In recent years Variation Autoencoders have become one of the most popular unsupervised learning of complicated distributions. Variational Autoencoder (VAE) provides more efficient reconstructive performance over a traditional autoencoder. Variational auto enocders make better approximaiton than MCMC. The VAE defines a generative process in terms of ancestral sampling through a cascade of hidde...

In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability. The kernel method is a powerful nonparametric modeling tool for pattern analysis and statistical signal processing. Through a nonlinear mapping, kernel methods...

This work presents the rst direct method for specii-cally tting ellipses in the least squares sense. Previous approaches used either generic conic tting or relied on iterative methods to recover elliptic solutions. The proposed method is (i) ellipse-speciic, (ii) directly solved by a generalised eigen-system, (iii) has a desirable low-eccentricity bias, and (iv) is robust to noise. We provide a...

This work presents a new e cient method for tting ellipses to scattered data. Previous algorithms either tted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4ac b = 1 the new method incorporates the ellipticity constraint into the normalization factor. The proposed method combines several advantages: (i) It is ellipse-speci c so ...

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The least-mean-square (LMS) algorithm is an adaptation scheme widely used in practice due to its simplicity. In some applications the involved signals are continuous-time. Then, usually either a fully analog implementation of the LMS algorithm is applied or the input data are sampled by analog-to-digital (AD) converters to be processed digitally. A purely digital realization is most often the p...

This paper considers the regularized learning algorithm associated with the leastsquare loss and reproducing kernel Hilbert spaces. The target is the error analysis for the regression problem in learning theory. A novel regularization approach is presented, which yields satisfactory learning rates. The rates depend on the approximation property and the capacity of the reproducing kernel Hilbert...

Many researchers have been interested in approximation properties of fuzzy logic systems (FLS), which like neural networks can be seen as approximation schemes. Almost all of them tackled Mamdani fuzzy model, which was shown to have many interesting features. This paper aims to present alternatives for traditional inference mechanisms and CRI method. The most attractive advantage of these new m...

PLS regression is a recent technique that generalizes and combines features from principal component analysis and multiple regression. Its goal is to predict or analyze a set of dependent variables from a set of independent variables or predictors. This prediction is achieved by extracting from the predictors a set of orthogonal factors called latent variables which have the best predictive pow...