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.
20836735
Kernel smoothing of periodograms under Kullback-Leibler discrepancy
Kernel smoothing on the periodogram is a popular nonparametric method for spectral density estimation. Most important in the implementation of this method is the choice of the bandwidth, or span, for smoothing. One idealized way of choosing the bandwidth is to choose it as the one that minimizes the Kullback-Leibler (KL) discrepancy between the smoothed estimate and the true spectrum. However, this method fails in practice, as the KL discrepancy is an unknown quantity. This paper introduces an estimator for this discrepancy, so that the bandwidth that minimizes the unknown discrepancy can be empirically approximated via the minimization of it. It is shown that this discrepancy estimator is consistent. Numerical results also suggest that this empirical choice of bandwidth often outperforms some other commonly used bandwidth choices. The same idea is also applied to choose the bandwidth for log-periodogram smoothing.
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.
18661216
A stabilized bandwidth selection method for kernel smoothing of the periodogram
One popular method for nonparametric spectral density estimation is to perform kernel smoothing on the periodogram, and one important component of this method is the choice of the bandwidth (or span) for smoothing. This paper proposes a new bandwidth selection method that is based on a coupling of the so-called plug-in and the unbiased risk estimation ideas. This new method is easy to describe, simple to implement, and does not impose severe conditions on the unknown spectrum. Numerical results suggest that this new method often outperforms some other commonly used bandwidth selection methods. The new methodology is also applied to choose the bandwidth for log-periodogram smoothing.
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.
6758538
Separable equilibrium state probabilities via time reversal in Markovian process algebra
The reversed compound agent theorem (RCAT) is a compositional result that uses Markovian process algebra (MPA) to derive the reversed process of certain interactions between two continuous time Markov chains at equilibrium. From this reversed process, together with the given, forward process, the joint state probabilities can be expressed as a product-form, although no general algorithm has previously been given. This paper first generalises RCAT to multiple (more than two) cooperating agents, which removes the need for multiple applications and inductive proofs in cooperations of an arbitrary number of processes. A new result shows a simple stochastic equivalence between cooperating, synchronised processes and corresponding parallel, asynchronous processes. This greatly simplifies the proof of the new, multi-agent theorem, which includes a statement of the desired product-form solution itself as a product of given state probabilities in the parallel components. The reversed process and product-form thus derived rely on a solution to certain rate equations and it is shown, for the first time, that a unique solution exists under mild conditions--certainly for queueing networks and G-networks.
42876940
An HMM-based speech recognition IC
This paper presents the design, simulation and measurement results of a Hidden Markov Model (HMM) based isolated word recognizer IC with double mixtures. Table look-up technique is employed in this design. The chip operates at 20 MHz at 3.3 V. The recognition time is 0.5 s for a 50-word speech library. The speech IC has been verified with 467 test speech data and the recognition accuracy is 93.8%. A reference software recognizer using the same algorithm and speech library has a recognition accuracy of 94.2%. The new speech IC that uses a table look up to reduce the complexity of the circuit has approximately the same recognition accuracy as an ideal software recognizer.
6741849
Blind Separation of Delayed and Convolved Sources
We address the difficult problem of separating multiple speakers with multiple microphones in a real room. We combine the work of Torkkola and Amari, Cichocki and Yang, to give Natural Gradient information maximisation rules for recurrent (IIR) networks, blindly adjusting delays, separating and deconvolving mixed signals. While they work well on simulated data, these rules fail in real rooms which usually involve non-minimum phase transfer functions, not-invertible using stable IIR filters. An approach that sidesteps this problem is to perform infomax on a feedforward architecture in the frequency domain (Lambert 1996). We demonstrate real-room separation of two natural signals using this approach.
17821880
Indentation and Protrusion Detection and Its Applications
In this paper, we investigated the mechanism of dividing a 2D-object border into a set of local and global indentation and protrusion segments by extending the classic curvature scale-space filtering method. The resultant segments, arranged in hierarchical structures, can represent the object shape. Applying this technique, we derived a border irregularity measure for pigmented skin lesions. The measure correlated well with experienced dermatologists' evaluations and may be useful for measuring the malignancy of the lesion. Furthermore, we can use the method to discover all the bays in an aerial map.
8163714
Scaling Laws in Natural Scenes and the Inference of 3D Shape
This paper explores the statistical relationship between natural images and their underlying range (depth) images. We look at how this relationship changes over scale, and how this information can be used to enhance low resolution range data using a full resolution intensity image. Based on our findings, we propose an extension to an existing technique known as shape recipes [3], and the success of the two methods are compared using images and laser scans of real scenes. Our extension is shown to provide a two-fold improvement over the current method. Furthermore, we demonstrate that ideal linear shape-from-shading filters, when learned from natural scenes, may derive even more strength from shadow cues than from the traditional linear-Lambertian shading cues.