82 citations · 103 across the 15 of their papers we have counts for
17 papers
On Regularization via Early Stopping for Least Squares Regression
Rishi Sonthalia, Jackie Lok, Elizaveta Rebrova
A fundamental problem in machine learning is understanding the effect of early stopping on the parameters obtained and the generalization capabilities of the model. Even for linear…
Error dynamics of mini-batch gradient descent with random reshuffling for least squares regression
Jackie Lok, Rishi Sonthalia, Elizaveta Rebrova
We study the discrete dynamics of mini-batch gradient descent with random reshuffling for least squares regression. We show that the training and generalization errors depend on a…
Near-Interpolators: Rapid Norm Growth and the Trade-Off between Interpolation and Generalization
Yutong Wang, Rishi Sonthalia, Wei Hu
We study the generalization capability of nearly-interpolating linear regressors: 's whose training error is positive but small, i.e., below the noise floor. Unde…
Spectral Neural Networks: Approximation Theory and Optimization Landscape
Chenghui Li, Rishi Sonthalia, Nicolas Garcia Trillos
There is a large variety of machine learning methodologies that are based on the extraction of spectral geometric information from data. However, the implementations of many of the…
Supermodular Rank: Set Function Decomposition and Optimization
Rishi Sonthalia, Anna Seigal, Guido Montufar
We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summa…
Double Descent and Overfitting under Noisy Inputs and Distribution Shift for Linear Denoisers
Chinmaya Kausik, Kashvi Srivastava, Rishi Sonthalia
Despite the importance of denoising in modern machine learning and ample empirical work on supervised denoising, its theoretical understanding is still relatively scarce. One conce…
Least Squares Regression Can Exhibit Under-Parameterized Double Descent
Xinyue Li, Rishi Sonthalia
The relationship between the number of training data points, the number of parameters, and the generalization capabilities of models has been widely studied. Previous work has show…
Predicting the Future of AI with AI: High-quality link prediction in an exponentially growing knowledge network
Mario Krenn, Lorenzo Buffoni, Bruno Coutinho +13
A tool that could suggest new personalized research directions and ideas by taking insights from the scientific literature could significantly accelerate the progress of science. A…
ICLR 2022 Challenge for Computational Geometry and Topology: Design and Results
Adele Myers, Saiteja Utpala, Shubham Talbar +25
This paper presents the computational challenge on differential geometry and topology that was hosted within the ICLR 2022 workshop ``Geometric and Topological Representation Learn…
How can classical multidimensional scaling go wrong?
Rishi Sonthalia, Gregory Van Buskirk, Benjamin Raichel +1
Given a matrix describing the pairwise dissimilarities of a data set, a common task is to embed the data points into Euclidean space. The classical multidimensional scaling (cM…
An Analysis of COVID-19 Knowledge Graph Construction and Applications
Dominic Flocco, Bryce Palmer-Toy, Ruixiao Wang +5
The construction and application of knowledge graphs have seen a rapid increase across many disciplines in recent years. Additionally, the problem of uncovering relationships betwe…
Dual Regularized Optimal Transport
Rishi Sonthalia, Anna C. Gilbert
In this paper, we present a new formulation of unbalanced optimal transport called Dual Regularized Optimal Transport (DROT). We argue that regularizing the dual formulation of opt…
Project and Forget: Solving Large-Scale Metric Constrained Problems
Rishi Sonthalia, Anna C. Gilbert
Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captu…
Tree! I am no Tree! I am a Low Dimensional Hyperbolic Embedding
Rishi Sonthalia, Anna C. Gilbert
Given data, finding a faithful low-dimensional hyperbolic embedding of the data is a key method by which we can extract hierarchical information or learn representative geometric f…
Generalized Metric Repair on Graphs
Chenglin Fan, Anna C. Gilbert, Benjamin Raichel +2
Many modern data analysis algorithms either assume or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metric lea…
Generalized Metric Repair on Graphs
Anna C. Gilbert, Rishi Sonthalia
Many modern data analysis algorithms either assume that or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metri…
Unsupervised Metric Learning in Presence of Missing Data
Anna C. Gilbert, Rishi Sonthalia
For many machine learning tasks, the input data lie on a low-dimensional manifold embedded in a high dimensional space and, because of this high-dimensional structure, most algorit…