984 research outputs found
Patterns of Scalable Bayesian Inference
Datasets are growing not just in size but in complexity, creating a demand
for rich models and quantification of uncertainty. Bayesian methods are an
excellent fit for this demand, but scaling Bayesian inference is a challenge.
In response to this challenge, there has been considerable recent work based on
varying assumptions about model structure, underlying computational resources,
and the importance of asymptotic correctness. As a result, there is a zoo of
ideas with few clear overarching principles.
In this paper, we seek to identify unifying principles, patterns, and
intuitions for scaling Bayesian inference. We review existing work on utilizing
modern computing resources with both MCMC and variational approximation
techniques. From this taxonomy of ideas, we characterize the general principles
that have proven successful for designing scalable inference procedures and
comment on the path forward
Parallel Adaptive Collapsed Gibbs Sampling
Rao-Blackwellisation is a technique that provably improves the performance of Gibbs sampling by summing-out variables from the PGM. However, collapsing variables is computationally expensive, since it changes the PGM structure introducing factors whose size is dependent upon the Markov blanket of the variable. Therefore, collapsing out several variables jointly is typically intractable in arbitrary PGM structures. This thesis proposes an adaptive approach for Rao-Blackwellisation, where additional parallel Markov chains are defined over different collapsed PGM structures. The collapsed variables are chosen based on their convergence diagnostics. Adding chains requires re-burn-in the chain, thus wasting samples. To address this, new chains are initialized from a mean field approximation for the distribution, that improves over time, thus reducing the burn-in period. The experiments on several UAI benchmarks shows that this approach is more accurate than state-of-the-art inference systems such as Merlin which have previously won the UAI inference challenge
Balancing Global Exploration and Local-connectivity Exploitation with Rapidly-exploring Random disjointed-Trees
Sampling efficiency in a highly constrained environment has long been a major
challenge for sampling-based planners. In this work, we propose
Rapidly-exploring Random disjointed-Trees* (RRdT*), an incremental optimal
multi-query planner. RRdT* uses multiple disjointed-trees to exploit
local-connectivity of spaces via Markov Chain random sampling, which utilises
neighbourhood information derived from previous successful and failed samples.
To balance local exploitation, RRdT* actively explore unseen global spaces when
local-connectivity exploitation is unsuccessful. The active trade-off between
local exploitation and global exploration is formulated as a multi-armed bandit
problem. We argue that the active balancing of global exploration and local
exploitation is the key to improving sample efficient in sampling-based motion
planners. We provide rigorous proofs of completeness and optimal convergence
for this novel approach. Furthermore, we demonstrate experimentally the
effectiveness of RRdT*'s locally exploring trees in granting improved
visibility for planning. Consequently, RRdT* outperforms existing
state-of-the-art incremental planners, especially in highly constrained
environments.Comment: Submitted to IEEE International Conference on Robotics and Automation
(ICRA) 201
Solving Factored MDPs with Hybrid State and Action Variables
Efficient representations and solutions for large decision problems with
continuous and discrete variables are among the most important challenges faced
by the designers of automated decision support systems. In this paper, we
describe a novel hybrid factored Markov decision process (MDP) model that
allows for a compact representation of these problems, and a new hybrid
approximate linear programming (HALP) framework that permits their efficient
solutions. The central idea of HALP is to approximate the optimal value
function by a linear combination of basis functions and optimize its weights by
linear programming. We analyze both theoretical and computational aspects of
this approach, and demonstrate its scale-up potential on several hybrid
optimization problems
A new hybrid meta-heuristic algorithm for solving single machine scheduling problems
A dissertation submitted in partial ful lment of the
degree of Master of Science in Engineering (Electrical) (50/50)
in the
Faculty of Engineering and the Built Environment
Department of Electrical and Information Engineering
May 2017Numerous applications in a wide variety of elds has resulted in a rich history of research
into optimisation for scheduling. Although it is a fundamental form of the problem, the
single machine scheduling problem with two or more objectives is known to be NP-hard.
For this reason we consider the single machine problem a good test bed for solution
algorithms. While there is a plethora of research into various aspects of scheduling
problems, little has been done in evaluating the performance of the Simulated Annealing
algorithm for the fundamental problem, or using it in combination with other techniques.
Speci cally, this has not been done for minimising total weighted earliness and tardiness,
which is the optimisation objective of this work.
If we consider a mere ten jobs for scheduling, this results in over 3.6 million possible
solution schedules. It is thus of de nite practical necessity to reduce the search space in
order to nd an optimal or acceptable suboptimal solution in a shorter time, especially
when scaling up the problem size. This is of particular importance in the application
area of packet scheduling in wireless communications networks where the tolerance for
computational delays is very low. The main contribution of this work is to investigate
the hypothesis that inserting a step of pre-sampling by Markov Chain Monte Carlo
methods before running the Simulated Annealing algorithm on the pruned search space
can result in overall reduced running times.
The search space is divided into a number of sections and Metropolis-Hastings Markov
Chain Monte Carlo is performed over the sections in order to reduce the search space for
Simulated Annealing by a factor of 20 to 100. Trade-o s are found between the run time
and number of sections of the pre-sampling algorithm, and the run time of Simulated
Annealing for minimising the percentage deviation of the nal result from the optimal
solution cost. Algorithm performance is determined both by computational complexity
and the quality of the solution (i.e. the percentage deviation from the optimal). We
nd that the running time can be reduced by a factor of 4.5 to ensure a 2% deviation
from the optimal, as compared to the basic Simulated Annealing algorithm on the full
search space. More importantly, we are able to reduce the complexity of nding the
optimal from O(n:n!) for a complete search to O(nNS) for Simulated Annealing to
O(n(NMr +NS)+m) for the input variables n jobs, NS SA iterations, NM Metropolis-
Hastings iterations, r inner samples and m sections.MT 201
Hierarchical relational models for document networks
We develop the relational topic model (RTM), a hierarchical model of both
network structure and node attributes. We focus on document networks, where the
attributes of each document are its words, that is, discrete observations taken
from a fixed vocabulary. For each pair of documents, the RTM models their link
as a binary random variable that is conditioned on their contents. The model
can be used to summarize a network of documents, predict links between them,
and predict words within them. We derive efficient inference and estimation
algorithms based on variational methods that take advantage of sparsity and
scale with the number of links. We evaluate the predictive performance of the
RTM for large networks of scientific abstracts, web documents, and
geographically tagged news.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS309 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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