Estimating the mean and variance of the target probability distribution

By D. Nix, Andreas S. Weigend. 1994

Subfields: Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision? (2017, background): “Heteroscedastic regression, on the other hand, assumes that observation noise can vary with input x [17, 18].”
Beauty and the Beast: Optimal Methods Meet Learning for Drone Racing (2018, methodology): “A similar network architecture for mean-variance estimation was proposed in [22].”
Learning to Pivot with Adversarial Networks (2016, background): “The j th output corresponds to the estimated value of the corresponding parameter γ j of that distribution (e.g., the mean, variance and mixing coefﬁcients of its components).”
High-Quality Self-Supervised Deep Image Denoising (2019, methodology): “To fit N (μy,Σy) to the observed noisy training data, we minimize the corresponding negative loglikelihood loss during training [22, 16, 13]:”
Chemprop: A Machine Learning Package for Chemical Property Prediction (2023, unknown): “The estimation methods include deep ensembles, 77 dropout, 78 mean-variance estimation (MVE), 71 and evidential, 72 as well as a special version of ensemble variance for spectral predictions, 28 and the inherently probabilistic outputs of classification models.”
Machine learning approaches for estimation of prediction interval for the model output (2006, unknown): “A machine learning technique is an algorithm that estimates (induces) a hitherto unknown mapping (or dependency) between a system’s inputs and its outputs from the available data (Mitchell, 1998).”
Uncertainty-Aware Learning for Zero-Shot Semantic Segmentation (2020, methodology): “The variance is related to the input sample’s uncertainty [37, 43], thus allowing the model to explicitly account for the observation noise of the training data.”
Single-Model Uncertainties for Deep Learning (2018, methodology): “Then, one can dedicate one output of the neural network to estimate the conditional variance of the target via maximum likelihood estimation [57, 44, 49].”
Neural networks for pattern recognition (1995, background): “More generally, we might wish to determine how the variance of the data depends on the input vector x (Nix and Weigend, 1994).”
Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles (2016, methodology): “Following [47], we use a network that outputs two values in the final layer, corresponding to the predicted mean μ(x) and variance2 2 (x) > 0.”
Practical Confidence and Prediction Intervals (1996, methodology): “, taking into account the uncertainty of the estimator and correcting for the tendency to overfit on the training data, and a simpler procedure similar to [7] which disregards both effects.”
Deep Evidential Regression (2019, methodology): “Our work builds on a large history of uncertainty estimation [25, 38, 37, 19] and modelling probability distributions using NNs [36, 4, 14, 26].”
On the Uncertainty of Self-Supervised Monocular Depth Estimation (2020, background): “Another popular strategy [49] consists of training the network to infer mean and variance of the distribution p(d|I,D) of parameters Θ.”
Data Uncertainty Learning in Face Recognition (2020, methodology): “This technique has been used by many tasks [22, 4, 30, 12, 2].”