no code implementations • 8 Feb 2023 • Mehrdad Ghadiri, Matthew Fahrbach, Gang Fu, Vahab Mirrokni
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition.
1 code implementation • 11 Sep 2022 • Matthew Fahrbach, Thomas Fu, Mehrdad Ghadiri
By extending our approach to block-design matrices where one block is a Kronecker product, we also achieve subquadratic-time algorithms for (1) Kronecker ridge regression and (2) updating the factor matrices of a Tucker decomposition in ALS, which is not a pure Kronecker regression problem, thereby improving the running time of all steps of Tucker ALS.
no code implementations • 22 Jun 2022 • Mehrdad Ghadiri, Mohit Singh, Santosh S. Vempala
We study approximation algorithms for the socially fair $(\ell_p, k)$-clustering problem with $m$ groups, whose special cases include the socially fair $k$-median ($p=1$) and socially fair $k$-means ($p=2$) problems.
no code implementations • 22 Jul 2021 • Matthew Fahrbach, Mehrdad Ghadiri, Thomas Fu
Low-rank tensor decomposition generalizes low-rank matrix approximation and is a powerful technique for discovering low-dimensional structure in high-dimensional data.
no code implementations • 23 Jun 2020 • Mehrdad Ghadiri, Richard Santiago, Bruce Shepherd
Submodular function maximization has found a wealth of new applications in machine learning models during the past years.
2 code implementations • 17 Jun 2020 • Mehrdad Ghadiri, Samira Samadi, Santosh Vempala
We show that the popular k-means clustering algorithm (Lloyd's heuristic), used for a variety of scientific data, can result in outcomes that are unfavorable to subgroups of data (e. g., demographic groups).
1 code implementation • 20 Oct 2019 • Saeid Naderiparizi, Adam Ścibior, Andreas Munk, Mehrdad Ghadiri, Atılım Güneş Baydin, Bradley Gram-Hansen, Christian Schroeder de Witt, Robert Zinkov, Philip H. S. Torr, Tom Rainforth, Yee Whye Teh, Frank Wood
Naive approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance.
no code implementations • pproximateinference AABI Symposium 2019 • Bradley Gram-Hansen, Christian Schroeder de Witt, Robert Zinkov, Saeid Naderiparizi, Adam Scibior, Andreas Munk, Frank Wood, Mehrdad Ghadiri, Philip Torr, Yee Whye Teh, Atilim Gunes Baydin, Tom Rainforth
We introduce two approaches for conducting efficient Bayesian inference in stochastic simulators containing nested stochastic sub-procedures, i. e., internal procedures for which the density cannot be calculated directly such as rejection sampling loops.
no code implementations • 19 Apr 2019 • Mehrdad Ghadiri, Richard Santiago, Bruce Shepherd
Using the multilinear framework and new matroid rounding techniques for quadratic objectives, we give an $\Omega(1/\sigma^{3/2})$-approximation for maximizing a $\sigma$-semi-metric diversity function subject to matroid constraint.
Data Structures and Algorithms Computational Geometry Discrete Mathematics
no code implementations • 20 Mar 2019 • Mehrdad Ghadiri, Mark Schmidt
In this paper, we consider this problem as an optimization problem that seeks to maximize the sum of a sum-sum diversity function and a non-negative monotone submodular function.
no code implementations • NeurIPS 2016 • Aditya Bhaskara, Mehrdad Ghadiri, Vahab Mirrokni, Ola Svensson
We first study the approximation quality of the algorithm by comparing with the LP objective.
no code implementations • 12 Dec 2015 • Mehrdad Ghadiri, Amin Aghaee, Mahdieh Soleymani Baghshah
k-medoids algorithm is a partitional, centroid-based clustering algorithm which uses pairwise distances of data points and tries to directly decompose the dataset with $n$ points into a set of $k$ disjoint clusters.
no code implementations • 7 Nov 2015 • Sepehr Abbasi Zadeh, Mehrdad Ghadiri
In many applications such as web-based search, document summarization, facility location and other applications, the results are preferable to be both representative and diversified subsets of documents.