11/19/2021 0 Comments Entropy Machine Learning
Difference between a discrete and a continuous loss function.Special Issue Machine Learning and Entropy: Discover Unknown Unknowns in Complex Data Sets. This procedure can be used to compute entropy, and consequently the free energy directly from a set of Monte Carlo configurations at a given. Subsequently, one can use virtually any machine learning classification algorithm for computing entropy. We translate the problem of calculating the entropy of a set of binary configurations/signals into a sequence of supervised classification tasks.The problem of induction has been given a modern machine learning form in the no-free lunch.In most cases, error function and loss function mean the same, but with a tiny difference.An error function measures/calculates how far our model deviates from correct prediction.A loss function operates on the error to quantify how bad it is to get an error of a particular size/direction, which is affected by the negative consequences that result in an incorrect prediction.A loss function can either be discrete or continuous.□ Keras Loss Functions: Everything You Need To Know□ PyTorch Loss Functions: The Ultimate GuideContinuous and discrete error/loss functionsWe’ll use two illustrations to understand continuous and discrete loss functions.Imagine you want to descend from the top of a big mountain on a cloudy day. Applying cross-entropy in deep learning frameworks PyTorch and TensorFlow.We define the cross-entropy cost function for this neuron by. We show that our method can calculate the entropy of various systems, both thermal and athermal, with state-of-the-art accuracy. (In binary classification and multi-class classification, understanding the cross-entropy formula)The estimation is performed with a recently proposed machine-learning algorithm which works with arbitrary network architectures that can be chosen to fit the structure and symmetries of the system at hand. The Cross-Entropy Loss Function. Machine learnings use of entropy isnt far from this concept of.In this case, the activation function applied is referred to as the sigmoid activation function.By doing the above, the error stops from being two students who failed SAT exams to more of a summation of each error on the student.Using probabilities for Illustration 2 will make it easier to sum the error(how far they are from passing) of each student, making it easier to move the prediction line in small steps until we get a minimum summation error.Exponential converts the probability to a range of 0-1We have n classes, and we want to find the probability of class x will be, with linear scores A1, A2… An, to calculate the probability of each class.The above function is the softmax activation function, where i is the class name.Understanding cross-entropy, it was essential to discuss loss function in general and activation functions, i.e., converting discrete predictions to continuous. Our example is what we call a binary classification, where you have two classes, either pass or fail. Sigmoid functionTo convert the error function from discrete to continuous error function, we need to apply an activation function to each student’s linear score value, which will be discussed later.For example, in Illustration 2, the model prediction output determines if a student will pass or fail the model answers the question, will student A pass the SAT exams?A continuous question would be, How likely is student A to pass the SAT exams? The answer to this will be 30% or 70% etc., possible.How do we ensure that our model prediction output is in the range of (0, 1) or continuous? We apply an activation function to each student’s linear scores. If we move small steps in the above example, we might end up with the same error, which is the case with discrete error functions.However, in Illustration 1, since the mountain slope is different, we can detect small variations in our height (error) and take the necessary step, which is the case with continuous error functions. We apply small steps to minimize the error. You step towards the chosen direction, thereby decreasing the height, repeating the same process, always decreasing the height until you reach your goal = the bottom of the mountain.To solve the error, we move the line to ensure all the positive and negative predictions are in the right area.In most real-life machine learning applications, we rarely make such a drastic move of the prediction line as we did above.We’ll discuss the differences when using cross-entropy in each case scenario. The average level of uncertainty refers to the error.Cross-entropy builds upon the idea of information theory entropy and measures the difference between two probability distributions for a given random variable/set of events.Cross entropy can be applied in both binary and multi-class classification problems. According to Shannon, the entropy of a random variable is the average level of “information,” “surprise,” or “uncertainty” inherent in the variable’s possible outcomes.We can see that the random variable’s entropy is related to our introduction concepts’ error functions. Cross-entropyClaude Shannon introduced the concept of information entropy in his 1948 paper, “A Mathematical Theory of Communication.
Entropy Hine Learning Free Energy DirectlyEntropy Hine Learning How To Apply CrossX = torch.randn( 10)Y = torch.randint( 2, ( 10,), dtype=torch.float)Let’s view the value of X: print(X) tensor([ 0.0421, -0.6606, 0.6276, 1.2491, -1.1535, -1.4137, 0.8967, -1.1786,Value of Y: print(y) tensor()In our discussions, we used the sigmoid function as the activation function of the inputs. Import torchUse the PyTorch random to generate the input features(X) and labels(y) values. Simple illustration of Binary cross Entropy using PytorchEnsure you have PyTorch installed follow the guidelines here. Let’s look at examples of how to apply cross-entropy: PyTorch1. Binary cross-entropy (BCE) formulaIn our four student prediction – model B:Yi = 1 if student passes else 0, therefore:We have discussed that cross-entropy loss is used in both binary classification and multi-class classification. House interior 3d modelBinary Cross Entropy: import tensorflow as tfLet’s say our actual and predicted values are as follows: actual_values = Predicted_values = Use the tensorflow BinaryCrossentropy() module: binary_cross_entropy = tf.keras.losses. Therefore we will not use an activation function as we did in the earlier example.We are still using the PyTorch random to generate the input features(X) and labels(y) values.Since this is a multi-class problem, the input features have five classes(class_0, class_1, class_2, class_3, class_4) X = torch.randn( 10, 5)Tensor(,]) y = torch.randint( 5, ( 10,))Print(y) tensor()The multi-class cross-entropy is calculated as follows: loss = nn.CrossEntropyLoss()(X, y)Calculating cross-entropy across different deep learning frameworks is the same let’s see how to implement the same in TensorFlow.1. Categorical Cross Entropy using PytorchPyTorch categorical Cross-Entropy module, the softmax activation function has already been applied to the formula. X_continous_values = torch.sigmoid(X)Tensor([ 0.5105, 0.3406, 0.6519, 0.7772, 0.2398, 0.1957, 0.7103, 0.2353, 0.2106,Pytorch Binary Cross-Entropy loss: loss = nn.BCELoss()(X_continous_values, y)2.
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