Search Results for author:
Found 68 papers, 18 papers with code
Causal Inference for Genomic Data with Multiple Heterogeneous Outcomes
In this paper, we propose a generic semiparametric inference framework for doubly robust estimation with multiple derived outcomes, which also encompasses the usual setting of multiple outcomes when the response of each unit is available.
Double Cross-fit Doubly Robust Estimators: Beyond Series Regression
Then, assuming the nuisance functions are H\"{o}lder smooth, but without assuming knowledge of the true smoothness level or the covariate density, we establish that DCDR estimators with several linear smoothers are semiparametric efficient under minimal conditions and achieve fast convergence rates in the non-$\sqrt{n}$ regime.
Semi-Supervised U-statistics
Semi-supervised datasets are ubiquitous across diverse domains where obtaining fully labeled data is costly or time-consuming.
Simultaneous inference for generalized linear models with unmeasured confounders
Tens of thousands of simultaneous hypothesis tests are routinely performed in genomic studies to identify differentially expressed genes.
The Fundamental Limits of Structure-Agnostic Functional Estimation
These first-order methods are however provably suboptimal in a minimax sense for functional estimation when the nuisance functions live in Holder-type function spaces.
Feature Importance: A Closer Look at Shapley Values and LOCO
We are particularly interested in the effect of correlation between features which can obscure interpretability.
Data fission: splitting a single data point
Rasines and Young (2022) offers an alternative approach that uses additive Gaussian noise -- this enables post-selection inference in finite samples for Gaussian distributed data and asymptotically when errors are non-Gaussian.
Decorrelated Variable Importance
We propose a method for mitigating the effect of correlation by defining a modified version of LOCO.
Universal Inference Meets Random Projections: A Scalable Test for Log-concavity
Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data.
Plugin Estimation of Smooth Optimal Transport Maps
Our work also provides new bounds on the risk of corresponding plugin estimators for the quadratic Wasserstein distance, and we show how this problem relates to that of estimating optimal transport maps using stability arguments for smooth and strongly convex Brenier potentials.
Forest Guided Smoothing
We use the output of a random forest to define a family of local smoothers with spatially adaptive bandwidth matrices.
Model-Independent Detection of New Physics Signals Using Interpretable Semi-Supervised Classifier Tests
Here we instead investigate a model-independent method that does not make any assumptions about the signal and uses a semi-supervised classifier to detect the presence of the signal in the experimental data.
Applications High Energy Physics - Phenomenology Data Analysis, Statistics and Probability
PLLay: Efficient Topological Layer based on Persistent Landscapes
We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure.
The huge Package for High-dimensional Undirected Graph Estimation in R
We describe an R package named huge which provides easy-to-use functions for estimating high dimensional undirected graphs from data.
Familywise Error Rate Control by Interactive Unmasking
We propose a method for multiple hypothesis testing with familywise error rate (FWER) control, called the i-FWER test.
Methodology
PLLay: Efficient Topological Layer based on Persistence Landscapes
We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure.
Trend Filtering -- II. Denoising Astronomical Signals with Varying Degrees of Smoothness
The remaining studies share broad themes of: (1) estimating observable parameters of light curves and spectra; and (2) constructing observational spectral/light-curve templates.
Instrumentation and Methods for Astrophysics Cosmology and Nongalactic Astrophysics Earth and Planetary Astrophysics Solar and Stellar Astrophysics Applications
Universal Inference
Constructing tests and confidence sets for such models is notoriously difficult.
Gaussian Mixture Clustering Using Relative Tests of Fit
We consider clustering based on significance tests for Gaussian Mixture Models (GMMs).
Minimax Confidence Intervals for the Sliced Wasserstein Distance
To motivate the choice of these classes, we also study minimax rates of estimating a distribution under the Sliced Wasserstein distance.
Trend Filtering: A Modern Statistical Tool for Time-Domain Astronomy and Astronomical Spectroscopy
The problem of denoising a one-dimensional signal possessing varying degrees of smoothness is ubiquitous in time-domain astronomy and astronomical spectroscopy.
Instrumentation and Methods for Astrophysics Cosmology and Nongalactic Astrophysics Applications
Cautious Deep Learning
Our construction is based on $p(x|y)$ rather than $p(y|x)$ which results in a classifier that is very cautious: it outputs the null set --- meaning "I don't know" --- when the object does not resemble the training examples.
Hypothesis Testing for High-Dimensional Multinomials: A Selective Review
The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson.
Hypothesis Testing For Densities and High-Dimensional Multinomials: Sharp Local Minimax Rates
In contrast to existing results, we show that the minimax rate and critical testing radius in these settings depend strongly, and in a precise way, on the null distribution being tested and this motivates the study of the (local) minimax rate as a function of the null distribution.
Topological Data Analysis
Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data.
Methodology
Least Ambiguous Set-Valued Classifiers with Bounded Error Levels
In most classification tasks there are observations that are ambiguous and therefore difficult to correctly label.
Finding Singular Features
We present a method for finding high density, low-dimensional structures in noisy point clouds.
Statistical Inference for Cluster Trees
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters.
Distribution-Free Predictive Inference For Regression
In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package.
Classification accuracy as a proxy for two sample testing
We prove two results that hold for all classifiers in any dimensions: if its true error remains $\epsilon$-better than chance for some $\epsilon>0$ as $d, n \to \infty$, then (a) the permutation-based test is consistent (has power approaching to one), (b) a computationally efficient test based on a Gaussian approximation of the null distribution is also consistent.
Minimax Lower Bounds for Linear Independence Testing
Linear independence testing is a fundamental information-theoretic and statistical problem that can be posed as follows: given $n$ points $\{(X_i, Y_i)\}^n_{i=1}$ from a $p+q$ dimensional multivariate distribution where $X_i \in \mathbb{R}^p$ and $Y_i \in\mathbb{R}^q$, determine whether $a^T X$ and $b^T Y$ are uncorrelated for every $a \in \mathbb{R}^p, b\in \mathbb{R}^q$ or not.
Nonparametric von Mises Estimators for Entropies, Divergences and Mutual Informations
We propose and analyse estimators for statistical functionals of one or moredistributions under nonparametric assumptions. Our estimators are derived from the von Mises expansion andare based on the theory of influence functions, which appearin the semiparametric statistics literature. We show that estimators based either on data-splitting or a leave-one-out techniqueenjoy fast rates of convergence and other favorable theoretical properties. We apply this framework to derive estimators for several popular informationtheoretic quantities, and via empirical evaluation, show the advantage of thisapproach over existing estimators.
Statistical Analysis of Persistence Intensity Functions
Persistence diagrams are two-dimensional plots that summarize the topological features of functions and are an important part of topological data analysis.
Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing
We formally characterize the power of popular tests for GDA like the Maximum Mean Discrepancy with the Gaussian kernel (gMMD) and bandwidth-dependent variants of the Energy Distance with the Euclidean norm (eED) in the high-dimensional MDA regime.
Statistical Inference using the Morse-Smale Complex
The Morse-Smale complex of a function $f$ decomposes the sample space into cells where $f$ is increasing or decreasing.
Optimal Ridge Detection using Coverage Risk
We introduce the concept of coverage risk as an error measure for density ridge estimation.
An Analysis of Active Learning With Uniform Feature Noise
For larger $\sigma$, the \textit{unflattening} of the regression function on convolution with uniform noise, along with its local antisymmetry around the threshold, together yield a behaviour where noise \textit{appears} to be beneficial.
Robust Topological Inference: Distance To a Measure and Kernel Distance
However, the empirical distance function is highly non-robust to noise and outliers.
Statistics Theory Computational Geometry Algebraic Topology Statistics Theory
Nonparametric modal regression
Modal regression estimates the local modes of the distribution of $Y$ given $X=x$, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods.
On the High-dimensional Power of Linear-time Kernel Two-Sample Testing under Mean-difference Alternatives
The current literature is split into two kinds of tests - those which are consistent without any assumptions about how the distributions may differ (\textit{general} alternatives), and those which are designed to specifically test easier alternatives, like a difference in means (\textit{mean-shift} alternatives).
Influence Functions for Machine Learning: Nonparametric Estimators for Entropies, Divergences and Mutual Informations
We propose and analyze estimators for statistical functionals of one or more distributions under nonparametric assumptions.
On Estimating $L_2^2$ Divergence
We give a comprehensive theoretical characterization of a nonparametric estimator for the $L_2^2$ divergence between two continuous distributions.
The functional mean-shift algorithm for mode hunting and clustering in infinite dimensions
We introduce the functional mean-shift algorithm, an iterative algorithm for estimating the local modes of a surrogate density from functional data.
Estimating the distribution of Galaxy Morphologies on a continuous space
The incredible variety of galaxy shapes cannot be summarized by human defined discrete classes of shapes without causing a possibly large loss of information.
Feature Selection For High-Dimensional Clustering
We provide explicit bounds on the error rate of the resulting clustering.
Efficient Sparse Clustering of High-Dimensional Non-spherical Gaussian Mixtures
We consider the problem of clustering data points in high dimensions, i. e. when the number of data points may be much smaller than the number of dimensions.
On the Decreasing Power of Kernel and Distance based Nonparametric Hypothesis Tests in High Dimensions
This paper is about two related decision theoretic problems, nonparametric two-sample testing and independence testing.
Subsampling Methods for Persistent Homology
Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets.
Algebraic Topology Computational Geometry Applications
A Comprehensive Approach to Mode Clustering
Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes.
Nonparametric Estimation of Renyi Divergence and Friends
We consider nonparametric estimation of $L_2$, Renyi-$\alpha$ and Tsallis-$\alpha$ divergences between continuous distributions.
Nonparametric Inference For Density Modes
We derive nonparametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate.
Stochastic Convergence of Persistence Landscapes and Silhouettes
Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram.
Statistics Theory Computational Geometry Algebraic Topology Statistics Theory
On the Bootstrap for Persistence Diagrams and Landscapes
Persistent homology probes topological properties from point clouds and functions.
Algebraic Topology Computational Geometry Applications
Estimating Undirected Graphs Under Weak Assumptions
In particular, we consider: cluster graphs, restricted partial correlation graphs and correlation graphs.
Tight Lower Bounds for Homology Inference
In this note we use a different construction based on the direct analysis of the likelihood ratio test to show that the upper bound of Niyogi, Smale and Weinberger is in fact tight, thus establishing rate optimal asymptotic minimax bounds for the problem.
Cluster Trees on Manifolds
In this paper we investigate the problem of estimating the cluster tree for a density $f$ supported on or near a smooth $d$-dimensional manifold $M$ isometrically embedded in $\mathbb{R}^D$.
Minimax Theory for High-dimensional Gaussian Mixtures with Sparse Mean Separation
While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings are not well-understood.
Confidence sets for persistence diagrams
Persistent homology is a method for probing topological properties of point clouds and functions.
A Conformal Prediction Approach to Explore Functional Data
This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data.
Nonparametric ridge estimation
Ridge estimation is an extension of mode finding and is useful for understanding the structure of a density.
Exponential Concentration for Mutual Information Estimation with Application to Forests
We prove a new exponential concentration inequality for a plug-in estimator of the Shannon mutual information.
Density-sensitive semisupervised inference
Semisupervised methods are techniques for using labeled data $(X_1, Y_1),\ldots,(X_n, Y_n)$ together with unlabeled data $X_{n+1},\ldots, X_N$ to make predictions.
Graph-Valued Regression
In this paper, we propose a semiparametric method for estimating $G(x)$ that builds a tree on the $X$ space just as in CART (classification and regression trees), but at each leaf of the tree estimates a graph.
Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models
In this paper, we present StARS: a new stability-based method for choosing the regularization parameter in high dimensional inference for undirected graphs.
Nonparametric regression and classification with joint sparsity constraints
We propose new families of models and algorithms for high-dimensional nonparametric learning with joint sparsity constraints.
Compressed Regression
Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data.
Treelets--An adaptive multi-scale basis for sparse unordered data
In many modern applications, including analysis of gene expression and text documents, the data are noisy, high-dimensional, and unordered--with no particular meaning to the given order of the variables.
Methodology
