Related papers: Robust and Trend-following Kalman Smoothers using …

Most Kalman filter extensions assume Gaussian noise and when the noise is non-Gaussian, usually other types of filters are used. These filters, such as particle filter variants, are computationally more demanding than Kalman type filters.…

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

Gaussian processes (GPs) are non-parametric probabilistic regression models that are popular due to their flexibility, data efficiency, and well-calibrated uncertainty estimates. However, standard GP models assume homoskedastic Gaussian…

Machine learning algorithms aim to find patterns from observations, which may include some noise, especially in robotics domain. To perform well even with such noise, we expect them to be able to detect outliers and discard them when…

We consider the problem of estimating the state transition matrix of a linear time-invariant (LTI) system, given access to multiple independent trajectories sampled from the system. Several recent papers have conducted a non-asymptotic…

The theory of Bayesian learning incorporates the use of Student-t Processes to model heavy-tailed distributions and datasets with outliers. However, despite Student-t Processes having a similar computational complexity as Gaussian…

Trajectory Reconstruction (TR) is vital for accurately mapping movement patterns and validating analyses, especially in fields like robotics, biomechanics, and environmental tracking, where data might be missing or affected by outliers.…

The Gaussian process (GP) is a powerful tool for nonparametric modeling, but its sensitivity to outliers limits its applicability to data distributions with heavy-tails. Studentt processes offer a robust alternative for heavy tail modeling,…

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise…

We show how to turn any classifier that classifies well under Gaussian noise into a new classifier that is certifiably robust to adversarial perturbations under the $\ell_2$ norm. This "randomized smoothing" technique has been proposed…

In this paper, instead of the usual Gaussian noise assumption, $t$-distribution noise is assumed. A Maximum Likelihood Estimator using the most recent N measurements is proposed for the Auto-Regressive-Moving-Average with eXogenous input…

Normalising flows are tractable probabilistic models that leverage the power of deep learning to describe a wide parametric family of distributions, all while remaining trainable using maximum likelihood. We discuss how these methods can be…

Sparse linear regression methods such as Lasso require a tuning parameter that depends on the noise variance, which is typically unknown and difficult to estimate in practice. In the presence of heavy-tailed noise or adversarial outliers,…

Real-world network applications must cope with failing nodes, malicious attacks, or nodes facing corrupted data - data classified as outliers. Our work addresses these concerns in the scope of the sensor network localization problem where,…

For the outlier problem in linear regression models, the Student-$t$ linear regression model is one of the common methods for robust modeling and is widely adopted in the literature. However, most of them applies it without careful…

Indoor localization is critical for IoT applications, yet challenges such as non-Gaussian noise, environmental interference, and measurement outliers hinder the robustness of traditional methods. Existing approaches, including Kalman…

A multi-sensor fusion Student's $t$ filter is proposed for time-series recursive estimation in the presence of heavy-tailed process and measurement noises. Driven from an information-theoretic optimization, the approach extends the single…

Student's $t$ statistic is finding applications today that were never envisaged when it was introduced more than a century ago. Many of these applications rely on properties, for example robustness against heavy tailed sampling…

We present a numerically-stable parallel-in-time linear Kalman smoother. The smoother uses a novel highly-parallel QR factorization for a class of structured sparse matrices for state estimation, and an adaptation of the SelInv…

Random effects meta-analysis model is an important tool for integrating results from multiple independent studies. However, the standard model is based on the assumption of normal distributions for both random effects and within-study…