Related papers: A random model for multidimensional fitting method
Computational difficulty of quadratic matching and the Gromov-Wasserstein distance has led to various approximation and relaxation schemes. One of such methods, relying on the notion of distance profiles, has been widely used in practice,…
We describe MPSE: a Multi-Perspective Simultaneous Embedding method for visualizing high-dimensional data, based on multiple pairwise distances between the data points. Specifically, MPSE computes positions for the points in 3D and provides…
Bias evaluation is fundamental to trustworthy AI, both in terms of checking data quality and in terms of checking the outputs of AI systems. In testing data quality, for example, one may study the distance of a given dataset, viewed as a…
In this study, we propose a novel model called the Markov-switching dynamic matrix factor (Ms-DMF) model, which serves the dual purpose of structural interpretation and prediction for high-dimensional matrix time series. When estimating the…
Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
Maximum mean discrepancy (MMD) has been widely employed to measure the distance between probability distributions. In this paper, we propose using MMD to solve continuous multi-objective optimization problems (MOPs). For solving MOPs, a…
Vector Fitting (VF) is a popular method of constructing rational approximants that provides a least squares fit to frequency response measurements. In an earlier work, we provided an analysis of VF for scalar-valued rational functions and…
We propose a novel distance-based regularization method for deep metric learning called Multi-level Distance Regularization (MDR). MDR explicitly disturbs a learning procedure by regularizing pairwise distances between embedding vectors…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
A Siamese Deep Forest (SDF) is proposed in the paper. It is based on the Deep Forest or gcForest proposed by Zhou and Feng and can be viewed as a gcForest modification. It can be also regarded as an alternative to the well-known Siamese…
The root-cause diagnostics of product quality defects in multistage manufacturing processes often requires a joint identification of crucial stages and process variables. To meet this requirement, this paper proposes a novel penalized…
Learning a Markov Decision Process (MDP) from a fixed batch of trajectories is a non-trivial task whose outcome's quality depends on both the amount and the diversity of the sampled regions of the state-action space. Yet, many MDPs are…
We consider the problem of approximating the moment generating function (MGF) of a truncated random variable in terms of the MGF of the underlying (i.e., untruncated) random variable. The purpose of approximating the MGF is to enable the…
A multivariate signal denoising method is proposed which employs a novel multivariate goodness of fit (GoF) test that is applied at multiple data scales obtained from discrete wavelet transform (DWT). In the proposed multivariate GoF test,…
\emph{Multiresolution mode decomposition} (MMD) is an adaptive tool to analyze a time series $f(t)=\sum_{k=1}^K f_k(t)$, where $f_k(t)$ is a \emph{multiresolution intrinsic mode function} (MIMF) of the form \begin{eqnarray*}…
Large high-dimensional datasets are becoming more and more popular in an increasing number of research areas. Processing the high dimensional data incurs a high computational cost and is inherently inefficient since many of the values that…
In recent years, a number of methods have been developed for the dimension reduction and decomposition of multiple linked high-content data matrices. Typically these methods assume that just one dimension, rows or columns, is shared among…
The Distributional Random Forest (DRF) is a recently introduced Random Forest algorithm to estimate multivariate conditional distributions. Due to its general estimation procedure, it can be employed to estimate a wide range of targets such…
Context: Adaptive monitoring is a method used in a variety of domains for responding to changing conditions. It has been applied in different ways, from monitoring systems' customization to re-composition, in different application domains.…