Related papers: Robustness in Chinese Remainder Theorem

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

Pulay's Residual Metric Minimization (RMM) method is one of the standard techniques for achieving self consistency in ab initio electronic structure calculations. We describe a reformulation of Pulay's RMM which guarantees reduction of the…

Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…

This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…

Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…

We investigate practical algorithms to find or disprove the existence of small subsets of a dataset which, when removed, reverse the sign of a coefficient in an ordinary least squares regression involving that dataset. We empirically study…

An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbolwise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…

Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…

In this paper, some issues concerning the Chinese remaindering representation are discussed. Some new converting methods, including an efficient probabilistic algorithm based on a recent result of von zur Gathen and Shparlinski…

We introduce the notion of fault-tolerant quantum metrology to overcome noise beyond our control -- associated with sensing the parameter, by reducing the noise in operations under our control -- associated with preparing and measuring…

This technical note presents a algorithmic approach for generating optimal sets of co-prime moduli within specified integer ranges. The proposed method addresses the challenge of balancing moduli bit-lengths while maximizing the dynamic…

A recent work of Harn and Fuyou presents the first multilevel (disjunctive) threshold secret sharing scheme based on the Chinese Remainder Theorem. In this work, we first show that the proposed method is not secure and also fails to work…

Recurrent Neural networks (RNN) have shown promising potential for learning dynamics of sequential data. However, artificial neural networks are known to exhibit poor robustness in presence of input noise, where the sequential architecture…

As we stride toward the exascale era, due to increasing complexity of supercomputers, hard and soft errors are causing more and more problems in high-performance scientific and engineering computation. In order to improve reliability…

PCA is a classical statistical technique whose simplicity and maturity has seen it find widespread use as an anomaly detection technique. However, it is limited in this regard by being sensitive to gross perturbations of the input, and by…

In this work, we study the robust subspace tracking (RST) problem and obtain one of the first two provable guarantees for it. The goal of RST is to track sequentially arriving data vectors that lie in a slowly changing low-dimensional…

Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable…

Regularization schemes for regression have been widely studied in learning theory and inverse problems. In this paper, we study distribution regression (DR) which involves two stages of sampling, and aims at regressing from probability…

Given collections A and B of residue classes modulo m and n, respectively, we investigate conditions on A and B that ensure that, for at least some a in A and b in B, the linear system x = a mod m, x = b mod n has an integer solution, and…

This paper revisits and extends the convergence and robustness properties of value and policy iteration algorithms for discrete-time linear quadratic regulator problems. In the model-based case, we extend current results concerning the…