25 research outputs found
GraphLab: A New Framework for Parallel Machine Learning
Designing and implementing efficient, provably correct parallel machine
learning (ML) algorithms is challenging. Existing high-level parallel
abstractions like MapReduce are insufficiently expressive while low-level tools
like MPI and Pthreads leave ML experts repeatedly solving the same design
challenges. By targeting common patterns in ML, we developed GraphLab, which
improves upon abstractions like MapReduce by compactly expressing asynchronous
iterative algorithms with sparse computational dependencies while ensuring data
consistency and achieving a high degree of parallel performance. We demonstrate
the expressiveness of the GraphLab framework by designing and implementing
parallel versions of belief propagation, Gibbs sampling, Co-EM, Lasso and
Compressed Sensing. We show that using GraphLab we can achieve excellent
parallel performance on large scale real-world problems
Stochastic Variational Inference for Hidden Markov Models
Variational inference algorithms have proven successful for Bayesian analysis
in large data settings, with recent advances using stochastic variational
inference (SVI). However, such methods have largely been studied in independent
or exchangeable data settings. We develop an SVI algorithm to learn the
parameters of hidden Markov models (HMMs) in a time-dependent data setting. The
challenge in applying stochastic optimization in this setting arises from
dependencies in the chain, which must be broken to consider minibatches of
observations. We propose an algorithm that harnesses the memory decay of the
chain to adaptively bound errors arising from edge effects. We demonstrate the
effectiveness of our algorithm on synthetic experiments and a large genomics
dataset where a batch algorithm is computationally infeasible.Comment: Appears in Advances in Neural Information Processing Systems (NIPS),
201
Kernel Belief Propagation
We propose a nonparametric generalization of belief propagation, Kernel
Belief Propagation (KBP), for pairwise Markov random fields. Messages are
represented as functions in a reproducing kernel Hilbert space (RKHS), and
message updates are simple linear operations in the RKHS. KBP makes none of the
assumptions commonly required in classical BP algorithms: the variables need
not arise from a finite domain or a Gaussian distribution, nor must their
relations take any particular parametric form. Rather, the relations between
variables are represented implicitly, and are learned nonparametrically from
training data. KBP has the advantage that it may be used on any domain where
kernels are defined (Rd, strings, groups), even where explicit parametric
models are not known, or closed form expressions for the BP updates do not
exist. The computational cost of message updates in KBP is polynomial in the
training data size. We also propose a constant time approximate message update
procedure by representing messages using a small number of basis functions. In
experiments, we apply KBP to image denoising, depth prediction from still
images, and protein configuration prediction: KBP is faster than competing
classical and nonparametric approaches (by orders of magnitude, in some cases),
while providing significantly more accurate results
Minimum Weight Perfect Matching via Blossom Belief Propagation
Max-product Belief Propagation (BP) is a popular message-passing algorithm
for computing a Maximum-A-Posteriori (MAP) assignment over a distribution
represented by a Graphical Model (GM). It has been shown that BP can solve a
number of combinatorial optimization problems including minimum weight
matching, shortest path, network flow and vertex cover under the following
common assumption: the respective Linear Programming (LP) relaxation is tight,
i.e., no integrality gap is present. However, when LP shows an integrality gap,
no model has been known which can be solved systematically via sequential
applications of BP. In this paper, we develop the first such algorithm, coined
Blossom-BP, for solving the minimum weight matching problem over arbitrary
graphs. Each step of the sequential algorithm requires applying BP over a
modified graph constructed by contractions and expansions of blossoms, i.e.,
odd sets of vertices. Our scheme guarantees termination in O(n^2) of BP runs,
where n is the number of vertices in the original graph. In essence, the
Blossom-BP offers a distributed version of the celebrated Edmonds' Blossom
algorithm by jumping at once over many sub-steps with a single BP. Moreover,
our result provides an interpretation of the Edmonds' algorithm as a sequence
of LPs
Approximate Decentralized Bayesian Inference
This paper presents an approximate method for performing Bayesian inference
in models with conditional independence over a decentralized network of
learning agents. The method first employs variational inference on each
individual learning agent to generate a local approximate posterior, the agents
transmit their local posteriors to other agents in the network, and finally
each agent combines its set of received local posteriors. The key insight in
this work is that, for many Bayesian models, approximate inference schemes
destroy symmetry and dependencies in the model that are crucial to the correct
application of Bayes' rule when combining the local posteriors. The proposed
method addresses this issue by including an additional optimization step in the
combination procedure that accounts for these broken dependencies. Experiments
on synthetic and real data demonstrate that the decentralized method provides
advantages in computational performance and predictive test likelihood over
previous batch and distributed methods.Comment: This paper was presented at UAI 2014. Please use the following BibTeX
citation: @inproceedings{Campbell14_UAI, Author = {Trevor Campbell and
Jonathan P. How}, Title = {Approximate Decentralized Bayesian Inference},
Booktitle = {Uncertainty in Artificial Intelligence (UAI)}, Year = {2014}