Related papers: Using scaling-region distributions to select embed…

Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…

We study the task of high-dimensional entangled mean estimation in the subset-of-signals model. Specifically, given $N$ independent random points $x_1,\ldots,x_N$ in $\mathbb{R}^D$ and a parameter $\alpha \in (0, 1)$ such that each $x_i$ is…

When building linear or nonlinear models one is faced with the problem of selecting the best set of variable with which to predict the future dynamics. In nonlinear time series analysis the problem is to select the correct time delays in…

We apply a recently proposed method for the analysis of time series from systems with delayed feedback to experimental data generated by a CO_2 laser. The method is able to estimate the delay time with an error of the order of the sampling…

Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…

The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors…

Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…

A general approach to selective inference is considered for hypothesis testing of the null hypothesis represented as an arbitrary shaped region in the parameter space of multivariate normal model. This approach is useful for hierarchical…

In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…

We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a…

High-dimensional linear models with endogenous variables play an increasingly important role in recent econometric literature. In this work we allow for models with many endogenous variables and many instrument variables to achieve…

A bottleneck of sufficient dimension reduction (SDR) in the modern era is that, among numerous methods, only the sliced inverse regression (SIR) is generally applicable under the high-dimensional settings. The higher-order inverse…

A key obstacle in automated analytics and meta-learning is the inability to recognize when different datasets contain measurements of the same variable. Because provided attribute labels are often uninformative in practice, this task may be…

With the recent surge in big data analytics for hyper-dimensional data there is a renewed interest in dimensionality reduction techniques for machine learning applications. In order for these methods to improve performance gains and…

Feature embeddings are one of the most essential steps when training deep learning based Click-Through Rate prediction models, which map high-dimensional sparse features to dense embedding vectors. Classic human-crafted embedding size…

Identifying the qualitative changes in time-series data provides insights into the dynamics associated with such data. Such qualitative changes can be detected through topological approaches, which first embed the data into a…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

This paper explores learning emulators for parameter estimation with uncertainty estimation of high-dimensional dynamical systems. We assume access to a computationally complex simulator that inputs a candidate parameter and outputs a…

Prediction algorithms, such as deep neural networks (DNNs), are used in many domain sciences to directly estimate internal parameters of interest in simulator-based models, especially in settings where the observations include images or…

An algorithmic limit of compressed sensing or related variable-selection problems is analytically evaluated when a design matrix is given by an overcomplete random matrix. The replica method from statistical mechanics is employed to derive…