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There is an emerging trend to leverage noisy image datasets in many visual recognition tasks. However, the label noise among the datasets severely degenerates the \mbox{performance of deep} learning approaches. Recently, one mainstream is…

The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…

The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We…

In the present paper we study the performance of linear denoisers for noisy data of the form $\mathbf{x} + \mathbf{z}$, where $\mathbf{x} \in \mathbb{R}^d$ is the desired data with zero mean and unknown covariance $\mathbf{\Sigma}$, and…

We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the…

Real-world large-scale datasets are both noisily labeled and class-imbalanced. The issues seriously hurt the generalization of trained models. It is hence significant to address the simultaneous incorrect labeling and class-imbalance, i.e.,…

Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modeled on the basis of simple assumptions such as bias, white noise, first…

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\mathfrak{X}$ of the sum of an approximately) low…

Uncovering causal relationships is a fundamental problem across science and engineering. However, most existing causal discovery methods assume acyclicity and direct access to the system variables -- assumptions that fail to hold in many…

Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of…

''Noisy'' datasets (regimes with low signal to noise ratios, small sample sizes, faulty data collection, etc) remain a key research frontier for classification methods with both theoretical and practical implications. We introduce FINDER, a…

This paper addresses the classic problem of regression, which involves the inductive learning of a map, $y=f(x,z)$, $z$ denoting noise, $f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$. Recently, Conditional GAN (CGAN) has been…

Classical Kullback-Leibler or entropic distances are known to enjoy certain desirable statistical properties in the context of decision-making with noiseless data. However, in most practical situations the data available to a decision maker…

This note presents a unified analysis of the identification of dynamical systems with low-rank constraints under high-dimensional scaling. This identification problem for dynamic systems are challenging due to the intrinsic dependency of…

We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…

As an example of the recently-introduced concept of rate of innovation, signals that are linear combinations of a finite number of Diracs per unit time can be acquired by linear filtering followed by uniform sampling. However, in reality,…

A central challenge in computational modeling of dynamic biological systems is parameter inference from experimental time course measurements. However, one would not only like to infer kinetic parameters but also study their variability…

In this paper, we consider the problem of estimating finite rate of innovation (FRI) signals from noisy measurements, and specifically analyze the interaction between FRI techniques and the underlying sampling methods. We first obtain a…

This paper presents a novel direct data-driven control framework for solving the linear quadratic regulator (LQR) under disturbances and noisy state measurements. The system dynamics are assumed unknown, and the LQR solution is learned…

We prove that output-feedback linear policies remain optimal for solving the Linear Quadratic Gaussian regulation problem in the face of worst-case process and measurement noise distributions when these are independent, stationary, and…