Related papers: Adversarially Perturbed Precision Matrix Estimatio…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that the errors…
This work studies sparse adversarial perturbations, including both unstructured and structured ones. We propose a framework based on a white-box PGD-like attack method named Sparse-PGD to effectively and efficiently generate such…
We consider a class of uncertain linear time-invariant overparametrized systems affected by bounded disturbances, which are described by a known exosystem with unknown initial conditions. For such systems an exponentially stable extended…
Calibration error is commonly adopted for evaluating the quality of uncertainty estimators in deep neural networks. In this paper, we argue that such a metric is highly beneficial for training predictive models, even when we do not…
Probabilistic time series forecasting has played critical role in decision-making processes due to its capability to quantify uncertainties. Deep forecasting models, however, could be prone to input perturbations, and the notion of such…
We identify three common cases that lead to overestimation of adversarial accuracy against bounded first-order attack methods, which is popularly used as a proxy for adversarial robustness in empirical studies. For each case, we propose…
Bayesian inference usually requires running potentially costly inference procedures separately for every new observation. In contrast, the idea of amortized Bayesian inference is to initially invest computational cost in training an…
This paper studies the theoretical construction and analytic error estimation of complex Bessel function-based conformal mappings in regions with randomly perturbed boundaries. First, we construct a conformal mapping applicable to such…
In this work, we revisit a classical distributed gradient-descent algorithm, introducing an interesting class of perturbed multi-agent systems. The state of each subsystem represents a local estimate of a solution to the global optimization…
Conformal inference is a statistical method used to construct prediction sets for point predictors, providing reliable uncertainty quantification with probability guarantees. This method utilizes historical labeled data to estimate the…
The paper deals with the nonparametric estimation problem at a given fixed point for an autoregressive model with unknown distributed noise. Kernel estimate modifications are proposed. Asymptotic minimax and efficiency properties for…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…
The escalating threat of adversarial attacks on deep learning models, particularly in security-critical fields, has underscored the need for robust deep learning systems. Conventional robustness evaluations have relied on adversarial…
Anomaly detection is to identify samples that do not conform to the distribution of the normal data. Due to the unavailability of anomalous data, training a supervised deep neural network is a cumbersome task. As such, unsupervised methods…
Adversarial training, in which a network is trained on both adversarial and clean examples, is one of the most trusted defense methods against adversarial attacks. However, there are three major practical difficulties in implementing and…
In recent years there has been significant interest in the effect of different types of adversarial perturbations in data classification problems. Many of these models incorporate the adversarial power, which is an important parameter with…
Community detection is an important problem in unsupervised learning. This paper proposes to solve a projection matrix approximation problem with an additional entrywise bounded constraint. Algorithmically, we introduce a new differentiable…
We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the error, whose components are balanced with respect to the…