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Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The $d$-th moment of an $n$-dimensional random variable is a symmetric $d$-way tensor of size…
We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…
Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable…
This study proposes a debiasing method for smooth nonparametric estimators. While machine learning techniques such as random forests and neural networks have demonstrated strong predictive performance, their theoretical properties remain…
Gaussian Mixture Models (GMMs) are a standard tool in data analysis. However, they face problems when applied to high-dimensional data (e.g., images) due to the size of the required full covariance matrices (CMs), whereas the use of…
Automated Machine Learning with ensembling (or AutoML with ensembling) seeks to automatically build ensembles of Deep Neural Networks (DNNs) to achieve qualitative predictions. Ensemble of DNNs are well known to avoid over-fitting but they…
Diffusion models generate samples by denoising along the score of a perturbed target distribution. In practice, one trains a neural diffusion model, which is computationally expensive. Recent work suggests that score matching implicitly…
Large pre-trained language models contain societal biases and carry along these biases to downstream tasks. Current in-processing bias mitigation approaches (like adversarial training) impose debiasing by updating a model's parameters,…
The asymptotic behavior of GMM estimators depends critically on whether the underlying moment condition model is correctly specified. Hong and Li (2023, Econometric Theory) showed that GMM estimators with nonsmooth (non-directionally…
Restricted Boltzmann machines (RBMs) and their extensions, called 'deep-belief networks', are powerful neural networks that have found applications in the fields of machine learning and artificial intelligence. The standard way to training…
Intelligent fault diagnosis has become an indispensable technique for ensuring machinery reliability. However, existing methods suffer significant performance decline in real-world scenarios where models are tested under unseen working…
Researchers and practitioners often wish to measure treatment effects in settings where units interact via markets and recommendation systems. In these settings, units are affected by certain shared states, like prices, algorithmic…
We propose an approach to better inform treatment decisions at an individual level by adapting recent advances in average treatment effect estimation to conditional average treatment effect estimation. Our work is based on doubly robust…
Federated learning has attracted considerable interest for collaborative machine learning in healthcare to leverage separate institutional datasets while maintaining patient privacy. However, additional challenges such as poor calibration…
Markov state models (MSMs) have been broadly adopted for analyzing molecular dynamics trajectories, but the approximate nature of the models that results from coarse-graining into discrete states is a long-known limitation. We show…
Assisted by the availability of data and high performance computing, deep learning techniques have achieved breakthroughs and surpassed human performance empirically in difficult tasks, including object recognition, speech recognition, and…
A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family…
Bayesian nonparametrics are a class of probabilistic models in which the model size is inferred from data. A recently developed methodology in this field is small-variance asymptotic analysis, a mathematical technique for deriving learning…
This paper considers the change point detection problem under dependent samples. In particular, we provide performance guarantees for the MMD-CUSUM test under exponentially $\alpha$, $\beta$, and fast $\phi$-mixing processes, which…
In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic…