14075649
Nonparametric log spectrum estimation using disconnected regression splines and genetic algorithms
This article proposes a new nonparametric procedure for estimating log spectra. This procedure consists of three major components: (1) a novel statistical model for modelling the unknown target log spectrum, (2) an AIC-based model selection criterion for choosing a 'best' fitting model, and (3) a genetic algorithm for effectively searching the 'best' fitting model. Numerical experiments are conducted to evaluate and compare the practical performance of the proposed procedure with some other common log spectral estimation procedures appearing in the literature. These other procedures include wavelet techniques, kernel smoothing and regression spline fitting. Empirical results suggest that the proposed procedure compares favourably against all these procedures, especially when the unknown log spectrum contains inhomogeneous structures.
39601893
Smoothing parameter selection for smoothing splines: a simulation study
Smoothing splines are a popular method for performing nonparametric regression. Most important in the implementation of this method is the choice of the smoothing parameter. This article provides a simulation study of several smoothing parameter selection methods, including two so-called risk estimation methods. To the best of the author's knowledge, the empirical performances of these two risk estimation methods have never been reported in the literature. Empirical conclusions from and recommendations based on the simulation results will be provided. One noteworthy empirical observation is that the popular method, generalized cross-validation, was outperformed by another method, an improved Akaike Information criterion, that shares the same assumptions and computational complexity.
16239260
Hybrid local polynomial wavelet shrinkage: wavelet regression with automatic boundary adjustment
An usual assumption underlying the use of wavelet shrinkage is that the regression function is assumed to be either periodic or symmetric. However, such an assumption is not always realistic. This paper proposes an effective method for correcting the boundary bias introduced by the inappropriateness of such periodic or symmetric assumption. The idea is to combine wavelet shrinkage with local polynomial regression, where the latter regression technique is known to possess excellent boundary properties. Simulation results from both the univariate and bivariate settings provide strong evidence that the proposed method is extremely effective in terms of correcting boundary bias.
7698976
Segmenting Images Corrupted by Correlated Noise
Image segmentation is fundamental to many image analysis problems. It aims to partition a digital image into a set of nonoverlapping homogeneous regions. The main contribution of this paper is the development of a new segmentation procedure which is designed to segment images corrupted by correlated noise. This new segmentation procedure is based on Rissanen's minimum description length (MDL) principle and consists of two components: 1) an MDL-based criterion in which the "best" segmentation is defined as its minimizer; and 2) a merging algorithm which attempts to locate this minimizer. The performance of this procedure is illustrated via a simulation study, with promising results.
2086088
Pattern generation using likelihood inference for cellular automata
Cellular automata are discrete dynamical systems which evolve on a discrete grid. Recent studies have shown that cellular automata with relatively simple rules can produce highly complex patterns. We develop likelihood-based methods for estimating rules of cellular automata aimed at the re-generation of observed regular patterns. Under noisy data, our approach is equivalent to estimating the local map of a stochastic cellular automaton. Direct computations of the maximum likelihood estimates are possible for regular binary patterns. The likelihood formulation of the problem is congenial with the use of the minimum description length principle as a model selection tool. We illustrate our method with a series of examples using binary images.
16063444
Nonparametric Estimation and Simulation of Two-Dimensional Gaussian Image Textures
Abstract The work to be described is motivated by the need to simulate a variety of real–world image textures, all of which can be well approximated by stationary Gaussian random fields (SGRFs). Specifically, given an observed SGRF T , we wish to simulate SGRFs which look like and possess similar statistical properties to T . The main contribution of this paper is the development of an automatic and nonparametric spectrum estimation procedure which is able to produce an estimated spectrum of T in such a way that SGRFs simulated from this estimated spectrum have these desirable characteristics. Two special features of the procedure are: (i) it relies on a different risk function to that commonly used in nonparametric spectrum estimation, and (ii) it chooses its smoothing parameters by the technique of unbiased risk estimation. Results from a simulation study and a practical example demonstrate the good performance of the procedure. The practical example also illustrates how the proposed procedure can be combined with Monte Carlo testing to tackle target testing problems. Finally, the procedure is applied to the synthesis of some Brodatz textures, with some success.
207739442
Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Subgaussian and Supergaussian Sources
An extension of the infomax algorithm of Bell and Sejnowski (1995) is presented that is able blindly to separate mixed signals with sub- and supergaussian source distributions. This was achieved by using a simple type of learning rule first derived by Girolami (1997) by choosing negentropy as a projection pursuit index. Parameterized probability distributions that have sub- and supergaussian regimes were used to derive a general learning rule that preserves the simple architecture proposed by Bell and Sejnowski (1995), is optimized using the natural gradient by Amari (1998), and uses the stability analysis of Cardoso and Laheld (1996) to switch between sub- and supergaussian regimes. We demonstrate that the extended infomax algorithm is able to separate 20 sources with a variety of source distributions easily. Applied to high-dimensional data from electroencephalographic recordings, it is effective at separating artifacts such as eye blinks and line noise from weaker electrical signals that arise from sources in the brain.
76211
Negative weights make adversaries stronger
The quantum adversary method is one of the most successful techniques for proving lower bounds on quantum query complexity. It gives optimal lower bounds for many problems, has application to classical complexity in formula size lower bounds, and is versatile with equivalent formulations interms of weight schemes, eigen values, and Kolmogorov complexity. All these formulations rely on the principlethat if an algorithm successfully computes a function then, in particular, itis able to distinguish between inputs which map to different values.
 We present a stronger version of the adversary method which goes beyond this principle to make explicit use of the stronger condition that the algorithm actually computes the function. This new method, which we call ADV+-, has all the advantages ofthe old: it is a lower bound on bounded-error quantum query complexity, its square is a lower bound on formula size, and it behaves well with respect tofunction composition. Moreover ADV+- is always at least as large as the adversary method ADV, and we show an example of a monotone function forwhich ADV+-(f)=Omega(ADV(f)1.098). We also give examples showing that ADV+- does not face limitations of ADV like the certificate complexity barrier and the property testing barrier.
16028378
Improving the Performance of Infomax Using Statistical Signal Processing Techniques
In this paper, we present a new method that speeds up the convergence of the infomax algorithm proposed by Bell and Sejnowski. One effect of the infomax algorithm is that the 2nd order and 4th order statistical correlations are reintroduced to the signals during the learning process due to the optimization with respect to the complete signal statistics. We show that repetitively forcing 2nd and 4th order correlations to zero speeds up the convergence and improves separating sources with fewer data points.
206754645
Statistical performance guarantees in large-scale cross-path packet switch
In this paper, we develop a general framework for a novel switch architecture, the cross-path switch, to provide persession statistical quality of service (QoS) guarantees. With characterizing the service each session receives by service curves, we derive a set of statistical bounds on the delay, backlog, and departure processes at the switch on a per-session manner using exponential bounded burstiness processes as source session traffic models. These bounds show that the service guarantees offered by the cross-path switch depend on the way of token assignment in the central stage of the switch. To provide better performance guarantees,we determine the criteria for designing a token assignment algorithm for the cross-path switch. Also, we quantify the service guaranteed by the cross-path switch with the central stage implemented in optical domain, which is important for the provision of QoS guarantees to each session in semioptical networks.
12361441
Computer-aided prototype system for nose surgery
Rhinoplasty, or surgery to reshape the nose, is one of the most common of all plastic-surgery procedures. Rhinoplasty can enhance a patient's appearance and self-confidence, may also correct a birth defect or injury, or help relieve some breathing problem. In this paper, we present a three-dimensional (3-D) surgical simulation system, which can assist surgeons in planning rhinoplasty procedures. This system employs computer graphics and image-processing techniques for the simulation of a rhinoplasty. Although the presented algorithms themselves are not new, the proposed system exploits the new idea to apply 3-D morphing for rhinoplasty, and simulation results are useful for the physicians. According to patients' expectation of what they would like their noses to look like, our system simulates expected results. Our tools provide quantitative measurements of a nose structure. Using these quantitative results, surgeons can arrange appropriate preoperative plans for patients. Finally, experimental results and experiences are reported to evaluate the usefulness of the proposed system.