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1.1.1 Examples. 1.1.2 Derivation of ... there is no net loss of kinetic energy into other forms such as heat, noise, ... These equations may be solved directly to ...
For example for an event that is 40% probable, one could say that the odds are "2 in 5", "2 to 3 in favor", or "3 to 2 against". When gambling, odds are often given as the ratio of the possible net profit to the possible net loss. However in many situations, you pay the possible loss ("stake" or "wager") up front and, if you win, you are paid ...
The loss function is a function that maps values of one or more variables onto a real number intuitively representing some "cost" associated with those values. For backpropagation, the loss function calculates the difference between the network output and its expected output, after a training example has propagated through the network.
In situation where one decision maker's gain (or loss) does not necessarily result in the other decision makers' loss (or gain), they are referred to as non-zero-sum. [10] Thus, a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the transaction, is in a non-zero-sum situation.
Expected loss is the sum of the values of all possible losses, each multiplied by the probability of that loss occurring. In bank lending (homes, autos, credit cards, commercial lending, etc.) the expected loss on a loan varies over time for a number of reasons. Most loans are repaid over time and therefore have a declining outstanding amount ...
For example, for any random variable with finite expectation, the Chebyshev inequality implies that there is at least a 75% probability of an outcome being within two standard deviations of the expected value. However, in special cases the Markov and Chebyshev inequalities often give much weaker information than is otherwise available.
In many applications, objective functions, including loss functions as a particular case, are determined by the problem formulation. In other situations, the decision maker’s preference must be elicited and represented by a scalar-valued function (called also utility function) in a form suitable for optimization — the problem that Ragnar Frisch has highlighted in his Nobel Prize lecture. [4]
In statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L 1 and L 2 penalties of the lasso and ridge methods. Nevertheless, elastic net regularization is typically more accurate than both methods with regard to reconstruction.