Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems.
- Keywords
- funkce hazardu, FLIPI, Follicular Lymphoma International Prognostic Index, overfitting,
- MeSH
- Algorithms MeSH
- Survival Analysis MeSH
- Bayes Theorem MeSH
- Confounding Factors, Epidemiologic MeSH
- Lymphoma, Follicular * MeSH
- Humans MeSH
- Logistic Models MeSH
- Decision Support Techniques MeSH
- Neural Networks, Computer MeSH
- Odds Ratio MeSH
- Probability MeSH
- Prognosis * MeSH
- Models, Statistical MeSH
- Statistics as Topic MeSH
- Support Vector Machine MeSH
- Check Tag
- Humans MeSH
... Contents -- Our Goal i -- 1 Like Programming, Mathematics has a Culture 1 -- 2 Polynomials 5 -- 2.1 Polynomials ... ... Optimization Flammer 263 -- 14.9 Gradients of Computation Graphs 264 -- 14.10 Application: Automatic Differentiation ... ... and a Simple Neural Network 267 -- 14.11 Cultural Review 283 -- 14.12 Exercises 283 -- 14.13 Chapter ...
First edition iii, 365 stran : ilustrace ; 25 cm
