11,977 research outputs found
Bayesian Agglomerative Clustering with Coalescents
We introduce a new Bayesian model for hierarchical clustering based on a
prior over trees called Kingman's coalescent. We develop novel greedy and
sequential Monte Carlo inferences which operate in a bottom-up agglomerative
fashion. We show experimentally the superiority of our algorithms over others,
and demonstrate our approach in document clustering and phylolinguistics.Comment: NIPS 200
Structured Sparsity: Discrete and Convex approaches
Compressive sensing (CS) exploits sparsity to recover sparse or compressible
signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity
is also used to enhance interpretability in machine learning and statistics
applications: While the ambient dimension is vast in modern data analysis
problems, the relevant information therein typically resides in a much lower
dimensional space. However, many solutions proposed nowadays do not leverage
the true underlying structure. Recent results in CS extend the simple sparsity
idea to more sophisticated {\em structured} sparsity models, which describe the
interdependency between the nonzero components of a signal, allowing to
increase the interpretability of the results and lead to better recovery
performance. In order to better understand the impact of structured sparsity,
in this chapter we analyze the connections between the discrete models and
their convex relaxations, highlighting their relative advantages. We start with
the general group sparse model and then elaborate on two important special
cases: the dispersive and the hierarchical models. For each, we present the
models in their discrete nature, discuss how to solve the ensuing discrete
problems and then describe convex relaxations. We also consider more general
structures as defined by set functions and present their convex proxies.
Further, we discuss efficient optimization solutions for structured sparsity
problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure
Multi-capacity bin packing with dependent items and its application to the packing of brokered workloads in virtualized environments
Providing resource allocation with performance
predictability guarantees is increasingly important in cloud
platforms, especially for data-intensive applications, in which
performance depends greatly on the available rates of data
transfer between the various computing/storage hosts underlying
the virtualized resources assigned to the application. Existing
resource allocation solutions either assume that applications
manage their data transfer between their virtualized resources, or
that cloud providers manage their internal networking resources.
With the increased prevalence of brokerage services in cloud
platforms, there is a need for resource allocation solutions that
provides predictability guarantees in settings, in which neither
application scheduling nor cloud provider resources can be
managed/controlled by the broker. This paper addresses this
problem, as we define the Network-Constrained Packing (NCP)
problem of finding the optimal mapping of brokered resources
to applications with guaranteed performance predictability. We
prove that NCP is NP-hard, and we define two special instances
of the problem, for which exact solutions can be found efficiently.
We develop a greedy heuristic to solve the general instance of the
NCP problem , and we evaluate its efficiency using simulations
on various application workloads, and network models.This work was done while author was at Boston University. It was partially supported by NSF CISE awards #1430145, #1414119, #1239021 and #1012798. (1430145 - NSF CISE; 1414119 - NSF CISE; 1239021 - NSF CISE; 1012798 - NSF CISE
Network-constrained packing of brokered workloads in virtualized environments
Providing resource allocation with performance predictability guarantees is increasingly important in cloud platforms, especially for data-intensive applications, in which performance depends greatly on the available rates of data transfer between the various computing/storage hosts underlying the virtualized resources assigned to the application. Existing resource allocation solutions either assume that applications manage their data transfer between their virtualized resources, or that cloud providers manage their internal networking resources.With the increased prevalence of brokerage services in cloud platforms, there is a need for resource allocation solutions that provides predictability guarantees in settings, in which neither application scheduling nor cloud provider resources can be managed/controlled by the broker. This paper addresses this problem, as we define the Network-Constrained Packing (NCP)problem of finding the optimal mapping of brokered resources to applications with guaranteed performance predictability. We prove that NCP is NP-hard, and we define two special instances of the problem, for which exact solutions can be found efficiently. We develop a greedy heuristic to solve the general instance of the NCP problem, and we evaluate its efficiency using simulations on various application workloads, and network models.This work is supported by NSF CISE CNS Award #1347522, # 1239021, # 1012798
Mapping constrained optimization problems to quantum annealing with application to fault diagnosis
Current quantum annealing (QA) hardware suffers from practical limitations
such as finite temperature, sparse connectivity, small qubit numbers, and
control error. We propose new algorithms for mapping boolean constraint
satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In
particular we develop a new embedding algorithm for mapping a CSP onto a
hardware Ising model with a fixed sparse set of interactions, and propose two
new decomposition algorithms for solving problems too large to map directly
into hardware.
The mapping technique is locally-structured, as hardware compatible Ising
models are generated for each problem constraint, and variables appearing in
different constraints are chained together using ferromagnetic couplings. In
contrast, global embedding techniques generate a hardware independent Ising
model for all the constraints, and then use a minor-embedding algorithm to
generate a hardware compatible Ising model. We give an example of a class of
CSPs for which the scaling performance of D-Wave's QA hardware using the local
mapping technique is significantly better than global embedding.
We validate the approach by applying D-Wave's hardware to circuit-based
fault-diagnosis. For circuits that embed directly, we find that the hardware is
typically able to find all solutions from a min-fault diagnosis set of size N
using 1000N samples, using an annealing rate that is 25 times faster than a
leading SAT-based sampling method. Further, we apply decomposition algorithms
to find min-cardinality faults for circuits that are up to 5 times larger than
can be solved directly on current hardware.Comment: 22 pages, 4 figure
S-TREE: Self-Organizing Trees for Data Clustering and Online Vector Quantization
This paper introduces S-TREE (Self-Organizing Tree), a family of models that use unsupervised learning to construct hierarchical representations of data and online tree-structured vector quantizers. The S-TREE1 model, which features a new tree-building algorithm, can be implemented with various cost functions. An alternative implementation, S-TREE2, which uses a new double-path search procedure, is also developed. S-TREE2 implements an online procedure that approximates an optimal (unstructured) clustering solution while imposing a tree-structure constraint. The performance of the S-TREE algorithms is illustrated with data clustering and vector quantization examples, including a Gauss-Markov source benchmark and an image compression application. S-TREE performance on these tasks is compared with the standard tree-structured vector quantizer (TSVQ) and the generalized Lloyd algorithm (GLA). The image reconstruction quality with S-TREE2 approaches that of GLA while taking less than 10% of computer time. S-TREE1 and S-TREE2 also compare favorably with the standard TSVQ in both the time needed to create the codebook and the quality of image reconstruction.Office of Naval Research (N00014-95-10409, N00014-95-0G57
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