Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality . This paper proposes joint dimensionality reduction and non-parametric density estimation framework, using novel estimator that can explicitl...

A novel approach for selecting an appropriate bin size for cell-based diversity assessment is presented. The method measures the sensitivity of the diversity index as a function of grid resolution, using a box-counting algorithm that is reminiscent of those used in fractal analysis. It is shown that the relative variance of the diversity score (sum of squared cell occupancies) of several common...

Abstract: We consider the problem of modeling heteroscedasticity in semiparametric regression analysis of cross-sectional data. Existing work in this setting is rather limited and mostly adopts a fully nonparametric variance structure. This approach is hampered by curse of dimensionality in practical applications. Moreover, the corresponding asymptotic theory is largely restricted to estimators...

We develop a novel dimension-reduction approach to consistent checks of parametric regression models when many regressors are present. The principle is to replace the nonparametric alternative by a class of semiparametric alternatives, namely single-index models, that is rich enough to allow detection of any nonparametric alternative. We propose an omnibus test based on the kernel method that p...

We propose a new family of kernels, based on the Kardashian family. We provide theoretical insights. We dance. As an application, we apply the new class of kernels to the problem of doing stuff. Figure 1: A motivation for the Kernel Trick. κ maps the real world of sane people into the subset of (R − Q)∞ spanned by Robert Kardashian, Sr. and Kris Jenner (formerly Kardashian). We would like to av...

Working with large amounts of unstructured data (e.g., text documents) has become important for many business, engineering and scientific applications. The purpose of this article is to demonstrate how the practical Data Scientist can implement a Locality Sensitive Hashing system from start to finish in order to drastically reduce the time required to perform a similarity search in high dimensi...

Studying model checking problems for partially linear singleindex models, we propose a variant of the integrated conditional moment test using a linear projection weighting function, which gains dimension reduction and makes the proposed method act as if there exists only one covariate even in the presence of multiple dimensional regressors. We derive asymptotic distributions of the proposed te...

Abstract – Nowadays large volumes of data with high dimensionality are being generated in many fields. Most existing indexing techniques degrade rapidly when dimensionality goes higher. ClusterTree is a new indexing approach representing clusters generated by any existing clustering approach. It is a hierarchy of clusters and subclusters which incorporates the cluster representation into the in...

A nonlinear programming approach for the optimal motion planning of robotic manipulators is presented. In this approach a standard optimal control problem of infinite dimensionality (in time) is converted into an optimization problem of finite dimensionality by approximating the manipulator trajectories by the sum of a polynomial and a set of appropriate eigenfunctions. The optimal control prob...