Projects
Generative Models with Statistical Guarantees
Generative modelling is the group’s most active line of work. Inferential Wasserstein GANs couple a generator with an encoder so that adversarial training also delivers valid statistical inference, and adaptive learning of the latent space of Wasserstein GANs lets the dimension and distribution of the latent variable be estimated from data rather than fixed in advance. On the likelihood-based side we study variational autoencoders under censoring and develop double-robust conditional VAEs with decode calibration and implicit KL annealing. Companion sampling work — tempered distribution flow for efficient multimodal sampling, unbiased contrastive divergence for energy-based latent variable models, and stochastic approximate gradient descent via the Langevin algorithm — makes these models tractable to fit, while Wasserstein coresets via the Sinkhorn loss compress the data they are trained on.
Simulation-Based Inference
Bayesian inference for jump diffusion processes is difficult: transition densities are intractable, and jump times and intensities are latent. NCoin-JDP (Neural Conformal Inference for Jump Diffusion Processes) is a likelihood-free, simulation-based approach that trains deep neural networks to map observed data directly to model parameters, eliminating discretization error. We develop the asymptotic theory for the resulting estimator and use conformal prediction to characterize its uncertainty, so the reported intervals carry validity guarantees rather than resting on the network alone. Applied to S&P 500 and NASDAQ data from 1993 to 2024, the method is used to examine the economic impact of COVID-19.
Understanding Weight Normalized Deep Neural Networks
We present a general framework for norm-based capacity control for Lp,q weight normalized deep neural networks, using the practical network architecture with a bias neuron per hidden layer. We first show how current norm-based constraints fail on fully connected networks with a bias neuron in each hidden layer — the output can diverge even when the product of layer norms is bounded. We then establish an upper bound on the Rademacher complexity of Lp,q weight normalized networks and, for regression, provide both generalization and approximation bounds. The approximation error can be controlled by the L1 norm of the output layer for any sufficiently large L1,∞ weight normalized network. Because L1,∞ weight normalization induces local sparsity, we further introduce sparse DNNs and an efficient algorithm for them, evaluated on synthetic and real-world experiments.
Nonlinear Feature Selection via Deep Neural Networks
A general framework for high-dimensional nonlinear feature selection with deep neural networks under supervised learning. The architecture includes both a selection layer and approximation layers, casting the problem as sparsity-constrained optimization with a sparse parameter in the selection layer. We propose a greedy algorithm, Deep Feature Selection (DFS), to estimate both sets of parameters, and establish a theoretical convergence guarantee when the objective has a Generalized Stable Restricted Hessian — generalizing known results for high-dimensional linear feature selection. DFS outperforms competing algorithms in simulation and on real data.
High-Dimensional Inference via Adaptive Bayes and Deep Learning
We develop Adaptive Bayes, a framework for high-dimensional inference that uses deep learning — specifically variational autoencoders — to adaptively learn prior sparsity information. Conditioning on this learned prior lets us make accurate inference on regression coefficients. The figure shows confidence intervals constructed by our approach with n = 500, p = 2000 and 40 non-zero coefficients.
Atrial Fibrillation Detection from Short Single-Lead ECGs
Detection of atrial fibrillation matters for stroke risk stratification. We developed a methodology to classify electrocardiograms as normal, atrial fibrillation, or other cardiac dysrhythmias, as defined by the PhysioNet Challenge 2017. The ECG waveform is fitted by a piecewise linear spline, morphological features related to the spline coefficients are extracted, and XGBoost classifies those coefficients together with heart-rate-variability features. Evaluated on the PhysioNet Challenge database of 3,658 expert-classified ECGs, the algorithm achieved an average F1 score of 81% under 10-fold cross-validation and 81% on the independent test set — comparable to the 9th-ranked score in the official phase of the Challenge.
Estimation of Heterogeneity for Multinomial Probit Models
Empirical studies suggest that utility functions are often irregularly shaped and that individuals deviate widely from one another. We introduce a multinomial probit model with both parametric and nonparametric covariates, combining heterogeneity with flexibility through two strategies: random effects for the parametric component, and an individual-level function for each subject in the nonparametric component. All nonparametric components share a common but unknown basis, which we recover by dictionary learning; an EM algorithm estimates the resulting multinomial probit models.
Local Region Image-on-Scalar Regression
We propose a regularization technique for estimating the coefficient image in an image-on-scalar regression model. The estimator is locally sparse where the coefficient image is zero within sub-regions, while explicitly accounting for the piecewise-smooth nature of most images. ADMM is used for estimation, with a distributed algorithm for big data. Simulation and real data analysis show superior performance against many existing approaches; the figure shows the truth alongside our recovered estimator.
