Logarithmic Loss Function Research Articles

Fault diagnosis method for elevator carriages based on temporal generative federated distillation

Addressing the ‘data silo’ issue among different elevator operating units and the temporal correlations in elevator vibration signals, a novel small-sample fault diagnosis method for elevator carriages based on temporal generative federated distillation is proposed. This method incorporates a temporal generative adversarial network into Federated Distillation via Generative Learning (FedGen). FedGen combines federated learning, knowledge distillation, and generative models to enhance model aggregation efficiency while mitigating data heterogeneity. However, the original generative model struggles to maintain dynamic correlations between signals when extracting temporal features. Therefore, an improved Time Series Generative Adversarial Networks (TimeGAN) model is introduced, substituting the initial logarithmic loss function with a least squares error function, thereby enhancing training stability and data quality. This approach eliminates the need for proxy datasets in knowledge distillation, avoiding the loss of temporal information during central server feature extraction. Simulation results demonstrate that this method enables data sharing while protecting data privacy, and enhances model generalization capabilities.

Mathematical Model of Logistic Regression for Binary Classification. Part 1. Regression Models of Data Generalization

In this article, the mathematical justification of logistic regression as an effective and simple to implement method of machine learning is performed. A review of literary sources was conducted in the direction of statistical processing, analysis and classification of data using the logistic regression method, which confirmed the popularity of this method in various subject areas. The logistic regression method was compared with the linear and probit regression methods regarding the possibility of predicting the probabilities of events. In this context, the disadvantages of linear regression and the advantages and affinity of logit and probit regression methods are noted. It is indicated that the possibility of forecasting probabilities and binary classification by the method of logistic regression is provided by the use of a sigmoid function with the property of compressive transformation of an argument with an unlimited numerical value into a limited range from 0 to 1 real value of the function. The derivation of the sigmoid function in two different ways is described: based on the model of the logarithm of the odds of events and the model of logistic population growth. Based on the method of maximum likelihood, the construction of a logarithmic loss function was demonstrated, the use of which made it possible to move from a multi-extremal nonlinear regression problem to a unimodal optimization problem. Methods of regularization of the loss function are presented to control the complexity and prevent retraining of the logistic regression model.

An efficient multi-metric learning method by partitioning the metric space

Metric learning has attracted significant attention due to its high effectiveness and efficiency for pattern recognition task. Traditional supervised metric learning algorithms attempt to seek a global distance metric with labeled samples. When data are represented with multimodal and only limited supervision information is available, these approaches are insufficient to obtain satisfactory results. In this paper, we develop a robust semi-supervised multi-metric learning method (RSMM) to improve classification performance. The proposed RSMM learns multiple local metrics and a background metric instead of a single global metric. Specifically, we divide the metric space into influential regions and background region, and then regulate the effectiveness of each local metric to be within the related regions. Simultaneously, a geometrically interpretable, symmetric distance is defined with local metrics and background metric. Based on the resultant learning bounds, we obtain the regularization term to improve the classifier’s generalization ability. Moreover, the manifold regularization term is introduced to preserve the supervision information as well as geometry structure. The substantial unlabeled samples may cause potential threats and large uncertainties, so the logarithmic loss function is utilized to enhance the robustness. An efficient gradient descent algorithm is exploited to solve the non-convex challenging problem. To further understand the proposed algorithm, we theoretically derive its robustness and generalization error bounds. Finally, numerical experiments on UCI datasets and image datasets demonstrate the feasibility and validity of the RSMM.

Construction of Integrated Platform for Eco-Sustainable Tourism and Marketing in Southeast Asia Based on Machine Learning

Southeast Asia is one of the most popular tourist destinations in the world, and its tourism model is mainly based on ecological and sustainable tourism characteristics. It is a special practical exploration of this region. However, with the rapid development of the tourism industry, the structural contradictions in the tourism industry have become increasingly prominent, coupled with the weak link of tourism development, making the development of tourism unbalanced. Therefore, this study proposed a platform-related algorithm based on machine learning to build the integration of eco-sustainable tourism and marketing in Southeast Asia and used a collaborative filtering algorithm and a route generation algorithm to recommend information or predict specific needs for specific tourists. The experimental results of this study showed that the difference between different loss functions of the improved transfer algorithm based on machine learning is not significant, which indicated that the method proposed in this study is robust to the choice of a loss function. Compared with the hinge loss function and the logarithmic loss function, the exponential loss function has the highest average classification accuracy of 0.91, of which the average accuracy of the logarithmic loss function is 0.85, and the average classification accuracy of the hinge loss function is 0.79. Therefore, applying the migration algorithm to the architecture of the platform is conducive to the stability of the dataset and to the better display of pages for tourists.

HighMLR: An open-source package for R with machine learning for feature selection in high dimensional cancer clinical genome time to event data

Machine learning techniques, popularly used as a tool for dimensionality reduction and pattern recognition of features, have been utilized extensively in data mining. In survival analysis, where the primary outcome is the time until a specific event occurs, identifying relevant features for building an efficient prediction model is essential. This is where machine learning can be a suitable option. However, there is an existing gap in utilizing machine learning techniques in high-dimensional survival data due to the non-availability of convenient programming functions and packages. In this article, we have developed an efficient machine learning procedure for analyzing survival data associated with high-dimensional gene expressions. Though there are several R libraries available for performing machine learning, no package support is available to implement machine learning with classification on high-dimensional survival data. highMLR, our developed R package, is capable of implementing machine learning methods on high dimensional survival data and provides a way of feature selection based on the logarithmic loss function. Several statistical methods for survival analysis have been incorporated into this machine learning algorithm. A high-dimensional gene expression dataset has been analyzed using the proposed R library to show its efficacy in feature selection.

Quantifying the risk of vector-borne disease transmission attributable to genetically modified vectors.

The relative risk of disease transmission caused by the potential release of transgenic vectors, such as through sterile insect technique or gene drive systems, is assessed with comparison with wild-type vectors. The probabilistic risk framework is demonstrated with an assessment of the relative risk of lymphatic filariasis, malaria and o'nyong'nyong arbovirus transmission by mosquito vectors to human hosts given a released transgenic strain of Anopheles coluzzii carrying a dominant sterile male gene construct. Harm is quantified by a logarithmic loss function that depends on the causal risk ratio, which is a quotient of basic reproduction numbers derived from mathematical models of disease transmission. The basic reproduction numbers are predicted to depend on the number of generations in an insectary colony and the number of backcrosses between the transgenic and wild-type lineages. Analogous causal risk ratios for short-term exposure to a single cohort release are also derived. These causal risk ratios were parametrized by probabilistic elicitations, and updated with experimental data for adult vector mortality. For the wild-type, high numbers of insectary generations were predicted to reduce the number of infectious human cases compared with uncolonized wild-type. Transgenic strains were predicted to produce fewer infectious cases compared with the uncolonized wild-type.

Machine learning approaches to predict peak demand days of cardiovascular admissions considering environmental exposure

BackgroundAccumulating evidence has linked environmental exposure, such as ambient air pollution and meteorological factors, to the development and severity of cardiovascular diseases (CVDs), resulting in increased healthcare demand. Effective prediction of demand for healthcare services, particularly those associated with peak events of CVDs, can be useful in optimizing the allocation of medical resources. However, few studies have attempted to adopt machine learning approaches with excellent predictive abilities to forecast the healthcare demand for CVDs. This study aims to develop and compare several machine learning models in predicting the peak demand days of CVDs admissions using the hospital admissions data, air quality data and meteorological data in Chengdu, China from 2015 to 2017.MethodsSix machine learning algorithms, including logistic regression (LR), support vector machine (SVM), artificial neural network (ANN), random forest (RF), extreme gradient boosting (XGBoost), and light gradient boosting machine (LightGBM) were applied to build the predictive models with a unique feature set. The area under a receiver operating characteristic curve (AUC), logarithmic loss function, accuracy, sensitivity, specificity, precision, and F1 score were used to evaluate the predictive performances of the six models.ResultsThe LightGBM model exhibited the highest AUC (0.940, 95% CI: 0.900–0.980), which was significantly higher than that of LR (0.842, 95% CI: 0.783–0.901), SVM (0.834, 95% CI: 0.774–0.894) and ANN (0.890, 95% CI: 0.836–0.944), but did not differ significantly from that of RF (0.926, 95% CI: 0.879–0.974) and XGBoost (0.930, 95% CI: 0.878–0.982). In addition, the LightGBM has the optimal logarithmic loss function (0.218), accuracy (91.3%), specificity (94.1%), precision (0.695), and F1 score (0.725). Feature importance identification indicated that the contribution rate of meteorological conditions and air pollutants for the prediction was 32 and 43%, respectively.ConclusionThis study suggests that ensemble learning models, especially the LightGBM model, can be used to effectively predict the peak events of CVDs admissions, and therefore could be a very useful decision-making tool for medical resource management.

Automatic segmentation of levator hiatus from ultrasound images using U-net with dense connections

In this paper, we propose a fully automatic method based on a densely connected convolutional network for the segmentation of the levator hiatus from ultrasound images. A densely connected path is incorporated into a U-net to achieve a deep architecture and improve the segmentation performance. The proposed network architecture provides dense connections between layers that encourage feature reuse and reduce the number of parameters while maintaining good performance. The parameters of the network are optimized by training with a binary cross entropy, i.e. logarithmic loss function. A dataset with 1000 levator hiatus images is used for training and 130 images are used for evaluating the performance of the proposed network architecture. The proposed model can get a mean Dice of . Experimental results show that the proposed method can achieve more accurate segmentation results than some of state-of-the-art methods.

Bayesian analysis of doubly censored lifetime data using two component mixture of Weibull distribution

In recent years analysis of the mixture models under Bayesian framework has received considerable attention. However, the Bayesian estimation of the mixture models under doubly censored samples has not yet been reported. This paper proposes a Bayesian estimation procedure for analyzing lifetime data under doubly censored sampling when the failure times belong to a two-component mixture of the Weibull model. An extended version of the likelihood function for doubly censored samples for the analysis of a mixture of lifetime models has been introduced. The posterior estimation has been considered under the assumption of gamma prior using a couple of loss functions. The performance of the different estimators has been investigated and compared through the analysis of simulated data. A real-life example has been included to demonstrate the practical applicability of the results. The results indicated the preference of the estimates under squared logarithmic loss function (SLLF) for the estimation of the mixture model. The proposed method can be extended for more than two component mixtures. DOI: http://dx.doi.org/10.4038/jnsfsr.v42i4.7731 J.Natn.Sci.Foundation Sri Lanka 2014 42 (4): 325-334

Bayesian Reliability Modeling Using Monte Carlo Integration

Bayesian Reliability Modeling Using Monte Carlo IntegrationThe aim of this article is to introduce the concept of Monte Carlo Integration in Bayesian estimation and Bayesian reliability analysis. Using the subject concept, approximate estimates of parameters and reliability functions are obtained for the three-parameter Weibull and the gamma failure models. Four different loss functions are used: square error, Higgins-Tsokos, Harris, and a logarithmic loss function proposed in this article. Relative efficiency is used to compare results obtained under the above mentioned loss functions.

On Complexity of Easy Predictable Sequences

Predictive complexity is a generalization of Kolmogorov complexity. It corresponds to an “optimal” prediction strategy and gives a natural lower bound to ability of any algorithm to predict elements of a sequence of outcomes. A natural question is studied: how complex can easy-to-predict sequences be? The standard measure of complexity, used in the paper, is Kolmogorov complexity K (which is close to predictive complexity for logarithmic loss function). The difficulty of prediction is measured by the notion of predictive complexity KG for bounded loss function (of nonlogarithmic type). We present an asymptotic relation sup x:l(x) = n K(x|n) KG(x) ∼ 1 a log n , when n →∞, where a is a constant and l(x) is the length of a sequence x . An analogous asymptotic relation holds for relative complexities K ( x | n )/ n and KG ( x )/ n , where n = l(x) . To obtain these results we present lower and upper bounds of the cardinality of all sequences of given predictive complexity.

On Complexity of Easy Predictable Sequences

Predictive complexity is a generalization of Kolmogorov complexity. It corresponds to an “optimal” prediction strategy and gives a natural lower bound to ability of any algorithm to predict elements of a sequence of outcomes. A natural question is studied: how complex can easy-to-predict sequences be? The standard measure of complexity, used in the paper, is Kolmogorov complexity K (which is close to predictive complexity for logarithmic loss function). The difficulty of prediction is measured by the notion of predictive complexity KG for bounded loss function (of nonlogarithmic type). We present an asymptotic relation sup x:l(x) = n K(x|n) KG(x) ∼ 1 a log n , when n →∞, where a is a constant and l(x) is the length of a sequence x . An analogous asymptotic relation holds for relative complexities K ( x | n )/ n and KG ( x )/ n , where n = l(x) . To obtain these results we present lower and upper bounds of the cardinality of all sequences of given predictive complexity.

C-V and G-V Measurements Showing Single Electron Trapping in Nanocrystalline Silicon Dot Embedded in MOS Memory Structure

AbstractWe prepared a SiO2/nanocrystalline Si (nc-Si)/SiO2 sandwich structure. A clear positive shift in C-V and G-V curves due to electrons trapped in nc-Si dots has been observed at room temperature. The peak in conductance around flat band condition indicates that a trap event had occurred where an electron is stored per nc-Si dot. A logarithmic charge loss function is found and this discharging process is independent of the thermal activation mechanism. The longer memory retention time and logarithmic charge loss in the dots are explained by a “built-in” electric field through the tunnel oxide, which varies with time, resulting in a variable tunneling probability. The electric repulsion induced by the built-in electric field hinders the discharging of electrons remained in the dots.

An Efficient Extension to Mixture Techniques for Prediction and Decision Trees

We present an efficient method for maintaining mixtures of prunings of a prediction or decision tree that extends the previous methods for “node-based” prunings (Buntine, 1990; Willems, Shtarkov, & Tjalkens, 1995; Helmbold & Schapire, 1997; Singer, 1997) to the larger class of edge-based prunings. The method includes an online weight-allocation algorithm that can be used for prediction, compression and classification. Although the set of edge-based prunings of a given tree is much larger than that of node-based prunings, our algorithm has similar space and time complexity to that of previous mixture algorithms for trees. Using the general online framework of Freund and Schapire (1997), we prove that our algorithm maintains correctly the mixture weights for edge-based prunings with any bounded loss function. We also give a similar algorithm for the logarithmic loss function with a corresponding weight-allocation algorithm. Finally, we describe experiments comparing node-based and edge-based mixture models for estimating the probability of the next word in English text, which show the advantages of edge-based models.

A Bayesian approach to sample size selection in a multiple hypotheses test for the Bernoulli model

The situation where a certain type of seed need to be classified into one of three different categories, according to its germination level, can be formulated as the simultaneous test of three statistical hypotheses. In this paper, the problem of assessing an optimal sample size for the simultaneous test of several hypotheses on a Bernoulli process is studied within the Bayesian framework, and a solution is obtained for a wide class of prior distributions and a logarithmic loss function.