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Uncertainty awareness is crucial to develop reliable machine learning models. In this work, we propose the Natural Posterior Network (NatPN) for fast and high-quality uncertainty estimation for any task where the target distribution belongs…

State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these…

In a network meta-analysis, some of the collected studies may deviate markedly from the others, for example having very unusual effect sizes. These deviating studies can be regarded as outlying with respect to the rest of the network and…

We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers. The guarantees of our algorithms improve in many cases significantly over the best previous ones, obtained…

We propose a new assumption in outlier detection: Normal data instances are commonly located in the area that there is hardly any fluctuation on data density, while outliers are often appeared in the area that there is violent fluctuation…

The point estimates of ReLU classification networks---arguably the most widely used neural network architecture---have been shown to yield arbitrarily high confidence far away from the training data. This architecture, in conjunction with a…

We explore the utility of information contained within a dropout based Bayesian neural network (BNN) for the task of detecting out of distribution (OOD) data. We first show how previous attempts to leverage the randomized embeddings induced…

The unscented Kalman filter is an algorithm capable of handling nonlinear scenarios. Uncertainty in process noise covariance may decrease the filter estimation performance or even lead to its divergence. Therefore, it is important to adjust…

Learning in a non-stationary environment is an inevitable problem when applying machine learning algorithm to real world environment. Learning new tasks without forgetting the previous knowledge is a challenge issue in machine learning. We…

Anomaly detection aims to detect data that do not conform to regular patterns, and such data is also called outliers. The anomalies to be detected are often tiny in proportion, containing crucial information, and are suitable for…

This paper focuses on the state estimation problem in distributed sensor networks, where intermittent packet dropouts, corrupted observations, and unknown noise covariances coexist. To tackle this challenge, we formulate the joint…

Kalman filter is a key tool for time-series forecasting and analysis. We show that the dependence of a prediction of Kalman filter on the past is decaying exponentially, whenever the process noise is non-degenerate. Therefore, Kalman filter…

Outlier detection and cleaning are essential steps in data preprocessing to ensure the integrity and validity of data analyses. This paper focuses on outlier points within individual trajectories, i.e., points that deviate significantly…

Outlier detection amounts to finding data points that differ significantly from the norm. Classic outlier detection methods are largely designed for single data type such as continuous or discrete. However, real world data is increasingly…

In this paper we consider the behavior of Kalman Filter state estimates in the case of distribution with heavy tails .The simulated linear state space models with Gaussian measurement noises were used. Gaussian noises in state equation are…

Characterizing uncertainty is a common issue in nuclear measurement and has important implications for reliable physical discovery. Traditional methods are either insufficient to cope with the heterogeneous nature of uncertainty or…

There exist multiple methods to detect outliers in multivariate data in the literature, but most of them require to estimate the covariance matrix. The higher the dimension, the more complex the estimation of the matrix becoming impossible…

The Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties…

In this paper, we aim to design and analyze distributed Bayesian estimation algorithms for sensor networks. The challenges we address are to (i) derive a distributed provably-correct algorithm in the functional space of probability…

Out-of-distribution detection (OOD) deals with anomalous input to neural networks. In the past, specialized methods have been proposed to reject predictions on anomalous input. Similarly, it was shown that feature extraction models in…