What Can Be Recovered Under Sparse Adversarial Corruption - Assumption-Free Theory for Linear Measurements

Explore the theoretical foundations of sparse adversarial corruption in linear measurements through this 49-minute academic lecture. Delve into the fundamental question of what can be recovered when dealing with arbitrary known matrices and sparse adversarial vectors, moving beyond traditional assumptions like restricted isometry or sparsity constraints. Learn about the main theoretical result that identifies the smallest robust solution set as the original solution plus the kernel of a unique projection matrix, derived from intersecting rowspaces of submatrices obtained by deleting specific rows. Discover how this framework provides a constructive approach to recovery through ℓ₀-norm minimization, offering assumption-free theory applicable to any matrix and solution vector. Gain insights into the mathematical foundations that bridge optimization theory with practical applications in adversarial learning, distributed systems, and network robustness from a researcher with extensive experience in applied mathematics, game theory, and industrial applications spanning predictive maintenance, IoT systems, and cybersecurity.