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In this work we show how to resolve, at least partially, the curse of dimensionality of likelihood ratios (LRs) while using importance sampling (IS) to estimate the performance of high-dimensional Mon...
We consider the statics and dynamics of dark matter-wave solitons in the dimensionality crossover regime from three dimensions (3D) to one dimension (1D). There, using the nonpolynomial Schröding...
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degre...
A numerical method is proposed to approximate the inverse of a general bi-Lipschitz nonlinear dimensionality reduction mapping, where the forward and consequently the inverse mappings are only explici...
The Indian banking industry is going through turbulent times. With the lowering of entry barriers and blurring product lines of banks and non-banks since the financial sector reforms, banks are functi...
We address the issue of variable selection in the regression model with very high ambient dimension, i.e., when the number of variables is very large. The main focus is on the situation where the numb...
A collaborative convex framework for factoring a data matrix $X$ into a non-negative product $AS$, with a sparse coefficient matrix $S$, is proposed. We restrict the columns of the dictionary matrix $...
High-dimensional classification has become an increasingly important problem. In this paper we propose a "Multivariate Adaptive Stochastic Search" (MASS) approach which first reduces the dimension of...
Ultrahigh dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statisti- cal research. Among others, Fan and Lv (2008) propose an indepen- ...
Consider a random field of tensor product-type X (t), ~ E [ O l, l d, given by where ( A ( ~ ) i , 0 ~ 1 2 , is an orthonormal system in L, KO, 11 and (tklkENd are non-correlated random variables w...
The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension)...
We consider tests of dimensionality in the multivariate analysis of variance (MANOVA). Three types of test criteria (Likelihood-Ratio-type, Lawley-Hotelling-type and Bartlett-Nanda-Pillai-type) are po...
We present the first tree-based regressorwhose convergence rate depends only on the intrinsic dimension of the data, namely its Assouad dimension. The regressor uses the RPtree partitioning procedu...

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