Research

My research develops mathematical methods for sparse and structured learning, with emphasis on exact sparsity, constrained optimization, and machine learning. Current work follows three directions that share a common base in nonconvex constrained optimization.

Research interests include:

• General: natural language processing, machine learning, deep learning, sparse optimization, large-scale optimization, mathematical finance, mathematical modeling, quantum computing, numerical linear algebra
• Methods and topics: support vector machines, penalty decomposition, L1-minimization, greedy algorithms, semidefinite programming, ADMM, inexact Newton methods, matrix decomposition, linear programming, quadratic optimization, and related areas

Current Research

1. Cardinality-Constrained Structured Optimization

   I develop penalty decomposition methods that enforce exact sparsity and related structural constraints directly, rather than through convex relaxations. This line includes mean-reverting and mean-variance portfolios under cardinality, volatility, and CVaR constraints, and an efficient quasi-Newton penalty decomposition algorithm for minimization over sparse symmetric sets (under review at Mathematical Programming Computation). Related work includes Weaver, a hybrid quantum-classical method for binary compressive sensing under matrix uncertainty (submitted to AAAI 2027), and a preprint with Mojtaba Soltanalian on the rank-collapse principle for low-rank quadratic optimization (arXiv:2608.07828).

2. Sparse And Structured Quadratic Surface Support Vector Machines

   Kernel-free quadratic surface SVMs model nonlinear boundaries without kernel selection, but the number of parameters grows quadratically with dimension. I develop sparsity-inducing and Universum-augmented QSVM models, including ℓ₁-regularized QSVMs, quadratic twin SVMs for imbalanced data, and ℓ₀-regularized QSVMs via explicit cardinality constraints. Ongoing work studies ensembles of random sparse quadratic twin parametric-margin SVMs (SSRN preprint).

3. Robust Multi-Scale And Multi-Modal Learning

   This direction develops lightweight, attention-based frameworks for settings with distribution shift, heterogeneous modalities, and nonstationary signals. Published and submitted work includes EMO-CARE (subject-independent EEG emotion recognition), E-CaTCH (event-centric multimodal misinformation detection), and MOMENTA (mixture-of-experts multimodal embeddings with temporal aggregation). Related projects include CAM-Soft for soft hate speech detection, MURAL for multimodal recommendation, BLADE for constrained bilevel LLM unlearning, and physics-conditioned attention for next-day wildfire spread prediction.