Confidence Probability Research Articles

Deep attention ConvLSTM-based adaptive fusion of clear-sky physical prior knowledge and multivariable historical information for probabilistic prediction of photovoltaic power

Photovoltaic (PV) power is an important way to utilize solar energy. Accurate PV power forecast is crucial to the large-scale application of PV power and the stability of electricity grid. This paper proposes a novel method for short-term photovoltaic power forecast using deep attention convolutional long short-term memory (ConvLSTM) network and kernel density estimation (KDE). ConvLSTM has strong ability to automatically extract the information from multiple variables related to PV power and the temporal information from historical PV data. Considering that clear-sky solar radiation is an important physical prior knowledge in PV power generation, attention mechanism is innovatively introduced into ConvLSTM to dynamically and adaptively adjust the weights of the physical prior knowledge and the historical PV data in forecast. KDE is used for estimating the joint probabilistic density function and giving the probabilistic confidence interval. Experiments in the three-year actual photovoltaic power data of two provinces in Belgium verified the effectiveness of the proposed method. Comparison experiments were made with naive persistence and other eight conventional methods including autoregressive integrated moving average with exogenous variable (ARIMAX) model, convolutional neural network (CNN), long short-term memory (LSTM) network, multilayer perceptron (MLP), support vector regression (SVR), extreme learning machine (ELM), classification and regression tree (CART) and gradient boosting decision tree (GBDT). Experiments show that the proposed method can realize the optimal fusion of the historical data and clear-sky prior knowledge, and significantly improve the PV power forecast accuracy in all seasons of a year.

Scene-Specialized Multitarget Detector with an SMC-PHD Filter and a YOLO Network.

You only look once (YOLO) is one of the most efficient target detection networks. However, the performance of the YOLO network decreases significantly when the variation between the training data and the real data is large. To automatically customize the YOLO network, we suggest a novel transfer learning algorithm with the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter and Gaussian mixture probability hypothesis density (GM-PHD) filter. The proposed framework can automatically customize the YOLO framework with unlabelled target sequences. The frames of the unlabelled target sequences are automatically labelled. The detection probability and clutter density of the SMC-PHD filter and GM-PHD are applied to retrain the YOLO network for occluded targets and clutter. A novel likelihood density with the confidence probability of the YOLO detector and visual context indications is implemented to choose target samples. A simple resampling strategy is proposed for SMC-PHD YOLO to address the weight degeneracy problem. Experiments with different datasets indicate that the proposed framework achieves positive outcomes relative to state-of-the-art frameworks.

Revisiting model’s uncertainty and confidences for adversarial example detection

Security-sensitive applications that rely on Deep Neural Networks (DNNs) are vulnerable to small perturbations that are crafted to generate Adversarial Examples. The (AEs) are imperceptible to humans and cause DNN to misclassify them. Many defense and detection techniques have been proposed. Model’s confidences and Dropout, as a popular way to estimate the model’s uncertainty, have been used for AE detection but they showed limited success against black- and gray-box attacks. Moreover, the state-of-the-art detection techniques have been designed for specific attacks or broken by others, need knowledge about the attacks, are not consistent, increase model parameters overhead, are time-consuming, or have latency in inference time. To trade off these factors, we revisit the model’s uncertainty and confidences and propose a novel unsupervised ensemble AE detection mechanism that 1) uses the uncertainty method called SelectiveNet, 2) processes model layers outputs, i.e. feature maps, to generate new confidence probabilities. The detection method is called SFAD. Experimental results show that the proposed approach achieves better performance against black- and gray-box attacks than the state-of-the-art methods and achieves comparable performance against white-box attacks. Moreover, results show that SFAD is fully robust against High Confidence Attacks (HCAs) for MNIST and partially robust for CIFAR10 datasets.1

METHODOLOGICAL ASPECTS OF ASSESSING THE COMPETENCE OF LABORATORY PERSONNEL DETERMINING THE QUALITY OF SEED POTATOES

Most of the quality indicators regulated by the standard for seed potato certification are determined by the subjective component, that is, the competence of the personnel. However, the regulatory framework does not establish criteria for assessing competence, which poses uncontrolled risks in the laboratory. The purpose of the study is to develop and investigate the methodology for assessing the competence of laboratory personnel involved in the testing of seed potatoes and determine the extent of application of the methodology. The methods of probability theory and mathematical statistics are used for the tasks of selection and research of statistical criteria that correspond to the law of distribution of the obtained data and provide the necessary reliability for the available sample volumes. The statistics and the method of determining the threshold value, which mathematically describes the decision-making on competence, are provided for the binomial distribution law. The properties of the proposed statistical method for assessing the competence of personnel in terms of finding the maximum differences in the results of the analysis, at which the personnel are recognised as competent, are investigated. The study demonstrates the dependence of the method capacity on the data volume. It is determined that to obtain a confidence probability of 0.95 for quality indicators, the content of which in the average sample according to the technical conditions is minimal, the sample size should be 600-1000 tubers. At the same time, up to 100 tubers are sufficient for indicators whose content is under 5%. The method proposed by the authors showed that the average sample of 250 tubers recommended by the standard is entirely justified in terms of attracting resources during certification but must be adjusted during competence monitoring in a testing laboratory that confirms its competence by the requirements of DSTU ISO IEC 17025:2019. The findings presented can be used by the personnel in the seed testing laboratories as a measure to minimise the risks caused by the impact of personnel incompetence

Hybrid Method for Detecting Anomalies in Cosmic ray Variations Using Neural Networks Autoencoder

Cosmic rays were discovered by the Austrian physicist Victor Hess in 1912 in a series of balloon experiments performed between 1911 and 1912. Cosmic rays are an integral part of fundamental and applied research in the field of solar–terrestrial physics and space weather. Cosmic ray data are applied in different fields from the discovery of high-energy particles coming to Earth from space, and new fundamental symmetries in the laws of nature, to the knowledge of residual matter and magnetic fields in interstellar space. The properties of interplanetary space are determined from intensity variations, angular distribution, and other characteristics of galactic cosmic rays. The measure of cosmic ray flux intensity variability is used as one of the significant space weather factors. The negative impact of cosmic rays is also known. The negative impact can significantly increase the level of radiation hazard and pose a threat to astronauts, crews, and passengers of high-altitude aircraft on polar routes and to modern space equipment. Therefore, methods aimed at timely detection and identification of anomalous manifestations in cosmic rays are of particular practical relevance. The article proposes a method for analyzing cosmic ray variations and detecting anomalous changes in the rate of galactic cosmic ray arrival to the Earth. The method is based on a combination of the Autoencoder neural network with wavelet transform. The use of non-linear activation functions and the ability to flexibly change the structure of the network provide the ability of the Autoencoder to approximate complex dependencies in the recorded variations of cosmic rays. The article describes the numerical operations of the method implementation. Verification of the adequacy of the neural network model is based on the use of Box–Ljung Q-statistics. On the basis of the wavelet transform constructions, data-adaptive operations for detecting complex singular structures are constructed. The parameters of the applied threshold functions are estimated with a given confidence probability based on the α-quantiles of Student’s distribution. Using data from high-latitude neutron monitor stations, it is shown that the proposed method provides efficient detection of anomalies in cosmic rays during increased solar activity and magnetic storms. Using the example of a moderate magnetic storm on 10–11 May 2019, the necessity of applying different methods and approaches to the study of cosmic ray variations is confirmed, and the importance of taking them into account when making space weather forecast is shown.

Constant Time Graph Neural Networks

The recent advancements in graph neural networks (GNNs) have led to state-of-the-art performances in various applications, including chemo-informatics, question-answering systems, and recommender systems. However, scaling up these methods to huge graphs, such as social networks and Web graphs, remains a challenge. In particular, the existing methods for accelerating GNNs either are not theoretically guaranteed in terms of the approximation error or incurred at least a linear time computation cost. In this study, we reveal the query complexity of the uniform node sampling scheme for Message Passing Neural Networks, including GraphSAGE, graph attention networks (GATs), and graph convolutional networks (GCNs). Surprisingly, our analysis reveals that the complexity of the node sampling method is completely independent of the number of the nodes, edges, and neighbors of the input and depends only on the error tolerance and confidence probability while providing a theoretical guarantee for the approximation error. To the best of our knowledge, this is the first article to provide a theoretical guarantee of approximation for GNNs within constant time. Through experiments with synthetic and real-world datasets, we investigated the speed and precision of the node sampling scheme and validated our theoretical results.

The Impacts of FDI, ODA, and LS on Gross Domestic Product in Cambodia: A Comparative Analysis

The study focus mainly on the impact of ODA, FDI, and LS on the GDP growth of Cambodia from 1995 to 2020 using the combined data generated from Macrotrends LLC (2021); Trading Economics (2021); World Bank Group (2021a; 2021b; 2021c & Cambodia Public Debt Statistical Bulletin (2015; 2016; 2017; 2018; 2019; 2020; 2021) and the Eviews 10 was used as a tool to analyze the data by applying the multivariate regression with ordinary least squares method. The result confirmed that FDI and LS are significant and positively contributed to the GDP growth of Cambodia with almost 100% confident interval or probability of 0.02%, and the ODA was evidently insignificant and also negatively impacted on the economic growth of Cambodia. The researcher also suggested for further researches in order to clarify the lapses of this study.

FEATURES OF QUANTITATIVE ESTIMATION OF FLAVONOID CONTENT IN JUGLANS NIGRA L. BARKS PREPARATIONS

The aim of the research is the development of quantification procedures of flavonoids in Juglans nigra L. barks preparations using modern instrumental analytical techniques (spectrophotometry, high performance liquid chromatography).Materials and methods. The subjects of research were tincture and dry extract of Juglans nigra L. bark, the samples of which were prepared in March and April 2020 in the Botanical Garden of Samara State Medical University (Samara); the standard samples (SS) of myricitrin, myricetin. The registration of the electronic spectra was carried out with a spectrophotometer «Specord 40» (Analytik Jena, Germany). The chromatographic analysis was carried out by the method of reversed-phase HPLC on a microcolumn liquid chromatograph “Milichrom-6” (NPAO “Nauchpribor”, Russia).Results. Using differential spectrophotometry, methods for the quantitative determination of the total amount of flavonoids in terms of myricitrin in the tincture and dry extract of Juglans nigra L. bark, has been developed. It has been determined that the content of the total amount of flavonoids in terms of myricitrin in the tincture and dry extract of Juglans nigra L., is 0.84±0.07% and 12.38±0.24%, respectively. The error of a single determination of the total amount of flavonoids in terms of myricitrin in the tincture and dry extract of Juglans nigra L. bark with a confidence probability of 95%, is ± 8.91% and ± 2.10%, respectively. Methods for the quantitative determination of myricitrin in the tincture and dry extract of Juglans nigra L. bark by HPLC has been developed. The content of the dominant flavonoid – myricitrin (myricetin-3-O-α-L-rhamnopyranoside) – in the tincture and dry extract of Juglans nigra L., was 0.42±0.06% and 8.45±0.24%, respectively. The error of the single determination of myricitrin in the tincture and dry extract of Juglans nigra L. with a confidence probability of 95% is ± 15.04% and ±2.96%, respectively.Conclusion. The developed methods for the quantitative determination of flavonoids in the preparations of Juglans nigra L. barks L. can be used in solving the problems of standardization of Juglans nigra L. preparations.

Improving a procedure for determining the factors that influence the need of higher education institutions for specialists of the highest qualification

A method for calculation of coefficients of the impact of factors on the need for specialists of the highest qualification was proposed. The method is based on expert evaluation methods, in particular, on determining the importance, degree of realization, and tendency of factors that affect the need for highly qualified specialists. The method implements the unit of data reliability verification based on the Kendall coefficient of concordance and Pearson criterion. The method applies an original approach to determining the competence of experts, in particular, by taking into consideration self-evaluation, mutual evaluation, and objective evaluation. The proposed method makes it possible to take into account the influence of factors on the need for specialists of the highest qualification with the possibility of forecasting. The totality of factors that influence the need for specialists of the highest qualification and the magnitude of their impact was determined. They were determined by calculating the indicators of each of the criteria regarding importance, realization, and tendency. Determining was carried out using the algorithm for calculating the coefficients of influence of the factors on the need for specialists of the highest qualification. In general, the following groups of factors were determined: conditions of scientific and scientific-pedagogical activity at a certain institution of higher education, the attractiveness of scientific and scientific-pedagogical activity in a certain country (region), development of industry (speciality). A group of 30 experts was selected to determine the numerical values of the factors, which satisfies the condition for achieving a confidence probability of 0.94. The results of the evaluation of expert judgments revealed that the most influential factors are: social protection (0.87), budget for higher education (0.99), remuneration (0.9), and prestige of scientific and pedagogical activities (0.91). The least influential are: the number of primary positions in the area (0.48) and self-realization opportunities at a higher education institution (0.58).

Taming the Green Swan: a criteria-based analysis to improve the understanding of climate-related financial risk assessment tools

ABSTRACT Understanding climate-related risks has become a key priority in financial decision-making and for regulatory supervision in the financial sector since the Task-force on Climate-related Financial Disclosures (TCFD) launched its recommendations on climate risk disclosures in 2017. However, a systematic approach to identify scientifically sound and decision-useful climate risk indicators and the tools to derive such risk metrics is still missing. Focusing on climate-related financial transition risks, we propose a set of analysis criteria rooted in climate science, economics, finance, and risk management, to assess whether climate transition risk analysis tools provide high quality, comparable, and decision-relevant results. We find that for a sample of 16 climate transition risk tools, some tools perform high on all criteria, but that especially model transparency, scenario flexibility, output-related uncertainties, and assumptions communication require considerable improvements. Financial supervisors and regulators should define appropriate ways to obtain comparable climate risk metrics, to ensure their interpretability, and to ensure that climate risk metric disclosures reflect the underlying assumptions and uncertainties surrounding the analyses. Researchers and any user of climate risk metrics should carefully understand and report the analysis tools’ setup, and interpret their findings in light of the analysis assumptions. Key policy insights Providers of climate risk analysis tools should increase transparency on the tools’ setup in standardized templates. Reporting templates should include information on whether the tool has been peer-reviewed, the depth of risk analysis, key modelling steps and underlying assumptions. Firms should report the tool setup and modelling assumptions in their voluntary climate-related disclosures. In addition, uncertainties surrounding the analysis should be reported, for example, via confidence intervals or probability distributions. Financial regulators and corporate reporting regulation should ensure that mandatory climate risk disclosures are understandable and comparable. Regulators should ask firms to disclose their risks based on harmonized climate risk metrics disclosure templates, to ensure that key assumptions, the model setup, limitations of the analyses and analysis uncertainties are reported alongside the metrics.

A Closed-Loop Assembly Network Optimization Based on Chance Constraint with Robust Approximation

In this paper, an optimization algorithm of forward-reverse cyclic assembly network under uncertainty is studied. A chance constrained algorithm based on robust approximation is adopted, in which the size of uncertain set is used to describe the violation probability of constraint. Further, some parameters are set to describe the confidence probability of the model. By implementing the proposed algorithm, we can reduce the manufacturing cost of the final forward-reverse cycle assembly network by 3.17% while ensuring a certain confidence probability, and relax the lower bound of the probability of the model, which makes the model more adaptable. By calculating the scheduling data and comparing with flexible robust optimization, the effectiveness of the algorithm is proved.

Constrained Gaussian Condensation Filter for Cooperative Target Tracking

Real-time high-precision navigation has many applications, such as pedestrian navigation, emergency rescue, and vehicle networks. In practice, the measurement models are often nonlinear, and sequential Bayesian filters, such as Kalman and particle filter, suffer from accumulative errors, which cannot provide long-time high-precision services for localization. To solve arbitrary noise distribution, this article proposes a Gaussian condensation filter (GCF) algorithm to achieve high-precision localization in a non-Gaussian noise environment. To this end, we proposed an error-ellipse resampling (EER)-based GCF (EER-GCF), which establishes error ellipses with different confidence probabilities and implements a resampling algorithm based on the sampling points’ geometrical positions. Furthermore, a cooperative EER-based GCF (CEER-GCF) is proposed to enhance information fusion in the multitarget network. This study accomplishes cooperative tracking based on spatial–temporal constraints to enhance error correction. The experimental results show that CEER-GCF can effectively eliminate the accumulative error and optimize state estimation, which outperforms state of the arts, such as unscented Kalman filter and particle filter.

Контроль и регулирование влажности бумажного полотна

Product quality is a key indicator of the positive outcome of pulp and paper production. Moisture content is one of the main paper quality characteristics. The moisture profile across the paper web width shows possible shortcomings of the process equipment which, if corrected, will improve the consumer properties of paper and enhance economic efficiency. The research aims to assess whether the moisture content measurement results meet the requirements of the process regulations in the steady-state and transient modes of paper machine operation as well as the uniformity of the moisture profile in the cross direction. Data from the scanning device at high and low resolution were processed using statistical methods in order to assess the quality of the automatic paper web moisture control system. It was determined that in the steady-state mode of paper machine operation the moisture content meets the requirements of the regulations with a confidence probability of 0.95; in the transient mode of operation it exceeds the upper limit by 6 %. It has been found that the automated moisture control system eliminates this fault in 340 s. The coefficient of variation was used as a criterion for evaluating the uniformity of the moisture profile across the paper web width. The hypothesis of a trend line in the moisture profile across the paper web width was confirmed and a trend line equation was obtained using regression analysis techniques. The moisture profile was modeled while eliminating the technological factor that systematically affects the uniformity. It is proven that the elimination of the fault will reduce the coefficient of variation and therefore improve the uniformity of the profile by 41.2 % in the steady-state mode of paper machine operation. In the transition mode of operation the moisture profile improves slightly. The proposed algorithm for studying the moisture profile of paper, its modeling after corrections of the control object can be used in systems for controlling the quality of paper in the transverse direction. For citation: Koryakovskaya N.V., Bederdinova O.I. Monitoring and Control of Paper Web Moisture. Lesnoy Zhurnal [Russian Forestry Journal], 2022, no. 1, pp. 188–204. DOI: 10.37482/0536-1036-2022-1-188-204

Economic Evaluation of Telemedicine Consultations to Reduce Unnecessary Neonatal Care Transfers

To perform an economic evaluation to estimate the return on investment (ROI) of making available telemedicine consultations from a healthcare payer perspective, and to estimate the economic impacts of telemedicine under a hypothetical scenario in which all rural hospitals providing level I neonatal care in California had access to telemedicine consultations from neonatologists at level III and level IV neonatal intensive care units (NICUs). We developed standard decision models with assumptions derived from primary data and the literature. Telemedicine costs included equipment installation and operation costs. Probabilistic analysis with Monte Carlo simulation was performed to address model uncertainties and to estimate 95% probabilistic confidence intervals (PCIs). All costs were adjusted to 2017 US dollars using the Consumer Price Index. Our probabilistic analysis estimated the ROI to have a mean value of 2.23 (95% PCI, -0.7 to 6.0). That is, a $1 investment in this telemedicine model would yield a net medical expenditure saving of $1.23. "Cost saving" was observed for 75% of the hypothetical 1000 Monte Carlo simulations. For the state of California, the estimated mean annual net savings was $661000. Providing telemedicine and making available consultations to rural hospitals providing level I neonatal care are likely to reduce medical expenditures by reducing potentially avoidable transfers of newborns to level III and IV NICUs, offsetting all telemedicine-related costs.

State-based confidence bounds for data-driven stochastic reachability using Hilbert space embeddings

In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides probabilistic assurances of safety for stochastic systems in a model-free manner. By implicitly embedding the stochastic kernel of a Markov control process in a reproducing kernel Hilbert space, we can approximate the safety probabilities for stochastic systems with arbitrary stochastic disturbances as simple matrix operations and inner products. We present finite sample bounds for point-based approximations of the safety probabilities through construction of probabilistic confidence bounds that are state- and input-dependent. One advantage of this approach is that the bounds are responsive to non-uniformly sampled data, meaning that tighter bounds are feasible in regions of the state- and input-space with more observations. We numerically evaluate the approach, and demonstrate its efficacy on a neural network-controlled pendulum system.

Hybrid probabilistic timing analysis with Extreme Value Theory and Copulas

The primary challenge of time-critical systems is to guarantee that a task completes its execution before its deadline. In order to ensure compliance with timing requirements, it is necessary to analyze the timing behavior of the overall software. Worst-Case Execution Time (WCET) represents the maximum amount of time an individual software unit takes to execute and is used for scheduling analysis in safety-critical systems. Recent studies focus on statistical approaches, which augments measurement-based timing analysis with probabilistic confidence level by applying stochastic methods. Common approaches either utilize Extreme Value Theory (EVT) for end-to-end measurements or convolution techniques for a group of program units to derive probabilistic upper bounds for the program. The former method does not ensure path coverage while the latter suffers from ignoring possible extreme cases. Furthermore, current state-of-the-art convolution methods employed in a commercial WCET analysis tool overestimates the results because of using the assumption of worst-case dependence between basic blocks. In this paper, we propose a hybrid probabilistic timing analysis framework and modeling the program units with EVT to capture extreme cases and use Copulas to model the dependency between the units to derive tighter distributional bounds in order to mitigate the effects of co-monotonic assumptions.

MPMR: Multi-Scale Feature and Probability Map for Melanoma Recognition.

Malignant melanoma (MM) recognition in whole-slide images (WSIs) is challenging due to the huge image size of billions of pixels and complex visual characteristics. We propose a novel automatic melanoma recognition method based on the multi-scale features and probability map, named MPMR. First, we introduce the idea of breaking up the WSI into patches to overcome the difficult-to-calculate problem of WSIs with huge sizes. Second, to obtain and visualize the recognition result of MM tissues in WSIs, a probability mapping method is proposed to generate the mask based on predicted categories, confidence probabilities, and location information of patches. Third, considering that the pathological features related to melanoma are at different scales, such as tissue, cell, and nucleus, and to enhance the representation of multi-scale features is important for melanoma recognition, we construct a multi-scale feature fusion architecture by additional branch paths and shortcut connections, which extracts the enriched lesion features from low-level features containing more detail information and high-level features containing more semantic information. Fourth, to improve the extraction feature of the irregular-shaped lesion and focus on essential features, we reconstructed the residual blocks by a deformable convolution and channel attention mechanism, which further reduces information redundancy and noisy features. The experimental results demonstrate that the proposed method outperforms the compared algorithms, and it has a potential for practical applications in clinical diagnosis.

Aliasing Black Box Adversarial Attack with Joint Self-Attention Distribution and Confidence Probability

Aliasing Black Box Adversarial Attack with Joint Self-Attention Distribution and Confidence Probability

КОРРЕЛЯЦИОННЫЙ АНАЛИЗ ФАКТОРОВ, ВЛИЯЮЩИХ НА УРОВЕНЬ БАКТЕРИАЛЬНОЙ ОБСЕМЕНЕННОСТИ МОЛОКА

When analyzing raw milk properties, we should take into account the complexity and ambiguity of the “bacterial contamination” criterion. The authors evaluated the influence of physico-chemical and microbiological parameters of milk on its contamination over a year period. Milk testing protocols for 2020 were used as a source of information. The values of acidity, the number of mesophilic aerobic and facultative anaerobic microorganisms (CMAFAnM), the number of somatic cells, the proportion of protein and fat, and the density of milk were studied. To assess the influence of environmental parameters, the authors took ionto account the values of air temperature and humidity at the moment of sampling. Sampling was carried out according to GOST 26809.1-2014 “Milk and dairy products. Acceptance rules, sampling methods, and sample preparation for analysis”. The research was carried out on three dairy farms of the Knyaginino district of the Nizhny Novgorod region. They included a dairy farm with tie-up housing for 200 heads with milking in a linear type milk pipeline; a dairy farm with loose housing for 400 heads with milking in a herringbone type milk pipeline; a dairy farm with combined (tie-up and loose) housing for 450 heads with milking in a linear-type milk pipeline. The lowest indicator of QMAFAnM (total viable content) was noticed in March, and the highest – in November. The correlation analysis showed that the greatest influence of the studied factors on the level of bacterial contamination is exerted by the number of somatic cells (Pearson correlation coefficient R = 0.71 with a confidence probability P = 0.0619). The authors suppose that this situation may result from improper hygienic condition of the udder, equipment, and premises. There was a weak influence on the level of bacterial contamination of milk density (R = –0.18 at P = 0.096) and ambient air temperature (R = –0.18 at P = 0.095), which may be result from insufficient cooling of milk before transportation.

Эффект перехода от применения бинарных искусственных нейронов к троичным нейронам при совместном использовании пяти классических статистических критериев проверки гипотез нормальности или равномерности распределений малых выборок

The work purpose is to show the advantages of moving from ordinary binary neurons to more complex neurons with ternary output quantization. As an example, a neural network combination of five classical statistical criteria is considered: Geary (1935), David-Hartley-Pearson (1954), Shapiro-Wilk (1965), Maximum deviation from the center (1965), Ali-Chergo-Revis (1992). A forecast of combining these criteria with others is given, built with confidence probability is equal to 0.99. The binary artificial neurons using will require the use of 280 statistical criteria. The conversion to the artificial neurons using with ternary quantizers should reduce the neurons number to 9 for small samples of 16 experiments. An exponential decreasing of the necessary neurons number is seen.