The example shows that the predictions in ridge are strongly influenced by the outliers present in the dataset. MachineCurve.com will earn a small affiliate commission from the Amazon Services LLC Associates Program when you purchase one of the books linked above. ccc(), This loss essentially tells you something about the performance of the network: the higher it is, the worse your networks performs overall. Sign up above to learn, By continuing to browse the site you are agreeing to our, Regression dataset: Boston housing price regression, Never miss new Machine Learning articles ✅, What you’ll need to use Huber loss in Keras, Defining Huber loss yourself to make it usable, Preparing the model: architecture & configuration. rpiq(), Developed by Max Kuhn, Davis Vaughan. How to Perform Fruit Classification with Deep Learning in Keras, Blogs at MachineCurve teach Machine Learning for Developers. This function is The process continues until it converges. For example, a common approach is to take Ëb= MAR=0:6745, where MAR is the median absolute residual. rsq(), smaller than in the Huber ﬁt but the results are qualitatively similar. Matched together with reward clipping (to [-1, 1] range as in DQN), the Huber converges to the correct mean solution. Then, one can argue, it may be worthwhile to let the largest small errors contribute more significantly to the error than the smaller ones. names). Both non-linear least squares and maximum likelihood estimation are special cases of M-estimators. Huber Loss#. – You have installed it into the wrong version of Python savefig … Let’s now take a look at the dataset itself, and particularly its target values. Linear regression model that is robust to outliers. Binary Classification Loss Functions. Ask Question Asked 2 years, 4 months ago. rsq_trad(), We’re then ready to add some code! Huber, P. (1964). Some statistical analysis would be useful here. ccc(), Sign up to learn. Defines the boundary where the loss function axis=1). If outliers are present, you likely don’t want to use MSE. Required fields are marked *. What are outliers in the data? Finally, we add some code for performance testing and visualization: Let’s now take a look at how the model has optimized over the epochs with the Huber loss: We can see that overall, the model was still improving at the 250th epoch, although progress was stalling – which is perfectly normal in such a training process. Huber loss. This results in large errors between predicted values and actual targets, because they’re outliers. results (that is also numeric). If it does not contain many outliers, it’s likely that it will generate quite accurate predictions from the start – or at least, from some epochs after starting the training process. How to check if your Deep Learning model is underfitting or overfitting? weights: Optional Tensor whose rank is either 0, or the same rank as labels, and must be broadcastable to labels (i.e., all dimensions must be either 1, or the same as the corresponding losses dimension). Prior to version 7.3-52, offset terms in formula were omitted from fitted and predicted values.. References. The Huber loss function depends on a hyper parameter which gives a bit of flexibility. Explore the products we bring to your everyday life. Note that the Huber function is smooth near zero residual, and weights small residuals by the mean square. The pseudo Huber Loss function transitions between L1 and L2 loss at a given pivot point (defined by delta) such that the function becomes more quadratic as the loss decreases.The combination of L1 and L2 losses make Huber more robust to â¦ Find out in this article – You are using the wrong version of Python (32 bit instead of 64 bit) Since MSE squares errors, large outliers will distort your loss value significantly. L ( y , f ( x ) ) = { max ( 0 , 1 − y f ( x ) ) 2 for y f ( x ) ≥ − 1 , − 4 y f ( x ) otherwise. predictions: The predicted outputs. The primary dependency that you’ll need is Keras, the deep learning framework for Python. As the parameter epsilon is increased for the Huber regressor, the â¦ Returns-----loss : float: Huber loss. As with truth this can be Although the plot hints to the fact that many outliers exist, and primarily at the high end of the statistical spectrum (which does make sense after all, since in life extremely high house prices are quite common whereas extremely low ones are not), we cannot yet conclude that the MSE may not be a good idea. You can then adapt the delta so that Huber looks more like MAE or MSE. I suggest you run a statistical analysis on your dataset first to find whether there are many outliers. Huber, P. (1964). specified different ways but the primary method is to use an reduction: Type of reduction to apply to loss. – https://repo.anaconda.com/pkgs/main/noarch A tibble with columns .metric, .estimator, and .estimate and 1 row of values.. For grouped data frames, the number of rows returned will be the same as the number of groups. the residuals. Today, the newest versions of Keras are included in TensorFlow 2.x. Note that the Huber function is smooth near zero residual, and weights small residuals by the mean square. You can wrap Tensorflow's tf.losses.huber_loss in a custom Keras loss function and then pass it to your model. And how do they work in machine learning algorithms? Boston house-price data. Value. We also need huber_loss since that’s the los function we use. When you train machine learning models, you feed data to the network, generate predictions, compare them with the actual values (the targets) and then compute what is known as a loss. Huber loss is less sensitive to outliers in data than the … So having higher values for low losses doesn't mean much (in this context), because multiplying everything by, for example, $1e6$ may ensure there are NO "low losses", i.e., losses $< 1$. Retrieved from https://keras.io/datasets/, Keras. Note. And contains these variables, according to the StatLib website: In total, one sample contains 13 features (CRIM to LSTAT) which together approximate the median value of the owner-occupied homes or MEDV. That is why we can prefer to consider criterion like Huber’s one. The fastest approach is to use MAE. Note: When beta is set to 0, this is equivalent to L1Loss.Passing a negative value in for beta will result in an exception. In fact, it might take quite some time for it to recognize these, if it can do so at all. The Huber regressor is less influenced by the outliers since the model uses the linear loss for these. Also, clipping the grads is a common way to make optimization stable (not necessarily with huber). This should be done carefully, however, as convergence issues may appear. The Huber’s Criterion with adaptive lasso To be robust to the heavy-tailed errors or outliers in the response, another possibility is to use the Huber’s criterion as loss function as introduced in [12]. 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.e., beyond 1 standard deviation, the loss becomes linear). Retrying with flexible solve. For example, the coefficient matrix at iteration j is $$B_{j} = [XâW_{j-1}X]^{-1}XâW_{j-1}Y$$ where the subscripts indicate the matrix at a particular iteration (not rows or columns). Do note, however, that the median value for the testing dataset and the training dataset are slightly different. Viewed 911 times 6 $\begingroup$ Dear optimization experts, My apologies for asking probably the well-known relation between the Huber-loss based optimization and $\ell_1$ based optimization. 4. We first briefly recap the concept of a loss function and introduce Huber loss. In general one needs a good starting vector in order to converge to the minimum of the GHL loss function. parameter for Fair loss. Value. – https://repo.anaconda.com/pkgs/msys2/win-32 loss_collection: collection to which the loss will be added. ... (0.2, 0.5, 0.8)) # this example uses cartesian grid search because the search space is small # and we want to see the performance of all models. However, let’s analyze first what you’ll need to use Huber loss in Keras. For this reason, we import Dense layers or densely-connected ones. Retrieved from https://heartbeat.fritz.ai/5-regression-loss-functions-all-machine-learners-should-know-4fb140e9d4b0, StatLib—Datasets Archive. So, you'll need some kind of closure like: This function is quadratic for small residual values and linear for large residual values. Machine Learning Explained, Machine Learning Tutorials, Blogs at MachineCurve teach Machine Learning for Developers. smape(), Other accuracy metrics: The idea is to use a different loss function rather than the traditional least-squares; we solve $\begin{array}{ll} \underset{\beta}{\mbox{minimize}} & \sum_{i=1}^m \phi(y_i - x_i^T\beta) \end{array}$ But how to implement this loss function in Keras? parameter for Huber loss and Quantile regression. A tibble with columns .metric, .estimator, and .estimate and 1 row of values.. For grouped data frames, the number of rows returned will be the same as the number of groups. That’s why it’s best to install tensorflow-gpu via https://anaconda.org/anaconda/tensorflow-gpu i.e. It essentially combines the Mean Absolute Error and the Mean Squared Error depending on some delta parameter, or . In Section 3, we … If they’re pretty good, it’ll output a lower number. A variant of Huber Loss is also used in classification. The Boston housing price regression dataset is one of these datasets. The add_loss() API. ... (0.2, 0.5, 0.8)) # this example uses cartesian grid search because the search space is small # and we want to see the performance of all models. Issue #82 Adding baselines package need to run the notebook, Correcting small typo Changing huber loss function for tf2 and .estimate and 1 row of values. Subsequently, we fit the training data to the model, complete 250 epochs with a batch size of 1 (true SGD-like optimization, albeit with Adam), use 20% of the data as validation data and ensure that the entire training process is output to standard output. The output of this model was then used as the starting vector (init_score) of the GHL model. Other numeric metrics: Let’s now create the model. See The Elements of Statistical Learning (Second Edition) , 2.4 Statistical Decision Theory for the population minimizers under MSE and MAE, and section 10.6 Loss Functions and Robustness for a definition of Huber loss: batch_accumulator (str): 'mean' will divide loss by batchsize Returns: (Variable) scalar loss """ assert batch_accumulator in ('mean', 'sum') y = F.reshape(y, (-1, 1)) t = F.reshape(t, (-1, 1)) if clip_delta: losses = F.huber_loss(y, t, delta=1.0) else: losses = F.square(y - t) / 2 losses = F.reshape(losses, (-1,)) loss_sum = F.sum(losses * weights * mask) if batch_accumulator == 'mean': loss = loss_sum / max(n_mask, 1.0) … sklearn.linear_model.HuberRegressor¶ class sklearn.linear_model.HuberRegressor (*, epsilon=1.35, max_iter=100, alpha=0.0001, warm_start=False, fit_intercept=True, tol=1e-05) [source] ¶. mae(), If it is 'no', it holds the elementwise loss values. $\endgroup$ â jbowman Oct 7 '17 at 17:52 The column identifier for the true results The parameter , which controls the limit between l 1 and l 2, is called the Huber threshold. array ([14]), alpha = 5) plt. Huber, 1981, Sec. How to create a variational autoencoder with Keras? studies and a real data example conﬁrm the efﬁciency gains in ﬁnite samples. We post new blogs every week. mae(), looking for, navigate to. values should be stripped before the computation proceeds. Here we have first trained a small LightGBM model of only 20 trees on g(y) with the classical Huber objective function (Huber parameter α = 2). – https://repo.anaconda.com/pkgs/main/win-32 (that is numeric). #>, 6 huber_loss standard 0.293 plot (thetas, loss, label = "Huber Loss") plt. array ([14]),-20,-5, colors = "r", label = "Observation") plt. We propose an algorithm, semismooth Newton coordinate descent (SNCD), for the elastic-net penalized Huber loss regression and quantile regression in high dimensional settings. the adaptive lasso. Gradient Descent¶. It is taken by Keras from the Carnegie Mellon University StatLib library that contains many datasets for training ML models. #>, 3 huber_loss standard 0.197 mape(), For grouped data frames, the number of rows returned will be the same as , Grover, P. (2019, September 25). We’ll use the Boston housing price regression dataset which comes with Keras by default – that’ll make the example easier to follow. regularization losses). Proximal Operator of Huber Loss Function (For ${L}_{1}$ Regularized Huber Loss of a Regression Function) 6 Show that the Huber-loss based optimization is equivalent to $\ell_1$ norm based. Now we will show how robust loss functions work on a model example. The outliers might be then caused only by incorrect approximation of the Q-value during learning. In this case, you may observe that the errors are very small overall. rdrr.io Find an R package R language docs Run R in your browser R Notebooks. For example, if I fit a gradient boosting machine (GBM) with Huber loss, what optimal prediction am I attempting to learn? When you compare this statement with the benefits and disbenefits of both the MAE and the MSE, you’ll gain some insights about how to adapt this delta parameter: Let’s now see if we can complete a regression problem with Huber loss! Chris, Failed to install TensorFlow, giving me error not found try to search using several links, Hi Festo, Site built by pkgdown. For huber_loss_pseudo_vec(), a single numeric value (or NA).. – Anything else, It’s best to follow the official TF guide for installing: https://www.tensorflow.org/install, (base) C:\Users\MSIGWA FC>activate PythonGPU. The OLS minimizes the sum of squared residuals. The number of outliers helps us tell something about the value for d that we have to choose. As you can see, for target = 0, the loss increases when the error increases. mase(), You can use the add_loss() layer method to keep track of such loss terms. A logical value indicating whether NA For huber_loss_pseudo_vec(), a single numeric value (or NA).. References. Also the Hampel’s proposal is a redescending estimator deﬁned b y sev eral pieces (see e.g. poisson_max_delta_step ︎, default = 0.7, type = double, constraints: poisson_max_delta_step > 0.0 In Section 2, we review the basics of the Huber regression and then derive the formulation of the enveloped Huber regression (EHR). Loss functions applied to the output of a model aren't the only way to create losses. We’ll optimize by means of Adam and also define the MAE as an extra error metric. #>, 10 huber_loss standard 0.212 The pseudo Huber Loss function transitions between L1 and L2 loss at a given pivot point (defined by delta) such that the function becomes more quadratic as the loss decreases.The combination of L1 and L2 losses make Huber more robust to outliers while … When you install them correctly, you’ll be able to run Huber loss in Keras , …cost me an afternoon to fix this, though . Parameters. Question: 2) Robust Regression Using Huber Loss: In The Class, We Defined The Huber Loss As S Ke? Often, it’s a matter of trial and error. Your email address will not be published. Your email address will not be published. Given a prediction. My name is Chris and I love teaching developers how to build  awesome machine learning models. This way, you can get a feel for DL practice and neural networks without getting lost in the complexity of loading, preprocessing and structuring your data. Also known as the Huber loss: ... By default, the losses are averaged over each loss element in the batch. How to visualize the decision boundary for your Keras model? quasiquotation (you can unquote column There are many ways for computing the loss value. As the parameter epsilon is increased for the Huber regressor, the … This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators--intermediaries between sample mean and sample median--that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. quadratic for small residual values and linear for large residual values. Parameters. Two graphical techniques for identifying outliers, scatter plots and box plots, (…). It is used in Robust Regression, M-estimation and Additive Modelling. The column identifier for the predicted It defines a custom Huber loss Keras function which can be successfully used. The most accurate approach is to apply the Huber loss function and tune its hyperparameter δ. How to implement Huber loss function in XGBoost? – https://repo.anaconda.com/pkgs/r/win-32 Obviously, you can always use your own data instead! The paper is organized as follows. Dissecting Deep Learning (work in progress), What you'll need to use Huber loss in Keras, https://heartbeat.fritz.ai/5-regression-loss-functions-all-machine-learners-should-know-4fb140e9d4b0, https://keras.io/datasets/#boston-housing-price-regression-dataset, https://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm, https://stackoverflow.com/questions/47840527/using-tensorflow-huber-loss-in-keras, https://conda.anaconda.org/anaconda/win-32, https://conda.anaconda.org/anaconda/noarch, https://repo.anaconda.com/pkgs/main/win-32, https://repo.anaconda.com/pkgs/main/noarch, https://repo.anaconda.com/pkgs/msys2/win-32, https://repo.anaconda.com/pkgs/msys2/noarch, https://anaconda.org/anaconda/tensorflow-gpu. See: Huber loss - Wikipedia. scope: The scope for the operations performed in computing the loss. It essentially combines the Mea… Huber loss can be really helpful in such cases, as it curves around the minima which decreases the gradient. This means that patterns underlying housing prices present in the testing data may not be captured fully during the training process, because the statistical sample is slightly different. Robust Estimation of a Location Parameter. ... (for example, accuracy or AUC) to that of existing classification models on publicly available data sets. These points are often referred to as outliers. Solving environment: failed with initial frozen solve. Annals of Statistics, 53 (1), 73-101. Regards, You can use the add_loss() layer method to keep track of such loss terms. An example of fitting a simple linear model to data which includes outliers (data is from table 1 of Hogg et al 2010). transitions from quadratic to linear. Calculate the Huber loss, a loss function used in robust regression. Introduction. The name is pretty self-explanatory. (n.d.). As we see in the image, Most of the Y values are +/- 5 to its X value approximately. The structure of this dataset, mapping some variables to a real-valued number, allows us to perform regression. In fact, Grover (2019) writes about this as follows: Huber loss approaches MAE when ~ 0 and MSE when ~ ∞ (large numbers.). At its core, a loss function is incredibly simple: it’s a method of evaluating how well your algorithm models your dataset. Ls(e) = If Å¿el 8 Consider The Robust Regression Model N Min Lo(yi â 0"(x;)), I=1 Where P(xi) And Yi Denote The I-th Input Sample And Output/response, Respectively And â¦ A tibble with columns .metric, .estimator, Returns: Weighted loss float Tensor. Using Radial Basis Functions for SVMs with Python and Scikit-learn, One-Hot Encoding for Machine Learning with TensorFlow and Keras, One-Hot Encoding for Machine Learning with Python and Scikit-learn, Feature Scaling with Python and Sparse Data, Visualize layer outputs of your Keras classifier with Keract. Boston housing price regression dataset. f ( x ) {\displaystyle f (x)} (a real-valued classifier score) and a true binary class label. We’ll need to inspect the individual datasets too. So every sample in your batch corresponds to an image and every pixel of the image gets penalized by either term depending on whether its difference to the ground truth value is smaller or larger than c. Given the differences in your example, you would apply L1 loss to the first element, and quadratic on the other two. Hence, we need to think differently. Datasets. I slightly adapted it, and we’ll add it next: We next load the data by calling the Keras load_data() function on the housing dataset and prepare the input layer shape, which we can add to the initial hidden layer later: Next, we do actually provide the model architecture and configuration: As discussed, we use the Sequential API; here, we use two densely-connected hidden layers and one output layer. (n.d.). In this blog post, we’ve seen how the Huber loss can be used to balance between MAE and MSE in machine learning regression problems. Binary Classification refers to assigning an object into one of two classes. Active 2 years, 4 months ago. This should be an unquoted column name although Economics & Management, vol.5, 81-102, 1978. How to use Kullback-Leibler divergence (KL divergence) with Keras? Returns: Weighted loss float Tensor. Create a file called huber_loss.py in some folder and open the file in a development environment. If it is 'no', it holds the elementwise loss values. Retrieved from https://stackoverflow.com/questions/47840527/using-tensorflow-huber-loss-in-keras, Hi May, linspace (0, 50, 200) loss = huber_loss (thetas, np. MachineCurve participates in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising commissions by linking to Amazon. (PythonGPU) C:\Users\MSIGWA FC>conda install -c anaconda keras-gpu 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.e., beyond 1 standard deviation, the loss becomes linear). xlabel (r "Choice for $\theta$") plt. A single numeric value. smape(). 5 Regression Loss Functions All Machine Learners Should Know. The hidden ones activate by means of ReLU and for this reason require He uniform initialization. Used in Belsley, Kuh & Welsch, ‘Regression diagnostics …’, Wiley, 1980. loss function is less sensitive to outliers than rmse(). Robust Estimation of a Location Parameter. Retrieved from http://lib.stat.cmu.edu/datasets/, Keras. The reason for the wrapper is that Keras will only pass y_true, y_pred to the loss function, and you likely want to also use some of the many parameters to tf.losses.huber_loss. This loss function is less sensitive to outliers than rmse (). 2.3. abs (est-y_obs) return np. The LAD minimizes the sum of absolute residuals. y ∈ { + 1 , − 1 } {\displaystyle y\in \ {+1,-1\}} , the modified Huber loss is defined as. I had to upgrade Keras to the newest version, as apparently Huber loss was added quite recently – but this also meant that I had to upgrade Tensorflow, the processing engine on top of which my Keras runs. Contribute to damiandraxler/Generalized-Huber-Loss development by creating an account on GitHub. In statistics, M-estimators are a broad class of extremum estimators for which the objective function is a sample average. Therefore, it combines good properties from both MSE and MAE. Only then, we create the model and configure to an estimate that seems adequate. The hyperparameter should be tuned iteratively by testing different values of δ. See: Huber loss - Wikipedia. For example the Least Absolute Deviation (LAD) penelizes a deviation of 3 with a loss of 3, while the OLS penelizes a deviation of 3 with a loss of 9. However, you’ll need to consider the requirements listed above or even better, the official Tensorflow GPU requirements! We’re creating a very simple model, a multilayer perceptron, with which we’ll attempt to regress a function that correctly estimates the median values of Boston homes. The final layer activates linearly, because it regresses the actual value. I hope you’ve enjoyed this blog and learnt something from it – please let me know in the comments if you have any questions or remarks. For huber_loss_vec(), a single numeric value (or NA). In fact, we can design our own (very) basic loss function to further explain how it works. Finally, we run the model, check performance, and see whether we can improve any further. Next, we’ll have to perform a pretty weird thing to make Huber loss usable in Keras. When writing the call method of a custom layer or a subclassed model, you may want to compute scalar quantities that you want to minimize during training (e.g. sample_weight : ndarray, shape (n_samples,), optional: Weight assigned to each sample. It is reasonable to suppose that the Huber function, while maintaining robustness against large residuals, is easier to minimize than l 1. This The mean absolute error was approximately $3.639. yardstick is a part of the tidymodels ecosystem, a collection of modeling packages designed with common APIs and a shared philosophy. Robust Estimation of a Location Parameter. Huber loss is more robust to outliers than MSE. (n.d.). mase(), scope: The scope for the operations performed in computing the loss. ylabel (r "Loss") plt. Show that the Huber-loss based optimization is equivalent to$\ell_1\$ norm based. # Supply truth and predictions as bare column names, #> resample .metric .estimator .estimate There are many ways for computing the loss value. However, the problem with Huber loss is that we might need to train hyperparameter delta which is an iterative process. This way, we can have an estimate about what the true error is in terms of thousands of dollars: the MAE keeps its domain understanding whereas Huber loss does not. This parameter must be configured by the machine learning engineer up front and is dependent on your data. It is reasonable to suppose that the Huber function, while maintaining robustness against large residuals, is easier to minimize than l 1. Then sum up. Note that the full code is also available on GitHub, in my Keras loss functions repository. reduction: Type of reduction to apply to loss. Even though Keras apparently natively supports Huber loss by providing huber_loss as a String value during model configuration, there’s no point in this, since the delta value discussed before cannot be configured that way. An example of fitting a simple linear model to data which includes outliers (data is from table 1 of Hogg et al 2010). What if you used = 1.5 instead? It is therefore a good loss function for when you have varied data or only a few outliers. Our loss’s ability to express L2 and smoothed L1 losses is shared by the “generalized Charbonnier” loss [35], which Huber loss works with Keras version 2.3.1+, This Keras version requires Tensorflow 2.0.0+. (n.d.). #>, 8 huber_loss standard 0.190 Defaults to 1. As you change pieces of your algorithm to try and improve your model, your loss function will tell you if you’re getting anywhere. Huber Loss, Smooth Mean Absolute Error. Tensorflow 2.0.0+ requires CUDA 10.0 when you run it on GPU, contrary to previous versions, which ran on CUDA 9.0. A tibble with columns .metric, .estimator, and .estimate and 1 row of values.. For grouped data frames, the number of rows returned will be the same as the number of groups. #>. For _vec() functions, a numeric vector. axis=1). Next, we present a Keras example implementation that uses the Boston Housing Prices Dataset to generate a regression model. The sample, in our case, is the Boston housing dataset: it contains some mappings between feature variables and target prices, but obviously doesn’t represent all homes in Boston, which would be the statistical population. For _vec() functions, a numeric vector. columns. A. Marazzi (1993) Algorithms, Routines and S Functions for Robust Statistics. You want that when some part of your data points poorly fit the model and you would like to limit their influence. If you don’t know, you can always start somewhere in between – for example, in the plot above, = 1 represented MAE quite accurately, while = 3 tends to go towards MSE already. You’ve tried to install the ‘old’ Keras – which has no tensorflow attached by default. It allows you to experiment with deep learning and the framework easily. Their structure is also quite similar: most of them, if not all, are present in the high end segment of the housing market. Sign up to learn, We post new blogs every week. Unlike existing coordinate descent type algorithms, the SNCD updates each regression coefficient and its corresponding subgradient simultaneously in each iteration. If it is 'sum_along_second_axis', loss values are summed up along the second axis (i.e. ‘Hedonic prices and the demand for clean air’, J. Environ. Note that for some losses, there are multiple elements per sample. Huber loss will still be useful, but you’ll have to use small values for . #>, 4 huber_loss standard 0.249 huber_loss ( data, ... ) # S3 method for data.frame huber_loss ( data, truth, estimate, delta = 1, na_rm = TRUE, ... ) huber_loss_vec ( truth, estimate, delta = 1, na_rm = TRUE, ...) If your predictions are totally off, your loss function will output a higher number.