Large VC-dimension classifiers can learn difficult tasks, but are usually impractical because they generalize well only if they are trained with huge quantities of data. In this paper we show that even very high-order polynomial classifiers can be trained with a small amount of training data and yet generalize better than classifiers with a smaller VC-dimension. This is achieved with a maximum margin algorithm (the Generalized Portrait).

Abstract not found

Most existing sparse Gaussian process (g.p.) models seek computational advantages by basing their computations on a set of m basis functions that are the covariance function of the g.p. with one of its two inputs fixed. We generalise this for the case of Gaussian covariance function, by basing our computations on m Gaussian basis functions with arbitrary diagonal covariance matrices (or length scales). For a fixed number of basis functions and any given criteria, this additional flexibility permits approximations no worse and typically better than was previously possible. We perform gradient based optimisation of the marginal likelihood, which costs O(m 2 n) time where n is the number of data points, and compare the method to various other sparse g.p. methods. Although we focus on g.p. regression, the central idea is applicable to all kernel based algorithms, and we also provide some results for the support vector machine (s.v.m.) and kernel ridge regression (k.r.r.). Our approach outperforms the other methods, particularly for the case of very few basis functions, i.e. a very high sparsity ratio. 1.

Accurate simulation of transient device thermal behavior is essential to predict CMOS VLSI circuit failures under electrical overstress (EOS). In this paper, we present an efficient transient electrothermal simulator that is built upon a SPICE-like engine. The transient device temperature is estimated by the convolution of the device power dissipation and its thermal impulse response which can be derived an analytical solution of the heat diffusion equation. New fast thermal simulation techniques are proposed including a regionwise-exponential (RWE) approximation of thermal impulse response and recursive convolution scheme. The recursive convolution provides a significant performance improvement over the numerical convolution by orders of magnitude, making it computationally feasible to simulate CMOS circuits with many devices. I. Introduction Smaller devices, higher packing density and rising power consumption lead to dramatic temperature increases in deep submicron VLSI circuits. C...

Robert E. Derr: Statistical Modeling of Microstructure with Applications to Effective Property Computation in Materials Science (Under the direction of Dr. Chuanshu Ji) We propose a class of models for microstructure in materials science, and conduct a statistical modeling process: perform image processing of the microstructure to summarize the data, perform inference and parameter estimation based on this summary data, use spatial birth-and-death processes to create Markov chain Monte Carlo simulations of the structures, perform post-modeling diagnostics and evaluate the goodness of fit via feature extraction. The proposed class of model is a hard-core/soft-shell elliptical point process---a special case of Markov point processes on geometric shapes, originally proposed by Ripley and Kelly (1977) and Baddeley and Mller (1989). This model may be utilized for the computation of certain properties, such as conductivity, of heterogeneous materials following the original work of Brown ...

Several numerical issues for valuing cliquet options using PDE methods are investigated. The use of a running sum of returns formulation is compared to an average return formulation. Methods for grid construction, interpolation of jump conditions, and application of boundary conditions are compared. The effect of various volatility modelling assumptions on the value of cliquet options is also studied. Numerical results are reported for jump diffusion models, calibrated volatility surface models, and uncertain volatility models.

In semi-supervised learning, at the limit of infinite unlabeled points while fixing labeled ones, the solutions of several graph Laplacian regularization based algorithms were shown by Nadler et al. (2009) to degenerate to constant functions with “spikes ” at labeled points in R d for d ≥ 2. These optimization problems all use the graph Laplacian regularizer as a common penalty term. In this paper, we address this problem by using regularization based on an iterated Laplacian, which is equivalent to a higher order Sobolev semi-norm. Alternatively, it can be viewed as a generalization of the thin plate spline to an unknown submanifold in high dimensions. We also discuss relationships between Reproducing Kernel Hilbert Spaces and Green’s functions. Experimental results support our analysis by showing consistently improved results using iterated Laplacians. 1

engineering.

introduce novel statistical simulation approaches to include the effect of surface roughness in coupled mechanical, electronic and thermal processes in N/MEMS and semiconductor devices in the 10 nm- 1 µm range. A model is presented to estimate roughness rms ∆ and autocorrelation L from experimental surfaces and edges, and subsequently generate statistical series of rough geometrical devices from these observable parameters. Using such series of rough electrodes under Holm’s theory, we present a novel simulation framework which predicts a contact resistance of 80 mΩ in MEMS gold-gold micro-contacts, for applied pressures above 0.3 mN on 1 µm × 1 µm surfaces. The non-contacting state of such devices is simulated through statistical Monte Carlo iterations on percolative networks to derive a time to electro-thermal failure through electrical discharges in the gas insulating metal electrodes. The observable parameters L and ∆ are further integrated in semi-classical solutions to the electronic and thermal Boltzman transport equation (BTE), and we show roughness limited heat and electronic transport