arXiv research

We identify and validate a model for PCR in high dimensions, improving prediction guarantees.

Novel Fréchet regression method handles errors-in-variables with low-rank covariates.

Bayesian deep learning accounts for input uncertainty using Errors-in-Variables models.

This paper addresses measurement errors in high-dimensional compositional data using a log-contrast model calibration approach.

In this note, we introduce a new algorithm to deal with finite dimensional clustering with errors in variables. The design of this algorithm is based on recent theoretical advances (see Loustau (2013a,b)) in statistical learning with errors in variables. As the previous mentioned papers, the algorithm mixes different t…

Suppose that we observe $y \in \mathbb{R}^f$ and $X \in \mathbb{R}^{f \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 β^* + ε\\ X & = & X_0 + W \end{eqnarray*} where $X_0$ is a $f \times m$ design matrix with independent subgaussian row vectors, $ε\in \mathbb{R}^f$ is a noise vector…

Adaptive PCR improves panel data analysis with uniform guarantees.

A new method ODR-BINDy improves model discovery from noisy data.

New EiV models correct bias in operator learning with noisy data.

The errors-in-variables (EIV) regression model, being more realistic by accounting for measurement errors in both the dependent and the independent variables, is widely adopted in applied sciences. The traditional EIV model estimators, however, can be highly biased by outliers and other departures from the underlying a…

We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions. Under restricted strong convexity on the loss and suitable regularity conditions on the penalty, we prove that \emph{any stationary point} of the composite objective f…

We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental errors, or malicious respondents in surveys/recommender systems, etc. Such non-stochas…

We address the problem of inferring the causal effect of an exposure on an outcome across space, using observational data. The data is possibly subject to unmeasured confounding variables which, in a standard approach, must be adjusted for by estimating a nuisance function. Here we develop a method that eliminates the …

In active learning, the user sequentially chooses values for feature $X$ and an oracle returns the corresponding label $Y$. In this paper, we consider the effect of feature noise in active learning, which could arise either because $X$ itself is being measured, or it is corrupted in transmission to the oracle, or the o…

The effect of errors in variables in quantization is investigated. We prove general exact and non-exact oracle inequalities with fast rates for an empirical minimization based on a noisy sample $Z_i=X_i+ε_i,i=1,\ldots,n$, where $X_i$ are i.i.d. with density $f$ and $ε_i$ are i.i.d. with density $η$. These rates depend …

GATs improve node regression on noisy graphs with provable advantage.

Several new estimation methods have been recently proposed for the linear regression model with observation error in the design. Different assumptions on the data generating process have motivated different estimators and analysis. In particular, the literature considered (1) observation errors in the design uniformly …

Suppose that we observe $y \in \mathbb{R}^n$ and $X \in \mathbb{R}^{n \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 β^* +ε\\ X & = & X_0 + W, \end{eqnarray*} where $X_0$ is an $n \times m$ design matrix with independent subgaussian row vectors, $ε\in \mathbb{R}^n$ is a noise vecto…

Corporate bond factor research is flawed due to measurement errors and ex-post filtering.

We demonstrate that the primal-dual witness proof method may be used to establish variable selection consistency and $\ell_\infty$-bounds for sparse regression problems, even when the loss function and/or regularizer are nonconvex. Using this method, we derive two theorems concerning support recovery and $\ell_\infty$-…

Estimating the effect of a treatment on a given outcome, conditioned on a vector of covariates, is central in many applications. However, learning the impact of a treatment on a continuous temporal response, when the covariates suffer extensively from measurement error and even the timing of the treatments is uncertain…

The maximum correntropy criterion (MCC) has recently been successfully applied in robust regression, classification and adaptive filtering, where the correntropy is maximized instead of minimizing the well-known mean square error (MSE) to improve the robustness with respect to outliers (or impulsive noises). Considerab…

The Grassmannian of affine subspaces is a natural generalization of both the Euclidean space, points being zero-dimensional affine subspaces, and the usual Grassmannian, linear subspaces being special cases of affine subspaces. We show that, like the Grassmannian, the affine Grassmannian has rich geometrical and topolo…

Bayesian method improves grid admittance matrix estimation from noisy data.

Dropout training is shown to be optimal for adversarial covariate corruption.

Paper tackles privacy-preserving data density issues using deconvolution.

New matching estimators correct bias in multivariate settings without smoothing parameters.

We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to make predictions. At the core of our analysis is a representation result, which st…

High-dimensional ConvNets detect patterns in 32+ dimensions for geometric registration.

This is an introductory article on high dimensional knots for the beginners. High dimensional knot theory is an exciting field. It is a field of knot theory, which is one of topology and is connected with many ones. In this article we use few literal expressions, equations, functions, etc. We barely suppose that the re…

An adaptive dropout approach improves high-dimensional Bayesian optimization.

The paper provides statistical guarantees for SGD and ASGD in high-dimensional settings.

i-flow uses normalizing flows for high-dimensional integration and sampling.

High-dimensional data simplifies problems, contrary to the curse of dimensionality.

PROD method improves high-dimensional regression by handling strong correlations.

A new BO method tackles high-dimensional optimization without reconstruction.

HD-BWDM improves clustering validation in high-dimensional data.

Solves clustering contradictions by high-dimensional embedding with wide gaps.

Machine learning improves high-dimensional matrix estimation.

In this paper, we propose the idea of radial scaling in frequency domain and activation functions with compact support to produce a multi-scale DNN (MscaleDNN), which will have the multi-scale capability in approximating high frequency and high dimensional functions and speeding up the solution of high dimensional PDEs…

New method estimates treatment effects from high dimensional data.

Estimates high-dimensional posterior densities by marginal distributions and neural networks.

AF improves sampling from high-dimensional, multi-modal distributions.

New method explains high-dimensional text classifiers.

A new machine learning method solves high-dimensional Kolmogorov PDEs efficiently.

Anomaly detection for high-dimensional data using large deviations principle.

Proposes GPLFR for predicting high-dimensional outputs with few data.

Paper proposes new density estimators for high-dimensional data.