Conditional Expectation Research Articles

Geriatric assessment - What should be done and considered before starting therapy of mHSPC and mCRPC?

The systemic treatment of prostate cancer nowadays is predominantly carried out with combination therapies. A range of aspects should be respected in older and comorbid patients, in order to avoid toxicities and to achieve a successful therapy alongside good quality of life. The definition of geriatric patients is not primarily based on chronological age but rather on the overall health condition and life expectancy. Comorbid patients > 70 years should undergo a three-step geriatric screening before treatment initiation. If the G8 screening and/or mini-COG shows abnormalities (taking into account nutrition, comorbidity/medication, mobility, and cognition), a simplified geriatric assessment is recommended. Patients can then be stratified into three groups (fit, vulnerable, frail). Only a few cases warrant a complete geriatric assessment. Treatable deficits in the above mentioned domains should be improved if possible. When choosing a systemic therapy, fit patients can be treated the same as non-geriatric patients. Vulnerable and frail patients are under a higher risk for toxicities, so special care should be taken. While the diverse substances of hormonal therapy are usually well tolerated (even though some substance-specific toxicities can occur), haematotoxic substances such as taxanes or olaparib can only be recommended in select cases. As falls - especially under hormonal therapy - are a common problem, osteoprotective therapy should especially be considered. Upon progression of the tumour disease, there should not be a reflex to simply switch to the next line of treatment, but an individual concept should be established together with the patient and his relatives, taking into account aspects of palliative care and patient needs and focussing on quality of life and also setting therapy limitations.

Capacity-constrained mean-excess equilibrium assignment method for railway networks

The reliability and unreliability of travel time variability caused by stochastic train delays considerably influence passengers’ travel path choices. This paper proposes an equilibrium assignment method that can capture the passengers’ path choice behaviors considering both the reliability and unreliability of travel time variability in the railway network. The passengers’ travel path choices are modeled using the mean-excess travel cost (METC), which is the combination of the conditional expectation of travel cost exceeding the effective travel cost, and the endogenous advanced ticket booking cost associated with the rigid train capacity. In general, heterogeneous passengers with different risk-aversion attitudes toward stochastic train delays evaluate their travel options differently and have different requirements for successful transfer. Therefore, first, the passengers’ transfer options are modeled with the concept of METC based on the delay distribution of the two connecting trains. Subsequently, the METC of the passenger trips is calculated. A mean-excess passenger flow assignment model is formulated based on the user equilibrium condition. A path-based capacity-constrained passenger assignment algorithm is designed to solve the model. Moreover, three illustrative examples are presented to demonstrate the effectiveness of the model and solution algorithm.

Machine learning approaches in microbiome research: challenges and best practices.

Microbiome data predictive analysis within a machine learning (ML) workflow presents numerous domain-specific challenges involving preprocessing, feature selection, predictive modeling, performance estimation, model interpretation, and the extraction of biological information from the results. To assist decision-making, we offer a set of recommendations on algorithm selection, pipeline creation and evaluation, stemming from the COST Action ML4Microbiome. We compared the suggested approaches on a multi-cohort shotgun metagenomics dataset of colorectal cancer patients, focusing on their performance in disease diagnosis and biomarker discovery. It is demonstrated that the use of compositional transformations and filtering methods as part of data preprocessing does not always improve the predictive performance of a model. In contrast, the multivariate feature selection, such as the Statistically Equivalent Signatures algorithm, was effective in reducing the classification error. When validated on a separate test dataset, this algorithm in combination with random forest modeling, provided the most accurate performance estimates. Lastly, we showed how linear modeling by logistic regression coupled with visualization techniques such as Individual Conditional Expectation (ICE) plots can yield interpretable results and offer biological insights. These findings are significant for clinicians and non-experts alike in translational applications.

Machine Learning Aided Prediction of Glass-Forming Ability of Metallic Glass

The prediction of the glass-forming ability (GFA) of metallic glasses (MGs) can accelerate the efficiency of their development. In this paper, a dataset was constructed using experimental data collected from the literature and books, and a machine learning-based predictive model was established to predict the GFA. Firstly, a classification model based on the size of the critical diameter (Dmax) was established to determine whether an alloy system could form a glass state, with an accuracy rating of 0.98. Then, regression models were established to predict the crystallization temperature (Tx), glass transition temperature (Tg), and liquidus temperature (Tl) of MGs. The R2 of the prediction model obtained in the test set was greater than 0.89, which showed that the model had good prediction accuracy. The key features used by the regression models were analyzed using variance, correlation, embedding, recursive, and exhaustive methods to select the most important features. Furthermore, to improve the interpretability of the prediction model, feature importance, partial dependence plot (PDP), and individual conditional expectation (ICE) methods were used for visualization analysis, demonstrating how features affect the target variables. Finally, taking Zr-Cu-Ni-Al system MGs as an example, a prediction model was established using a genetic algorithm to optimize the alloy composition for high GFA in the compositional space, achieving the optimal design of alloy composition.

A posteriori error estimates for fully coupled McKean–Vlasov forward-backward SDEs

Abstract Fully coupled McKean–Vlasov forward-backward stochastic differential equations (MV-FBSDEs) arise naturally from large population optimization problems. Judging the quality of given numerical solutions for MV-FBSDEs, which usually require Picard iterations and approximations of nested conditional expectations, is typically difficult. This paper proposes an a posteriori error estimator to quantify the $L^2$-approximation error of an arbitrarily generated approximation on a time grid. We establish that the error estimator is equivalent to the global approximation error between the given numerical solution and the solution of a forward Euler discretized MV-FBSDE. A crucial and challenging step in the analysis is the proof of stability of this Euler approximation to the MV-FBSDE, which is of independent interest. We further demonstrate that, for sufficiently fine time grids, the accuracy of numerical solutions for solving the continuous MV-FBSDE can also be measured by the error estimator. The error estimates justify the use of residual-based algorithms for solving MV-FBSDEs. Numerical experiments for MV-FBSDEs arising from mean field control and games confirm the effectiveness and practical applicability of the error estimator.

Conditional supremum in Riesz spaces and applications

We extend the concept of conditional supremum to the measure-free setting of Riesz spaces via the conditional expectation operator. We explore its properties and show how this tool is crucial in generalizing various results across multiple disciplines to the framework of Riesz spaces. Among other applications, we utilize this concept in finance to derive characterizations of certain financial conditions.

Beurling type representation for certain invariant subspaces of maximal subdiagonal algebras

Let A be a maximal subdiagonal algebra in a σ-finite von Neumann algebra M with respect to a faithful normal conditional expectation Φ. We consider certain invariant subspaces of A in the Haagerup noncommutative Lp space Lp(M) (1≤p≤∞). Suppose that φ is a faithful normal state on M with φ∘Φ=φ and {σtφ:t∈R} is the modular automorphism group of M associated with φ, we give a Beurling type representation for those right invariant subspaces of A in Lp(M) which are also invariant under {σtφ:t∈R}. Furthermore, we give an algebraic characterization for a subdiagonal algebra to be type 1 and also give a type decomposition for a central projection in M associated with the center of D.

Beyond prediction: An integrated post-hoc approach to interpret complex model in hydrometeorology

With the increasing application of machine learning (ML) in hydrometeorology, we face the urge to demystify the ML's black-box nature because it usually does not provide physically interpretable information to users. Here, we demonstrate multiple post-hoc interpretation methods to evaluate feature effects for hydrometeorological prediction. These methods were integrated and applied to soil moisture (SM) as an example, and random forest was used to establish a prediction model based on a FLUXNET site in Haibei, China. Different views of interpretability, feature importance, Shapley values, partial dependence plot, individual conditional expectation, and accumulated local effect were used to investigate how features affect the prediction. The result shows that a comprehensive understanding can be achieved of the relationship between predicted SM and affecting variables, including lagged SM, precipitation, and soil temperature. Thus, we advocated integrated interpretation tools to enhance the practicability of ML for hydrologists and other physical scientists. A toolbox named ExplainAI is provided.

Mixed $q$-deformed Araki–Woods von Neumann algebras

Given a strongly continuous orthogonal representation (U_t)_{t\in \mathbb{R}} of \mathbb{R} on a real Hilbert space {\mathcal{H}}_{\mathbb{R}} , a decomposition {\mathcal{H}}_{\mathbb{R}}:=\bigoplus_{i\in N}\mathcal{H}_{\mathbb{R}}^{(i)} consisting of invariant subspaces of (U_t)_{t\in\mathbb{R}} and an appropriate matrix ((q_{ij}))_{N\times N} of real parameters, we associate representations of the mixed commutation relations on twisted Fock spaces. The associated von Neumann algebras are (usually) non-tracial and are generalizations of those constructed by Bożejko–Speicher and Hiai. We investigate the factoriality of these von Neumann algebras. Along the process, we show that the generating abelian subalgebras associated with the blocks of the aforesaid decomposition are strongly mixing masas when they admit appropriate conditional expectations. On the contrary, the generating abelian algebras which fail to admit appropriate conditional expectations are quasi-split. We also discuss non-injectivity and the Haagerup approximation property.

Significance test for semiparametric conditional average treatment effects and other structural functions

The paper investigates a hypothesis testing problem concerning the potential additional contributions of other covariates to the structural function, given the known covariates. The structural function is the conditional expectation given covariates in which the response may depend on unknown nuisance functions. It includes classic regression functions and the conditional average treatment effects as illustrative instances. Based on Neyman's orthogonality condition, the proposed distance-based test exhibits the quasi-oracle property in the sense that the nuisance function asymptotically does not influence on the limiting distributions of the test statistic under both the null and alternatives. This novel test can effectively detect the local alternatives distinct from the null at the fastest possible rate in hypothesis testing. This is particularly noteworthy given the involvement of nonparametric estimation of the conditional expectation. Numerical studies are conducted to examine the performance of the test. In the real data analysis section, the proposed tests are applied to identify significantly explanatory covariates that are associated with AIDS treatment effects, yielding noteworthy insights.

Reliability Estimation of Inverse Weibull Distribution Based on Intuitionistic Fuzzy Lifetime Data

As a commonly used model in reliability analysis, the inverse Weibull distribution (IWD) is widely applied in various scientific fields. This paper considers the reliability estimation of the IWD based on intuitionistic fuzzy lifetime data. Firstly, the related concepts of the fuzzy set theory are reviewed, and the concepts of the intuitionistic fuzzy conditional density, intuitionistic fuzzy likelihood function, and intuitionistic fuzzy conditional expectation are obtained by extension. In classical estimations, the maximum likelihood estimators of parameters and reliability are derived. Due to the nonlinearity, the EM algorithm is used to obtain the maximum likelihood estimates. In the Bayesian estimation, the gamma prior is selected, and the Bayesian estimation of the parameters and reliability is conducted under the symmetric entropy and the scale square error loss function, respectively. Since the integrals are complicated, the Lindley approximation is used to approximate the Bayesian estimates. Then, the performance of these estimators is evaluated by the Monte Carlo simulation. The simulation results show that the Bayesian estimation is more suitable than the maximum likelihood estimation for the reliability estimation. Finally, a set of real data is used to prove the effectiveness of these proposed methods. Through these methods, the reliability of the intuitive fuzzy life data is accurately estimated, which provides an important reference for the reliability analysis in the scientific field.

Partially observed mean-field Stackelberg stochastic differential game with two followers

This paper studies a partially observed stochastic Stackelberg game with two followers, where state satisfies a linear stochastic differential equation of mean-field type, and cost functionals are quadratic. Using decomposition technique and backward separation approach, we derive the followers' optimal strategy. The leader focuses on an optimal control problem driven by a fully coupled mean-field forward–backward stochastic differential equation with conditional expectation. By layer-by-layer decomposition technique, some inequalities and Riccati equations, we not only get the existence and uniqueness of solution to the corresponding Hamiltonian system but also give a feedback form of Stackelberg solution. Finally, we tackle a government debt problem by the above theoretical results.

Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators

The class of doubly robust (DR) functionals studied by Rotnitzky et al. (2021) is of central importance in economics and biostatistics. It strictly includes both (i) the class of mean-square continuous functionals that can be written as an expectation of an affine functional of a conditional expectation studied by Chernozhukov et al. (2022b) and the class of functionals studied by Robins et al. (2008). The present state-of-the-art estimators for DR functionals ψ are double-machine-learning (DML) estimators (Chernozhukov et al., 2018a). A DML estimator ψ̂1 of ψ depends on estimates p̂(x) and b̂(x) of a pair of nuisance functions p(x) and b(x), and is said to satisfy “rate double-robustness” if the Cauchy–Schwarz upper bound of its bias is o(n−1/2). Rate double-robustness implies that the bias is o(n−1/2), but the converse is false. Were it achievable, our scientific goal would have been to construct valid, assumption-lean (i.e. no complexity-reducing assumptions on b or p) tests of the validity of a nominal (1−α) Wald confidence interval (CI) centered at ψ̂1. But this would require a test of the bias to be o(n−1/2), which can be shown not to exist. We therefore adopt the less ambitious goal of falsifying, when possible, an analyst’s justification for her claim that the reported (1−α) Wald CI is valid. In many instances, an analyst justifies her claim by imposing complexity-reducing assumptions on b and p to ensure “rate double-robustness”. Here we exhibit valid, assumption-lean tests of H0: “rate double-robustness holds”, with non-trivial power against certain alternatives. If H0 is rejected, we will have falsified her justification. However, no assumption-lean test of H0, including ours, can be a consistent test. Thus, the failure of our test to reject is not meaningful evidence in favor of H0.

Prediction of rheological properties and ageing performance of recycled plastic modified bitumen using Machine learning models

Recycled plastics can be used to improve the rheological properties of neat bitumen. The rheological properties of recycled plastic modified bitumen (RPMB) depend on multiple factors, including the modified bitumen composition and ageing conditions. In this study, four ensemble machine learning (EML) models were developed based on experimental data records, aimed at predicting the rheological properties of RPMB in terms of complex shear modulus and phase angle at both unaged and short-term aged conditions. The performance of four EML models was evaluated using various metrics such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), coefficient of determination (R2) and Objective Function Value (OBJ). The results indicated that CatBoost exhibited the highest accuracy, achieving a coefficient of determination of 0.98 for complex shear modulus prediction and 0.93 for phase angle prediction. Additionally, SHapley Additive exPlanations (SHAP) analysis, individual conditional expectation and partial dependence plots were utilised to identify the magnitude and impact of inputs variables on complex shear modulus and phase angle, as well as analyse the relationship between input and output variables. The findings highlighted that the temperature and frequency of the dynamic shear rheometer test, the amount of polymer and the penetration of the base bitumen are key factors influencing the rheological properties of RPMBs. The proposed approach provides useful information to decision-makers for effectively evaluating the composition of bitumen mixtures and the rheological properties of RPMBs based on specific project conditions.

Temperature-Dependent Density and Viscosity Prediction for Hydrocarbons: Machine Learning and Molecular Dynamics Simulations.

Machine learning-based predictive models allow rapid and reliable prediction of material properties and facilitate innovative materials design. Base oils used in the formulation of lubricant products are complex hydrocarbons of varying sizes and structure. This study developed Gaussian process regression-based models to accurately predict the temperature-dependent density and dynamic viscosity of 305 complex hydrocarbons. In our approach, strongly correlated/collinear predictors were trimmed, important predictors were selected by least absolute shrinkage and selection operator (LASSO) regularization and prior domain knowledge, hyperparameters were systematically optimized by Bayesian optimization, and the models were interpreted. The approach provided versatile and quantitative structure-property relationship (QSPR) models with relatively simple predictors for determining the dynamic viscosity and density of complex hydrocarbons at any temperature. In addition, we developed molecular dynamics simulation-based descriptors and evaluated the feasibility and versatility of dynamic descriptors from simulations for predicting the material properties. It was found that the models developed using a comparably smaller pool of dynamic descriptors performed similarly in predicting density and viscosity to models based on many more static descriptors. The best models were shown to predict density and dynamic viscosity with coefficient of determination (R2) values of 99.6% and 97.7%, respectively, for all data sets, including a test data set of 45 molecules. Finally, partial dependency plots (PDPs), individual conditional expectation (ICE) plots, local interpretable model-agnostic explanation (LIME) values, and trimmed model R2 values were used to identify the most important static and dynamic predictors of the density and viscosity.

LQG Differential Stackelberg Game Under Nested Observation Information Patterns

We investigate the linear quadratic Gaussian Stackelberg game under a class of nested observation information patterns. The follower uses its observation data to design its strategy, whereas the leader implements its strategy using global observation data. We show that the solution requires solving a new type of forward-backward stochastic differential equation, whose drift components contain two conditional expectation terms associated to the adjoint variables. We then propose a method to find the functional relations between each adjoint pair, i.e., each pair formed by an adjoint variable and the conditional expectation of its associated state. The proposed method follows a layered pattern. More precisely, in the inner layer, we seek the functional relation for the adjoint pair under the sigma-sub-algebra generated by follower's observation information; and in the outer layer, we look for the functional relation for the adjoint pair under the sigma-sub-algebra generated by leader's observation information. Our result shows that the optimal open-loop solution admits an explicit feedback type representation.

Interpretable Machine Learning for COVID-19: An Empirical Study on Severity Prediction Task.

The black-box nature of machine learning models hinders the deployment of some high-accuracy medical diagnosis algorithms. It is risky to put one's life in the hands of models that medical researchers do not fully understand or trust. However, through model interpretation, black-box models can promptly reveal significant biomarkers that medical practitioners may have overlooked due to the surge of infected patients in the COVID-19 pandemic. This research leverages a database of 92 patients with confirmed SARS-CoV-2 laboratory tests between 18th January 2020 and 5th March 2020, in Zhuhai, China, to identify biomarkers indicative of infection severity prediction. Through the interpretation of four machine learning models, decision tree, random forests, gradient boosted trees, and neural networks using permutation feature importance, partial dependence plot, individual conditional expectation, accumulated local effects, local interpretable model-agnostic explanations, and Shapley additive explanation, we identify an increase in N-terminal pro-brain natriuretic peptide, C-reaction protein, and lactic dehydrogenase, a decrease in lymphocyte is associated with severe infection and an increased risk of death, which is consistent with recent medical research on COVID-19 and other research using dedicated models. We further validate our methods on a large open dataset with 5644 confirmed patients from the Hospital Israelita Albert Einstein, at São Paulo, Brazil from Kaggle, and unveil leukocytes, eosinophils, and platelets as three indicative biomarkers for COVID-19.

Doubly truncated expectation and variance of univariate generalized skew-elliptical distributions with applications

In this article, doubly truncated expectation (DTE) and variance (DTV) of univariate generalized skew-elliptical (GSE) distributions are investigated. In addition, we present an alternative form of DTE and DTV for this class of distributions in terms of the hazard function. This class of distributions includes many skewing distributions, for instance, generalized skew-normal, skew-Student-t, skew-logistic, skew-Laplace, and skew-Pearson type VII distributions. Also, we define truncated generalized skew-elliptical distributions and give the relations between moments of truncated distributions and truncated moments of distributions. Specially, we use the EM algorithm to give maximum likelihood estimation of parameters for generalized skew-elliptical distributions. Further, we apply our results to present tail conditional expectation (TCE) and tail variance (TV) for GSE distributions. We also structure an optimal portfolio selection involving DTE and DTV, and give its optimal solution. As an illustrative example, DTE and DTV of a skew-normal random variable are estimated by the Monte Carlo method. Finally, we use real data to fit and select the best distributions, and analysis TCE and TV for the logarithm of adjusted price of three companies (stocks) from S & P (Standard & Poor’s) sectors.

A Novel Bivariate Generalized Weibull Distribution with Properties and Applications

Univariate Weibull distribution is a well known lifetime distribution and has been widely used in reliability and survival analysis. In this paper, we introduce a new family of bivariate generalized Weibull (BGW) distributions, whose univariate marginals are exponentiated Weibull distribution. Different statistical quantiles like marginals, conditional distribution, conditional expectation, product moments, correlation and a measure component reliability are derived. Various measures of dependence and statistical properties along with aging properties are examined. Further, the copula associated with BGW distribution and its various important properties are also considered. The methods of maximum likelihood and Bayesian estimation are employed to estimate unknown parameters of the model. A Monte Carlo simulation and real data study are carried out to demonstrate the performance of the estimators and results have proven the effectiveness of the distribution in real-life situations.

Contingent capital conversion under dual asset and equity jump–diffusions

We model contingent capital with market trigger under dual jump–diffusion processes in asset values and equity prices. Under the dual jump–diffusions, we show that the conversion ratio is no longer deterministic under the jump–diffusion. The conversion ratio becomes a stochastic process related to the jump process of the underlying equity and the conditional expectation of the contingent capital at the conversion time. Thus, making the implementation of contingent capital impossible. The best we can hope to practically implement this conversion design, is to give the minimal conversion ratio (at least the portion required to convert) to conform with Basel III.