Search Results for author: Alessandro Rinaldo

Found 31 papers, 8 papers with code

Mitigating multiple descents: A model-agnostic framework for risk monotonization

no code implementations25 May 2022 Pratik Patil, Arun Kumar Kuchibhotla, Yuting Wei, Alessandro Rinaldo

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.

E-detectors: a nonparametric framework for online changepoint detection

no code implementations7 Mar 2022 Jaehyeok Shin, Aaditya Ramdas, Alessandro Rinaldo

Sequential changepoint detection is a classical problem with a variety of applications.

The Performance of the MLE in the Bradley-Terry-Luce Model in $\ell_{\infty}$-Loss and under General Graph Topologies

1 code implementation20 Oct 2021 Wanshan Li, Shamindra Shrotriya, Alessandro Rinaldo

However, beyond very few well-studied cases, such as the complete and Erd\"os-R\'enyi comparison graphs, little is known about the performance of the maximum likelihood estimator (MLE) of the BTL model parameters in the $\ell_{\infty}$-loss under more general graph topologies.

Lattice partition recovery with dyadic CART

1 code implementation NeurIPS 2021 Oscar Hernan Madrid Padilla, Yi Yu, Alessandro Rinaldo

We study piece-wise constant signals corrupted by additive Gaussian noise over a $d$-dimensional lattice.

Optimal network online change point localisation

no code implementations14 Jan 2021 Yi Yu, Oscar Hernan Madrid Padilla, Daren Wang, Alessandro Rinaldo

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.

Change Point Detection

Nonparametric Estimation in the Dynamic Bradley-Terry Model

1 code implementation28 Feb 2020 Heejong Bong, Wanshan Li, Shamindra Shrotriya, Alessandro Rinaldo

We propose a time-varying generalization of the Bradley-Terry model that allows for nonparametric modeling of dynamic global rankings of distinct teams.

On conditional versus marginal bias in multi-armed bandits

no code implementations ICML 2020 Jaehyeok Shin, Aaditya Ramdas, Alessandro Rinaldo

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.

Multi-Armed Bandits

Statistical Analysis of Nearest Neighbor Methods for Anomaly Detection

1 code implementation NeurIPS 2019 Xiaoyi Gu, Leman Akoglu, Alessandro Rinaldo

Nearest-neighbor (NN) procedures are well studied and widely used in both supervised and unsupervised learning problems.

Anomaly Detection

Are sample means in multi-armed bandits positively or negatively biased?

no code implementations NeurIPS 2019 Jaehyeok Shin, Aaditya Ramdas, Alessandro Rinaldo

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.

Multi-Armed Bandits Selection bias

Time Series Featurization via Topological Data Analysis

no code implementations7 Dec 2018 Kwangho Kim, Jisu Kim, Alessandro Rinaldo

We develop a novel algorithm for feature extraction in time series data by leveraging tools from topological data analysis.

Dimensionality Reduction Feature Engineering +2

Markov Properties of Discrete Determinantal Point Processes

no code implementations4 Oct 2018 Kayvan Sadeghi, Alessandro Rinaldo

Determinantal point processes (DPPs) are probabilistic models for repulsion.

Point Processes

A Sharp Error Analysis for the Fused Lasso, with Application to Approximate Changepoint Screening

no code implementations NeurIPS 2017 Kevin Lin, James L. Sharpnack, Alessandro Rinaldo, Ryan J. Tibshirani

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.

Statistical Inference for Cluster Trees

no code implementations NeurIPS 2016 Jisu Kim, Yen-Chi Chen, Sivaraman Balakrishnan, Alessandro Rinaldo, Larry Wasserman

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

5 code implementations14 Apr 2016 Jing Lei, Max G'Sell, Alessandro Rinaldo, Ryan J. Tibshirani, Larry Wasserman

In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package.

Prediction Intervals

Statistical Analysis of Persistence Intensity Functions

no code implementations8 Oct 2015 Yen-Chi Chen, Daren Wang, Alessandro Rinaldo, Larry Wasserman

Persistence diagrams are two-dimensional plots that summarize the topological features of functions and are an important part of topological data analysis.

Topological Data Analysis

Robust Topological Inference: Distance To a Measure and Kernel Distance

2 code implementations22 Dec 2014 Frédéric Chazal, Brittany T. Fasy, Fabrizio Lecci, Bertrand Michel, Alessandro Rinaldo, Larry Wasserman

However, the empirical distance function is highly non-robust to noise and outliers.

Statistics Theory Computational Geometry Algebraic Topology Statistics Theory

Statistical Models for Degree Distributions of Networks

no code implementations14 Nov 2014 Kayvan Sadeghi, Alessandro Rinaldo

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.

Subsampling Methods for Persistent Homology

no code implementations7 Jun 2014 Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Bertrand Michel, Alessandro Rinaldo, Larry Wasserman

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

Consistency of spectral clustering in stochastic block models

no code implementations7 Dec 2013 Jing Lei, Alessandro Rinaldo

We analyze the performance of spectral clustering for community extraction in stochastic block models.

Stochastic Convergence of Persistence Landscapes and Silhouettes

no code implementations2 Dec 2013 Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman

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

1 code implementation2 Nov 2013 Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Aarti Singh, Larry Wasserman

Persistent homology probes topological properties from point clouds and functions.

Algebraic Topology Computational Geometry Applications

Estimating Undirected Graphs Under Weak Assumptions

no code implementations26 Sep 2013 Larry Wasserman, Mladen Kolar, Alessandro Rinaldo

In particular, we consider: cluster graphs, restricted partial correlation graphs and correlation graphs.

DeBaCl: A Python Package for Interactive DEnsity-BAsed CLustering

1 code implementation30 Jul 2013 Brian P. Kent, Alessandro Rinaldo, Timothy Verstynen

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.

Tight Lower Bounds for Homology Inference

no code implementations29 Jul 2013 Sivaraman Balakrishnan, Alessandro Rinaldo, Aarti Singh, Larry Wasserman

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

no code implementations NeurIPS 2013 Sivaraman Balakrishnan, Srivatsan Narayanan, Alessandro Rinaldo, Aarti Singh, Larry Wasserman

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 $\mathbb{R}^D$.

Confidence sets for persistence diagrams

no code implementations28 Mar 2013 Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman, Sivaraman Balakrishnan, Aarti Singh

Persistent homology is a method for probing topological properties of point clouds and functions.

A Conformal Prediction Approach to Explore Functional Data

no code implementations26 Feb 2013 Jing Lei, Alessandro Rinaldo, Larry Wasserman

This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data.

Recovering Block-structured Activations Using Compressive Measurements

no code implementations15 Sep 2012 Sivaraman Balakrishnan, Mladen Kolar, Alessandro Rinaldo, Aarti Singh

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.

Minimax Localization of Structural Information in Large Noisy Matrices

no code implementations NeurIPS 2011 Mladen Kolar, Sivaraman Balakrishnan, Alessandro Rinaldo, Aarti Singh

We consider the problem of identifying a sparse set of relevant columns and rows in a large data matrix with highly corrupted entries.

Two-sample testing

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