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Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…
In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…
Symmetric positive definite (SPD) matrices are useful for capturing second-order statistics of visual data. To compare two SPD matrices, several measures are available, such as the affine-invariant Riemannian metric, Jeffreys divergence,…
Ensembles of Convolutional neural networks have shown remarkable results in learning discriminative semantic features for image classification tasks. Though, the models in the ensemble often concentrate on similar regions in images. This…
It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
We study semiparametric factor models in high-dimensional panels where the factor loadings consist of a nonparametric component explained by observed covariates and an idiosyncratic component capturing unobserved heterogeneity. A key…
This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability,…
In lifelong learning, tasks (or classes) to be learned arrive sequentially over time in arbitrary order. During training, knowledge from previous tasks can be captured and transferred to subsequent ones to improve sample efficiency. We…
We extend the validity of a Gromov's dimension comparison estimate for topological hypersurfaces to sufficiently large classes of rectifiable sets, arising from Sobolev mappings. Our tools are a suitably weak exterior differentiation for…
Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various…
Deep Convolutional Neural Networks (DCNNs) and their variants have been widely used in large scale face recognition(FR) recently. Existing methods have achieved good performance on many FR benchmarks. However, most of them suffer from two…
Unsupervised domain adaptation is critical in various computer vision tasks, such as object detection, instance segmentation, etc. They attempt to reduce domain bias-induced performance degradation while also promoting model application…
We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…
Deepfake detection remains a challenging task due to the difficulty of generalizing to new types of forgeries. This problem primarily stems from the overfitting of existing detection methods to forgery-irrelevant features and…
Many computer vision and medical imaging problems are faced with learning from large-scale datasets, with millions of observations and features. In this paper we propose a novel efficient learning scheme that tightens a sparsity constraint…
$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler…
This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset…
Data augmentation methods are commonly integrated into the training of anomaly detection models. Previous approaches have primarily focused on replicating real-world anomalies or enhancing diversity, without considering that the standard of…
Unsupervised representation learning has been extensively employed in anomaly detection, achieving impressive performance. Extracting valuable feature vectors that can remarkably improve the performance of anomaly detection are essential in…