Related papers: Nonparametric Testing under Random Projection
We propose statistical inferential procedures for panel data models with interactive fixed effects in a kernel ridge regression framework.Compared with traditional sieve methods, our method is automatic in the sense that it does not require…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
The goal of nonparametric regression is to recover an underlying regression function from noisy observations, under the assumption that the regression function belongs to a pre-specified infinite dimensional function space. In the online…
A core challenge in causal inference is how to extrapolate long term effects, of possibly continuous actions, from short term experimental data. It arises in artificial intelligence: the long term consequences of continuous actions may be…
We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…
This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…
This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline…
It is often of interest to assess whether a function-valued statistical parameter, such as a density function or a mean regression function, is equal to any function in a class of candidate null parameters. This can be framed as a…
We present a machine learning approach for model-independent new physics searches. The corresponding algorithm is powered by recent large-scale implementations of kernel methods, nonparametric learning algorithms that can approximate any…
With appropriately chosen sampling probabilities, sampling-based random projection can be used to implement large-scale statistical methods, substantially reducing computational cost while maintaining low statistical error. However,…
We propose new reproducing kernel-based tests for model checking in conditional moment restriction models. By regressing estimated residuals on kernel functions via kernel ridge regression (KRR), we obtain a coefficient function in a…
We study the problem of estimating the derivatives of a regression function, which has a wide range of applications as a key nonparametric functional of unknown functions. Standard analysis may be tailored to specific derivative orders, and…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
Adaptive psychophysical procedures aim to increase the efficiency and reliability of measurements. With increasing stimulus and experiment complexity in the last decade, estimating multi-dimensional psychometric functions has become a…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions. While this assumption leads to efficient algorithms, it limits…
Kernel ridge regression (KRR) is a well-known and popular nonparametric regression approach with many desirable properties, including minimax rate-optimality in estimating functions that belong to common reproducing kernel Hilbert spaces…
A Two-Stage approach enables researchers to make optimal non-linear predictions via Generalized Ridge Regression using models that contain two or more x-predictor variables and make only realistic minimal assumptions. The optimal regression…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
We analyze the Nystr\"om approximation of a positive definite kernel associated with a probability measure. We first prove an improved error bound for the conventional Nystr\"om approximation with i.i.d. sampling and singular-value…