In this paper, we present a new and straightforward approximation methodology for pricing call option in Black Scholes market, characterized by stochastic interest rates. The method relies on Gaussian moment matching technique applied to conditional formula, used disentangle the distributional complexity of underlying price process. problem then reduces exploiting density expression bond induce...

We present an algorithm based on maximum likelihood for the estimation and renormalization (marginalization) of exponential densities. The moment-matching problem resulting from the maximization of the likelihood is solved as an optimization problem using the Levenberg-Marquardt algorithm. In the case of renormalization, the moments needed to set up the moment-matching problem are evaluated usi...

In this paper we present a new algorithm for computing reduced-order models of interconnect which utilizes the dominant controllable sub-space of the system. The dominant controllable modes are computed via a new iterative Lya-punov equation solver, Vector ADI. This new algorithm is as inexpensive as Krylov subspace-based moment matching methods, and often produces a better approximation over a...

Sum-product networks (SPNs) have recently emerged as an attractive representation due to their dual interpretation as a special type of deep neural network with clear semantics and a tractable probabilistic graphical model. We explore online algorithms for parameter learning in SPNs with continuous variables. More specifically, we consider SPNs with Gaussian leaf distributions and show how to d...

In physical design and optimization for VLSI/ULSI, parameterized model order reduction can be used to handle large design objectives. In this paper we propose an efficient yet accurate parameterized model order reduction method EMPIRE for physical design with multiple parameters. It is the first practical algorithm using implicit moment matching to handle high order moments of very large number...