get_inverse_GRAM

check_positive_definite

Function <code>get_inverse_GRAM()</code> allows to get inverse Gram matrix based on given
positive regularization constant lambda
Function <code>check_positive_definite()</code> returns logical value about n trials on
'is Gram matrix positive definite or not?' Just incorrect trial returns FALSE

internal

Incorporates Approximate Bayesian Computation to get a posterior distribution and to select a model optimal parameter for an observation point. Additionally, the meta-sampling heuristic algorithm is realized for parameter estimation, which requires no model runs and is dimension-independent. A sampling scheme is also presented that allows model runs and uses the meta-sampling for point generation. A predictor is realized as the meta-sampling for the model output. All the algorithms leverage a machine learning method utilizing the maxima weighted Isolation Kernel approach, or 'MaxWiK'. The method involves transforming raw data to a Hilbert space (mapping) and measuring the similarity between simulated points and the maxima weighted Isolation Kernel mapping corresponding to the observation point. Comprehensive details of the methodology can be found in the papers Iurii Nagornov (2024) <doi:10.1007/978-3-031-66431-1_16> and Iurii Nagornov (2023) <doi:10.1007/978-3-031-29168-5_18>.

Yuri Nagornov

MaxWiK

Machine Learning Method Based on Isolation Kernel Mean Embedding

get_inverse_GRAM function

<dl><dt>G</dt>
<dd>Gram matrix gotten via <code>GRAM_iKernel()</code> function</dd>
<dt>l</dt>
<dd>Lambda parameter or positive regularization constant</dd>
<dt>check_pos_def</dt>
<dd>Logical parameter to check the Gram matrix is positive definite or do not check</dd>
<dt>n</dt>
<dd>Number of iterations to check the positive definite property</dd></dl>

Arguments

<ul>
<li><code>check_positive_definite()</code>: The function to check the positive definite property of Gram matrix</li>
</ul>

Functions

The function to get inverse Gram matrix — get_inverse_GRAM

<dl>

<dt>G</dt>
<dd>Gram matrix gotten via <code>GRAM_iKernel()</code> function</dd>


<dt>l</dt>
<dd>Lambda parameter or positive regularization constant</dd>


<dt>check_pos_def</dt>
<dd>Logical parameter to check the Gram matrix is positive definite or do not check</dd>


<dt>n</dt>
<dd>Number of iterations to check the positive definite property</dd>

</dl>

get_inverse_GRAM: The function to get inverse Gram matrix

Description

Usage

Value

Arguments

Functions

Examples