281,366 research outputs found
Maximum Likelihood Estimation of Closed Queueing Network Demands from Queue Length Data
Resource demand estimation is essential for the application of analyical models, such as queueing networks, to real-world systems. In this paper, we investigate maximum likelihood (ML) estimators for service demands in closed queueing networks with load-independent and load-dependent service times. Stemming from a characterization of necessary conditions for ML estimation, we propose new estimators that infer demands from queue-length measurements, which are inexpensive metrics to collect in real systems. One advantage of focusing on queue-length data compared to response times or utilizations is that confidence intervals can be rigorously derived from the equilibrium distribution of the queueing network model. Our estimators and their confidence intervals are validated against simulation and real system measurements for a multi-tier application
Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics
We show how to extend a recently proposed multi-level Monte Carlo approach to
the continuous time Markov chain setting, thereby greatly lowering the
computational complexity needed to compute expected values of functions of the
state of the system to a specified accuracy. The extension is non-trivial,
exploiting a coupling of the requisite processes that is easy to simulate while
providing a small variance for the estimator. Further, and in a stark departure
from other implementations of multi-level Monte Carlo, we show how to produce
an unbiased estimator that is significantly less computationally expensive than
the usual unbiased estimator arising from exact algorithms in conjunction with
crude Monte Carlo. We thereby dramatically improve, in a quantifiable manner,
the basic computational complexity of current approaches that have many names
and variants across the scientific literature, including the
Bortz-Kalos-Lebowitz algorithm, discrete event simulation, dynamic Monte Carlo,
kinetic Monte Carlo, the n-fold way, the next reaction method,the
residence-time algorithm, the stochastic simulation algorithm, Gillespie's
algorithm, and tau-leaping. The new algorithm applies generically, but we also
give an example where the coupling idea alone, even without a multi-level
discretization, can be used to improve efficiency by exploiting system
structure. Stochastically modeled chemical reaction networks provide a very
important application for this work. Hence, we use this context for our
notation, terminology, natural scalings, and computational examples.Comment: Improved description of the constants in statement of Theorem
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
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