On robust estimation of the location parameter

By F. Forst. 1980

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Citations in the corpus

Training Compute-Optimal Large Language Models (2022, positive): “To estimate ( 𝐴, 𝐵, 𝐸, 𝛼, 𝛽 ) , we minimize the Huber loss (Huber, 1964) between the predicted and observed log loss using the L-BFGS algorithm (Nocedal, 1980): We account for possible local minima by selecting the best ﬁt from a grid of initialisations.”
Speed/Accuracy Trade-Offs for Modern Convolutional Object Detectors (2016, methodology): “Following [10, 30, 25], we use the Smooth L1 (or Huber [15]) loss function in all experiments.”
Autoregressive Quantile Networks for Generative Modeling (2018, background): “This results in the Huber quantile loss (Huber, 1964; Dabney et al., 2018b): (2) 3.”
Multiset-Equivariant Set Prediction with Approximate Implicit Differentiation (2021, methodology): “We use the Hungarian loss with Huber loss (Huber, 1964) as pairwise loss.”
Observe and Look Further: Achieving Consistent Performance on Atari (2018, background): “…weights θ (0) and then iterates where the expectation is taken with respect to a random sample of states and actions and L is the Huber loss [9] deﬁned as In practice, the minimization problem in (1) is only approximately solved by performing a ﬁnite and ﬁxed number of stochastic gradient…”
Neural Programmer: Inducing Latent Programs with Gradient Descent (2015, methodology): “When the answer is a scalar, we use Huber loss (Huber, 1964) given by: , otherwise where a = | scalar answer T − y | is the absolute difference between the predicted and true answer, and δ is the Huber constant treated as a model hyper-parameter.”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “…the kernel density estimator (KDE) by replacing the squared loss L(k(xi, ·), g) = ‖g − k(xi, ·)‖2H in (3.24) by the loss which is less sensitive to outliers such as Huber loss (Huber 1964) and k is assumed to be non-negative and to integrate to one, e.g., Gaussian kernel and Student’s-t kernel.”
Robust Aggregation for Federated Learning (2019, methodology): “[42] P. J. Huber.”
Manipulating Machine Learning: Poisoning Attacks and Countermeasures for Regression Learning (2018, methodology): “Robust regression has been extensively studied in statistics as a method to provide resilience against noise and outliers [27], [28], [52], [56].”
Striving for Simplicity in Off-policy Deep Reinforcement Learning (2019, neutral): “The Q-heads with different random initialization are optimized with complete data sharing between heads using the loss L ( θ ) given by where l δ is the Huber loss.”
Distributional Reinforcement Learning with Quantile Regression (2017, methodology): “The Huber loss is given by (Huber 1964), The quantile Huber loss is then simply the asymmetric variant of the Huber loss, For notational simplicity we will denote ρ 0 τ = ρ τ , that is, it will revert to the standard quantile regression loss.”
Implicit Quantile Networks for Distributional Reinforcement Learning (2018, methodology): “…each θ i assigned a ﬁxed quantile target, ˆ τ i = τ i − 1 + τ i 2 for 1 ≤ i ≤ N , where τ i = i/N . trained These quantile estimates are using the Huber (1964) quantile regression loss, with threshold κ , on the pairwise TD-errors At the time of this writing, QR-DQN achieves the best performance…”
What Matters In On-Policy Reinforcement Learning? A Large-Scale Empirical Study (2020, methodology): “References [1] Peter J Huber.”
Agnostic Estimation of Mean and Covariance (2016, background): “Such robust statistics have been proposed and studied for mean and covariance estimation in high dimension as well (see [Hub64, Tuk74, Mar76, SJD81, Don82, Dav87, HPL91, DG92, MSY92, MZ12, CGR15] and the references therein).”
PREDICTIVE LEARNING VIA RULE ENSEMBLES (2008, background): “For the simulated regression problems illustrated in the following squared-error loss, (15) is used, whereas for the real data example Huber loss, (16) with α = 0 .”
Benchmarking Batch Deep Reinforcement Learning Algorithms (2019, background): “…algorithm (DQN) [Mnih et al., 2015], this value function Q θ is updated in a manner that approximates the optimality operator, through Q-learning [Watkins, 1989]: where l κ deﬁnes the Huber loss [Huber et al., 1964]: but is generally interchangeable with other losses such as mean-squared error.”
Being Robust (in High Dimensions) Can Be Practical (2017, background): “Robust statistics was founded in the seminal works of (Tukey, 1960) and (Huber, 1964).”
From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification (2016, methodology): “Coincidentally, as we next show, the sparsemax loss in the binary case reduces to the Huber classiﬁcation loss, an important loss function in robust statistics (Huber, 1964).”
Robust kernel density estimation (2008, methodology): “Fortunately, the iteratively re-weighted least squares (IRWLS) algorithm used in classical M -estimation (Huber, 1964) can be extended to a RKHS using the kernel trick.”
Real-time user-guided image colorization with learned deep priors (2017, background): “In cases where there is ambiguity, the smooth-ℓ 1 is also a robust estimator (Huber 1964), which can help avoid the averaging problem.”