Conditional Probability Distribution Research Articles

Seismic Fragility and Risk Assessment of a Nuclear Power Plant Containment Building for Seismic Input Based on the Conditional Spectrum

A procedure for the seismic fragility assessment of nuclear power plants by applying ground motions compatible with the conditional probability distribution of a conditional spectrum (CS) is presented with a case study of a containment building. Three CSs were constructed using different control frequencies to investigate the influence of the control frequency. Horizontal component-to-component directional variability was introduced by randomly rotating the horizontal axes of the recorded ground motions. Nonlinear lumped mass stick models were constructed using variables distributed by Latin hypercube sampling to model the uncertainty. An incremental dynamic analysis was performed, and seismic fragility curves were calculated. In addition, a seismic input based on a uniform hazard response spectrum (UHRS) was applied to the seismic fragility assessment for comparison. By selecting a control frequency dominating the seismic response, the CS-based seismic input produces an enhanced ‘high confidence of low probability of failure’ capacity and lower seismic risk than the UHRS-based seismic input.

Multi-Source Selection Transfer Learning with Privacy-Preserving

Transfer learning has ability to create learning task of weakly labeled or unlabeled target domain by using knowledge of source domain to help, which can effectively improve the performance of target learning task. At present, the increased awareness of privacy protection restricts access to data sources and poses new challenges to the development of transfer learning. However, the research on privacy protection in transfer learning is very rare. The existing work mainly uses differential privacy technology and does not consider the distribution difference between data sources, or does not consider the conditional probability distribution of data, which causes negative transfer to harm the effect of algorithm. Therefore, this paper proposes multi-source selection transfer learning algorithm with privacy-preserving MultiSTLP, which is used in scenarios where target domain contains unlabeled data sets with only a small amount of group probability information and multiple source domains with a large number of labeled data sets. Group probability means that the class label of each sample in target data set is unknown, but the probability of each class in a given data group is available, and multiple source domains indicate that there are more than two source domains. The number of data set contains more than two data sets of source domain and one data set of target domain. The algorithm adapts to the marginal probability distribution and conditional probability distribution differences between domains, and can protect the privacy of target data and improve classification accuracy by fusing the idea of multi-source transfer learning and group probability into support vector machine. At the same time, it can select the representative dataset in source domains to improve efficiency relied on speeding up the training process of algorithm. Experimental results on several real datasets show the effectiveness of MultiSTLP, and it also has some advantages compared with the state-of-the-art transfer learning algorithm.

Lost data neural semantic recovery framework for structural health monitoring based on deep learning

AbstractStructural condition perception is a crucial step in structural health monitoring (SHM). Random loss or corruption of sensing data seriously hinders the reliability of the monitoring system. This paper discusses the recovery of randomly lost data in SHM from the perspective of conditional probability generation. A novel data‐driven neural semantic recovery framework is proposed, transforming data recovery into a conditional probability modeling problem. This framework uses deep fully convolutional neural networks with an encoder–decoder architecture to capture the overall semantic features of the vibration data, allowing accurate modeling of the behavior of complex conditional probability distributions. Advanced techniques such as dense connections, skip connections, and residual connections significantly improved the network's parameter utilization and recovery performance. Moreover, a novel perceptual loss function is proposed, enabling the network to integrate data loss patterns effectively. The proposed network can be trained end‐to‐end in a self‐supervised manner and perform efficient inferences. Based on the long‐term measured acceleration response under the ambient excitation of a pedestrian bridge, the recovery performance and robustness of the model are sufficiently verified and evaluated. The network exhibits excellent recovery accuracy and robustness, even if the loss ratio is as high as 90%. Preliminary evaluation results show that the proposed model can be seamlessly transferred to scenarios with continuous data loss without retraining the network. Finally, the application prospects of the framework in modal identification and anomaly monitoring of structural conditions are demonstrated.

Molecular formations and spectra due to electron correlations in three-electron hybrid double-well qubits

We show that systematic full configuration-interaction (FCI) calculations enable prediction of the energy spectra and the intrinsic spatial and spin structures of the many-body wave functions as a function of the detuning parameter for the case of three-electron hybrid qubits based on GaAs asymmetric double quantum dots. Specifically, in comparison with the case of weak interactions and treating the entire three-electron double-dot hybrid qubit as an integral unit, it is shown that the predicted spectroscopic patterns, originating from strong electron correlations, manifest the formation of Wigner molecules (WMs). Signatures of WM formation include: (1) a strong suppression of the energy gaps relative to the non-interacting-electrons modeling, and (2) the appearance of a pair of avoided crossings arising between states associated with two-electron occupancies in the left and right wells. The Wigner molecule is a physical entity associated with electron localization within each well and it cannot be captured by the previously employed independent-particle or two-site-Hubbard theoretical modeling of the hybrid qubits. The emergence of strong WMs is investigated in depth through the concerted use of FCI-adapted diagnostic tools like charge and spin densities, as well as conditional probability distributions. Furthermore, the energy spectrum as a function of the strength of the Coulomb repulsion (at constant detuning) is calculated in order to complement the thorough analysis of the factors contributing to WM emergence. We report remarkable agreement with recent experimental measurements. The present FCI methodology for multi-well quantum dots can be straightforwardly extended to treat valleytronic two-band Si/SiGe hybrid qubits, where the central role of the WMs was confirmed recently.

Design of infinite‐dimensional distributed consensus filter for mobile sensor networks with packet losses

In this paper, design of infinite dimensional distributed consensus filter is addressed for a class of spatially distributed processes utilising mobile sensor networks with multiple packet losses. The missing information is drawn into a sensor network in such a way that it conforms to a conditional probability distribution. A new framework for optimisation of mobile sensors is presented to enhance the performance of the filter. The goal of filtering issue is to construct a distributed consensus filter, for any possible measurements that are missing, such that the filtering error converge to bounded consensus in the mean square. Using the Lyapunov direct method and the spatial operator, certain sufficient criteria for the desired filter to satisfy the consensus performance criterion are developed. Lastly, a numerical simulation is performed to show that the suggested filter presented is effective.

Changes in Large Lake Water Level Dynamics in Response to Climate Change

Understanding impacts of climate change on water level fluctuations across Earth's large lakes has critical implications for commercial and recreational boating and navigation, coastal planning, and ecological function and management. A common approach to advancing this understanding is the propagation of climate change scenarios (often from global circulation models) through regional hydrological models. We find, however, that this approach does not always fully capture water supply spatiotemporal features evolving from complex relationships between hydrologic variables. Here, we present a statistical approach for projecting plausible climate-related regional water supply scenarios into localized net basin supply sequences utilizing a parametric vine copula. This approach preserves spatial and temporal correlations between hydrologic components and allows for explicit representation and manipulation of component marginal and conditional probability distributions. We demonstrate the capabilities of our new modeling framework on the Laurentian Great Lakes by coupling our copula-derived net basin supply simulations with a newly-formulated monthly lake-to-lake routing model. This coupled system projects monthly average water levels on Lake Superior, Michigan-Huron, and Erie (we omit Lake Ontario from our study due to complications associated with simulating strict regulatory controls on its outflow). We find that our new method faithfully replicates marginal and conditional probability distributions, as well as serial autocorrelation, within and among historical net basin supply sequences. We find that our new method also reproduces seasonal and interannual water level dynamics. Using readily-available climate change simulations for the Great Lakes region, we then identified two plausible, transient, water supply scenarios and propagated them through our model to understand potential impacts on future water levels. Both scenarios result in an average water level increase of <10 cm on Lake Superior and Erie, with slightly larger increases on Michigan-Huron, as well as elevated variability of monthly water levels and a shift in seasonal water level modality. Our study contributes new insights into plausible impacts of future climate change on Great Lakes water levels, and supports the application and advancement of statistical modeling tools to forecast water supplies and water levels on not just the Great Lakes, but on other large lakes around the world as well.

A Method of Value Measurement Based on Probability Theory in Economics

Value is one of the most fundamental concepts in economics. The existing main definitions of value have certain limitations and are difficult to be unified and quantified. Thus, this article presents a method of quantifying value based on the conditional probability theory; we set value as a random variable,a price is the value of the good in terms of money, according to the price’s historical records, quantitative statistics and human experiences, and thus uses conditional probability distribution to measure value. Furthermore, the mean and variance of random variables are used to describe the weighted average of the possible values and the dispersion of values distribution. This method provides a new perspective for the measurement of value.

Multiplicative Non‐Gaussian Model Error Estimation in Data Assimilation

AbstractModel uncertainty quantification is an essential component of effective data assimilation. Model errors associated with sub‐grid scale processes are often represented through stochastic parameterizations of the unresolved process. Many existing Stochastic Parameterization schemes are only applicable when knowledge of the true sub‐grid scale process or full observations of the coarse scale process are available, which is typically not the case in real applications. We present a methodology for estimating the statistics of sub‐grid scale processes for the more realistic case that only partial observations of the coarse scale process are available. Model error realizations are estimated over a training period by minimizing their conditional sum of squared deviations given some informative covariates (e.g., state of the system), constrained by available observations and assuming that the observation errors are smaller than the model errors. From these realizations a conditional probability distribution of additive model errors given these covariates is obtained, allowing for complex non‐Gaussian error structures. Random draws from this density are then used in actual ensemble data assimilation experiments. We demonstrate the efficacy of the approach through numerical experiments with the multi‐scale Lorenz 96 system using both small and large time scale separations between slow (coarse scale) and fast (fine scale) variables. The resulting error estimates and forecasts obtained with this new method are superior to those from two existing methods.

A Method of Probability Distribution Modeling of Multi-Dimensional Conditions for Wind Power Forecast Error Based on MNSGA-II-Kmeans

How to consider both the influence of weather and wind power in the modeling process of probability distribution of wind power forecast error (WPFE), and to emphasize the application value of conditional modeling, is rarely studied at present. This paper proposes a novel method of conditional probability distribution modeling for WPFE. This method uses a proposed MNSGA-II-Kmeans algorithm to perform multi-objective clustering of multi-dimensional influencing factors (MDIF), including weather and wind power. It can maximize the difference between the probability distributions of each MDIF mode’s WPFE while clustering, thus ensuring the application value of the conditional modeling way. Based on the clustering results, by using the versatile distribution to simulate the probability distribution of WPFE and the support vector machine to realize the recognition of MDIF modes, the specific conditional probability distribution function of WPFE can be provided to stochastic economic dispatch by identifying the forecast MDIF data. A wind plant of north China with historical data is selected for calculation. The results verify the effectiveness of the proposed method, and by comparison with the non-conditional probability distribution of WPFE that does not consider MDIF, it can effectively increase the wind power consumption of the power system.

Pocket2Drug: An Encoder-Decoder Deep Neural Network for the Target-Based Drug Design.

Computational modeling is an essential component of modern drug discovery. One of its most important applications is to select promising drug candidates for pharmacologically relevant target proteins. Because of continuing advances in structural biology, putative binding sites for small organic molecules are being discovered in numerous proteins linked to various diseases. These valuable data offer new opportunities to build efficient computational models predicting binding molecules for target sites through the application of data mining and machine learning. In particular, deep neural networks are powerful techniques capable of learning from complex data in order to make informed drug binding predictions. In this communication, we describe Pocket2Drug, a deep graph neural network model to predict binding molecules for a given a ligand binding site. This approach first learns the conditional probability distribution of small molecules from a large dataset of pocket structures with supervised training, followed by the sampling of drug candidates from the trained model. Comprehensive benchmarking simulations show that using Pocket2Drug significantly improves the chances of finding molecules binding to target pockets compared to traditional drug selection procedures. Specifically, known binders are generated for as many as 80.5% of targets present in the testing set consisting of dissimilar data from that used to train the deep graph neural network model. Overall, Pocket2Drug is a promising computational approach to inform the discovery of novel biopharmaceuticals.

An online resilience assessment method for islanded distribution systems considering uncertainty of intermittent RESs and loads

The frequent natural disasters caused by global warming have been threatening the safety of power systems for decades. A resilient power system has the ability to recover quickly following a disaster and has been continuously studied these years. However, with the progress of energy transition, a large quantity of renewable energy sources (RESs) has been integrated into the power distribution systems and the uncertainty has complicated the decision and operation of resilient distribution systems. This paper proposes an online resilience assessment method for islanded distribution systems considering the time-varying uncertainty of RESs and loads, based on only the measured data without any forecasting tools. An offline probabilistic modeling and online conditional probability distribution derivation method is proposed to generate short-term power scenarios of RESs and loads dynamically, and an online resilience assessment framework is established with an optimization-based system response model in different outage scenarios of distribution systems. The case study to a modified IEEE 37-node test feeder validates the advantages of the proposed method in generating accurate short-term scenarios of uncertainties and providing reliable resilience assessment results. The proposed framework can be used as a basic tool for the online operation of resilient distribution systems.

A Bayesian Network Analysis of the Probabilistic Relationships Between Various Obesity Phenotypes and Cardiovascular Disease Risk in Chinese Adults: Chinese Population-Based Observational Study.

BackgroundCardiovascular disease (CVD) risk among individuals with different BMI levels might depend on their metabolic health. The extent to which metabolic health status and BMI affect CVD risk, either directly or through a mediator, in the Chinese population remains unclear.ObjectiveIn this study, the Bayesian network (BN) perspective is adopted to characterize the multivariable probabilistic connections between CVD risk and metabolic health and obesity status and identify potential factors that influence these relationships among Chinese adults.MethodsThe study population comprised 6276 Chinese adults aged 30 to 74 years who participated in the China Health and Nutrition Survey 2009. BMI was used to categorize participants as normal weight, overweight, or obese, and metabolic health was defined by the Adult Treatment Panel-3 criteria. Participants were categorized into 6 phenotypes according to their metabolic health and BMI categorization. The 10-year risk of CVD was determined using the Framingham Risk Score. BN modeling was used to identify the network structure of the variables and compute the conditional probability of CVD risk for the different metabolic obesity phenotypes with the given structure.ResultsOf 6276 participants, 64.67% (n=4059), 20.37% (n=1279), and 14.95% (n=938) had a low, moderate, and high 10-year CVD risk. An averaged BN with a stable network structure was constructed by learning 300 bootstrapped networks from the data. Using BN reasoning, the conditional probability of high CVD risk increased as age progressed. The conditional probability of high CVD risk was 0.43% (95% CI 0.2%-0.87%) for the 30 to 40 years age group, 2.25% (95% CI 1.75%-2.88%) for the 40 to 50 years age group, 16.13% (95% CI 14.86%-17.5%) for the 50 to 60 years age group, and 52.02% (95% CI 47.62%-56.38%) for those aged ≥70 years. When metabolic health and BMI categories were instantiated to their different statuses, the conditional probability of high CVD risk increased from 7.01% (95% CI 6.27%-7.83%) for participants who were metabolically healthy normal weight to 10.47% (95% CI 7.63%-14.18%) for their metabolically healthy obese (MHO) counterparts and up to 21.74% and 34.48% among participants who were metabolically unhealthy normal weight and metabolically unhealthy obese (MUO), respectively. Sex was a significant modifier of the conditional probability distribution of metabolic obesity phenotypes and high CVD risk, with a conditional probability of high CVD risk of only 2.02% and 22.7% among MHO and MUO women, respectively, compared with 21.92% and 48.21% for their male MHO and MUO counterparts, respectively.ConclusionsBN modeling was applied to investigate the relationship between CVD risk and metabolic health and obesity phenotypes in Chinese adults. The results suggest that both metabolic health and obesity status are important for CVD prevention; closer attention should be paid to BMI and metabolic status changes over time.

Multisource Data Fusion Outage Location in Distribution Systems via Probabilistic Graphical Models

Efficient outage location is critical to enhancing the resilience of power distribution systems. However, accurate outage location requires combining massive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">evidence</i> received from diverse data sources, including smart meter (SM) last gasp signals, customer trouble calls, social media messages, weather data, vegetation information, and physical parameters of the network. This is a computationally complex task due to the high dimensionality of data in distribution grids. In this paper, we propose a multi-source data fusion approach to locate outage events in partially observable distribution systems using Bayesian networks (BNs). A novel aspect of the proposed approach is that it takes multi-source evidence and the complex structure of distribution systems into account using a probabilistic graphical method. Our method can radically reduce the computational complexity of outage location inference in high-dimensional spaces. The graphical structure of the proposed BN is established based on the network’s topology and the causal relationship between random variables, such as the states of branches/customers and evidence. Utilizing this graphical model, accurate outage locations are obtained by leveraging a Gibbs sampling (GS) method, to infer the probabilities of de-energization for all branches. Compared with commonly-used exact inference methods that have exponential complexity in the size of the BN, GS quantifies the target conditional probability distributions in a timely manner. A case study of several real-world distribution systems is presented to validate the proposed method.

Multi-Agent Reinforcement Learning Based Fully Decentralized Dynamic Time Division Configuration for 5G and B5G Network.

Future network services must adapt to the highly dynamic uplink and downlink traffic. To fulfill this requirement, the 3rd Generation Partnership Project (3GPP) proposed dynamic time division duplex (D-TDD) technology in Long Term Evolution (LTE) Release 11. Afterward, the 3GPP RAN#86 meeting clarified that 5G NR needs to support dynamic adjustment of the duplex pattern (transmission direction) in the time domain. Although 5G NR provides a more flexible duplex pattern, how to configure an effective duplex pattern according to services traffic is still an open research area. In this research, we propose a distributed multi-agent deep reinforcement learning (MARL) based decentralized D-TDD configuration method. First, we model a D-TDD configuration problem as a dynamic programming problem. Given the buffer length of all UE, we model the D-TDD configuration policy as a conditional probability distribution. Our goal is to find a D-TDD configuration policy that maximizes the expected discount return of all UE’s sum rates. Second, in order to reduce signaling overhead, we design a fully decentralized solution with distributed MARL technology. Each agent in MARL makes decisions only based on local observations. We regard each base station (BS) as an agent, and each agent configures uplink and downlink time slot ratio according to length of intra-BS user (UE) queue buffer. Third, in order to solve the problem of overall system revenue caused by the lack of global information in MARL, we apply leniency control and binary LSTM (BLSTM) based auto-encoder. Leniency controller effectively controls Q-value estimation process in MARL according to Q-value and current network conditions, and auto-encoder makes up for the defect that leniency control cannot handle complex environments and high-dimensional data. Through the parallel distributed training, the global D-TDD policy is obtained. This method deploys the MARL algorithm on the Mobile Edge Computing (MEC) server of each BS and uses the storage and computing capabilities of the server for distributed training. The simulation results show that the proposed distributed MARL converges stably in various environments, and performs better than distributed deep reinforcement algorithm.

Aligning the achievement of SDGs with long-term sustainability and resilience: An OOBN modelling approach

This research utilizes an Object-Oriented Bayesian Network (OOBN) to model the relationships between the Sustainable Development Goal (SDGs) and resilience and sustainability at national, regional, and global levels. The ability of the OOBN to learn the parameters, i.e., the conditional probability distributions between the variables included in the network, was exploited to explore the impacts of progress of SDGs on the sustainability and resilience of nations. The resulting OOBN is used to examine different situations pertinent to policy analysis and design at the times of disasters, particularly in the wake of the COVID-19 pandemic. Three case studies are used to illustrate the step by step process of using the proposed OOBN as well as the expected results of its application in policy analysis and evaluation contexts. The proposed is able to provide insight regarding which SDGs will have more significant impacts on both resilience and sustainability as well as their constituent components. The results of this research indicate how data induced OOBNs can be utilised by policy makers to prioritize new policies and evaluate the impacts of existing policies on both the resilience and sustainability of societies.

Comparison between bivariate and trivariate flood frequency analysis using the Archimedean copula functions, a case study of the Karun River in Iran

Historically, severe floods have caused great human and financial losses. Therefore, the flood frequency analysis based on the flood multiple variables including flood peak, volume and duration poses more motivation for hydrologists to study. The main goal of this paper is conducting a tri-variate flood frequency analysis through simultaneously processing the three main variables of any flood event. In addition to this analysis, three bi-variate flood frequency analyses are also performed considering the variables pairwise. Meanwhile, the Archimedean copula functions are employed to conduct such analyses, and finally compared based on their performance in estimating the accurate and reliable flood frequencies. Bivariate and trivariate flood frequency analysis and modeling using Archimedean copula functions is focused. For this purpose, the annual flood data over a 55-year historical period recorded at the Dez Dam hydrometric station were used. According to the goodness-of-fit criteria along with the analytical tail dependence results based on the extreme value theory, the Frank function built upon the couple of the flood peak-volume and the couple of the flood peak-duration as well as the Clayton function built upon the flood volume-duration were identified to be the best copula families to be adopted. The trivariate analysis was conducted and the Clayton family was chosen as the best copula function. Thereafter, the common and conditional cumulative probability distribution functions were built and analyzed to determine the periodic "and", "or" and "conditional" bivariate and trivariate flood return periods. The results suggest that the bivariate conditional return period obtained for short-term periods is more reliable than the trivariate conditional return period. Additionally, the trivariate conditional return period calculated for long-term periods is more reliable than the bivariate conditional return period.

Factors affecting marine ranching risk in China and their hierarchical relationships based on DEMATEL, ISM, and BN

Marine ranching have attracted wide attention in the marine fishery in recent years owing to numerous benefits for sustainable development. However, existing research efforts on marine ranching risk management are very limited, and no prior in-depth research has focused on studying the risk interdependencies in marine ranching from the perspectives of multiple risks. This paper begins by identifying 29 marine ranching risks using a systematic literature review and experts propose. Next, the cause-effect diagram and hierarchical network model of marine ranching are obtained using the combined DEMATEL - ISM method, which clearly confirms the interdependent relationships among various risk factors. It also identifies the most critical factors, which enables the operators of the marine ranching to make decisions to reduce risks. Then the hierarchical network model is mapped to a BN and expert judgments are further transformed into the conditional probability distribution by software Netica, in order to quantify the strength of the interdependent relationships among the marine ranching risk system, and determine main paths resulting in risk occurrence. According to the research results, the risk occurrence probability of marine ranching is high, with a probability of 85.1%，and the most approximate cause path leading to the occurrence of risk are determined—namely, X 27 (Long construction cycle) → X 10 (Financing difficulties) → X 15 (Safety hazards) → X 11 (Investment return risk) → Y(Marine ranching risk) and X 9 (Lack of technical talent) → X 8 (Monitoring failure) → X 2 (Habitat destruction) → X 26 (Large preinvestment) → X 10 → X 15 → X 11 (Investment return risk) → Y. Through the established risk analysis model, the key risk factors in the implementation process of marine ranching can be obtained, which is helpful for in-depth understanding of the risk information of marine ranching and more effective risk management of marine ranching. • The risk factors of marine ranching in China are identified. • DEMATEL, ISM and BN are used in the research of risk assessment of marine ranching. • The hierarchical relationship of risk factors of marine ranching is figured out. • The most approximate cause path leading to the occurrence of risk is determined.

A Method of Value Measurement Based on Probability Theory in Economics

Value is one of the most fundamental concepts in economics. The existing main definitions of value have certain limitations and are difficult to be unified and quantified. Thus, this article presents a method of quantifying value based on the conditional probability theory; we set value as a random variable,a price is the value of the good in terms of money, according to the price’s historical records, quantitative statistics and human experiences, and thus uses conditional probability distribution to measure value. Furthermore, the mean and variance of random variables are used to describe the weighted average of the possible values and the dispersion of values distribution. This method provides a new perspective for the measurement of value.

Bayesian Maximal Information Coefficient (BMIC) to reason novel trends in large datasets

The Bayesian network (BN) is a probability inference model to describe the explicit relationship between cause and effect, which may be examined in the complex system of rice price with data uncertainty. However, discovering the optimized structure from a super-exponential number of graphs in the search space is an NP-hard problem. In this paper, Bayesian Maximal Information Coefficient (BMIC) is proposed to uncover the causal correlations from a large data set in a random system by integrating probabilistic graphical model (PGM) and maximal information coefficient (MIC) with Bayesian linear regression (BLR). First, MIC is to capture the strong dependence between predictor variables and a target variable to reduce the number of variables for the BN structural learning of PGM. Second, BLR is responsible for assigning orientation in a graph resulting from a posterior probability distribution. It conforms to what BN needs to acquire a conditional probability distribution when given the parents for each node by the Bayes’ Theorem. Third, the Bayesian information criterion (BIC) is treated as an indicator to determine the well-explained model with its data to ensure correctness. The score shows that the proposed BMIC obtains the highest score compared to the two traditional learning algorithms. Finally, the proposed BMIC is applied to discover the causal correlations from the large data set on Thai rice price by identifying the causal changes in the paddy price of Jasmine rice. The results of the experiments show that the proposed BMIC returns directional relationships with clues to identify the cause(s) and effect(s) of paddy price with a better heuristic search.

Semi-controlled Learning in Information Processing Problems

The article substantiates the need for further research of known methods and the development of new methods of machine learning – semi-supervized learning. It is shown that knowledge of the probability distribution density of the initial data obtained using unlabeled data should carry information useful for deriving the conditional probability distribution density of labels and input data. If this is not the case, semi-supervised learning will not provide any improvement over supervised learning. It may even happen that the use of unlabeled data reduces the accuracy of the prediction. For semi-supervised learning to work, certain assumptions must hold, namely: the semi-supervised smoothness assumption, the clustering assumption (low-density partitioning), and the manifold assumption. A new hybrid semi-supervised learning algorithm using the label propagation method has been developed. An example of using the proposed algorithm is given.