Class Of Statistical Models Research Articles

Testing biological network motif significance with exponential random graph models

Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions. However, there is disagreement as to the statistical significance of these motifs, and there are potential problems with standard methods for estimating this significance. Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over 10 years ago but have had limited application to biological networks, possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein–protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network, and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an E. coli and a yeast regulatory network. We also confirm, using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features.

Nonparametric estimation and inference for spatiotemporal epidemic models

Epidemic modelling is an essential tool to understand the spread of the novel coronavirus and ultimately assist in disease prevention, policymaking, and resource allocation. In this article, we establish a state-of-the-art interface between classic mathematical and statistical models and propose a novel space-time epidemic modelling framework to study the spatial-temporal pattern in the spread of infectious diseases. We propose a quasi-likelihood approach via the penalised spline approximation and alternatively reweighted least-squares technique to estimate the model. The proposed estimators are consistent, and the asymptotic normality is established for the constant coefficients. Utilizing spatiotemporal analysis, our proposed model enhances the dynamics of the epidemiological mechanism and dissects the spatiotemporal structure of the spreading disease. We evaluate the numerical performance of the proposed method through a simulation example. Finally, we apply the proposed method in the study of the devastating COVID-19 pandemic.

Validation of statistic and deterministic asperity contact models using experimental Stribeck data

Contact models are used, among others, to describe the asperity contact in lubricated contacts. In recent decades, a large number of contact models have been developed based on different approaches. In this article a selection of classical statistical contact models are compared with a deterministic FE model. The validation of the different approaches was carried out applying an indirect methodology. By comparing a numerically determined Stribeck curve, on which the characteristics of the contact model has a significant influence, and experimentally determined Stribeck curves, the applicability of the different contact models can be evaluated. The influence of elastic and elastoplastic material behaviour in the deterministic contact model on the asperity contact pressure curves and Stribeck curves, respectively, was examined during the investigations. The results show, that the elastic FEM contact model and the statistical model according to Greenwood and Tripp provide the best agreement with the experimental Stribeck data. This can be attributed to the fact that the roughness peaks are smoothed immediately in the early contact stage and the smoothed surface behaves almost elastically.

Artificial Intelligence Methods: Toward a New Decision Making Tool

ABSTRACT This work is based on a mixe between the dynamics of investor decision making and the effectiveness of the forecasting models used to model market movements. Thus, it appears that the determination of adequate models can help to explain the behavior of agents and result to easier decision making through the anticipation of future prices. For this reason, we will use artificial intelligence models, in particular Machine Learning and Deep Learning algorithms, in order to better understand the variation of asset prices and their future evolution. In order to do so, we will use Recurrent Neural Networks (RNN), which has proven to be very suitable in the case of the Moroccan banking sector. The comparison between classical models and advanced artificial intelligence (AI) algorithms has demonstrated the inadequacy of classical statistical models. The latter are based on certain assumptions not verified in the framework of financial series, which reduces the capacity of classical models to correctly predict new data. The integration of AI has also made it possible to overcome the assumption of market efficiency by modeling the behavior of irrational agents, who trade on rumors and false news.

An introduction to Random Forests for modeling tasks - theory and practice in python with public health case studies

Abstract RFs are a powerful, volatile, and easy to use method, making it an excellent benchmark method for different types of analysis, notably in the public health domain. RFs offer outstanding performance with minimal effort from the user (given its low sensitivity to its hyperparameters) and can be used for many different modeling tasks (classification, regression, clustering, outlier detection). In practice, RFs are easily applicable through libraries in Python and R languages, allowing users to benefit from their capabilities with minimal coding knowledge. In addition to their pure performance abilities, RFs have some practical advantages when compared to many classical statistical models: it does not require any normalization of the data, handles very large datasets (in population or variables) and all kinds of data types (e.g., binary, categorical, continuous); it handles outliers and is insensitive to multicollinearity within the input variables. Their main limitation is their less straightforward interpretation of the final model they build. However, they offer additional tools, such as variable importance and proximity metrics, that improve the understanding of their results and potentially provide insights that traditional models cannot. Finally, its construction based on decision trees grants it additional capabilities, notably the possibility to extract prediction intervals and to handle efficiently imbalanced data problems with a variant of the algorithm called Balanced Random Forests.

Emergent Statistical Mechanics from Properties of Disordered Random Matrix Product States

The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well approximated by matrix product states. In this work, we introduce a picture of generic states within the trivial phase of matter with respect to their non-equilibrium and entropic properties: We do so by rigorously exploring non-translation-invariant matrix product states drawn from a local i.i.d. Haar-measure. We arrive at these results by exploiting techniques for computing moments of random unitary matrices and by exploiting a mapping to partition functions of classical statistical models, a method that has lead to valuable insights on local random quantum circuits. Specifically, we prove that such disordered random matrix product states equilibrate exponentially well with overwhelming probability under the time evolution of Hamiltonians featuring a non-degenerate spectrum. Moreover, we prove two results about the entanglement Renyi entropy: The entropy with respect to sufficiently disconnected subsystems is generically extensive in the system-size, and for small connected systems the entropy is almost maximal for sufficiently large bond dimensions.

A Novel Matrix Profile-Guided Attention LSTM Model for Forecasting COVID-19 Cases in USA.

Background: The outbreak of the novel coronavirus disease 2019 (COVID-19) has been raging around the world for more than 1 year. Analysis of previous COVID-19 data is useful to explore its epidemic patterns. Utilizing data mining and machine learning methods for COVID-19 forecasting might provide a better insight into the trends of COVID-19 cases. This study aims to model the COVID-19 cases and perform forecasting of three important indicators of COVID-19 in the United States of America (USA), which are the adjusted percentage of daily admitted hospitalized COVID-19 cases (hospital admission), the number of daily confirmed COVID-19 cases (confirmed cases), and the number of daily death cases caused by COVID-19 (death cases).Materials and Methods: The actual COVID-19 data from March 1, 2020 to August 5, 2021 were obtained from Carnegie Mellon University Delphi Research Group. A novel forecasting algorithm was proposed to model and predict the three indicators. This algorithm is a hybrid of an unsupervised time series anomaly detection technique called matrix profile and an attention-based long short-term memory (LSTM) model. Several classic statistical models and the baseline recurrent neural network (RNN) models were used as the baseline models. All models were evaluated using a repeated holdout training and test strategy.Results: The proposed matrix profile-assisted attention-based LSTM model performed the best among all the compared models, which has the root mean square error (RMSE) = 1.23, 31612.81, 467.17, mean absolute error (MAE) = 0.95, 26259.55, 364.02, and mean absolute percentage error (MAPE) = 0.25, 1.06, 0.55, for hospital admission, confirmed cases, and death cases, respectively.Conclusion: The proposed model is more powerful in forecasting COVID-19 cases. It can potentially aid policymakers in making prevention plans and guide health care managers to allocate health care resources reasonably.

Comparative analysis of the forecasting quality of the classical statistical model and the machine learning model on the data of the Russian stock market

The main objective of this work is to compare the predictive ability of the classical machine learning model — ARIMA, as the most common and well-studied baseline model, and the ML model based on a sequential neural network — in this case, LSTM. The goal is to maximize accuracy and minimize error — selecting the most appropriate model for predicting time series with the highest accuracy. A description is given for these mathematical models. An algorithm is also proposed for forecasting time series using these models, based on the «Rolling window» approach. Practical implementation is implemented using the Python programming environment with the Pandas, Numpy, pmdarima, Keras, Statsmodels libraries. To train the models, we used stock data at the closing price per share of the leading Russian companies: Yandex, VTB, KamAZ, Kiwi, Gazprom, NLMK, Rosneft, Alrosa for the period. The studies carried out demonstrate the predictive superiority of the approach based on neural networks, while the RMSE is 71% less than the same indicator for the ARIMA model, which allows us to conclude that the use of the LSTM model is preferable for this class of problems.

A novel deep learning prediction model for concrete dam displacements using interpretable mixed attention mechanism

Dam displacements can effectively reflect its operational status, and thus establishing a reliable displacement prediction model is important for dam health monitoring. The majority of the existing data-driven models, however, focus on static regression relationships, which cannot capture the long-term temporal dependencies and adaptively select the most relevant influencing factors to perform predictions. Moreover, the emerging modeling tools such as machine learning (ML) and deep learning (DL) are mostly black-box models, which makes their physical interpretation challenging and greatly limits their practical engineering applications. To address these issues, this paper proposes an interpretable mixed attention mechanism long short-term memory (MAM-LSTM) model based on an encoder-decoder architecture, which is formulated in two stages. In the encoder stage, a factor attention mechanism is developed to adaptively select the highly influential factors at each time step by referring to the previous hidden state. In the decoder stage, a temporal attention mechanism is introduced to properly extract the key time segments by identifying the relevant hidden states across all the time steps. For interpretation purpose, our emphasis is placed on the quantification and visualization of factor and temporal attention weights. Finally, the effectiveness of the proposed model is verified using monitoring data collected from a real-world dam, where its accuracy is compared to a classical statistical model, conventional ML models, and homogeneous DL models. The comparison demonstrates that the MAM-LSTM model outperforms the other models in most cases. Furthermore, the interpretation of global attention weights confirms the physical rationality of our attention-based model. This work addresses the research gap in interpretable artificial intelligence for dam displacement prediction and delivers a model with both high-accuracy and interpretability.

A novel fractional discrete grey model with an adaptive structure and its application in electricity consumption prediction

PurposeElectricity consumption prediction has been an important topic for its significant impact on electric policies. Due to various uncertain factors, the growth trends of electricity consumption in different cases are variable. However, the traditional grey model is based on a fixed structure which sometimes cannot match the trend of raw data. Consequently, the predictive accuracy is variable as cases change. To improve the model's adaptability and forecasting ability, a novel fractional discrete grey model with variable structure is proposed in this paper.Design/methodology/approachThe novel model can be regarded as a homogenous or non-homogenous exponent predicting model by changing the structure. And it selects the appropriate structure depending on the characteristics of raw data. The introduction of fractional accumulation enhances the predicting ability of the novel model. And the relative fractional order r is calculated by the numerical iterative algorithm which is simple but effective.FindingsTwo cases of power load and electricity consumption in Jiangsu and Fujian are applied to assess the predicting accuracy of the novel grey model. Four widely-used grey models, three classical statistical models and the multi-layer artificial neural network model are taken into comparison. The results demonstrate that the novel grey model performs well in all cases, and is superior to the comparative eight models.Originality/valueA fractional-order discrete grey model with an adaptable structure is proposed to solve the conflict between traditional grey models' fixed structures and variable development trends of raw data. In applications, the novel model has satisfied adaptability and predicting accuracy.

Development of Algorithms for Choosing the Best Time Series Models and Neural Networks to Predict COVID-19 Cases

Time series analysis became one of the most investigated fields of knowledge during spreading of the COVID-19 around the world. The problem of modeling and forecasting infection cases of COVID-19, deaths, recoveries and other parameters is still urgent. Purpose of the study. Our article is devoted to investigation of classical statistical and neural network models that can be used for forecasting COVID-19 cases. Materials and methods. We discuss neural network model NNAR, compare it with linear and nonlinear models (BATS, TBATS, Holt's linear trend, ARIMA, classical epidemiological SIR model). In our article we discuss the Epemedic.Network algorithm using the R programming language. This algorithm takes the time series as input data and chooses the best model from SIR, statistical models and neural network model. The model selection criterion is the MAPE error. We consider the implementation of our algorithm for analysis of time series for COVID -19 spreading in Chelyabinsk region, and predicting the possible peak of the third wave using three possible scenarios. We mention that the considered algorithm can work for any time se-ries, not only for epidemiological ones. Results. The developed algorithm helped to identify the pat-tern of COVID -19 infection for Chelyabinsk region using the models realized as parts of the consi-dered algorithm. It should be noted that the considered models make it possible to form short-term forecasts with sufficient accuracy. We show that the increase in the number of neurons led to in-creasing accuracy, as there are other cases where the error is reduced in case of reducing the number of neurons, and this depends on COVID -19 infection spreading pattern. Conclusion. Hence, to get a very accurate forecast, we recommend re-running the algorithm weekly. For medium-range fore-casting, only the NNAR model can be used from among those considered but it also allows to get good forecasts only with horizon 1–2 weeks.

Effectiveness of resampling methods in coping with imbalanced crash data: Crash type analysis and predictive modeling

Crash data analysis is commonly subjected to imbalanced data. Varied by facility and control types, some crash types are more frequent than others. However, uncommon crash types are routinely more severe and associated with higher economic and societal costs, and thus crucial to prevent. It is paramount to develop inferential models that can reliably predict crash types and identify attributing factors, especially for the severe types. The current process of modeling towards infrequent events generally disregards disparity in data representation, which can lead to biased models. Therefore, mitigating and managing imbalanced data is essential to the development of meaningful and robust models that help reveal effective countermeasures. This study focuses on comparing the effects of resampling techniques on the performance of both machine learning and classical statistical models for classifying and predicting different crash types on freeways. Specifically, a mixed sampling approach featuring a cluster-based under-sampling coupled with three popular over-sampling methods (i.e., random over-sampling, synthetic minority over-sampling, and adaptive synthetic sampling) were investigated with respect to four crash classification models, including three ensemble machine learning models (CatBoost, XGBoost, and Random Forests) and one classic statistical model (Nested Logit). This study concluded that all three resampling methods consistently enhanced the performance of all models. Among the three over-sampling methods, the adaptive synthetic sampling approach performed best and tremendously improved the prediction of minority crash types without impeding the prediction of the majority crash type. This is likely due to the density-based approach of adaptive synthetic sampling in creating synthetic instances that are more congruent with the underlying manifold structure embodied in the high-dimensional feature space.

Classical and machine learning modeling of crude oil production in Nigeria: Identification of an eminent model for application

The production and exportation of petroleum plays a dominant role in Nigeria’s economy. A drastic fall in the quantity of crude oil produced is fatal to the Nigerian economy since Nigeria depends heavily on the oil sector. Different classical statistical methods have been used to model the crude oil production but the application of machine learning models on crude oil production has been grossly understudied. In this study, we identified a high-performance model between a classical statistical model (ARIMA) and two machine learning models (ANN and RF) in modeling the crude oil production in Nigeria. The monthly data on crude oil production in Nigeria collected from January, 2006 to October, 2020 used in this study is secondary data from Nigerian National Petroleum Corporation (NNPC) and Reuters. The ANN model has a significant modified Diebold–Mariano test when compared with the ARIMA and RF models in the test set. The ANN model had the best trade-off of Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and Nash–Sutcliffe Efficiency (NSE) values and was used for forecasting crude oil production in Nigeria. The crude oil production is predicted to increase slightly from March, 2021 (1.67 mmbd) to September, 2021 (1.685 mmbd) before it begins a downward trend from October, 2021 (1.684 mmbd) till it gets to 1.628 mmbd in December, 2023. This predicted fall in the quantity of crude oil produced will obviously affect the Nigerian economy since Nigeria depends solely on the oil sector. There is need to diversify the monoculture economic system in Nigeria to explore and harness untapped natural resources.

Explainable AI methods in cyber risk management

AbstractArtificial intelligence (AI) methods are becoming widespread, especially when data are not sufficient to build classical statistical models, as is the case for cyber risk management. However, when applied to regulated industries, such as energy, finance, and health, AI methods lack explainability. Authorities aimed at validating machine learning models in regulated fields will not consider black‐box models, unless they are supplemented with further methods that explain why certain predictions have been obtained, and which are the variables that mostly concur to such predictions. Recently, Shapley values have been introduced for this purpose: They are model agnostic, and powerful, but are not normalized and, therefore, cannot become a standardized procedure. In this paper, we provide an explainable AI model that embeds Shapley values with a statistical normalization, based on Lorenz Zonoids, particularly suited for ordinal measurement variables that can be obtained to assess cyber risk.

Variability and Randomness of the Instantaneous Firing Rate.

The apparent stochastic nature of neuronal activity significantly affects the reliability of neuronal coding. To quantify the encountered fluctuations, both in neural data and simulations, the notions of variability and randomness of inter-spike intervals have been proposed and studied. In this article we focus on the concept of the instantaneous firing rate, which is also based on the spike timing. We use several classical statistical models of neuronal activity and we study the corresponding probability distributions of the instantaneous firing rate. To characterize the firing rate variability and randomness under different spiking regimes, we use different indices of statistical dispersion. We find that the relationship between the variability of interspike intervals and the instantaneous firing rate is not straightforward in general. Counter-intuitively, an increase in the randomness (based on entropy) of spike times may either decrease or increase the randomness of instantaneous firing rate, in dependence on the neuronal firing model. Finally, we apply our methods to experimental data, establishing that instantaneous rate analysis can indeed provide additional information about the spiking activity.

Statistical mechanical models for quantum codes with correlated noise

We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl, and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or subsystem codes subject to correlated Pauli noise models, including models of fault tolerance. This mapping connects the error correction threshold of the quantum code to a phase transition in the statistical mechanical model. Thus, any existing method for finding phase transitions, such as Monte Carlo simulations, can be applied to approximate the threshold of any such code, without having to perform optimal decoding. By way of example, we numerically study the threshold of the surface code under mildly correlated bit-flip noise, showing that noise with bunching correlations causes the threshold to drop to p_{\textup{corr}}=10.04(6)\% , from its known iid value of p_{\text{iid}}=10.917(3)\% . Complementing this, we show that the mapping also allows us to utilise any algorithm which can calculate/approximate partition functions of classical statistical mechanical models to perform optimal/approximately optimal decoding. Specifically, for 2D codes subject to locally correlated noise, we give a linear-time tensor network-based algorithm for approximate optimal decoding which extends the MPS decoder of Bravyi, Suchara and Vargo.

Using Model Averaging to Determine Suitable Risk Measure Estimates

Recent research in loss modeling resulted in a growing number of classes of statistical models as well as additional models being proposed within each class. Empirical results indicate that a range of models within or between model classes perform similarly well, as measured by goodness-of-fit or information criteria, when fitted to the same data set. This leads to model uncertainty and makes model selection a challenging task. This problem is particularly virulent if the resulting risk measures vary greatly between and within the model classes. We propose an approach to estimate risk measures that accounts for model selection uncertainty based on model averaging. We exemplify the application of the approach considering the class of composite models. This application considers 196 different left-truncated composite models previously used in the literature for loss modeling and arrives at point estimates for the risk measures that take model uncertainty into account. A simulation study highlights the benefits of this approach. The data set on Norwegian fire losses is used to illustrate the proposed methodology.

Pattern similarity-based machine learning methods for mid-term load forecasting: A comparative study

Pattern similarity-based frameworks are widely used for classification and regression problems. Repeated, similar-shaped cycles observed in seasonal time series encourage the use of such frameworks for forecasting. In this paper, we use pattern similarity-based models for mid-term load forecasting. An integral part of these models is the use of patterns of time series sequences for time series representation. Pattern representation ensures input and output data unification through trend filtering and variance equalization. This simplifies the forecasting problem and allows us to use models based on pattern similarity. We consider four such models: nearest-neighbor model, fuzzy neighborhood model, kernel regression model, and general regression neural network. Three variants of the approach were proposed. A basic one and two hybrid solutions combining similarity-based and statistical methods (ARIMA and exponential smoothing).In the experimental part of the work, the proposed models were used to forecast the monthly electricity demand in 35 European countries. The results show the high performance of the proposed models, which outperform both the comparative classical statistical models and machine learning models in terms of accuracy, simplicity, and ease of optimization. Among the proposed variants, a hybrid approach combining similarity-based methods with exponential smoothing turned out to be the most accurate. The study highlights the many advantages of the proposed pattern similarity-based models such as clear operation principles, a small number of parameters to adjust, no training procedure, fast optimization procedure, good generalization ability, ability to work on the newest data without retraining, and delivery of multi-step forecasts.

Separation of au, Ag, As, Cd, Cu, Hg, Mo and Sb geochemical anomalies using the concentration-number (C-N) fractal and classical statistical models in Nahavand 1: 100,000 sheet, Iran

The main aim of this research is finding the most promising concentration areas of the Au and their paragenesis in order to prospect the most accurate anomalies in Nahavand 1:100,000 sheet. Based on the generated models, the results of the C-N model are more accurate than the conventional ones although they have good correlations with each other. The anomalies are correlated with faults and structure trending NW-SE, which correlate with main structural trends in Sanandaj-Sirjan Zone. Gold mineralization was very well reflected by the geochemical signature of these elements in the sediment samples of the area. The results derived via C-N fractal model exhibit Au anomalies in the northwest, west and southeast parts of the area. The use of a multivariate statistical method such as the factor analysis greatly helped the interpretation of the data set in this study. The application of this technique gave rise to a significant conception of the geochemistry of the stream sediments in the study area. Based on correlation between obtained results with geological data, the major anomalies of Au and related factors are mostly situated around slates and metavolcanic rocks.

Spatial modeling of individual‐level infectious disease transmission: Tuberculosis data in Manitoba, Canada

Geographically dependent individual level models (GD-ILMs) are a class of statistical models that can be used to study the spread of infectious disease through a population in discrete-time in which covariates can be measured both at individual and area levels. The typical ILMs to illustrate spatial data are based on the distance between susceptible and infectious individuals. A key feature of GD-ILMs is that they take into account the spatial location of the individuals in addition to the distance between susceptible and infectious individuals. As a motivation of this article, we consider tuberculosis (TB) data which is an infectious disease which can be transmitted through individuals. It is also known that certain areas/demographics/communities have higher prevalent of TB (see Section 4 for more details). It is also of interest of policy makers to identify those areas with higher infectivity rate of TB for possible preventions. Therefore, we need to analyze this data properly to address those concerns. In this article, the expectation conditional maximization algorithm is proposed for estimating the parameters of GD-ILMs to be able to predict the areas with the highest average infectivity rates of TB. We also evaluate the performance of our proposed approach through some simulations. Our simulation results indicate that the proposed method provides reliable estimates of parameters which confirms accuracy of the infectivity rates.