Multidimensional Data Approximation

Statistical medical data analysis encounters challenges such as missing data, model uncertainty, small datasets, and limited applicability of certain methods. The Approximation using Stochastic Kernel (ASK) method offers a solution by addressing these issues and improving interpolation, extrapolation, and approximation accuracy.

There are various problems in statistical medical data analysis. Missing data, or missing values, occur when no data value is stored for the variable in an observation.

Another data analysis problem is so-called model data uncertainty, if the proposed scientific model has more parameters than experimental data can supply. Small data also create an analysis problem for parametric approximation application and ensuring the continuity properties of a function during approximation.

These properties of the data do not allow the use of many effective methods, such as neural networks.
The accuracy of interpolation and extrapolation also depends on the methods used and may not be mutually supported at the same time.

Approximation using stochastic kernel (ASK) method is proposed to solve the following data point set analysis problems:

• Missing data • Small data • Model uncertainty • Model parameter independency • Interpolation accuracy • Extrapolation accuracy • Approximation accuracy

Theoretical Basis

The skilled team of specialists at AIDATO,  use a comprehensive approach to care, which means we look at each aspect of your data to find out which variables are contributing to or exacerbating your data.

Probabilistic Hypercube

Transforming multidimensional data to a unit probabilistic hypercube

Uncertainty minimization

Operator norm second order moment minimization

How to Achieve the Smallest Possible Error

Choosing the best kernel estimate

Example

Given Function

The function is given as z=F(x,y)

Approximation using Two points

Approximation using Four points

Approximation using Nine points

The given examples of approximation show convergence and precision process

Accuracy and Stability(Robustness)

The AIDATO method can beapplied to various classes of research tasks. Classification Task is one ofthem. Let's look at the accuracy and stability of themethod using the example of a classification problem and compare with otherknown methods.

Accuracy and Stability (Robustness)

Let’s define the following three geometrical zones

A set of random points are distributed as train points. This means that it is known exactly which zone each point belongs to. Note that the size and configuration of the zones are initially unknown to the methods

Now we randomly distribute new points and ask the mathematical method to "guess" which zone this point belongs to. Simulating this task several trails we can obtain the accuracy and stability of the methods

 As you can see from the comparative analysis of the accuracy of different methods the AITATO method is more precise and stable methods

Welcome to your small data analysis

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Prepare

Prepare your data in a simple table format file

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Upload

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Results

Get 3D charts or reports

The skilled team of specialists at AIDATO,  use a comprehensive approach to care,
which means we look at each aspect of your data to find out which
variables are contributing to or exacerbating your data.

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