We discuss an approach to signal recovery in Generalized Linear Models (GLM) in which the signal estimationproblem is reduced to the problem of solving a stochastic monotone Variational Inequality (VI). The solution ...
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We discuss an approach to signal recovery in Generalized Linear Models (GLM) in which the signal estimationproblem is reduced to the problem of solving a stochastic monotone Variational Inequality (VI). The solution to the stochastic VI can be found in a computationally efficient way, and in the case when the VI is strongly monotone we derive finite-time upper bounds on the expected || center dot ||(2)(2) error converging to 0 at the rate O(1/K) as the number K of observation grows. Our structural assumptions are essentially weaker than those necessary to ensure convexity of the optimization problem resulting from Maximum Likelihood estimation. In hindsight, the approach we promote can be traced back directly to the ideas behind the Rosenblatt's perceptron algorithm.
The existence of an estimator constrained to lie in a certain type of bounded set is established for a fairly wide class of probability density functions. The necessary and sufficient conditions thus obtained provide ...
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The existence of an estimator constrained to lie in a certain type of bounded set is established for a fairly wide class of probability density functions. The necessary and sufficient conditions thus obtained provide a convenient means of finding such an estimator by mathematical programming methods. This result is a generalization of Cramer’s demonstration of the existence of an unconstrained maximum likelihood estimator and of Aitchison and Silvey’s demonstration of the existence of a maximum likelihood estimator constrained to satisfy certain equations.
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