Huber loss derivative

Huber loss derivative. Huber loss. The hinge loss is used for "maximum-margin" classification, most notably for support vector machines (SVMs). ) — which cannot be compensated for with data preprocessing — or use in unsupervised learning (as we will discuss later). Huber (1964) defines the loss function piecewise by[1] Apr 23, 2021 · The Tukey loss function The Tukey loss function, also known as Tukey’s biweight function, is a loss function that is used in robust statistics. 345) Laplace | Gaussian | Huber. Usage psi. However, there may be cases where these traditional/main loss functions may not be sufficient. It is used in Robust Regression, M-estimation, and Additive Modelling. Next Previous Oct 24, 2023 · Derivative of Huber's loss function. It is linear in the tails and so is not affected by outliers like with absolute loss and unlike with squared loss. 012 when the actual observation label is 1 would be bad and result in a high loss value. This loss function is less sensitive to outliers than rmse(). •To utilize the Huber loss, a parameter that controls the transitions from a quadratic function to an absolute value function needs to be selected. •In this work, we propose an alternative probabilistic interpretation of the Huber loss, The hybrid nature of Huber Loss makes it less sensitive to outliers, just like MAE, but also penalizes minor errors within the data sample, similar to MSE. 我们知道在梯度下降时 MSE较MAE更为准确 而在异常值出现时 MAE较MSE更加鲁棒 那么能否将两者的优势集中在一起而尽可能的规避劣势呢？ Jun 1, 2023 · As an outlier-resistant loss function, the Huber's loss with a scaling parameter τ h τ (u) = {u 2 2, if | u | ≤ τ, τ | u | − τ 2 2, if | u | > τ, was proposed in the seminal work [12] in the context of robust estimation of location parameters. ca, Alejandra Martinez Jan 27, 2024 · In recent times, the significance of variable selection has amplified because of the advent of high-dimensional data. In this context, the mean (average) is the estimator optimising L2-loss, and the median is the estimator optimising L1-loss. Instead of having a partial derivative that looks like step function, as it is the case for the L1 loss partial derivative, we want a smoother version of it that is similar to the smoothness of the sigmoid activation function. </p> Aug 14, 2021 · We can achieve this using the Huber Loss (Smooth L1 Loss), a combination of L1 (MAE) and L2 (MSE) losses. loss (as it behaves like quadratic loss near the origin and like absolute loss far from the origin) or a Pseudo-Huber loss (due to its resemblance to the classic Huber loss func-tion [7]). Some examples would be if there is too much noise in your training data (outliers, erroneous attribute values, etc. Advantages of Huber Loss. We can approximate it using the Psuedo-Huber function. The important thing to note here is that operator() is a templated method, which assumes that all its inputs and outputs are of some type T. One of the ways to tackle this problem is the selection of a proper loss function showing insensitivity to noise present in the data. Mean square loss and log loss are some examples of loss functi Feb 24, 2022 · Huber loss with delta = 5 Because of the clipping gradient capabilities, the Pseudo-Huber was used in the Fast R-CNN model to prevent the exploding gradients . 3. While a twice differentiable loss function is not required for vanilla SGD, other solvers and SGD variants may require the second derivative's existence to converge properly. This comes from the shape of the Huber loss function. It combines the best properties of L2 squared loss and L1 absolute loss by being strongly convex when close to the target/minimum and less steep for extreme values –Common example is Huber loss: –Note that h is differentiable: h(ε) = εand h(-ε) = -ε. It is shown that this class of P-spline estimators enjoys the same optimal asymptotic properties as least-squares P-splines, thereby providing strong theoretical Sep 21, 2023 · It has all the advantages of Huber loss, and it’s twice differentiable everywhere, unlike Huber loss. eters of the Huber loss and the parameters of the Laplace distributions. Huber Loss is used for Regression problems, it is more robust to outliers due to its form. The Huber estimator exhibits superior performance compared with the N Q A R 0. A variant of Huber Loss is also used in classification. Appendices: Appendices containing the background on convex analysis and properties of Newton derivative, the derivation of SNA for penalized Huber loss regression, and proof for theoretical results. Note that we have E[j‘0(X> ;Y)Xjj1+ ] = E[jYXjj1+ ] for = 0 2 , which makes (5) somewhat minimal in order to ensure the existence of the moment we need for the loss derivative for all 2 . See HuberLoss for details. The use of templating here allows Ceres to call CostFunctor::operator<T>(), with T=double when just the value of the residual is needed, and with a special type T=Jet when the Jacobians are needed. estimate #> <chr> <chr> <dbl> #> 1 huber_loss_pseudo standard 0. Aug 10, 2021 · Huber Loss. Our loss’s ability to express L2 and smoothed L1 losses is sharedby the “generalizedCharbonnier”loss[34], which Oct 24, 2023 · Derivative of Huber's loss function. Oct 2, 2019 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have The computed Pseudo-Huber loss function values. Calculate the Huber loss, a loss function used in robust regression. Cross-entropy loss, or log loss, measures the performance of a classification model whose output is a probability value between 0 and 1. In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. Similar function which this function approximates. The regression paradigm that is associated with the Huber loss is termed as Huber regression and the resulting estimator is termed as the Huber regression estimator. A loss function measures the performance of a model by measuring the difference between the output expected from the model and the actual output obtained from the model. Huber loss function is usually solved by gradient descent (GD) method or stochastic gradient descent (SGD) method, but these methods are easy to fall into local optimum and cannot find the global optimal solution. This function evaluates the first derivative of Huber's loss function. It is a smooth approximation to the Huber loss function. This article proposes a robust regularization regression estimator Download scientific diagram | Huber loss and derivative as a function of x for δ = 1. With this formulation, we show that a linear convergence algorithm can be utilized to find a minimizer. We believe the standard probabilistic interpretation that relates the Huber loss to the Huber density fails to provide adequate intuition for identifying the The Huber loss function describes the penalty incurred by an estimation procedure f. To take advantage of such a local strong convexity, we employ the gradient descent method with a Barzilai-Borwein update step (GD-BB) ( Barzilai and Borwein Dec 1, 2023 · The asymptotic properties of the Huber estimator in the NAR model are derived. ubc. Nov 1, 2020 · The Huber norm is designed to be quadratic for small deviations but grows linearly for large deviations. The Huber Regressor optimizes the squared loss for the samples where |(y-Xw-c) / sigma| < epsilon and the absolute loss for the samples where |(y-Xw-c) / sigma| > epsilon, where the model coefficients w, the intercept c and the scale sigma are parameters to be optimized. Our focus is to keep the joints as smooth as possible. squared loss is strongly convex (hence, has a fast learning rate) and the absolute loss is robust. 为什么说 Huber Loss 集MAE与MSE的优势于一身. Nov 5, 2019 · The Huber loss is a robust loss function used for a wide range of regression tasks. The most popular one is Pseudo-Huber loss [22], i. Comparison The Huber loss function is quadratic on a symmetric interval about the origin and linear everywhere else. , The Huber loss function describes the penalty incurred by an estimation procedure f. Figure 1 shows the Huber loss function for k = 1. A quadratic function with a positive coefficient is convex (you can verify this by taking the second derivative and seeing that it is positive) . … Continue reading → Jun 30, 2023 · It’s another function used in regression tasks that’s much smoother than MSE loss. Author(s) Matias Salibian-Barrera, matias@stat. Aug 9, 2022 · We also provide a comparison of robust estimators from several other loss functions, including the Huber loss function and the rank dispersion function. 345) Jun 29, 2020 · The ordinary least squares estimate for linear regression is sensitive to errors with large variance. Learn R Programming. A necessary condition is established for global minimizers, as well as non-emptiness of the set of global minimizers. [1] May 1, 2022 · Moreover, since the Huber loss is locally strongly convex around zero, we will show that L ˜ (t) (⋅) is locally strongly convex in a neighborhood of β ˜ (t) with high probability. A variant for classification is also sometimes used. In line with this notation, we use h ∞ to denote the least squares loss h ∞ (u) = u 2 2 This is often referred to as Charbonnier loss [6], pseudo-Huber loss (as it resembles Huber loss [19]), or L1-L2 loss [40] (as it behaves like L2 loss near the origin and like L1 loss elsewhere). This becomes the easiest when the two slopes are equal. Dec 13, 2019 · Construction of robust regression learning models to fit data with noise is an important and challenging problem of data regression. In this paper, we propose to use a Huber loss function with a generalized penalty to achieve robustness in estimation and variable selection. Jan 10, 2021 · Huber loss function compared against Z and Z². e. Feb 17, 2019 · Proximal Operator of Huber Loss Function (For $ {L}_{1} $ Regularized Huber Loss of a Regression Function) 8 Show that the Huber-loss based optimization is equivalent to $\ell_1$ norm based. Aug 7, 2024 · In machine learning, optimizers and loss functions are two components that help improve the performance of the model. Linear regression fits a line or hyperplane that best describes the linear relationship between inputs and the […] Explore math with our beautiful, free online graphing calculator. We can implement the Pseudo-Huber-Loss using ‘reg:pseudohubererror’ as the parameter for void gtsam::noiseModel::mEstimator::Huber::print (const std::string & s = "": const The plot shows that the Hinge loss penalizes predictions y < 1, corresponding to the notion of a margin in a support vector machine. Another loss function we could use is the Huber loss, parameterized by a hyperparameter : L (y;t) = H (y t) H a formula for the derivative H0 (a), Mar 21, 2020 · A MATLAB implementation is given in my answer to Proximal Operator of Huber Loss Function (For $ {L}_{1} Derivative of the Prox / Proximal Operator. Can be called Huber Loss or Smooth MAE Less sensitive to outliers in data than the squared Huber loss, also called smooth L1 loss, aims to balance the strengths of both MAE and MSE. Next, we show you how to use Huber loss with Keras to create a regression model. Pseudo-Huber loss is a more smooth function also behaving like MSE in one-dimensional case in the neighbourhood of zero and like MAE in the neighbourhood of infinity: Calculate the Huber loss, a loss function used in robust regression. For the Huber loss, we have q= 1 and the only requirement on Yis EjYj<+1and Apr 22, 2019 · Huber loss is defined as. The Huber Loss Function. We believe the standard probabilistic interpretation that relates the Huber loss to the Huber density fails to provide adequate intuition for identifying the This loss combines advantages of both L1Loss and MSELoss; the delta-scaled L1 region makes the loss less sensitive to outliers than MSELoss, while the L2 region provides smoothness over L1Loss near 0. However, spatial data is more intricate than ordinary data because of spatial correlation and non-stationarity. This smoothing of the second derivative is achieved by piecewise interpolation with a cubic polynomial. 2 except the part involving SNA. Algorithms used for regression tasks are also referred to as “regression” algorithms, with the most widely known and perhaps most successful being linear regression. –But we can minimize the Huber loss using gradient descent. Huber loss, log-cosh loss and absolute loss are robust to outliers. Huber Loss: A robust loss function for regression tasks with a focus on handling outliers. The mean is very vulnerable to extreme outliers. Sep 1, 2023 · Derivative of Huber's loss function. 2. Monte Carlo simulations are conducted to demonstrate the advantages of the Huber estimation. Mar 25, 2024 · It is easy to see that derivative of Huber loss is continuous, but not differentiable in points | x | = δ 𝑥 𝛿 |x|=\delta | italic_x | = italic_δ. # Supply truth and predictions as bare column names huber_loss_pseudo (solubility_test, solubility, prediction) #> # A tibble: 1 × 3 #>. 将huber loss 应用到ekf, 减小outlier的影响． huber loss在最小二乘中的使用最小二乘的求解: \pmb{x}^{*} = argmin |\pmb{f}(\pmb{x})|_{\pmb{\Omega}}^{2} \tag{1} 观测 \pmb{f}(\pmb{x}) 满足0均值，方差为\pmb… Jun 6, 2021 · I'd like to proof $\gamma=median\{y_1,y_N \}$ minimizes the Huber Loss so i've taken its first derivate for $\gamma\neq y_i$: I've tried to proof that first derivate change its signal before and after the median, i mean $\frac{\partial R}{\partial \gamma}<0$ when $\lambda< median$ and $\frac{\partial R}{\partial \gamma}>0$ when $\lambda Oct 12, 2019 · Let's now see if we can complete a regression problem with Huber loss! Huber loss example with TensorFlow 2/Keras. However, it is not smooth so we cannot guarantee smooth derivatives. The regularization method is a popular technique for variable selection and parameter estimation. A preliminary scale estimator can also be included in the loss function. And even under normal errors, it Aug 14, 2019 · Huber loss is more robust to outliers than MSE. Binary Classification Loss Functions. For a batch of size N N N, the unreduced loss can be described as: The optimizing constant for Huber loss is close to the value that minimizes absolute loss. . Huber loss and derivative as a function of xfor δ= 1. Since Huber function has the property that inputs with large deviations of misfit are penalized linearly and small errors are Mar 1, 2023 · For small values of delta, the Huber loss behaves like the MSE loss and is more sensitive to outliers. This is motivated by a desire for the second derivative of the Huber loss to decay smoothly from 1 to zero over an interval of length "h". We'll use the Boston housing price regression dataset which comes with Keras by default - that'll make the example easier to follow. However, not even those formulations are smooth. seed (1234) size <-100 times <-10 # create 10 resamples solubility_resampled <-bind_rows (replicate (n = times Jan 1, 2024 · Robust estimators are obtained by well-chosen loss functions, such as the Huber or Tukey loss function. 345) loss = huber(Y,targets) returns the Huber loss between the formatted dlarray object Y containing the predictions and the target values targets for regression tasks. The generalized Charbonnier loss function takes the Charbonnier loss and, instead of applying a square-root, raises the loss to an arbitrary power parameter : In the following sections, we survey the related work (Section 2), review the Huber loss and maximum likelihood estimation in detail (Section 3), propose our alternative probabilistic interpretation of the Huber loss (Section 4), utilize a toy problem to illustrate the relationship between the optimal transition point of the Huber loss and the noise distribution of the ground-truth (Section 5 This repository provides a modification to the Huber loss function proposed in (reference to Huber 1964). Why do we need a 2nd derivative? Many ML model implementations like XGBoost use Newton’s method to find the optimum, which is why the second derivative (Hessian) is needed. The loss you've implemented is its smooth approximation, the Pseudo-Huber loss: The problem with this loss is that its second derivative gets too close to zero. The performance of estimation and variable Feb 1, 2022 · R( ) and its partial derivatives to be well-defined. Why do we need a 2nd derivative? Feb 1, 2023 · In this paper, we consider the robust regression problem associated with Huber loss in the framework of functional linear model and reproducing kernel Hilbert spaces. , Nov 30, 2023 · However, in multivariate datasets, the performance of MAE, MSE, and Log-cosh was similar to that of the Huber loss. We would be happy to share the code for SNA on request. The Huber loss function has several advantages over other loss functions commonly used in regression problems: Jan 10, 2021 · On the day I was introduced to Huber loss by Michal Fabinger, the very first thing that came to my mind was the question: “How did someone joined these two functions in a mathematical way?”. As a beginner, these losses are more than enough, but if you still want to dig deeper and explore more loss functions, I highly recommend you to go through Charbonnier loss, pseudo-Huber loss, and generalized Charbonnier loss functions. Lange [12], proposed a set of potential functions for im-age reconstruction that behave like the Huber loss, but un-like the Huber loss, these functions are more than once dif-ferentiable. We want to classify a tumor as ‘Malignant’ or ‘Benign’ based on features like average radius, area, perimeter, etc. Obviously, you Aug 23, 2023 · Recently, uncertainty quantification is getting more and more attention, especially for computer model calibration. Further, we examine the use of the log-cosh Aug 10, 2021 · Without reading the linked paper: Huber's loss was introduced by Huber in 1964 in the context of estimating a one-dimensional location of a distribution. Nov 6, 2023 · Derivative Computation: Calculate the derivatives of the loss with respect to the model’s parameters. Overall, the Huber loss had the best performance score compared to other loss functions. , beyond 1 standard deviation, the loss becomes linear). The Huber loss function is given by, (1 jtj k. The Huber loss with unit weight is defined as, $\mathcal{L}_{huber}(y, \hat{y}) = \begin{cases} 1/2(y - \hat{y})^{2} & |y - \hat{y}| \leq 1 \\ |y - \hat{y}| - 1/2 & |y - \hat{y}| > 1 \end{cases}$ In a single figure the second derivative (not shown) is discontinuous. 5 estimator in both the light-tailed and heavy-tailed cases. metric . We show that using the log-exp transform together with the logistic function, we can create a loss which combines the desirable properties of the strictly convex losses with robust loss functions. huber. Pseudo-Huber-Loss. Aug 4, 2022 · Image Source: Author. Our loss’s ability to express L2 and smoothed L1 losses is shared by the “generalized Charbonnier” loss [35], which Feb 22, 2022 · We propose an extended generalization of the pseudo Huber loss formulation. A comparison of linear regression using the squared-loss function (equivalent to ordinary least-squares regression) and the Huber loss function, with c = 1 (i. powered by. 199 library set. Huber (1964) defines the loss function piecewise by[1] In literature, there are some nice properties to have for centralizing metrics like the equivariance under scaling, translation, rotation or some other transform []. R Code: R code for the timing experiments in Section 5. Cross-entropy loss increases as the predicted probability diverges from the actual label. (1) Derivative. We characterize local minimizers and establish conditions that are necessary and sufficient for a local minimizer to be strict. It can be implemented in python XGBoost as follows,. Feb 14, 2021 · The main advantage of the Pseudo-Huber is that it is twice differentiable (i. Thus, it is less sensitive to heavy-tailed observations. See also. In general, Huber loss differs from SmoothL1Loss by a factor of delta (AKA beta in Smooth L1). parameter. The generalized Charbonnier loss function takes the Charbonnier loss and, instead of applying a square-root, raises the loss to an arbitrary shape parameter : Jun 12, 2020 · Regression is a modeling task that involves predicting a numerical value given an input. This function is quadratic for small residual values and linear for large residual values. The introduction of Huber regression led This is often referred to as Charbonnier loss [5], pseudo-Huber loss (as it resembles Huber loss [18]), or L1-L2 loss [39] (as it behaves like L2 loss near the origin and like L1 loss elsewhere). The Huber Loss function is also utilized in regression machine learning tasks. To overcome the limitation of the traditional calibration procedures, the authors develop a robust calibration procedure based on Huber Jul 10, 2017 · Huber Loss is a well documented loss function. The Huber loss Description. So let’s differentiate both functions and equalize them. Linear functions are also technically convex (since their second derivative is non-negative). May 20, 2023 · Learn how Huber Regression strikes a balance between ordinary least squares (OLS) and absolute deviation (L1) regression, providing reliable parameter estimates while mitigating the impact of The Huber loss is a robust loss function used for a wide range of regression tasks. Apr 8, 2019 · The Huber loss is another way to deal with the outlier problem and is very closely linked to the LASSO regression loss function. 0. Absolute loss, quantile loss and \(\epsilon \)-insensitivity loss are not smooth, Huber loss is first derivative, and square loss and log-cosh loss are second derivative. The squared loss has the disadvantage that it can be dominated by outliers, and when the underlying distribution of the nominal data is heavy-tailed, the efficiency of its minimi. However, most of the existing papers assume the errors follow a Gaussian or sub-Gaussian distribution, which would not be satisfied in practice. Parameter Update: Update the model’s parameters iteratively until you reach the global minimum of the loss function. 3) loss (as it behaves like quadratic loss near the origin and like absolute loss far from the origin) or a Pseudo-Huber loss (due to its resemblance to the classic Huber loss func-tion [7]). To achieve smoothness, alternative formulations have been proposed for the combination of square and absolute losses [21]. Dec 7, 2017 · Pseudo-Huber Loss Function. –This f is convex but setting f(x) = 0 does not give a linear system. Next, it calculates the Huber Loss with a specified delta value (delta=1. Tensor. Apr 8, 2020 · Instead of having a partial derivative that looks like step function, as it is the case for the L1 loss partial derivative, we want a smoother version of it that is similar to the smoothness of the sigmoid activation function. Notes. For large values of delta, the Huber loss behaves like the L1 loss and is less sensitive to outliers. To this matter, we start by defining our loss function partial derivative before defining the loss function itself. Based on our findings, we conclude that the Huber loss is the most effective loss function among the ones tested. It has all the advantages of Huber loss because it’s twice differentiable everywhere, unlike Huber loss, because some learning algorithms like XGBoost use Newton’s method to find the optimum, and hence the second derivative (Hessian). So predicting a probability of . Hence, the Hessian is not defined at those points. Return type. It incorporates an adjustable hyperparameter, δ, that acts as a transition point: for loss values below or equal to δ, Huber loss is quadratic (such as MSE); for loss values greater than δ, Huber loss is linear (such as MAE). See Huber loss for more information. We point out that every loss function (including ours) that depends on the difference between the parameter x 𝑥 x and the samples x n subscript 𝑥 𝑛 x_{n} will be equivariant under translation. The mathematical equation for Huber Loss is as follows: L(δ, y, f(x)) = (1/2) * (f(x) - y)^2 if |f(x) - y Jan 1, 2022 · The Huber loss and the theoretical findings in location parameter estimation then applied and carried over to robust regression problems. (2) Robustness. The Huber Loss offers the best of both worlds by balancing the MSE and MAE together. Rdocumentation. Let’s first start with a brief recap of the Huber loss function and the basics of Generalized Linear Models (GLM). Tukey’s loss is similar to Huber loss in that it demonstrates quadratic behavior near the origin. 0) using the implemented huber_loss function. In this lecture we will get an intuitive. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Description. The joint can be figured out by equating the derivatives of the two functions. rmargint (version 2. In this work, we propose a loss function which is similar to a potential function in Aug 20, 2019 · We will discuss how to optimize this loss function with gradient boosted trees and compare the results to classical loss functions on an artificial data set. To this matter, we start by defining our loss function partial derivative before defining the loss function itself. Jun 14, 2023 · This means that ‘logcosh’ works mostly like the mean squared error, but will not be so strongly affected by the occasional wildly incorrect prediction. A vector of the same length as x. Huber loss is, as Wikipedia defines it, “a loss function used in robust An example of fitting a simple linear model to data which includes outliers (data is from table 1 of Hogg et al 2010). We propose an Ivanov regularized empirical risk minimization estimation procedure to approximate the slope function of the linear model in the presence of outliers or heavy-tailed Aug 2, 2021 · Loss functions are mainly classified into two different categories Classification loss and Regression Loss. estimator . Note that this loss is not differentiable and for-mulations like Huber loss [3] are needed for differentiability. The input Y is a formatted dlarray. It has all the advantages of Huber loss, and it’s twice differentiable everywhere, unlike Huber loss. The output loss is an unformatted dlarray scalar. "smooth"), whereas the Huber is only differentiable once. It is clear that ρ′′ H (x) will be discontinuous at both −δand +δ. Sep 19, 2020 · We investigate the structure of the local and global minimizers of the Huber loss function regularized with a sparsity inducing L0 norm term. Here k is a parameter and the idea behind the loss function is to penalize outliers (beyond k) linearly instead of quadratically. Value. Huber(t) = 2t2; 1 k jtj : (1) 2k2; jtj > k. We further discuss Jul 29, 2024 · Then, it defines a custom function huber_loss to compute the Huber Loss, which is a combination of MSE and MAE, offering a balance between robustness to outliers and smoothness. Classification loss is the case where the aim is to predict the output from the different categorical values for example, if we have a dataset of handwritten images and the digit is to be predicted that lies between (0–9), in these kinds of scenarios classification loss is used. To speed up their algorithm, lightgbm uses Newton method's approximation to find the optimal leaf value: y = - L' / L'' (See this blogpost for details). Details. It is not robust to heavy-tailed errors or outliers, which are commonly encountered in applications. In machine learning, the hinge loss is a loss function used for training classifiers. Apr 12, 2020 · Below, we will summarize and compare them briefly from several aspects. from publication: Statistical Properties of the log-cosh Loss Function Used in Machine Learning | This paper •The Huber loss is a robust loss function used for a wide range of regression tasks. Apart from that, the usage of Huber loss was pretty straightforward to understand when he May 20, 2022 · The alternative supported implementation of the MAE is the Pseudo-Huber-Loss. This loss function is less sensitive to outliers than rmse() . huber(r, k = 1. To utilize the Huber loss, a parameter that controls the transitions from a quadratic function to an absolute value function needs to be selected. The parameter sigma makes sure that if y is scaled up or down by a certain Mar 11, 2024 · Implementing the Huber loss requires comparing the absolute value against some small kappa, then behaving linearly with the absolute value outside this bound, but quadratic inside. We can define it using the following piecewise function: What this equation essentially says is: for loss values less than delta, use the MSE; for loss values greater than delta, use the MAE. This function is quadratic for small residual values and linear for large residual values. In this study, to address the top (or low) tails of data points, we integrated the Huber norm with the asymmetric loss function to obtain an asymmetric Huber norm. Fig. In this work, we propose a loss function which is similar to a potential function in The popular method in the field of AI is to use Huber loss function, which combines the advantages of both MAE and MSE, as a framework. lizyxm gxtewi paxvphh fegnsm lcaau rwstu duhjnojl floiuu hdijwoy lhnozd