Asymptotic Convergence of Soft-Constrained Neural Networks for Density Estimation

Trentin, Edmondo

doi:10.3390/math8040572

Cited by 5 publications

(5 citation statements)

References 30 publications

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“…The asymptotic convergence of the resulting technique to the correct solution was formally proven in Ref. [25]. The ideas behind such integration methods are exploited in this paper, as well.…”

Section: Earlier Approaches To Ann-based Density Estimationmentioning

confidence: 89%

Multivariate Density Estimation with Deep Neural Mixture Models

Trentin

2023

Neural Process Lett

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Albeit worryingly underrated in the recent literature on machine learning in general (and, on deep learning in particular), multivariate density estimation is a fundamental task in many applications, at least implicitly, and still an open issue. With a few exceptions, deep neural networks (DNNs) have seldom been applied to density estimation, mostly due to the unsupervised nature of the estimation task, and (especially) due to the need for constrained training algorithms that ended up realizing proper probabilistic models that satisfy Kolmogorov’s axioms. Moreover, in spite of the well-known improvement in terms of modeling capabilities yielded by mixture models over plain single-density statistical estimators, no proper mixtures of multivariate DNN-based component densities have been investigated so far. The paper fills this gap by extending our previous work on neural mixture densities (NMMs) to multivariate DNN mixtures. A maximum-likelihood (ML) algorithm for estimating Deep NMMs (DNMMs) is handed out, which satisfies numerically a combination of hard and soft constraints aimed at ensuring satisfaction of Kolmogorov’s axioms. The class of probability density functions that can be modeled to any degree of precision via DNMMs is formally defined. A procedure for the automatic selection of the DNMM architecture, as well as of the hyperparameters for its ML training algorithm, is presented (exploiting the probabilistic nature of the DNMM). Experimental results on univariate and multivariate data are reported on, corroborating the effectiveness of the approach and its superiority to the most popular statistical estimation techniques.

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Section: Earlier Approaches To Ann-based Density Estimationmentioning

confidence: 89%

Multivariate Density Estimation with Deep Neural Mixture Models

Trentin

2023

Neural Process Lett

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“…the DNN parameters within the gradient-descent scheme used for the optimization. The asymptotic convergence of the resulting technique to the correct solution was formally proven in [23]. The ideas behind such integration methods are exploited in this paper, as well.…”

Section: Earlier Approaches To Ann-based Density Estimationmentioning

confidence: 96%

Multivariate Density Estimation with Deep Neural Mixture Models

Trentin¹

2020

Preprint

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Albeit worryingly underrated in the recent literature on machine learning in general (and, on deep learning in particular), multivariate density estimation is a fundamental task in many applications, at least implicitly, and still an open issue. With a few exceptions, deep neural networks (DNNs) have seldom been applied to density estimation, mostly due to the unsupervised nature of the estimation task, and (especially) due to the need for constrained training algorithms that ended up realizing proper probabilistic models that satisfy Kolmogorov's axioms. Moreover, in spite of the well-known improvement in terms of modeling capabilities yielded by mixture models over plain single-density statistical estimators, no proper mixtures of multivariate DNN-based component densities have been investigated so far. The paper fills this gap by extending our previous work on Neural Mixture Densities (NMMs) to multivariate DNN mixtures. A maximum-likelihood (ML) algorithm for estimating Deep NMMs (DN-MMs) is handed out, which satisfies numerically a combination of hard and soft constraints aimed at ensuring satisfaction of Kolmogorov's axioms. The class of probability density functions that can be modeled to any degree of precision via DNMMs is formally defined. A procedure for the automatic selection of the DNMM architecture, as well as of the hyperparameters for its ML training algorithm, is presented (exploiting the probabilistic nature of the DNMM). Experimental results on univariate and multivariate data are reported on, corroborating the effectiveness of the approach and its superiority to the most popular statistical estimation techniques.

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“…For that purpose we downloaded data of 36 samples of cancer genes (Table 1) from the online database Catalogue of Somatic Mutations in Cancer (COSMIC) with sample name PD7301a and COSMIC sample ID COSS1540693 [34]; the tumour location is in the bone; the pelvis (chondrosarcoma; central); see also Appendix E for the AX1 gene. In Figure 9, one can see the difference in the calculation of the Chern-Simons current in the ALX1 gene for cancer (red) and normal (blue) gene versions; the change is better visible in the computation of (ITD − IMF)chain 1 (8). In Figures 10 and 11 are presented results for the tensor correlation of the Chern-Simons current from (ITD − IMF)chain 1 (1) and (ITD − IMF)chain 1 (6) between normal (blue) and cancer (red) genes in selected 28 samples of bone cancer.…”

Section: Empirical Analysis Of Cancer Gene Signaturementioning

confidence: 99%

“…The suppersymetry approach [7] was also used for the model of graphene wormhole and for the computation of the Chern-Simons current in a Josephson junction of superconductor states in the graphene. Additionally, the applications of neural networks for density estimation [8] outperformed parametric and non-parametric approaches.…”

Section: Introductionmentioning

confidence: 99%

A Supersymmetry and Quantum Cryptosystem with Path Integral Approach in Biology

2020

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The source of cancerous mutations and the relationship to telomeres is explained in an alternative way. We define the smallest subunit in the genetic code as a loop braid group element. The loop braid group is suitable to be defined as a configuration space in the process of converting the information written in the DNA into the structure of a folded protein. This smallest subunit, or a flying ring in our definition, is a representation of 8-spinor field in the supermanifold of the genetic code. The image of spectral analysis from the tensor correlation of mutation genes as our biological system is produced. We apply the loop braid group for biology and authentication in quantum cryptography to understand the cell cocycle and division mechanism of telomerase aging. A quantum biological cryptosystem is used to detect cancer signatures in 36 genotypes of the bone ALX1 cancer gene. The loop braid group with the RSA algorithm is applied for the calculation of public and private keys as cancer signatures in genes. The key role of this approach is the use of the Chern–Simons current and then the fiber bundle representation of the genetic code that allows a quantization procedure.

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Asymptotic Convergence of Soft-Constrained Neural Networks for Density Estimation

Cited by 5 publications

References 30 publications

Multivariate Density Estimation with Deep Neural Mixture Models

Multivariate Density Estimation with Deep Neural Mixture Models

Multivariate Density Estimation with Deep Neural Mixture Models

A Supersymmetry and Quantum Cryptosystem with Path Integral Approach in Biology

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