View source for Objective vs. Cost vs. Loss vs. Error Function

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* [[Agents#AI Agent Optimization|AI Agent Optimization]] ... [[Optimization Methods]] ... [[Optimizer]] ... [[Objective vs. Cost vs. Loss vs. Error Function]] ... [[Exploration]]
* [[Backpropagation]] ... [[Feed Forward Neural Network (FF or FFNN)|FFNN]] ... [[Forward-Forward]] ... [[Activation Functions]] ...[[Softmax]] ... [[Loss]] ... [[Boosting]] ... [[Gradient Descent Optimization & Challenges|Gradient Descent]] ... [[Algorithm Administration#Hyperparameter|Hyperparameter]] ... [[Manifold Hypothesis]] ... [[Principal Component Analysis (PCA)|PCA]]
* [[AI Solver]] ... [[Algorithms]] ... [[Algorithm Administration|Administration]] ... [[Model Search]] ... [[Discriminative vs. Generative]] ... [[Train, Validate, and Test]]
* [http://towardsdatascience.com/error-analysis-to-your-rescue-773b401380ef Error Analysis to Your Rescue! | Kritika Jalan] 
* [http://heartbeat.fritz.ai/5-regression-loss-functions-all-machine-learners-should-know-4fb140e9d4b0 5 Regression Loss Functions All Machine Learners Should Know | Prince Grover]
* [[Process Supervision]]


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"The function we want to minimize or maximize is called the objective function, or criterion. When we are minimizing it, we may also call it the cost function, [[Loss|loss function]], or error function - these terms are synonymous. The cost function is used more in optimization problem and [[Loss|loss function]] is used in parameter estimation.

The [[Loss|loss function (or error)]] is for a single training example, while the cost function is over the entire training set (or mini-batch for mini-batch gradient descent). Therefore, a [[loss]] function is a part of a cost function which is a type of an objective function.  [http://stats.stackexchange.com/questions/179026/objective-function-cost-function-loss-function-are-they-the-same-thing Objective function, cost function, loss function: are they the same thing? | StackExchange]

* <b>[[Loss|Loss function]]</b> is usually a function defined on a data point, prediction and label, and measures the penalty. For example:
** square loss l(f(xi|θ),yi)=(f(xi|θ)−yi)2, used in linear [[Regression]]
** hinge loss l(f(xi|θ),yi)=max(0,1−f(xi|θ)yi), used in SVM
** 0/1 loss l(f(xi|θ),yi)=1⟺f(xi|θ)≠yi, used in theoretical analysis and definition of accuracy

* <b>Cost function</b> is usually more general. It might be a sum of [[Loss|loss functions]] over your training set plus some model complexity penalty (regularization). For example:
** Mean Squared Error MSE(θ)=1N∑Ni=1(f(xi|θ)−yi)2
** SVM cost function SVM(θ)=∥θ∥2+C∑Ni=1ξi (there are additional constraints connecting ξi with C and with training set)

* <b>Objective function</b> is the most general term for any function that you optimize during training. For example, a probability of generating training set in maximum likelihood approach is a well defined objective function, but it is not a [[Loss|loss function]] nor cost function (however you could define an equivalent cost function). For example:
** MLE is a type of objective function (which you maximize)
**Divergence between classes can be an objective function but it is barely a cost function, unless you define something artificial, like 1-Divergence, and name it a cost

* <b>Error function</b> - [[Backpropagation]]; or automatic differentiation, is commonly used by the gradient descent optimization algorithm to adjust the [[Activation Functions#Weights|weight]] of neurons by calculating the gradient of the [[Loss|loss function]]. This technique is also sometimes called backward propagation of errors, because the error is calculated at the output and distributed back through the network layers. [http://en.wikipedia.org/wiki/Backpropagation Backpropagation | Wikipedia]


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