Parameters Of Probabilistic Model Research Articles

Poisson Modeling Predicts Acute Telestroke Patient Call Volume.

Background: Predicting the frequency of calls for telestroke and emergency teleneurology consultation is essential to prepare staffing for the immediate management of time-sensitive strokes. In this study, we evaluate Poisson distribution count data using a generalized linear model that predicts the volume of hourly telestroke calls over a 24-h period. Methods: We performed an Institutional Review Board approved retrospective cohort review of patients (January 2019-December 2022) from an institutional telestroke database at a large nonprofit multihospital system in the United States. All patients ≥18 years with a telestroke activation were included. Telestroke calls were quantified in frequency per day and analyzed by multiple time and date intervals. Poisson probability mass function (PMF) and cumulative distribution function (CDF) were used to predict call probabilities. A univariable Poisson regression model was fit to predict call volumes. Results: A total of 8,499 patients at 21 hospitals met inclusion criteria, the mean calls/day were 5.82 ± 2.54, and mean calls/day within each hour increment ranged from a minimum of 0.07 from 5 a.m. to 6 a.m. to a maximum of 0.45 from 7 p.m. to 8 p.m. The Poisson distribution was the most appropriate parametric probability model for these data, confirmed by the fit of the data to the expected distributions corresponding to the calculated means. The predicted probabilities of call frequencies by hour were calculated using the Poisson PMF and CDF; the probability of two or fewer calls/day by hour ranged from 98.9% to 99.9%. Univariable Poisson regression modeled an increase of future calls/day from 6.7 calls/day in July 2023 to 7.6 calls/day in October 2025. Conclusion: Poisson modeling closely fits telestroke call volumes, predicts the future volumes, and can be applied to any health system in which the mean call volume is known, which may inform the number of physicians needed to cover calls in real-time.

Inferring from an imprecise Plackett–Luce model: Application to label ranking

The Plackett–Luce model is a popular parametric probabilistic model to define distributions between rankings of objects, modelling for instance observed preferences of users or ranked performances of algorithms. Since such observations may be scarce (users may provide partial preferences, or not all algorithms are run for a given experiment), it may be useful to consider the case where the parameters of the Plackett–Luce model are imprecisely known. In this paper, we first introduce the imprecise Plackett–Luce model, induced by a set of parameters (for instance, parameters with a high relative likelihood). Given a set of possible parameters for the model, we then provide an efficient algorithm to make cautious inferences, returning sets of possible optimal rankings (for instance in the form of partial orders). We illustrate the use of our imprecise model on label ranking, a specific kind of supervised learning.

Stochastic Thermodynamics of Learning Parametric Probabilistic Models.

We have formulated a family of machine learning problems as the time evolution of parametric probabilistic models (PPMs), inherently rendering a thermodynamic process. Our primary motivation is to leverage the rich toolbox of thermodynamics of information to assess the information-theoretic content of learning a probabilistic model. We first introduce two information-theoretic metrics, memorized information (M-info) and learned information (L-info), which trace the flow of information during the learning process of PPMs. Then, we demonstrate that the accumulation of L-info during the learning process is associated with entropy production, and the parameters serve as a heat reservoir in this process, capturing learned information in the form of M-info.

OFDM-Based Massive Connectivity for LEO Satellite Internet of Things

Low earth orbit (LEO) satellite has been considered as a potential supplement for the terrestrial Internet of Things (IoT). In this paper, we consider grant-free non-orthogonal random access (GF-NORA) in the orthogonal frequency division multiplexing (OFDM) system to increase access capacity and reduce access latency for LEO satellite-IoT. We focus on the joint device activity detection (DAD) and channel estimation (CE) problem at the satellite access point. The delay and the Doppler effect of the LEO satellite channel are assumed to be partially compensated. We propose an OFDM-symbol repetition technique to better distinguish the residual Doppler frequency shifts, and present a grid-based parametric probability model to characterize channel sparsity in the delay-Doppler-user domain, as well as to characterize the relationship between the channel states and the device activity. Based on that, we develop a robust Bay esian message-passing algorithm named modified variance state propagation (MVSP) for joint DAD and CE. Moreover, to tackle the mismatch between the real channel and its on-grid representation, an expectation–maximization (EM) framework is proposed to learn the grid parameters. Simulation results demonstrate that our proposed algorithms significantly outperform the existing approaches in both activity detection probability and channel estimation accuracy.

Accelerated Maximum Entropy Method for Time Series Models Estimation

The work is devoted to the development of a maximum entropy estimation method with soft randomization for restoring the parameters of probabilistic mathematical models from the available observations. Soft randomization refers to the technique of adding regularization to the functional of information entropy in order to simplify the optimization problem and speed up the learning process compared to the classical maximum entropy method. Entropic estimation makes it possible to restore probability distribution functions for model parameters without introducing additional assumptions about the likelihood function; thus, this estimation method can be used in problems with an unspecified type of measurement noise, such as analysis and forecasting of time series.

Modelling Wind Turbine Power Curves based on Frank’s copula

In the study of wind turbines, one of the most relevant and useful indicators is the power curve. It has been shown to be of paramount importance in evaluating turbine performance and therefore reducing operation and maintenance (O&M) costs. Various techniques can be applied to model and obtain the shape of this curve, which relates the electrical power generated by a turbine to the wind speed. Statistical copulas are used in this paper, a tool used in other fields such as econometrics, and whose potential lies in its ability to capture the complex dependency between the variables involved. In particular, the Frank copula is applied to obtain a probabilistic model of the power curve of a wind turbine. This model is compared with the Gaussian Mixture Model, a technique widely used to obtain parametric probabilistic models. As a result of this comparison, it is observed that the Frank copula model fits the power curve of the wind turbine with greater precision and reliability, which would allow its use for prediction and fault detection.

Tensor train factorization under noisy and incomplete data with automatic rank estimation

As a powerful tool in analyzing multi-dimensional data, tensor train (TT) decomposition shows superior performance compared to other tensor decomposition formats. Existing TT decomposition methods, however, either easily overfit with noise, or require substantial fine-tuning to strike a balance between recovery accuracy and model complexity. To avoid the above shortcomings, this paper treats the TT decomposition in a fully Bayesian perspective, which includes automatic TT rank determination and noise power estimation. Theoretical justification on adopting the Gaussian-product-Gamma priors for inducing sparsity on the slices of the TT cores is provided, thus allowing the model complexity to be automatically determined even when the observed tensor data is noisy and contains many missing values. Furthermore, using the variational inference framework, an effective learning algorithm on the probabilistic model parameters is derived. Simulations on synthetic data demonstrate that the proposed algorithm accurately recovers the underlying TT structure from incomplete noisy observations. Further experiments on image and video data also show its superior performance to other existing TT decomposition algorithms.

Random partitions with two-side bounds and $(r,s)$-Bell polynomials in a parametric probabilistic model

Рассматриваются $A_{r,s}$-разбиения $n$-множества $X_n = $ $\{1,2,\ldots,n\}$, т. е. такие разбиения, когда все блоки разбиения имеют размеры, являющиеся элементами заданного подмножества натуральных чисел $A_{r,s} = \{i: r < i \leqslant s \}$, $0 \leqslant r < s \leqslant n$. На множестве таких разбиений задается вероятностная мера, согласно которой любому разбиению с $k$ блоками приписывается вероятность, пропорциональная $\theta^k$, где $\theta > 0$ - параметр меры. Для такой модели изучается распределение общего числа блоков $\xi_{n,r,s}$ случайного разбиения множества $X_n$. Определяются $(r,s)$-полиномы Белла и исследуется их асимптотическое поведение, когда параметры $n,r,s$ стремятся к бесконечности согласованным образом. На этой основе доказывается асимптотическая нормальность $\xi_{n,r,s}$. Построены статистические критерии проверки гипотезы равновероятности $H_0\colon \theta = 1$ относительно альтернатив $H_1\colon \theta \ne 1$.

A method to characterize climate, Earth or environmental vector random processes

We propose a general methodology to characterize a non-stationary random process that can be used for simulating random realizations that keep the probabilistic behavior of the original time series. The probability distribution of the process is assumed to be a piecewise function defined by several weighted parametric probability models. The weights are obtained analytically by ensuring that the probability density function is well defined and that it is continuous at the common endpoints. Any number of subintervals and continuous probability models can be chosen. The distribution is assumed to vary periodically in time over a predefined time interval by defining the model parameters and the common endpoints as truncated generalized Fourier series. The coefficients of the expansions are obtained with the maximum likelihood method. Different sets of orthogonal basis functions are tested. The method is applied to three time series with different particularities. Firstly, it is shown its good behavior to capture the high variability of the precipitation projected at a semiarid location of Spain for the present century. Secondly, for the Wolf sunspot number time series, the Schwabe cycle and time variations close to the 7.5 and 17 years are analyzed along a 22-year cycle. Finally, the method is applied to a bivariate time series that contains (1) freshwater discharges at the last regulation point of a dam located in a semiarid zone in Andalucía (Spain) which is influenced not only by the climate variability but also by management decisions and (2) the salinity at the mouth of the river. For this case, the analysis, that was combined with a vectorial autoregressive model, focus on the assessment of the goodness of the methodology to replicate the statistical features of the original series. In particular, it is found that it reproduces the marginal and joint distributions and the duration of sojourns above/below given thresholds.

The risk of death in newborn businesses during the first years in market

In this paper, we analysed how business age and mortality are related during the first years of life, and tested the different hypotheses proposed in the literature. For that, we used data on US business establishments, with 1-year resolution in the range of age of 0–5 years, in the period 1978–2019, published by the US Census Bureau. First, we explored the adaptation of classical techniques of survival analysis (the life table and Peto–Turnbull methods) to business survival analysis. Then, we considered nine parametric probabilistic models, most of them well known in reliability analysis and in the actuarial literature, with different shapes of the hazard function, that we fitted by maximum-likelihood method and compared with the Akaike information criterion. Our findings show that newborn firms seem to have a decreasing failure rate with age during the first 5 years in market, with the exception of the first months of some years in which the risk can rise.

Probabilistic Assessment of the Dynamic Viscosity of Self-Compacting Steel-Fiber Reinforced Concrete through a Micromechanical Model.

This article develops a probabilistic approach to a micromechanical model to calculate the dynamic viscosity in self-compacting steel-fiber reinforced concrete (SCSFRC), which implies a paradigm shift in the approach of the deterministic models used. It builds on a previous work by the authors in which Bayesian analysis is applied to rheological micromechanical models in cement paste, self-compacting mortar, and self-compacting concrete. As a consequence of the varied characteristics of the particles in these suspensions (in terms of materials, shapes, size distributions, etc.), as well as their random nature, it seems appropriate to study these systems with probabilistic models. The Bayesian analysis, thorough Markov Chain Monte Carlo and Gibbs Sampling methods, allows the conversion of parametric-deterministic models into parametric-probabilistic models, which results in enrichment in engineering and science. The incorporation of steel fibers requires a new term in the model to account for their effect on the dynamic viscosity of SCSFRC, and this new term is also treated here with the Bayesian approach. The paper uses an extensive collection of experimental data to obtain the probability density functions of the parameters for assessing the dynamic viscosity in SCSFRC. The results obtained with these parameters’ distributions are much better than those calculated with the theoretical values of the parameters, which indicates that Bayesian methods are appropriated to respond to questions in complex systems with complex models.

D3p - A Python Package for Differentially-Private Probabilistic Programming

Abstract We present d3p, a software package designed to help fielding runtime efficient widely-applicable Bayesian inference under differential privacy guarantees. d3p achieves general applicability to a wide range of probabilistic modelling problems by implementing the differentially private variational inference algorithm, allowing users to fit any parametric probabilistic model with a differentiable density function. d3p adopts the probabilistic programming paradigm as a powerful way for the user to flexibly define such models. We demonstrate the use of our software on a hierarchical logistic regression example, showing the expressiveness of the modelling approach as well as the ease of running the parameter inference. We also perform an empirical evaluation of the runtime of the private inference on a complex model and find a ~10 fold speed-up compared to an implementation using TensorFlow Privacy.

Using a Probabilistic Model and Local Parameters to Improve the Reliability of Ambient Water Quality Criteria for the Protection of Human Health: A Case Study of Organophosphate Esters in China

Water quality criteria for the protection of human health (HHWQC) are crucial for the management of aquatic environmental quality. However, previous studies derived HHWQC using only deterministic approaches, which may under/overprotect target populations. This paper improved the methodology for criteria development and applied it to organophosphate esters (OPEs). Missing model parameters, including the trophic level-specific fish consumption rate (FIn) and lipid fraction (fl(TL,n)), were derived according to China’s conditions. The trophic level-specific national bioaccumulation factors (BAFs) for OPEs (5.05–14,281 L/kg) were calculated based on field-measured BAFs in surface freshwater across China and were dominated by the hydrophobicity of compounds. Then, the probabilistic approach was introduced to HHWQC derivation (0.1120–400.5 μg/L), and the results were compared with those derived by the deterministic method (0.1024–664.5 μg/L), which demonstrated that the probabilistic approach derived HHWQC more accurately. The contributions of organism ingestion to the HHWQC for OPEs were steady (<10%) with log Kow<3.5, increased linearly (10–90%) within a log Kow of 3.5–5.5, and then leveled off. Regarding the effects of carcinogenic OPEs, approximately 10% of the studied freshwater in China displays significant risks to human health. This study is significant for the scientific development of HHWQC worldwide and the management of pollutants in water.

Multi-vehicle interaction safety of connected automated vehicles in merging area: A real-time risk assessment approach

The risky lane-changing manoeuvre of vehicles often occurs at expressway entrances, which would result in a high crash risk in the freeway system and significantly impact its safety. The highly anticipated environment of connected and autonomous vehicles (CAVs) is expected to reduce the associated crash risk of lane changing by offering various types of driving support, which utilise surrounding traffic information. The modelling crash risk under the environment of CAV driving during mandatory lane changing in merging areas faces new challenges due to the novelty of CAVs and subsequent shortage of data. To explore such risk situation of multi-vehicle interaction at expressway entrances, this study proposed a supervised learning algorithm and a Bayesian hierarchical model to assess risk levels and predict the probability of risk occurrence at different risk levels of interactive vehicles in real time of mandatory driving behaviour during the merging process. The learning algorithm, based on XGBoost, was exploited to classify risk levels. The Bayesian hierarchical model was used to analyse the probability of real-time risk comprising vehicle physical state layer, multi-vehicle interaction layer and risk probability layer. The probabilistic model parameters were calibrated using Markov Chain Monte Carlo (MCMC) Gibbs sampling method. The K-fold cross validation method was used to validate the proposed model of risk level. The probabilistic model validity was tested through posterior prediction of P-value. The quantitative risk estimation of CAVs through a few merging cases was conducted. Results show that the identification accuracy of slight, low, moderate and high risk is 94.24%, 85.82%, 84.16% and 79.69%, respectively. The P-value of Durbin–Watson’s posterior, normal hypothesis, test distribution symmetry and kurtosis are all close to 0.5. Therefore, the method of real-time risk assessment is convergent and has good fitting. This research can promote cautious driving behaviours and provide reference for driver’s decision making in the long term under the environment of CAVs.

Probabilistic prediction and calibration for residual shear strength of corroded reinforced concrete columns

Degradation of shear strength for reinforced concrete (RC) columns caused by steel corrosion is one of the prominent factors for shortening the entire service life of RC structures. In this work, probabilistic prediction and calibration methods for residual shear strength of corroded RC columns were developed by combining theoretical analysis with available experimental data. Deterministic shear strength degradation model accounting for the cross-sectional area reduction and mechanical properties degradation of steel reinforcement and concrete was derived first based on the truss and arch mechanisms. Then probabilistic prediction model was proposed by introducing probabilistic model parameters and systematic error. Meanwhile, probabilistic model parameters regarding the influences of prior variation coefficients and update times were investigated using the Bayesian theory. Moreover, probabilistic method was implemented to calibrate seven available deterministic shear strength models based on probability density function and confidence interval. Results indict that the proposed model can not only quantify the probabilistic characteristics of shear strength and predict the residual shear strength for any given corrosion level and guarantee rate, but also provide a suitable approach for calibrating the applicability of conventional deterministic shear strength models.

Sampling the Variational Posterior with Local Refinement.

Variational inference is an optimization-based method for approximating the posterior distribution of the parameters in Bayesian probabilistic models. A key challenge of variational inference is to approximate the posterior with a distribution that is computationally tractable yet sufficiently expressive. We propose a novel method for generating samples from a highly flexible variational approximation. The method starts with a coarse initial approximation and generates samples by refining it in selected, local regions. This allows the samples to capture dependencies and multi-modality in the posterior, even when these are absent from the initial approximation. We demonstrate theoretically that our method always improves the quality of the approximation (as measured by the evidence lower bound). In experiments, our method consistently outperforms recent variational inference methods in terms of log-likelihood and ELBO across three example tasks: the Eight-Schools example (an inference task in a hierarchical model), training a ResNet-20 (Bayesian inference in a large neural network), and the Mushroom task (posterior sampling in a contextual bandit problem).

Maximum Probability Theorem: A Framework for Probabilistic Machine Learning

We present a theoretical framework of probabilistic learning derived from the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">maximum probability (MP) theorem</i> shown in this article. In this probabilistic framework, a model is defined as an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">event</i> in the probability space, and a model or the associated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">event</i> —either the true underlying model or the parameterized model—has a quantified probability measure. This quantification of a model's probability measure is derived by the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MP theorem</i> , in which we have shown that an event's probability measure has an upper bound given its conditional distribution on an arbitrary random variable. Through this alternative framework, the notion of model parameters is encompassed in the definition of the model or the associated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">event</i> . Therefore, this framework deviates from the conventional approach of assuming a prior on the model parameters. Instead, the regularizing effects of assuming prior over parameters are imposed through maximizing probabilities of models or, according to information theory, minimizing the information content of a model. The probability of a model in our framework is invariant to reparameterization and is solely dependent on the model's likelihood function. In addition, rather than maximizing the posterior in a conventional Bayesian setting, the objective function in our alternative framework is defined as the probability of set operations (e.g., intersection) on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">event</i> of the true underlying model and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">event</i> of the model at hand. Our theoretical framework adds clarity to probabilistic learning through solidifying the definition of probabilistic models, quantifying their probabilities, and providing a visual understanding of objective functions. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>Impact Statement</i>—The choice of prior distribution over the parameters of probabilistic machine learning models determines the regularization of learning algorithms in the Bayesian perspective. The complexity in choice of prior over the parameters and the form of regularization is relative to the complexity of the models being used. Thereby, finding priors for parameters of complex models is often not tractable. We address this problem by uncovering the maximum probability (MP) theorem as a direct consequence of Kolmogorov's probability theory. Through the lens of the MP theorem, the process of regularizing models is understood and automated. The regularization process is defined as the maximization of the probability of the model. The probability of the model is understood by the MP theorem and is determined by the behavior of the model. The effects of maximizing the probability of the model can be backpropagated in a gradient-based optimization process. Consequently, the MP framework provides a form of black-box regularization and eliminates the need for case-by-case analysis of models to determine priors.

Inferring Urban Social Networks from Publicly Available Data

The definition of suitable generative models for synthetic yet realistic social networks is a widely studied problem in the literature. By not being tied to any real data, random graph models cannot capture all the subtleties of real networks and are inadequate for many practical contexts—including areas of research, such as computational epidemiology, which are recently high on the agenda. At the same time, the so-called contact networks describe interactions, rather than relationships, and are strongly dependent on the application and on the size and quality of the sample data used to infer them. To fill the gap between these two approaches, we present a data-driven model for urban social networks, implemented and released as open source software. By using just widely available aggregated demographic and social-mixing data, we are able to create, for a territory of interest, an age-stratified and geo-referenced synthetic population whose individuals are connected by “strong ties” of two types: intra-household (e.g., kinship) or friendship. While household links are entirely data-driven, we propose a parametric probabilistic model for friendship, based on the assumption that distances and age differences play a role, and that not all individuals are equally sociable. The demographic and geographic factors governing the structure of the obtained network, under different configurations, are thoroughly studied through extensive simulations focused on three Italian cities of different size.

Calculation of Dynamic Viscosity in Concentrated Cementitious Suspensions: Probabilistic Approximation and Bayesian Analysis.

We present a new focus for the Krieger–Dougherty equation from a probabilistic point of view. This equation allows the calculation of dynamic viscosity in suspensions of various types, like cement paste and self-compacting mortar/concrete. The physical meaning of the parameters that intervene in the equation (maximum packing fraction of particles and intrinsic viscosity), together with the random nature associated with these systems, make the application of the Bayesian analysis desirable. This analysis permits the transformation of parametric-deterministic models into parametric-probabilistic models, which improves and enriches their results. The initial limitations of the Bayesian methods, due to their complexity, have been overcome by numerical methods (Markov Chain Monte Carlo and Gibbs Sampling) and the development of specific software (OpenBUGS). Here we use it to compute the probability density functions that intervene in the Krieger–Dougherty equation applied to the calculation of viscosity in several cement pastes, self-compacting mortars, and self-compacting concretes. The dynamic viscosity calculations made with the Bayesian distributions are significantly better than those made with the theoretical values.

Probabilistic inductive constraint logic

Probabilistic logical models deal effectively with uncertain relations and entities typical of many real world domains. In the field of probabilistic logic programming usually the aim is to learn these kinds of models to predict specific atoms or predicates of the domain, called target atoms/predicates. However, it might also be useful to learn classifiers for interpretations as a whole: to this end, we consider the models produced by the inductive constraint logic system, represented by sets of integrity constraints, and we propose a probabilistic version of them. Each integrity constraint is annotated with a probability, and the resulting probabilistic logical constraint model assigns a probability of being positive to interpretations. To learn both the structure and the parameters of such probabilistic models we propose the system PASCAL for “probabilistic inductive constraint logic”. Parameter learning can be performed using gradient descent or L-BFGS. PASCAL has been tested on 11 datasets and compared with a few statistical relational systems and a system that builds relational decision trees (TILDE): we demonstrate that this system achieves better or comparable results in terms of area under the precision–recall and receiver operating characteristic curves, in a comparable execution time.