Inference Procedures Research Articles

A Unified Multi-task Learning Framework for Multi-goal Conversational Recommender Systems

Recent years witnessed several advances in developing multi-goal conversational recommender systems (MG-CRS) that can proactively attract users’ interests and naturally lead user-engaged dialogues with multiple conversational goals and diverse topics. Four tasks are often involved in MG-CRS, including Goal Planning, Topic Prediction, Item Recommendation, and Response Generation. Most existing studies address only some of these tasks. To handle the whole problem of MG-CRS, modularized frameworks are adopted where each task is tackled independently without considering their interdependencies. In this work, we propose a novel Unified MultI-goal conversational recommeNDer system (UniMIND). Specifically, we unify these four tasks with different formulations into the same sequence-to-sequence paradigm. Prompt-based learning strategies are investigated to endow the unified model with the capability of multi-task learning. Finally, the overall learning and inference procedure consists of three stages, including multi-task learning, prompt-based tuning, and inference. Experimental results on two MG-CRS benchmarks (DuRecDial and TG-ReDial) show that UniMIND achieves state-of-the-art performance on all tasks with a unified model. Extensive analyses and discussions are provided for shedding some new perspectives for MG-CRS.

Improved inference for doubly robust estimators of heterogeneous treatment effects.

We propose a doubly robust approach to characterizing treatment effect heterogeneity in observational studies. We develop a frequentist inferential procedure that utilizes posterior distributions for both the propensity score and outcome regression models to provide valid inference on the conditional average treatment effect even when high-dimensional or nonparametric models are used. We show that our approach leads to conservative inference in finite samples or under model misspecification and provides a consistent variance estimator when both models are correctly specified. In simulations, we illustrate the utility of these results in difficult settings such as high-dimensional covariate spaces or highly flexible models for the propensity score and outcome regression. Lastly, we analyze environmental exposure data from NHANES to identify how the effects of these exposures vary by subject-levelcharacteristics.

Evaluating Dynamic Discrimination Performance of Risk Prediction Models for Survival Outcomes.

Risk prediction models for survival outcomes are widely applied in medical research to predict future risk for the occurrence of the event. In many clinical studies, the biomarker data are measured repeatedly over time. To facilitate timely disease prognosis and decision making, many dynamic prediction models have been developed and generate predictions on a real-time basis. As a dynamic prediction model updates an individual's risk prediction over time based on new measurements, it is often important to examine how well the model performs at different measurement times and prediction times. In this article, we propose a two-dimensional area under curve (AUC) measure for dynamic prediction models and develop associated estimation and inference procedures. The estimation procedures are discussed under two types of biomarker measurement schedules: regular visits and irregular visits. The model parameters are estimated effectively by maximizing a pseudo-partial likelihood function. We apply the proposed method to a renal transplantation study to evaluate the discrimination performance of dynamic prediction models based on longitudinal biomarkers for graft failure.

A Conway–Maxwell–Poisson Type Generalization of Hypergeometric Distribution

The hypergeometric distribution has gained its importance in practice as it pertains to sampling without replacement from a finite population. It has been used to estimate the population size of rare species in ecology, discrete failure rate in reliability, fraction defective in quality control, and the number of initial faults present in software coding. Recently, Borges et al. considered a COM type generalization of the binomial distribution, called COM–Poisson–Binomial (CMPB) and investigated many of its characteristics and some interesting applications. In the same spirit, we develop here a generalization of the hypergeometric distribution, called the COM–hypergeometric distribution. We discuss many of its characteristics such as the limiting forms, the over- and underdispersion, and the behavior of its failure rate. We write its probability-generating function (pgf) in the form of Kemp’s family of distributions when the newly introduced shape parameter is a positive integer. In this form, closed-form expressions are derived for its mean and variance. Finally, we develop statistical inference procedures for the model parameters and illustrate the results by extensive Monte Carlo simulations.

Inequities in the Number of Days Assigned to an Exclusionary Discipline Consequence by the Ethnicity/Race of Texas High School Girls: A Statewide, Multiyear Investigation

Ascertained in this analysis was the extent to which inequities existed in the number of days that Texas Grade 9, 10, and 11 students were assigned to an exclusionary discipline consequence (i.e., in-school suspension, out-of-school suspension) by the ethnicity/race for the 2015-2016, 2016-2017, and 2017-2018 school years. Inferential statistical procedures revealed the presence of statistically significant disparities in all three school years and at all three grade levels. At every grade level and school year, Black girls were assigned to more days in an in-school suspension than were Hispanic girls and White girls. For out-of-school suspensions across all three school years, Black girls were assigned to an out-of-school suspension statistically significantly more days than Hispanic girls and White girls, and Hispanic girls were assigned statistically significantly more days than White girls with the exception of Grade 10 in 2016-2017, and Grade 11 in 2016-2017 and 2017-2018.

Conditional predictive inference for stable algorithms

We investigate generically applicable and intuitively appealing prediction intervals based on k-fold cross-validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training sample (hence, training conditional validity), and show that it is close to the nominal level, in an appropriate sense, provided that the underlying algorithm used for computing point predictions is sufficiently stable when feature-response pairs are omitted. Our results are based on a finite sample analysis of the empirical distribution function of k-fold cross-validation residuals and hold in nonparametric settings with only minimal assumptions on the error distribution. To illustrate our results, we also apply them to high-dimensional linear predictors, where we obtain uniform asymptotic training conditional validity as both sample size and dimension tend to infinity at the same rate and consistent parameter estimation typically fails. These results show that despite the serious problems of resampling procedures for inference on the unknown parameters (cf. in A Festschrift for Erich L. Lehmann (1983) 28–48 Wadsworth; Ann. Statist. 24 (1996) 307–335; J. Mach. Learn. Res. 19 (2018) 5), cross-validation methods can be successfully applied to obtain reliable predictive inference even in high dimensions and conditionally on the training data.

Characterizing the Functional Density Power Divergence Class

Divergence measures have a long association with statistical inference, machine learning and information theory. The density power divergence and related measures have produced many useful (and popular) statistical procedures, which provide a good balance between model efficiency on one hand and outlier stability or robustness on the other. The logarithmic density power divergence, a particular logarithmic transform of the density power divergence, has also been very successful in producing efficient and stable inference procedures; in addition it has also led to significant demonstrated applications in information theory. The success of the minimum divergence procedures based on the density power divergence and the logarithmic density power divergence (which also go by the names <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> -divergence and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> -divergence, respectively) make it imperative and meaningful to look for other, similar divergences which may be obtained as transforms of the density power divergence in the same spirit. With this motivation we search for such transforms of the density power divergence, referred to herein as the functional density power divergence class. The present article characterizes this functional density power divergence class, and thus identifies the available divergence measures within this construct that may be explored further for possible applications in statistical inference, machine learning and information theory.

Gravitational wave inference on a numerical-relativity simulation of a black hole merger beyond general relativity

We apply common gravitational wave inference procedures on binary black hole merger waveforms beyond general relativity. We consider dynamical Chern-Simons gravity, a modified theory of gravity with origins in string theory and loop quantum gravity. This theory introduces an additional parameter $\ell$, corresponding to the length-scale below which beyond-general-relativity effects become important. We simulate data based on numerical relativity waveforms produced under an approximation to this theory, which differ from those of general relativity in the strongly nonlinear merger regime. We consider a system with parameters similar to GW150914 with different values of $\ell$ and signal-to-noise ratios. We perform two analyses of the simulated data. The first is a template-based analysis that uses waveforms derived under general relativity and allows us to identify degeneracies between the two waveform morphologies. The second is a morphology-independent analysis based on BayesWave that does not assume that the signal is consistent with general relativity. The BayesWave analysis faithfully reconstructs the simulated signals. However, waveform models derived under general relativity are unable to fully mimic the simulated modified-gravity signals and such a deviation would be identifiable with existing inference tools. Depending on the magnitude of the deviation, we find that the templated analysis can under perform the morphology-independent analysis in fully recovering simulated beyond-GR waveforms even for achievable signal-to-noise ratios $\gtrsim 20{-}30$.

Covariate adjustment in multiarmed, possibly factorial experiments

AbstractRandomized experiments are the gold standard for causal inference and enable unbiased estimation of treatment effects. Regression adjustment provides a convenient way to incorporate covariate information for additional efficiency. This article provides a unified account of its utility for improving estimation efficiency in multiarmed experiments. We start with the commonly used additive and fully interacted models for regression adjustment in estimating average treatment effects (ATE), and clarify the trade-offs between the resulting ordinary least squares (OLS) estimators in terms of finite sample performance and asymptotic efficiency. We then move on to regression adjustment based on restricted least squares (RLS), and establish for the first time its properties for inferring ATE from the design-based perspective. The resulting inference has multiple guarantees. First, it is asymptotically efficient when the restriction is correctly specified. Second, it remains consistent as long as the restriction on the coefficients of the treatment indicators, if any, is correctly specified and separate from that on the coefficients of the treatment-covariate interactions. Third, it can have better finite sample performance than the unrestricted counterpart even when the restriction is moderately misspecified. It is thus our recommendation when the OLS fit of the fully interacted regression risks large finite sample variability in case of many covariates, many treatments, yet a moderate sample size. In addition, the newly established theory of RLS also provides a unified way of studying OLS-based inference from general regression specifications. As an illustration, we demonstrate its value for studying OLS-based regression adjustment in factorial experiments. Importantly, although we analyse inferential procedures that are motivated by OLS, we do not invoke any assumptions required by the underlying linear models.

Correlated product of experts for sparse Gaussian process regression

Gaussian processes (GPs) are an important tool in machine learning and statistics. However, off-the-shelf GP inference procedures are limited to datasets with several thousand data points because of their cubic computational complexity. For this reason, many sparse GPs techniques have been developed over the past years. In this paper, we focus on GP regression tasks and propose a new approach based on aggregating predictions from several local and correlated experts. Thereby, the degree of correlation between the experts can vary between independent up to fully correlated experts. The individual predictions of the experts are aggregated taking into account their correlation resulting in consistent uncertainty estimates. Our method recovers independent Product of Experts, sparse GP and full GP in the limiting cases. The presented framework can deal with a general kernel function and multiple variables, and has a time and space complexity which is linear in the number of experts and data samples, which makes our approach highly scalable. We demonstrate superior performance, in a time vs. accuracy sense, of our proposed method against state-of-the-art GP approximations for synthetic as well as several real-world datasets with deterministic and stochastic optimization.

Determining Tilapia Quality Using the Fuzzy Logic

Fish are living things with the highest trophic level in a body of water. Fish are living creatures that live in aquatic environments in fresh, brackish and marine waters. Tilapia is one of the leading commodities of aquaculture and is a widely used freshwater fish, and its production is quite high. Fuzzy logic is a logic that deals with the concept of partial truth, where classical logic states that everything can be expressed in binary terms (0 or 1). Various theories in the development of fuzzy logic show that fuzzy logic can be used to model various systems. A very adaptable and data-tolerant approach is mamdani fuzzy. Therefore, in this research, a mamdani fuzzy model will be developed to evaluate the quality of tilapia. This research uses fuzzy logic to evaluate the quality of tilapia based on its texture, taste, and size. In this study, researchers modeled 4 fuzzy variables, with 3 inputs (texture, taste, and size), 1 output (price), and a total of 4 fuzzy variables. The MIN IMPLICATION function was used in the inference procedure in the fuzzy operator application. Next, the MAX approach is used in the compilation of all fuzzy outputs. Then comes the affirmation, also known as defuzzification which is done using the Centroid method. The results show with 10 trial data it is seen that the higher the input value of size, the higher the output value of price.

Inferring ASF transmission in domestic pigs and wild boars using a paired model iterative approach

The rapid spread of African swine fever (ASF) in recent years has once again raised awareness of the need to improve our preparedness in preventing and managing outbreaks, for which modelling-based forecasts can play an important role. This is even more important in the case of a disease such as ASF, involving several types of hosts, characterised by a high case-fatality rate and for which there is currently no treatment or vaccine. Within the framework of the ASF challenge, we proposed a modelling approach based on a stochastic mechanistic model and an inference procedure to estimate key transmission parameters from provided data (incomplete and noisy) and generate forecasts for unobserved time horizons. The model is partly data driven and composed of two modules, corresponding to epidemic and demographic dynamics in domestic pig and wild boar (WB) populations, interconnected through the networks of animal trade and/or spatial proximity. The inference consists in an iterative procedure, alternating between the two models and based on a criterion optimisation. Estimates of transmission and detection parameters appeared to be of similar magnitude for each of the three periods of the challenge, except for the transmission rates in WB population through contact with infectious individuals and carcasses, higher during the first period. The predicted number of infected domestic pig farms was in overall agreement with the data. The proportion of positive tested WB was overestimated, but with a trend close to that observed in the data. Comparison of the spatial simulated and observed distributions of detected cases also showed an overestimation of the spread of the pathogen within WB metapopulation. Beyond the quantitative results and the inherent difficulties of real-time forecasting, we built a modelling framework that is flexible enough to accommodate changes in transmission processes and control measures that may occur during an epidemic emergency.

Optimal Subsampling Bootstrap for Massive Data

The bootstrap is a widely used procedure for statistical inference because of its simplicity and attractive statistical properties. However, the vanilla version of bootstrap is no longer feasible computationally for many modern massive datasets due to the need to repeatedly resample the entire data. Therefore, several improvements to the bootstrap method have been made in recent years, which assess the quality of estimators by subsampling the full dataset before resampling the subsamples. Naturally, the performance of these modern subsampling methods is influenced by tuning parameters such as the size of subsamples, the number of subsamples, and the number of resamples per subsample. In this article, we develop a novel hyperparameter selection methodology for selecting these tuning parameters. Formulated as an optimization problem to find the optimal value of some measure of accuracy of an estimator subject to computational cost, our framework provides closed-form solutions for the optimal hyperparameter values for subsampled bootstrap, subsampled double bootstrap and bag of little bootstraps, at no or little extra time cost. Using the mean square errors as a proxy of the accuracy measure, we apply our methodology to study, compare and improve the performance of these modern versions of bootstrap developed for massive data through numerical study. The results are promising.

Robust causal inference of drug-drug interactions.

There is growing interest in developing causal inference methods for multi-valued treatments with a focus on pairwise average treatment effects. Here we focus on a clinically important, yet less-studied estimand: causal drug-drug interactions (DDIs), which quantifies the degree to which the causal effect of drug A is altered by the presence versus the absence of drug B. Confounding adjustment when studying the effects of DDIs can be accomplished via inverse probability of treatment weighting (IPTW), a standard approach originally developed for binary treatments and later generalized to multi-valued treatments. However, this approach generally results in biased results when the propensity score model is misspecified. Motivated by the need for more robust techniques, we propose two empirical likelihood-based weighting approaches that allow for specifying a set of propensity score models, with the second method balancing user-specified covariates directly, by incorporating additional, nonparametric constraints. The resulting estimators from both methods are consistent when the postulated set of propensity score models contains a correct one; this property has been termed multiple robustness. In this paper, we derive two multiply-robust estimators of the causal DDI, and develop inference procedures. We then evaluate their finite sample performance through simulation. The results demonstrate that the proposed estimators outperform the standard IPTW method in terms of both robustness and efficiency. Finally, we apply the proposed methods to evaluate the impact of renin-angiotensin system inhibitors (RAS-I) on the comparative nephrotoxicity of nonsteroidal anti-inflammatory drugs (NSAID) and opioids, using data derived from electronic medical records from a large multi-hospital health system.

A Flexible Zero-Inflated Poisson-Gamma Model with Application to Microbiome Sequence Count Data

In microbiome studies, it is of interest to use a sample from a population of microbes, such as the gut microbiota community, to estimate the population proportion of these taxa. However, due to biases introduced in sampling and preprocessing steps, these observed taxa abundances may not reflect true taxa abundance patterns in the ecosystem. Repeated measures, including longitudinal study designs, may be potential solutions to mitigate the discrepancy between observed abundances and true underlying abundances. Yet, widely observed zero-inflation and over-dispersion issues can distort downstream statistical analyses aiming to associate taxa abundances with covariates of interest. To this end, we propose a Zero-Inflated Poisson Gamma (ZIPG) model framework to address these aforementioned challenges. From a perspective of measurement errors, we accommodate the discrepancy between observations and truths by decomposing the mean parameter in Poisson regression into a true abundance level and a multiplicative measurement of sampling variability from the microbial ecosystem. Then, we provide a flexible ZIPG model framework by connecting both the mean abundance and the variability of abundances to different covariates, and build valid statistical inference procedures for both parameter estimation and hypothesis testing. Through comprehensive simulation studies and real data applications, the proposed ZIPG method provides significant insights into distinguished differential variability and mean abundance. Supplementary materials for this article are available online.

Computationally efficient adaptive decompression for whole slide image processing.

Whole slide image (WSI) analysis is increasingly being adopted as an important tool in modern pathology. Recent deep learning-based methods have achieved state-of-the-art performance on WSI analysis tasks such as WSI classification, segmentation, and retrieval. However, WSI analysis requires a significant amount of computation resources and computation time due to the large dimensions of WSIs. Most of the existing analysis approaches require the complete decompression of the whole image exhaustively, which limits the practical usage of these methods, especially for deep learning-based workflows. In this paper, we present compression domain processing-based computation efficient analysis workflows for WSIs classification that can be applied to state-of-the-art WSI classification models. The approaches leverage the pyramidal magnification structure of WSI files and compression domain features that are available from the raw code stream. The methods assign different decompression depths to the patches of WSIs based on the features directly retained from compressed patches or partially decompressed patches. Patches from the low-magnification level are screened by attention-based clustering, resulting in different decompression depths assigned to the high-magnification level patches at different locations. A finer-grained selection based on compression domain features from the file code stream is applied to select further a subset of the high-magnification patches that undergo a full decompression. The resulting patches are fed to the downstream attention network for final classification. Computation efficiency is achieved by reducing unnecessary access to the high zoom level and expensive full decompression. With the number of decompressed patches reduced, the time and memory costs of downstream training and inference procedures are also significantly reduced. Our approach achieves a 7.2× overall speedup, and the memory cost is reduced by 1.1 orders of magnitudes, while the resulting model accuracy is comparable to the original workflow.

Bayesian Log-Rank Test

Comparison of two survival curves is a fundamental problem in survival analysis. Although abundant frequentist methods have been developed for comparing survival functions, inference procedures from the Bayesian perspective are rather limited. In this article, we extract the quantity of interest from the classic log-rank test and propose its Bayesian counterpart. Monte Carlo methods, including a Gibbs sampler and a sequential importance sampling procedure, are developed to draw posterior samples of survival functions and a decision rule of hypothesis testing is constructed for making inference. Via simulations and real data analysis, the proposed Bayesian log-rank test is shown to be asymptotically equivalent to the classic one when noninformative prior distributions are used, which provides a Bayesian interpretation of the log-rank test. When using the correct prior information from historical data, the Bayesian log-rank test is shown to outperform the classic one in terms of power. R codes to implement the Bayesian log-rank test are also provided with step-by-step instructions.

Uniform predictive inference for factor models with instrumental and idiosyncratic betas

This paper investigates the impact of allowing for characteristic-based time-varying factor betas on the diffusion-index type forecasts. The factor beta consists of two distinct components: the “instrumental beta” is a function of some observable characteristics, while the “idiosyncratic beta” captures more volatile residual movements. To estimate these characteristic-based time-varying betas and the corresponding factors, we apply the projected principal component analysis (P-PCA) method on high-frequency returns data. The primary advantage of this method is that it refines the estimators of latent factors, which shall be used in the forecasting models. We show that various leading components of the conditional mean forecast error are all asymptotically normal and pairwise independent. Extensive simulation studies show the good finite-sample properties of the P-PCA estimators and demonstrate the advantage of the P-PCA method relative to the classic PCA method in forecasting. In our empirical experiments of volatility prediction, we find that the factor-augmented model associated with the P-PCA method is more parsimonious and achieves better performance for a wide variety of target assets. We also find evidence on different levels of variation over time in the idiosyncratic beta, which necessitates our uniform predictive inference procedure.

Heterogeneity in choice experiment data: A Bayesian investigation

Discrete mixture (DM) models recognize the presence of heterogeneity across individuals in a given population. In the context of a public land use discrete choice experiment, we use DM models to allow for respondent behavior to probabilistically mix over multiple competing process heuristics. We pairwise combine the Random Utility Model (RUM), Contextual Concavity Model (CCM), and Random Regret Minimization (RRM) heuristic into three DM models, in which the probability of an individual adhering to a particular heuristic is modeled as a function of sociodemographic characteristics. We present a comprehensive Bayesian analysis for which we explicitly describe prior selection, inferential procedures, and model comparison metrics. We use a fully Bayesian information criterion to rank the models. We find evidence that responses are best modeled using random regret. After accounting for preference heterogeneity, the DM models estimate two latent groups of decision makers. For the DM models, we develop a novel algorithm to calculate posterior-weighted willingness to pay estimates for improvements in different public park amenities in Polk County, Iowa.

Guidance counseling services expenditures at Texas schools: A multiyear statewide investigation

This study was conducted to determine the degree to which differences were present in the distribution of Guidance Counseling Services dollars spent per student at the elementary, middle, and high school levels for the 2009-2010 through the 2018-2019 school years in Texas. Texas statewide data were obtained from the Texas Education Agency Public Education Information Management System for 10 school years. Specifically targeted in this multiyear investigation was the expenditure, out of the total amount of available dollars, of monies toward providing guidance counseling services to students. Through the use of inferential statistical procedures, statistically significant differences were established. The amount of school counseling dollars spent per pupil were highest at the high school level, followed by the middle school level, and were lowest at the elementary school level. From the 2009-2010 school year through the 2018-2019 school year, expenditures for elementary, middle, and high schools across the State of Texas increased by only $60, $95, and $100, respectively. Implications and recommendations for future research were discussed.