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- W4300920385 abstract "In this paper we study the problem of recovering a structured but unknown parameter ${bf{theta}}^*$ from $n$ nonlinear observations of the form $y_i=f(langle {bf{x}}_i,{bf{theta}}^*rangle)$ for $i=1,2,ldots,n$. We develop a framework for characterizing time-data tradeoffs for a variety of parameter estimation algorithms when the nonlinear function $f$ is unknown. This framework includes many popular heuristics such as projected/proximal gradient descent and stochastic schemes. For example, we show that a projected gradient descent scheme converges at a linear rate to a reliable solution with a near minimal number of samples. We provide a sharp characterization of the convergence rate of such algorithms as a function of sample size, amount of a-prior knowledge available about the parameter and a measure of the nonlinearity of the function $f$. These results provide a precise understanding of the various tradeoffs involved between statistical and computational resources as well as a-prior side information available for such nonlinear parameter estimation problems." @default.
- W4300920385 created "2022-10-04" @default.
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- W4300920385 date "2016-10-22" @default.
- W4300920385 modified "2023-09-26" @default.
- W4300920385 title "Fast and Reliable Parameter Estimation from Nonlinear Observations" @default.
- W4300920385 doi "https://doi.org/10.48550/arxiv.1610.07108" @default.
- W4300920385 hasPublicationYear "2016" @default.
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