Minimum maximum mean discrepancy (MMD) estimation has emerged as a robust and likelihood-free alternative to maximum likelihood estimation for parameter estimation. Yet, despite its practical success, the associated optimization problem remains poorly understood, with theoretical guarantees for existing algorithms hinging on convexity assumptions that rarely hold in practice. We address this gap by proposing a preconditioned gradient descent (PGD) scheme, establishing its asymptotic \emph{global} convergence under explicit gradient-dominance and projection-residual conditions. Our approach is inspired by recent progress on MMD gradient flows, a nonparametric descent scheme on the space of probability measures. We provide extensive empirical evidence that our PGD scheme outperforms standard gradient descent across a range of challenging parameter estimation and composite hypothesis testing problems.
Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distributions driven by an energy functional. Though there are multiple mathematical characterizations of a…
Boosting is one of the most successful learning techniques for standard classification and regression tasks. Its extension to multi-output prediction problems has found an increasing number of applications in recent years. Among them is the prediction of entire conditional distri…
The global minimum-variance portfolio (GMVP) is the canonical decision built from an estimated covariance matrix, yet covariance estimators are universally evaluated by matrix-norm loss, which is not the object the decision depends on. We characterise exactly how covariance-estim…
Backpropagation makes training deep networks memory intensive because it must store intermediate activations. Forward-mode methods avoid this cost, but their gradient estimates become increasingly noisy as the number of trained parameters grows. We introduce Split Forward Gradien…
Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map. In applications like generative modeling, the transport co…
We develop an adjoint-sensitivity framework for positional influence in causal residual Transformers and separate unconditional analytic results from conditional boundary-shape conclusions. The principal unconditional theorem is the residual-to-depth-flow estimate for layer contr…