34 citations · 63 across the 26 of their papers we have counts for
31 papers
Mixture and separation of log-concave measures
March T. Boedihardjo, Yao Xie
For a two-component log-concave mixture model, we investigate the extent to which the weight, mean, and covariance of each component distribution can be accurately recovered when g…
Testing the mixture model hypothesis via spectral gap
March T. Boedihardjo, Joe Kileel, Vandy Tombs
In this paper, we study the problem of testing whether or not a given probability measure on can be decomposed as a mixture of two probability measures whose s…
Optimality of empirical measures as quantizers
March T. Boedihardjo
A common way to discretize a probability measure is to use an empirical measure as a discrete approximation. But how far from being optimal is this approximation in the p-Wasserste…
On Extended Concentration Inequalities for Fast JL Embeddings of Infinite Sets
Edem Boahen, March T. Boedihardjo, Rafael Chiclana +1
The Johnson-Lindenstrauss (JL) lemma allows subsets of a high-dimensional space to be embedded into a lower-dimensional space while approximately preserving all pairwise Euclidean…
Injective norm of random tensors with independent entries
March T. Boedihardjo
We obtain a non-asymptotic bound for the expected injective norm of a random tensor with independent entries. This bound is similar to the bound by Bandeira and van Handel (2016) f…
Embedding C*-algebras into the Calkin algebra of
March T. Boedihardjo
Let . We show that there is an isomorphism from any separable unital subalgebra of onto a subalgebra of that pre…
Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distances
Jie Wang, March Boedihardjo, Yao Xie
Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is d…
Metric geometry of the privacy-utility tradeoff
March Boedihardjo, Thomas Strohmer, Roman Vershynin
Synthetic data are an attractive concept to enable privacy in data sharing. A fundamental question is how similar the privacy-preserving synthetic data are compared to the true dat…
Max-sliced 2-Wasserstein distance
March T. Boedihardjo
This note is a continuation of the author's previous work on "Sharp bounds for the max-sliced Wasserstein distance." We use the same technique to obtain an upper bound for the expe…
Sharp bounds for max-sliced Wasserstein distances
March T. Boedihardjo
We obtain essentially matching upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirica…
Certified private data release for sparse Lipschitz functions
Konstantin Donhauser, Johan Lokna, Amartya Sanyal +3
As machine learning has become more relevant for everyday applications, a natural requirement is the protection of the privacy of the training data. When the relevant learning ques…
Covariance loss, Szemeredi regularity, and differential privacy
March Boedihardjo, Thomas Strohmer, Roman Vershynin
We show how randomized rounding based on Grothendieck's identity can be used to prove a nearly tight bound on the covariance loss--the amount of covariance that is lost by taking c…
Private measures, random walks, and synthetic data
March Boedihardjo, Thomas Strohmer, Roman Vershynin
Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guarante…
Private sampling: a noiseless approach for generating differentially private synthetic data
March Boedihardjo, Thomas Strohmer, Roman Vershynin
In a world where artificial intelligence and data science become omnipresent, data sharing is increasingly locking horns with data-privacy concerns. Differential privacy has emerge…
Privacy of synthetic data: a statistical framework
March Boedihardjo, Thomas Strohmer, Roman Vershynin
Privacy-preserving data analysis is emerging as a challenging problem with far-reaching impact. In particular, synthetic data are a promising concept toward solving the aporetic co…
Matrix Concentration Inequalities and Free Probability
Afonso S. Bandeira, March T. Boedihardjo, Ramon van Handel
A central tool in the study of nonhomogeneous random matrices, the noncommutative Khintchine inequality, yields a nonasymptotic bound on the spectral norm of general Gaussian rando…
Covariance's Loss is Privacy's Gain: Computationally Efficient, Private and Accurate Synthetic Data
March Boedihardjo, Thomas Strohmer, Roman Vershynin
The protection of private information is of vital importance in data-driven research, business, and government. The conflict between privacy and utility has triggered intensive res…
The spectral norm of Gaussian matrices with correlated entries
Afonso S. Bandeira, March T. Boedihardjo
We give a non-asymptotic bound on the spectral norm of a matrix with centered jointly Gaussian entries in terms of the covariance matrix of the entries. In some cas…
A Performance Guarantee for Spectral Clustering
March Boedihardjo, Shaofeng Deng, Thomas Strohmer
The two-step spectral clustering method, which consists of the Laplacian eigenmap and a rounding step, is a widely used method for graph partitioning. It can be seen as a natural r…
Estimation of expected value of function of i.i.d. Bernoulli random variables
March T. Boedihardjo
We estimate the expected value of certain function . For example, with computer assistance, we show that if is the Laplacian of the Cayley graph of…
DP-LSSGD: A Stochastic Optimization Method to Lift the Utility in Privacy-Preserving ERM
Bao Wang, Quanquan Gu, March Boedihardjo +2
Machine learning (ML) models trained by differentially private stochastic gradient descent (DP-SGD) have much lower utility than the non-private ones. To mitigate this degradation,…
-algebras isomorphically representable on
March T. Boedihardjo
Let . We show that every homomorphism from a -algebra into satisfies a compactness property where is any set.…
Multiplication operators on L^p
March Boedihardjo
We show that every operator on , defined by multiplication by the identity function on is a compact perturbation of an operator that is diagonal wi…
Calkin representations for
March T. Boedihardjo
We identify the weak closures of the ranges of certain Calkin representations for , . As a consequence, assuming the continuum hypothesis, we show that the commu…