19 citations · 69 across the 35 of their papers we have counts for
38 papers
Convexification of mixed-integer quadratic optimization via decision diagrams
Soobin Choi, Salar Fattahi, Andres Gomez +2
We study mixed-integer quadratic optimization (MIQO) problems with indicator variables. We propose a unified framework, based on decision diagrams, that serves both to solve the as…
On the Absence of Identifiable Manifolds in Finite-Max Composite Optimization
Yifan Wang, Jianhao Ma, Salar Fattahi
In nonsmooth optimization, identifiable sets describe the local region eventually reached by sequences converging to a prescribed critical point. When such a set is a manifol…
Oracle-Based Distributionally Robust Optimization under Optimal Transport Ambiguity Sets
Guixian Chen, Salar Fattahi, Soroosh Shafiee
Distributionally robust optimization (DRO) with optimal transport ambiguity sets is traditionally solved by reformulating the minimax problem into a single-level convex program. Wh…
Coordinate Optimality Reformulation for Mixed-Integer Convex Programs with Indicators
Tong Xu, Salar Fattahi, Andrés Gómez +1
We consider mixed-integer convex optimization problems in which binary indicators control continuous variables. We introduce the \emph{Coordinate Optimality Reformulation} (CORe) f…
Solving Convex Quadratic Optimization with Indicators Over Structured Graphs
Aaresh Bhathena, Salar Fattahi, Andrés Gómez +1
This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where th…
Risk-Averse Wasserstein Distributionally Robust Online Learning
Guixian Chen, Salar Fattahi, Soroosh Shafiee
We study distributionally robust online learning, where a risk-averse learner updates decisions sequentially to guard against worst-case distributions drawn from a Wasserstein ambi…
Efficient inference of dynamic gene regulatory networks using discrete penalty
Visweswaran Ravikumar, Aaresh Bhathena, Wajd N Al-Holou +2
Gene regulatory networks (GRNs) orchestrate cellular decision making and survival strategies. Inferring the structure of these networks from high-dimensional transcriptomics data i…
Understanding the Implicit Regularization of Gradient Descent in Over-parameterized Models
Jianhao Ma, Geyu Liang, Salar Fattahi
Implicit regularization refers to the tendency of local search algorithms to converge to low-dimensional solutions, even when such structures are not explicitly enforced. Despite i…
Preconditioned Gradient Descent for Over-Parameterized Nonconvex Matrix Factorization
Gavin Zhang, Salar Fattahi, Richard Y. Zhang
In practical instances of nonconvex matrix factorization, the rank of the true solution is often unknown, so the rank of the model can be overspecified as $r>r^{\st…
RANSAC Revisited: An Improved Algorithm for Robust Subspace Recovery under Adversarial and Noisy Corruptions
Guixian Chen, Jianhao Ma, Salar Fattahi
In this paper, we study the problem of robust subspace recovery (RSR) in the presence of both strong adversarial corruptions and Gaussian noise. Specifically, given a limited numbe…
Enhancing Performance of Explainable AI Models with Constrained Concept Refinement
Geyu Liang, Senne Michielssen, Salar Fattahi
The trade-off between accuracy and interpretability has long been a challenge in machine learning (ML). This tension is particularly significant for emerging interpretable-by-desig…
A Parametric Approach for Solving Convex Quadratic Optimization with Indicators Over Trees
Aaresh Bhathena, Salar Fattahi, Andrés Gómez +1
This paper investigates convex quadratic optimization problems involving indicator variables, each associated with a continuous variable, particularly focusing on scenarios whe…
Triple Component Matrix Factorization: Untangling Global, Local, and Noisy Components
Naichen Shi, Salar Fattahi, Raed Al Kontar
In this work, we study the problem of common and unique feature extraction from noisy data. When we have N observation matrices from N different and associated sources corrupted by…
Convergence of Gradient Descent with Small Initialization for Unregularized Matrix Completion
Jianhao Ma, Salar Fattahi
We study the problem of symmetric matrix completion, where the goal is to reconstruct a positive semidefinite matrix of rank-, paramete…
Solution Path of Time-varying Markov Random Fields with Discrete Regularization
Salar Fattahi, Andres Gomez
We study the problem of inferring sparse time-varying Markov random fields (MRFs) with different discrete and temporal regularizations on the parameters. Due to the intractability…
Personalized Dictionary Learning for Heterogeneous Datasets
Geyu Liang, Naichen Shi, Raed Al Kontar +1
We introduce a relevant yet challenging problem named Personalized Dictionary Learning (PerDL), where the goal is to learn sparse linear representations from heterogeneous datasets…
Heterogeneous Matrix Factorization: When Features Differ by Datasets
Naichen Shi, Raed Al Kontar, Salar Fattahi
In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics…
Sparse Mean Estimation in Adversarial Settings via Incremental Learning
Jianhao Ma, Rui Ray Chen, Yinghui He +2
In this paper, we study the problem of sparse mean estimation under adversarial corruptions, where the goal is to estimate the -sparse mean of a heavy-tailed distribution from s…
Can Learning Be Explained By Local Optimality In Robust Low-rank Matrix Recovery?
Jianhao Ma, Salar Fattahi
We explore the local landscape of low-rank matrix recovery, focusing on reconstructing a matrix with rank from linear measurements, some potential…
Behind the Scenes of Gradient Descent: A Trajectory Analysis via Basis Function Decomposition
Jianhao Ma, Lingjun Guo, Salar Fattahi
This work analyzes the solution trajectory of gradient-based algorithms via a novel basis function decomposition. We show that, although solution trajectories of gradient-based alg…
Simple Alternating Minimization Provably Solves Complete Dictionary Learning
Geyu Liang, Gavin Zhang, Salar Fattahi +1
This paper focuses on the noiseless complete dictionary learning problem, where the goal is to represent a set of given signals as linear combinations of a small number of atoms fr…
Blessing of Nonconvexity in Deep Linear Models: Depth Flattens the Optimization Landscape Around the True Solution
Jianhao Ma, Salar Fattahi
This work characterizes the effect of depth on the optimization landscape of linear regression, showing that, despite their nonconvexity, deeper models have more desirable optimiza…
Efficient Inference of Spatially-varying Gaussian Markov Random Fields with Applications in Gene Regulatory Networks
Visweswaran Ravikumar, Tong Xu, Wajd N. Al-Holou +2
In this paper, we study the problem of inferring spatially-varying Gaussian Markov random fields (SV-GMRF) where the goal is to learn a network of sparse, context-specific GMRFs re…
Preconditioned Gradient Descent for Overparameterized Nonconvex Burer--Monteiro Factorization with Global Optimality Certification
Gavin Zhang, Salar Fattahi, Richard Y. Zhang
We consider using gradient descent to minimize the nonconvex function over an factor matrix , in which is an underlying smooth convex cost funct…