Search Results for author:
Found 33 papers, 9 papers with code
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.
DeBaCl: A Python Package for Interactive DEnsity-BAsed CLustering
The package is intended to promote the practical use of level set trees through improvements in computational efficiency and a high degree of user customization.
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
Statistical Analysis of Nearest Neighbor Methods for Anomaly Detection
Nearest-neighbor (NN) procedures are well studied and widely used in both supervised and unsupervised learning problems.
Nonparametric Estimation in the Dynamic Bradley-Terry Model
We propose a time-varying generalization of the Bradley-Terry model that allows for nonparametric modeling of dynamic global rankings of distinct teams.
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.
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.
Consistency of spectral clustering in stochastic block models
We analyze the performance of spectral clustering for community extraction in stochastic block models.
Confidence sets for persistence diagrams
Persistent homology is a method for probing topological properties of point clouds and functions.
Statistical Models for Degree Distributions of Networks
We define and study the statistical models in exponential family form whose sufficient statistics are the degree distributions and the bi-degree distributions of undirected labelled simple graphs.
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 $\mathbb{R}^D$.
Recovering Block-structured Activations Using Compressive Measurements
We consider the problems of detection and localization of a contiguous block of weak activation in a large matrix, from a small number of noisy, possibly adaptive, compressive (linear) measurements.
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
On the Bootstrap for Persistence Diagrams and Landscapes
Persistent homology probes topological properties from point clouds and functions.
Algebraic Topology Computational Geometry Applications
Markov Properties of Discrete Determinantal Point Processes
Determinantal point processes (DPPs) are probabilistic models for repulsion.
Time Series Featurization via Topological Data Analysis
We develop a novel algorithm for feature extraction in time series data by leveraging tools from topological data analysis.
A Sharp Error Analysis for the Fused Lasso, with Application to Approximate Changepoint Screening
In the 1-dimensional multiple changepoint detection problem, we derive a new fast error rate for the fused lasso estimator, under the assumption that the mean vector has a sparse number of changepoints.
Minimax Localization of Structural Information in Large Noisy Matrices
We consider the problem of identifying a sparse set of relevant columns and rows in a large data matrix with highly corrupted entries.
On the bias, risk and consistency of sample means in multi-armed bandits
For example, when is it consistent, how large is its bias, and can we bound its mean squared error?
Are sample means in multi-armed bandits positively or negatively biased?
It is well known that in stochastic multi-armed bandits (MAB), the sample mean of an arm is typically not an unbiased estimator of its true mean.
Cryptocurrency Price Prediction and Trading Strategies Using Support Vector Machines
Few assets in financial history have been as notoriously volatile as cryptocurrencies.
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 conditional versus marginal bias in multi-armed bandits
The bias of the sample means of the arms in multi-armed bandits is an important issue in adaptive data analysis that has recently received considerable attention in the literature.
Optimal network online change point localisation
The goal is to detect the change point as quickly as possible, if it exists, subject to a constraint on the number or probability of false alarms.
Lattice partition recovery with dyadic CART
We study piece-wise constant signals corrupted by additive Gaussian noise over a $d$-dimensional lattice.
$\ell_{\infty}$-Bounds of the MLE in the BTL Model under General Comparison Graphs
In this paper, we derive novel, general upper bounds on the $\ell_{\infty}$ estimation error of the BTL MLE that depend explicitly on the algebraic connectivity of the comparison graph, the maximal performance gap across items and the sample complexity.
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.
E-detectors: a nonparametric framework for sequential change detection
Sequential change detection is a classical problem with a variety of applications.
Mitigating multiple descents: A model-agnostic framework for risk monotonization
Recent empirical and theoretical analyses of several commonly used prediction procedures reveal a peculiar risk behavior in high dimensions, referred to as double/multiple descent, in which the asymptotic risk is a non-monotonic function of the limiting aspect ratio of the number of features or parameters to the sample size.
Sharp high-probability sample complexities for policy evaluation with linear function approximation
This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes.
On Least Squares Estimation in Softmax Gating Mixture of Experts
Mixture of experts (MoE) model is a statistical machine learning design that aggregates multiple expert networks using a softmax gating function in order to form a more intricate and expressive model.
