Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 106 for “"Curse of dimensionality"”.
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Breaking the curse of dimensionality in electronic structure methods: towards optimal utilization of the canonical polyadic decomposition
… methods and severely limits the modeling of interesting chemistry problems, introduction and application of higher-order tensor (HOT) decompositions, specifically the canonical polyadic (CP) decomposition, is fairly limited. The CP decomposition is an incredibly useful sparse tensor …
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Numerical Methods for the Chemical Master Equation
… equation, formulated on the Markov assumption of underlying chemical kinetics, offers an accurate stochastic description of general chemical reaction systems on the mesoscopic scale. The chemical master equation is especially useful when formulating mathematical models of gene regulatory …
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A tensor-train-decomposition-based algorithm for high-dimensional pursuit-evasion games
… methods used to solve pursuit-evasion games often require unrealistic computation time. This problem, called the curse of dimensionality, can be mitigated under certain circumstances by utilizing tensor-train (TT) decomposition. By using this intuition, a new algorithm for solving high …
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Particle filtering for EEG source localization and constrained state spaces
… models. However, the numerical nature of PFs cause them to have major weakness in two important areas: (1) handling constraints on the state, and (2) dealing with high-dimensional states. In the first area, handling constraints within the PF framework is crucial in dynamical systems, …
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Statistical aspects of optimal transport
… several statistical problems at the forefront of applied optimal transport, prioritizing statistically and computationally practical results. We begin by considering one of the most popular applications of OT in practice, the barycenter problem, providing dimension-free rates of statistical …
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Simulation-based optimization of Markov decision processes
… problems involve very large state spaces ( "curse of dimensionality"), which prohibits the application of dynamic programming. In addition, dynamic programming assumes the availability of an exact model, in the form of transition probabilities ( "curse of modeling"). In many situations, such …
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Approximation of prices for average-type options via bounds
The problem of pricing multi-dimensional arithmetic average-type options is a complex problem both analytically and numerically, analytically because the distribution of the average on which the payoff function depends is unknown in closed-form and numerically because of the high dimensionality of …
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Derivative-Free Methods for High-Dimensional Optimization with Application to Centrifugal Pump Design
… acquiring derivative information from many of these simulation codes is often infeasible or intractable. For such problems, derivative-free optimization (DFO) methods offer a means of optimizing using only function evaluations. Unfortunately, many of these methods suffer from the curse of …
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COMBINING QUANTUM TRAJECTORIES AND TIME-DEPENDENT VARIATIONAL MONTE CARLO FOR MANY-BODY OPEN QUANTUM SYSTEMS
Simulating quantum systems is complex due to the “curse of dimensionality”, which is exacerbated in open quantum systems that interact with their environment. Indeed, tra- ditional computational methods struggle with the exponential growth of Hilbert space in these systems. This thesis introduces …
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Inexact methods for the chemical master equation with constant or time-varying propensities, and application to parameter inference
… molecular biology and many other different fields of science such as ecology and social study. A familiar approach to modeling such problems is to find their master equation. In systems biology, the equation is called the chemical master equation (CME), and solving the CME is a difficult task, …
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Robust and Constrained Dimension Reduction
"The well-known ""curse of dimensionality"" makes high-dimensional data analysis unusually challenging. Dimension reduction plays a valuable role in enabling certain statistical analyses performed in a parsimonious way. The canonical correlation (CANCOR) method developed by Fung et al. (2002) is …
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An approximate dynamic programming approach to discrete optimization
… the value function in order to break the curse of dimensionality. Through an extensive computational study we illustrate that our ADP approach to integer programming competes successfully with existing methodologies including state of art commercial packages like CPLEX. Our benchmarks for …
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Modern challenges in distribution testing
Hypothesis testing is one of the most classical problems in statistics. While it has enjoyed over a century of intense study, only recent focus has been on the small-sample regime, with interest in sample complexities and minimax rates. Our understanding of many fundamental problems is now quite …
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Reinforcement Learning with Gaussian Processes for Unmanned Aerial Vehicle Navigation
We study the problem of Reinforcement Learning (RL) for Unmanned Aerial Vehicle (UAV) navigation with the smallest number of real world samples possible. This work is motivated by applications of learning autonomous navigation for aerial robots in structural inspec- tion. A naive RL implementation …
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Interpreting Dimension Reductions through Gradient Visualization
… in data analysis to reduce the complexity of high dimensional data while preserving information to the greatest extent. However, the complex processes involved in DRs attribute to their inability to reason the relationship between the projection and the original data features (dimensions). …
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Machine learning approach for high speed link modeling and IBIS-AMI model generation
The high-speed link system is one of the major components in the networking infrastructure. Developing a high-performance behavioral model for such a system is crucial but challenging, especially when taking nonlinearity into account. This work reports modeling the high-speed link (HSL) system …
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Machine learning methods based on diffusion processes
… on the mathematical formalism and physical idea of diffusion processes. First, the idea of using heat diffusion on a hypersphere to measure similarity has been previously proposed and tested by computer scientists, demonstrating promising results based on a heuristic heat kernel obtained from the …
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Towards Out-of-distribution Problem for Reinforcement Learning
… high-quality models require a large amount of data, parameters as well as computation power. This originates from the curse of dimensionality and poor out-of-distribution generalization of current probabilistic models. Current machine learning models requires data points to be independently …
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Decision tools for electricity transmission service and pricing : a dynamic programming approach
… that the system users can hedge the volatility of the real-time market. From a Transmission Service Provider's point of view, optimal transmission resource allocation between these two markets poses a very interesting decision making problem for a defined performance criteria under …
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