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IQN is a technique for minimizing a function which can be expressed as a sum of other functions. More...
Public Member Functions  
IQN (const double stepSize=0.01, const size_t batchSize=10, const size_t maxIterations=100000, const double tolerance=1e5)  
Construct the IQN optimizer with the given function and parameters. More...  
size_t  BatchSize () const 
Get the batch size. More...  
size_t &  BatchSize () 
Modify the batch size. More...  
size_t  MaxIterations () const 
Get the maximum number of iterations (0 indicates no limit). More...  
size_t &  MaxIterations () 
Modify the maximum number of iterations (0 indicates no limit). More...  
template < typename DecomposableFunctionType >  
double  Optimize (DecomposableFunctionType &function, arma::mat &iterate) 
Optimize the given function using IQN. More...  
double  StepSize () const 
Get the step size. More...  
double &  StepSize () 
Modify the step size. More...  
double  Tolerance () const 
Get the tolerance for termination. More...  
double &  Tolerance () 
Modify the tolerance for termination. More...  
Detailed Description
IQN is a technique for minimizing a function which can be expressed as a sum of other functions.
That is, suppose we have
IQN is the first stochastic quasi Newton method proven to converge superlinearly in a local neighborhood of the optimal solution.
For more information, please refer to:
This class is useful for datadependent functions whose objective function can be expressed as a sum of objective functions operating on an individual point. Then, IQN considers the gradient of the objective function operating on an individual point in its update of .
For IQN to work, the class must implement the following function:
size_t NumFunctions(); double Evaluate(const arma::mat& coordinates, const size_t i); void Gradient(const arma::mat& coordinates, const size_t i, arma::mat& gradient);
NumFunctions() should return the number of functions ( ), and in the other two functions, the parameter i refers to which individual function (or gradient) is being evaluated. So, for the case of a datadependent function, such as NCA (see mlpack::nca::NCA), NumFunctions() should return the number of points in the dataset, and Evaluate(coordinates, 0) will evaluate the objective function on the first point in the dataset (presumably, the dataset is held internally in the DecomposableFunctionType).
Constructor & Destructor Documentation
◆ IQN()
IQN  (  const double  stepSize = 0.01 , 
const size_t  batchSize = 10 , 

const size_t  maxIterations = 100000 , 

const double  tolerance = 1e5 

) 
Construct the IQN optimizer with the given function and parameters.
The defaults here are not necessarily good for the given problem, so it is suggested that the values used be tailored to the task at hand. The maximum number of iterations refers to the maximum number of points that are processed (i.e., one iteration equals one point; one iteration does not equal one pass over the dataset).
 Parameters

stepSize Step size for each iteration. batchSize Size of each batch. maxIterations Maximum number of iterations allowed (0 means no limit). tolerance Maximum absolute tolerance to terminate algorithm.
Member Function Documentation
◆ BatchSize() [1/2]
◆ BatchSize() [2/2]
◆ MaxIterations() [1/2]

inline 
◆ MaxIterations() [2/2]

inline 
◆ Optimize()
double Optimize  (  DecomposableFunctionType &  function, 
arma::mat &  iterate  
) 
Optimize the given function using IQN.
The given starting point will be modified to store the finishing point of the algorithm, and the final objective value is returned.
 Template Parameters

DecomposableFunctionType Type of the function to be optimized.
 Parameters

function Function to optimize. iterate Starting point (will be modified).
 Returns
 Objective value of the final point.
◆ StepSize() [1/2]
◆ StepSize() [2/2]
◆ Tolerance() [1/2]

inline 
◆ Tolerance() [2/2]

inline 
The documentation for this class was generated from the following file:
 /var/www/www.mlpack.org/mlpackgit/src/mlpack/core/optimizers/iqn/iqn.hpp
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