Inverse Regression Model Research Articles

Extreme partial least-squares

We propose a new approach, called Extreme-PLS, for dimension reduction in conditional extreme values settings. The objective is to find linear combinations of covariates that best explain the extreme values of the response variable in a non-linear inverse regression model. The asymptotic normality of the Extreme-PLS estimator is established in the single-index framework and under mild assumptions. The performance of the method is assessed on simulated data. A statistical analysis of French farm income data, considering extreme cereal yields, is provided as an illustration.

Rapid design centering of multi-band antennas using knowledge-based inverse models and response features

Accounting for manufacturing tolerances as well as uncertainties concerning operating conditions and material parameters is one of the important yet often neglected aspects of antenna development. Appropriate quantification of uncertainties allows for estimating the fabrication yield but also to carry out robust design (e.g., yield maximization). For reliability reasons, statistical analysis should be executed at the accuracy level of full-wave electromagnetic (EM) simulation. Unfortunately, the associated computational cost is normally unmanageable when using traditional methods, e.g., Monte Carlo (MC) simulation, in a brute force manner. Computationally tractable approaches are based on surrogate modeling techniques, where the fast metamodel is either used to run MC at low cost, or to directly extract statistical moments of the system output (e.g., polynomial chaos expansion). The bottleneck of surrogate-based frameworks is a potentially large number of training data samples necessary to render the surrogate, which may become problematic especially for higher-dimensional parameter spaces. This paper proposes a novel approach to design centering of multi-band antennas, which involves knowledge-based inverse regression models constructed at the level of appropriately-defined response features. Our methodology capitalizes on establishing – in​ the form of the inverse model – a functional relationship between the feature point coordinates affecting satisfaction of the prescribed design specification and geometry parameters of the antenna under analysis. The inverse model predicts the parameter vectors featuring improved likelihood of fulfilling the requirements under uncertainties. Due to low-dimensionality of the feature space, only a handful of EM analyses is necessary to render the model, which translates into a low cost of the entire design centering procedure. The presented algorithm is demonstrated using three microstrip antennas and favorably compared to several benchmark methods

Effect of Socio-Economic Status on Perioperative Outcomes After Robotic-Assisted Pulmonary Lobectomy

Background: Lower socioeconomic status (SES) has been correlated with poor survival rates and surgical outcomes following lung cancer resection. This study sought to determine whether this disparity exists perioperatively in lung cancer patients following robotic-assisted video-thoracoscopic pulmonary lobectomy. Methods: We retrospectively reviewed 447 consecutive patients who underwent robotic-assisted pulmonary lobectomy by one surgeon for known or suspected lung cancer. Ten patients were excluded due to incomplete data. We used median income by residential ZIP code as a surrogate for SES status and grouped patients based on whether ZIP-based median income was less than (Group 1) or greater than (Group 2) 300% of the federal poverty income level. The effects of SES status groups on incidence of postoperative complications, chest tube duration, hospital length of stay (LOS), and in-hospital mortality were evaluated by the logistic regression model and Inverse Gaussian regression model, respectively.Results: Without adjustment, Group 1 tended to have a higher rate of postoperative complications, with 54% of patients experiencing complications compared to 34% of patients in Group 2 (p=0.007). Median chest tube duration and hospital LOS were also significantly longer in Group 1 than in Group 2 (p=0.034). In multivariable logistical regression analysis, while controlling for covariates and considering effect modifications, lower SES was significantly and positively associated with postoperative complications (odds ratio (OR)=1.98, p=0.039). Preoperative chronic obstructive pulmonary disease (COPD) was also a positive and significant predictor of postoperative complications (OR=1.89, p=0.017), chest tube duration (p=0.020), and LOS (p=0.010).Conclusions: Lower median income is associated with a greater number of postoperative complications following pulmonary resection for lung cancer when controlling for covariates.

Peroral Endoscopic Myotomy; Novice Surgeon Learning Curve.

Peroral endoscopic myotomy (POEM) is a novel endoscopic procedure used to treat achalasia and other spastic esophageal disorders that is an alternative to Heller myotomy. We seek to define the learning curve of POEM for a foregut surgeon with no formal endoscopic or POEM training by analyzing different intraoperative factors in a single series. The first 38 consecutive patients undergoing POEM by a single foregut surgeon were included in this retrospective study. Inverse curve regression models were used to analyze total operative time (TOT) and total operative time per centimeter of myotomy (TOT-CM), in addition to other intraoperative variables. Clinical outcomes were reported as pre- and post-operative Eckardt Scores. All patients had type II achalasia with no post-operative complications observed. Eckardt scores improved postoperatively (median (range): 1 (0-4)) compared with the preoperative scores (10 (8-12)) (P < .001). The total operative time (median 76minutes, range 51-129) decreased significantly over the course of the series (R2 = .38, P < .001), with a learning plateau at 70minutes and a learning rate of 12 cases. Total operative time per centimeter of myotomy (median 7.08min/cm, range 4.25 to 15.38) decreased over time (R2 = .45, P < .001), with a learning plateau at 7minutes/cm and a learning rate of 12 cases. The number of cases for a foregut surgeon to become proficient in a POEM procedure was found to be 12-14 cases. The learning curve for a POEM in a formally trained foregut surgeon may be comparable to an endoscopically trained interventionist.

Effectiveness of CoronaVac in children 3–5 years of age during the SARS-CoV-2 Omicron outbreak in Chile

The outbreak of the B.1.1.529 lineage of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) (Omicron) has caused an unprecedented number of Coronavirus Disease 2019 (COVID-19) cases, including pediatric hospital admissions. Policymakers urgently need evidence of vaccine effectiveness in children to balance the costs and benefits of vaccination campaigns, but, to date, the evidence is sparse. Leveraging a population-based cohort in Chile of 490,694 children aged 3–5 years, we estimated the effectiveness of administering a two-dose schedule, 28 days apart, of Sinovac’s inactivated SARS-CoV-2 vaccine (CoronaVac). We used inverse probability-weighted survival regression models to estimate hazard ratios of symptomatic COVID-19, hospitalization and admission to an intensive care unit (ICU) for children with complete immunization over non-vaccination, accounting for time-varying vaccination exposure and relevant confounders. The study was conducted between 6 December 2021 and 26 February 2022, during the Omicron outbreak in Chile. The estimated vaccine effectiveness was 38.2% (95% confidence interval (CI), 36.5–39.9) against symptomatic COVID-19, 64.6% (95% CI, 49.6–75.2) against hospitalization and 69.0% (95% CI, 18.6–88.2) against ICU admission. The effectiveness against symptomatic COVID-19 was modest; however, protection against severe disease was high. These results support vaccination of children aged 3–5 years to prevent severe illness and associated complications and highlight the importance of maintaining layered protections against SARS-CoV-2 infection.

The 2021 Western North American heat dome increased climate change anxiety among British Columbians: Results from a natural experiment

Extreme weather events caused by climate change pose a risk to mental health. Illustrating this reality, this study estimates the impact of the 2021 Western North American heat dome (June 25th, 2021 – July 1st, 2021) on climate change anxiety among British Columbians. We conducted an online survey of British Columbians, aged ≥ 16. Participants were recruited using paid advertisements on social media. Data were collected pre- and post- heat dome between May 12th, 2021 – June 21st, 2021 (n = 439), and July 15th, 2021 – July 18th, 2021 (n = 420), respectively. A multivariable inverse Gaussian regression model tested differences in Climate Change Anxiety Scale (CCAS) scores pre- and post- heat dome. Potential confounders measured included age, gender, ethnicity, education, income, and political orientation. CCAS reliability was assessed using Cronbach's alpha. Most participants indicated that they were much (40.1%) or somewhat (18.4%) more worried about climate change due to the heat dome. Mean CCAS scores increased from 1.66 (standard deviation [SD]= 0.80) to 1.87 (SD = 0.87) pre- and post- heat dome, respectively. In multivariable modeling, this effect was significant after controlling for potential confounders (Estimate = 0.057, standard error = 0.148, p < 0.001). The CCAS reliability was high (Cronbach's alpha = 0.94). Our results found that British Columbians had significantly higher climate change anxiety following the 2021 Western North American heat dome. Ongoing monitoring of climate change anxiety is needed to understand the impact of individual and compounding climate change-related weather events over time.

A new improved Liu estimator for the QSAR model with inverse Gaussian response

The regression model is one of the important quantitative structure-activity relationship (QSAR) model tools that is used chiefly in chemometrics studies. In chemometrics, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, then the inverse Gaussian regression model (IGRM) is a better choice QSAR model. Multicollinearity in the IGRM affects the IGRM estimation and inferences. To overcome the effect of multicollinearity, biased estimators such as ridge and Liu are discussed in the literature. However, the disadvantage of using the traditional Liu estimator is that the shrinkage parameter, d, returns a negative value that severely affects the estimator's performance. To mitigate this problem, we propose a new improved Liu estimator for the IGRM. The new estimator's performance is compared with the maximum likelihood estimator (MLE) and the other biased estimators. A Monte Carlo simulation study is conducted to assess the newly proposed estimator's performance under different parametric conditions. A QSAR chemometric application is also considered to see the clear picture of the proposed estimator. The simulation and QSAR application findings demonstrate that the newly proposed estimator consistently dominates the other competitive estimators in all the evaluated conditions.

Principal component ridge type estimator for the inverse Gaussian regression model

The inverse Gaussian regression model (IGRM) is applied when the response variable is continuous, positively skewed and well fitted to the inverse Gaussian distribution. In the presence of multicollinearity, the maximum likelihood estimation (MLE) is not a right choice. Therefore, we proposed a new estimator called the principal component ridge estimator for the IGRM which combines the principal component estimator and the ridge estimator. We also consider a two-parameter estimator (TPE) and other biased estimators to see a clear image of our proposed estimator. A Monte Carlo simulation study is also presented to examine the performance of the proposed estimators. Furthermore, we analysed a dataset to assess the superiority of the proposed estimator. Based on the simulation and application results, it is evident that the proposed estimator dominates the classical MLE, and other considered biased estimation methods.

Age-at-death standards for Mesoamerican Prehispanic and colonial infant, child, and juvenile skeletons.

This study aims to develop age-at-death standards for Valley of Mexico skeletal collections. Using 159 individuals, with a dental age-at-death between 0 to 15 years, we develop linear and quadratic inverse regression models of age-at-death estimation between dental age and the diaphyseal length of the six long bones. A blind test for both regressions was performed, also a regression developed for a Maya group was carried out. We also compared skeletal growth of our sample by applying regressions developed for Maya and North American populations to assess the magnitude of the differences among ethnically unrelated populations. Our regressions yielded a close correlation between the diaphyseal length and dental age, especially femur and radius. It is noticeable that the disparities between younger and older age categories, the latter presenting larger standard deviations. Quadratic regression fitted better than linear and Maya regressions, and the differences of age-at-death distributions are significant. The skeletal growth curve of the Valley of Mexico is statistically different from other Native American groups. We conclude that for the present standards, despite the high degree of variance, the quadratic regression is a better applicable age estimator, when it is applied to biologically close populations.

Statistical guarantees for Bayesian uncertainty quantification in nonlinear inverse problems with Gaussian process priors

Bayesian inference and uncertainty quantification in a general class of nonlinear inverse regression models is considered. Analytic conditions on the regression model {G(θ):θ∈Θ} and on Gaussian process priors for θ are provided such that semiparametrically efficient inference is possible for a large class of linear functionals of θ. A general Bernstein–von Mises theorem is proved that shows that the (non-Gaussian) posterior distributions are approximated by certain Gaussian measures centred at the posterior mean. As a consequence, posterior-based credible sets are valid and optimal from a frequentist point of view. The theory is illustrated with two applications with PDEs that arise in nonlinear tomography problems: an elliptic inverse problem for a Schrödinger equation, and inversion of non-Abelian X-ray transforms. New analytical techniques are deployed to show that the relevant Fisher information operators are invertible between suitable function spaces.

The Neutrophil to Lymphocyte Ratio Is Associated With the Risk of Subsequent Dementia in the Framingham Heart Study.

Objective: Active neutrophils are important contributors to Alzheimer’s disease (AD) pathology through the formation of capillary stalls that compromise cerebral blood flow (CBF) and through aberrant neutrophil signaling that advances disease progression. The neutrophil to lymphocyte ratio (NLR) is a proxy of neutrophil-mediated inflammation, and higher NLR is found in persons diagnosed with clinical AD. The objective of this study was to investigate whether increased NLR in older adults is independently associated with the risk of subsequent dementia.Methods: We examined associations of baseline NLR with incident dementia risk in the community-based Framingham Heart Study (FHS) longitudinal cohorts. The association between NLR and risk of dementia was evaluated using the cumulative incidence function (CIF) and inverse probability-weighted Cox proportional cause-specific hazards regression models, with adjustment for age, sex, body mass index (BMI), systolic and diastolic blood pressure, diabetes, current smoking status, low-density lipoprotein (LDH), high-density lipoprotein (LDL), total cholesterol, triglycerides, and history of cardiovascular disease (CVD). Random forest survival models were used to evaluate the relative predictive value of the model covariates on dementia risk.Results: The final study sample included 1,648 participants with FHS (average age, 69 years; 56% women). During follow-up (median, 5.9 years), we observed 51 cases of incident dementia, of which 41 were AD cases. Results from weighted models suggested that the NLR was independently associated with incident dementia, and it was preceded in predictive value only by age, history of CVD, and blood pressure at baseline.Conclusion: Our study shows that individuals with higher NLR are at a greater risk of subsequent dementia during a 5.9-year follow-up period. Further evaluating the role of neutrophil-mediated inflammation in AD progression may be warranted.

Knowledge-based performance-driven modeling of antenna structures

The importance of surrogate modeling techniques in the design of modern antenna systems has been continuously growing over the recent years. This phenomenon is a matter of practical necessity rather than simply a fashion. On the one hand, antenna design procedures rely on full-wave electromagnetic (EM) simulation tools. On the other hand, the computational costs incurred by repetitive EM analyses involved in solving common tasks (parameter tuning, uncertainty quantification, multi-criterial design, etc.), are often prohibitive. The replacement of full-wave simulations by fast surrogates may mitigate these issues; as a matter of fact, it is the only viable option for carrying out EM-driven design in many cases. Among available modeling approaches, data-driven surrogates are by far the most popular due to their accessibility and versatility. At the same time, a construction of reliable models is hindered by the curse of dimensionality, high nonlinearity of antenna characteristics, as well as broad ranges of parameters and operating conditions that the model has to cover to ensure its design utility. Recently proposed performance-driven modeling frameworks offer a workaround these issues by restricting the model domain to the parameter space regions that contain high-quality designs (w.r.t. the assumed performance metrics). However, the domain determination requires acquisition of a set of pre-optimized reference designs, which adds to the overall computational cost of the surrogate model setup in a significant manner. This work proposes a novel two-stage knowledge-based approach, where the confined domain is defined without using any reference designs. Instead, a preselected set of random observables is employed to establish an inverse regression model being a basis for domain determination of the final surrogate. Comprehensive numerical validation involving three antenna structures indicates that our methodology offers the computational benefits similar to those of the previous performance-driven methods while considerably reducing the initial setup cost, by a factor of sixty percent on the average, which has been achieved by exploiting the problem-specific knowledge.

Does the use of multiple agricultural technologies affect household welfare? Evidence from Northern Ghana

ABSTRACT Agricultural intensification has been encouraged through the promotion of various agricultural technologies, but the synergies between different technologies have not been fully explored among various specific crops. Using the multinomial endogenous switching regression model complemented with the multivalued inverse probability regression model, this study determines the impacts of the adoption of combinations of chemical fertiliser, improved rice seeds, and herbicides on household welfare. Data were collected from 900 farm households in Northern Ghana. Our results indicate that the adoption of combinations of agricultural technologies is affected by various socio-economic attributes, resource constraints, institutional factors, and production shocks. We find that adopting multiple technologies improves rice yields, gross rice income, and per capita consumption expenditure. The results point out the crucial synergistic effects of the adoption of agricultural technologies on household welfare. We suggest that policies aimed at strengthening farm household welfare should encourage adopting multiple agricultural technologies in rice-producing farm households to realise the most welfare.

Inverse Gaussian Liu-type estimator

The inverse Gaussian regression (IGR) model parameters are generally estimated using the maximum likelihood (ML) estimation method. Since the multicollinearity problem exists among the explanatory variables, the ML estimation method becomes inflated. When the multicollinearity problem occurs, biased estimators can be used to estimate the parameters of the model. One of the most widely used biased estimators is the Liu-type estimator. In this study, we extend the Liu-type estimator for the IGR model. The proposed estimator is compared with the Ridge and Liu estimators defined for the IGR model in terms of the mean squared error (MSE) criterion. Also, a real data example is presented to illustrate the superiority of the proposed estimator. Experimental results show that the Liu-type estimator outperforms the Ridge and Liu estimators when multicollinearity exists.

Modified ridge-type estimator for the inverse Gaussian regression model

This paper considers the parameter estimation for the inverse Gaussian regression model (IGRM) in the presence of multicollinearity. The inverse Gaussian modified ridge-type estimator (IGMRTE) is developed for efficient parameter estimation and compared with other estimation methods such as the maximum likelihood estimator (MLE), ridge and Liu estimator. We derived the properties of the proposed estimator and conducted a theoretical comparison with some of the existing estimators using the matrix mean squared error and mean squared error criterions. Furthermore, the statistical properties of these estimators are systematically scrutinized via a Monte Carlo simulation study under different conditions. The findings of the simulation study demonstrate that the proposed IGMRTE showed a much more robust behavior in the presence of severe multicollinearity. A real life example is also analyzed to evaluate the effectiveness of the estimators under study. Both the simulation and the application results confirm the use of IGMRTE for the estimation of unknown regression coefficients of the IGRM when the explanatory variables are highly correlated.

Inverse Lindley power series distributions: a new compounding family and regression model with censored data

This paper introduces a new class of distributions by compounding the inverse Lindley distribution and power series distributions which is called compound inverse Lindley power series (CILPS) distributions. An important feature of this distribution is that the lifetime of the component associated with a particular risk is not observable, rather only the minimum lifetime value among all risks is observable. Further, these distributions exhibit an unimodal failure rate. Various properties of the distribution are derived. Besides, two special models of the new family are investigated. The model parameters of the two sub-models of the new family are obtained by the methods of maximum likelihood, least square, weighted least square and maximum product of spacing and compared them using the Monte Carlo simulation study. Besides, the log compound inverse Lindley regression model for censored data is proposed. Three real data sets are analyzed to illustrate the flexibility and importance of the proposed models.

Deep molecular dreaming: inverse machine learning for de-novo molecular design and interpretability with surjective representations

Computer-based de-novo design of functional molecules is one of the most prominent challenges in cheminformatics today. As a result, generative and evolutionary inverse designs from the field of artificial intelligence have emerged at a rapid pace, with aims to optimize molecules for a particular chemical property. These models ‘indirectly’ explore the chemical space; by learning latent spaces, policies, and distributions, or by applying mutations on populations of molecules. However, the recent development of the SELFIES (Krenn 2020 Mach. Learn.: Sci. Technol. 1 045024) string representation of molecules, a surjective alternative to SMILES, have made possible other potential techniques. Based on SELFIES, we therefore propose PASITHEA, a direct gradient-based molecule optimization that applies inceptionism (Mordvintsev 2015) techniques from computer vision. PASITHEA exploits the use of gradients by directly reversing the learning process of a neural network, which is trained to predict real-valued chemical properties. Effectively, this forms an inverse regression model, which is capable of generating molecular variants optimized for a certain property. Although our results are preliminary, we observe a shift in distribution of a chosen property during inverse-training, a clear indication of PASITHEA’s viability. A striking property of inceptionism is that we can directly probe the model’s understanding of the chemical space on which it is trained. We expect that extending PASITHEA to larger datasets, molecules and more complex properties will lead to advances in the design of new functional molecules as well as the interpretation and explanation of machine learning models.

Graph informed sliced inverse regression

A new method is developed for performing sufficient dimension reduction when probabilistic graphical models are being used to estimate parameters. The procedure enriches the domain of application of dimension reduction techniques to settings where (i) p the number of variables in the model is much larger than the available sample size n, (ii) p is much larger than the number of slices H the model uses and (iii) D the number of projection vectors can be larger than the number of slices H. The methodology is developed for the case of the sliced inverse regression model, but extensions to other dimension reduction techniques such as sliced average variance estimation or other methods are straightforward.

Association of Parathyroidectomy With 5-Year Clinically Significant Kidney Stone Events in Patients With Primary Hyperparathyroidism

ObjectivePatients with primary hyperparathyroidism (PHPT) are at increased risk of kidney stones. Guidelines recommend parathyroidectomy in patients with PHPT with a history of stone disease. This study aimed to compare the 5-year incidence of clinically significant kidney stone events in patients with PHPT treated with parathyroidectomy versus nonoperative management. MethodsWe performed a longitudinal cohort study of patients with PHPT in a national commercial insurance claims database (2006-2019). Propensity score inverse probability weighting-adjusted multivariable regression models were calculated. ResultsWe identified 7623 patients aged ≥35 years old with continuous enrollment >1 year before and >5 years after PHPT diagnosis. A total of 2933 patients (38.5%) were treated with parathyroidectomy. The cohort had a mean age of 66.5 years, 5953 (78.1%) were female, and 5520 (72.4%) were White. Over 5 years, the unadjusted incidence of ≥1 kidney stone event was higher in patients who were managed with parathyroidectomy compared with those who were managed nonoperatively overall (5.4% vs 4.1%, respectively) and among those with a history of kidney stones at PHPT diagnosis (17.9% vs 16.4%, respectively). On multivariable analysis, parathyroidectomy was associated with no statistically significant difference in the odds of a 5-year kidney stone event among patients with a history of kidney stones (odds ratio, 1.03; 95% CI, 0.71-1.50) or those without a history of kidney stones (odds ratio, 1.16; 95% CI, 0.84-1.60). ConclusionBased on this claim analysis, there was no difference in the odds of 5-year kidney stone events in patients with PHPT who were treated with parathyroidectomy versus nonoperative management. Time horizon for benefit should be considered when making treatment decisions for PHPT based on the risk of kidney stone events.

Two parameter Ridge estimator in the inverse Gaussian regression model

It is well known that multicollinearity, which occurs among the explanatory variables, has adverse effects on the maximum likelihood estimator in the inverse Gaussian regression model. Biased estimators are proposed to cope with the multicollinearity problem in the inverse Gaussian regression model. The main interest of this article is to introduce a new biased estimator. Also, we compare newly proposed estimator with the other estimators given in the literature. We conduct a Monte Carlo simulation and provide a real data example to illustrate the performance of the proposed estimator over the maximum likelihood and Ridge estimators. As a result of the simulation study and real data example, the newly proposed estimator is superior to the other estimators used in this study.