dec 05)
Producing the Bayesian network structure that maximizes a
score function is known as model selection. A common
approach to model selection involves local search in the
space of acyclic digraphs, which is prone to local
maxima. Under a wide variety of assumptions the problem is
NP-hard. Moreover, exhaustive enumeration requires
super-exponential time in the number of variables. We
present an exponential space/time algorithm for finding a
structure that corresponds to the global maxima of a
decomposable scoring function, such as BDeu or BIC.
[Paper]
[Slides]
[3 Node Example]