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Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering…
Learning with label dependent label noise has been extensively explored in both theory and practice; however, dealing with instance (i.e., feature) and label dependent label noise continues to be a challenging task. The difficulty arises…
Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…
In this paper, we propose an approach to address the problems with ambiguity in tuning the process and observation noises for a discrete-time linear Kalman filter. Conventional approaches to tuning (e.g. using normalized estimation error…
Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…
Distant and weak supervision allow to obtain large amounts of labeled training data quickly and cheaply, but these automatic annotations tend to contain a high amount of errors. A popular technique to overcome the negative effects of these…
Reliability analysis aims at estimating the failure probability of an engineering system. It often requires multiple runs of a limit-state function, which usually relies on computationally intensive simulations. Traditionally, these…
We consider functional data which are measured on a discrete set of observation points. Often such data are measured with additional noise. We explore in this paper the factor structure underlying this type of data. We show that the latent…
Fr\'echet regression extends linear regression to model complex responses in metric spaces, making it particularly relevant for multi-label regression, where eachinstance can have multiple associated labels. However, addressing noise and…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…
Managing noisy data is a central challenge in direct data-driven control design. We propose an approach for synthesizing model-reference controllers for linear time-invariant (LTI) systems using noisy state-input data, employing novel noise…
In this paper, we extend our research concerning the standard and linearized monotonicity methods for the inverse problem of the time harmonic elastic wave equation and introduce the modification of these methods for noisy data. In more…
This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional…
Label noise is a critical factor that degrades the generalization performance of deep neural networks, thus leading to severe issues in real-world problems. Existing studies have employed strategies based on either loss or uncertainty to…
High-dimensional inference refers to problems of statistical estimation in which the ambient dimension of the data may be comparable to or possibly even larger than the sample size. We study an instance of high-dimensional inference in…
We study the problem of estimation and testing in logistic regression with class-conditional noise in the observed labels, which has an important implication in the Positive-Unlabeled (PU) learning setting. With the key observation that the…
We demonstrate the first algorithms for the problem of regression for generalized linear models (GLMs) in the presence of additive oblivious noise. We assume we have sample access to examples $(x, y)$ where $y$ is a noisy measurement of…
Motivated by data-rich experiments in transcriptional regulation and sensory neuroscience, we consider the following general problem in statistical inference. When exposed to a high-dimensional signal S, a system of interest computes a…
The presence of noise in acquired data invariably leads to performance degradation in cross-modal matching. Unfortunately, obtaining precise annotations in the multimodal field is expensive, which has prompted some methods to tackle the…
In large-scale, data-driven applications, parameters are often only known approximately due to noise and limited data samples. In this paper, we focus on high-dimensional optimization problems with linear constraints under uncertain…