Conditional Independence Assumption Research Articles

Modeling Neural Connectivity in a Point-Process Analogue of Kalman Filter.

A neural encoding model describes how single neuron tunes to external stimuli as well as its connectivity with other neurons. The connectivity illustrates the neuronal interaction within populations in response to the shared latent brain states. Understanding these interactions is crucial to computationally predict the neural activity, which elucidates the neural encoding mechanism A computational analysis on the neural connectivity also facilitates developing more point process decoding model to interpret movement state from neural spike observations for brain machine interfaces (BMI). Most of the previous point process models only consider single neural tuning property and assumes conditional independence among multiple neurons. The connectivity among neurons is not considered in such a Bayesian approach to derive the state. In this work, we propose a point-process analogue of Kalman Filter to model the neural connectivity in a closed-form Bayesian filter. Neural connectivity corrects the posterior of the state given the multi-dimension observation, and a Gaussian distribution is used to approximate the updated posterior distribution. We validate the proposed method on simulation data and compared with traditional point process filtering with conditional independent assumption. The result shows that our method models the neural connectivity information and the single neuronal tuning property at the same time and achieves a better performance of the state decoding. Clinical Relevance - This paper proposes a closed-form derivation of a point process filter based on Gaussian approximations. It can model both single neuronal tuning property and the neural connectivity, which is potential to understanding the neural connectivity computationally.

Efficient Estimation for Censored Quantile Regression

ABSTRACT Censored quantile regression (CQR) has received growing attention in survival analysis because of its flexibility in modeling heterogeneous effect of covariates. Advances have been made in developing various inferential procedures under different assumptions and settings. Under the conditional independence assumption, many existing CQR methods can be characterized either by stochastic integral-based estimating equations (see, e.g., Peng and Huang) or by locally weighted approaches to adjust for the censored observations (see, for instance, Wang and Wang). While there have been proposals of different apparently dissimilar strategies in terms of formulations and the techniques applied for CQR, the inter-relationships amongst these methods are rarely discussed in the literature. In addition, given the complicated structure of the asymptotic variance, there has been limited investigation on improving the estimation efficiency for censored quantile regression models. This article addresses these open questions by proposing a unified framework under which many conventional approaches for CQR are covered as special cases. The new formulation also facilitates the construction of the most efficient estimator for the parameters of interest amongst a general class of estimating functions. Asymptotic properties including consistency and weak convergence of the proposed estimator are established via the martingale-based argument. Numerical studies are presented to illustrate the promising performance of the proposed estimator as compared to existing contenders under various settings. Supplementary materials for this article are available online.

Approximate Bayesian inference for analysis of spatiotemporal flood frequency data

Extreme floods cause casualties and widespread damage to property and vital civil infrastructure. Predictions of extreme floods, within gauged and ungauged catchments, is crucial to mitigate these disasters. In this paper a Bayesian framework is proposed for predicting extreme floods, using the generalized extreme-value (GEV) distribution. A major methodological challenge is to find a suitable parametrization for the GEV distribution when multiple covariates and/or latent spatial effects are involved and a time trend is present. Other challenges involve balancing model complexity and parsimony, using an appropriate model selection procedure and making inference based on a reliable and computationally efficient approach. We here propose a latent Gaussian modeling framework with a novel multivariate link function designed to separate the interpretation of the parameters at the latent level and to avoid unreasonable estimates of the shape and time trend parameters. Structured additive regression models, which include catchment descriptors as covariates and spatially correlated model components, are proposed for the four parameters at the latent level. To achieve computational efficiency with large datasets and richly parametrized models, we exploit a highly accurate and fast approximate Bayesian inference approach which can also be used to efficiently select models separately for each of the four regression models at the latent level. We applied our proposed methodology to annual peak river flow data from 554 catchments across the United Kingdom. The framework performed well in terms of flood predictions for both ungauged catchments and future observations at gauged catchments. The results show that the spatial model components for the transformed location and scale parameters as well as the time trend are all important, and none of these should be ignored. Posterior estimates of the time trend parameters correspond to an average increase of about 1.5% per decade with range 0.1% to 2.8% and reveal a spatial structure across the United Kingdom. When the interest lies in estimating return levels for spatial aggregates, we further develop a novel copula-based postprocessing approach of posterior predictive samples in order to mitigate the effect of the conditional independence assumption at the data level, and we demonstrate that our approach indeed provides accurate results.

Bayesian Consumer Profiling: How to Estimate Consumer Characteristics from Aggregate Data

Firms use aggregate data from data brokers (e.g., Acxiom, Experian) and external data sources (e.g., Census) to infer the likely characteristics of consumers in a target list and thus better predict consumers’ profiles and needs unobtrusively. The authors demonstrate that the simple count method most commonly used in this effort relies implicitly on an assumption of conditional independence that fails to hold in many settings of managerial interest. They develop a Bayesian profiling introducing different conditional independence assumptions. They also show how to introduce additional observed covariates into this model. They use simulations to demonstrate that in managerially relevant settings, the Bayesian method will outperform the simple count method, often by an order of magnitude. The authors then compare different conditional independence assumptions in two case studies. The first example estimates customers’ age on the basis of their first names; prediction errors decrease substantially. In the second example, the authors infer the income, occupation, and education of online visitors of a marketing analytic software company based exclusively on their IP addresses. The face validity of the predictions improves dramatically and reveals an interesting (and more complex) endogenous list-selection mechanism than the one suggested by the simple count method.

Developing Economic Models for Assessing the Cost-Effectiveness of Multiple Diagnostic Tests: Methods and Applications.

Clinical pathways with multiple diagnostic tests are complex to model, but problematic and simplistic approaches are often used in economic evaluations. We analyzed statistical methods of handling multiple diagnostic tests and provided guidance on applying these methods in economic modeling. We first introduced a statistical model to quantify the correlations between 2 tests and how those correlations can be incorporated within an economic model. We also presented the general form of conditional dependence among multiple tests. We then introduced net reclassification improvement (NRI), a measure that evaluates the added value of a new risk factor (e.g., biomarker) for risk prediction. We further provided 2 examples to illustrate the application of these methods. Our first example illustrated how to model an add-on test to an existing test, in the absence of a perfect reference standard. After accounting for the imperfect nature of both tests and the conditional dependence between tests, the potential health benefits from the additional test were reduced. This led to differential cost-effectiveness results when comparing models using the perfect test and conditional independence assumptions. The second example illustrated how to evaluate the added value of a new risk factor using the NRI measure. Using the new risk classification provides greater precision in risk prediction, and in the example, the strategy using the new risk classification with treatment for selected individuals led to more favorable cost-effectiveness results. These innovative methods for handling multiple diagnostic tests have improved the methodology within the field and should be adopted to provide more accurate estimates within cost-effectiveness analyses. Economic evaluations of multiple diagnostic tests often apply problematic simplistic approaches, such as ignoring conditional dependence between 2 tests or assuming a perfect final test in the diagnostic pathway. We provided guidance on how to apply improved methods for economic modeling.We introduced methods to model conditional dependence between 2 imperfect tests. We used an example to illustrate how assumptions about perfect diagnostic test accuracy and conditional independence between tests affect cost-effectiveness.Compared with the results of the area under the receiver-operating-characteristic curve, net reclassification improvement has distinct advantages in measuring the added value of a new risk factor for model-based economic evaluation.Economic evaluations that appropriately account for the complexities of diagnostic test pathways can help decision makers ensure efficient use of resources.

Accurate summary-based cardinality estimation through the lens of cardinality estimation graphs

This paper is an experimental and analytical study of two classes of summary-based cardinality estimators that use statistics about input relations and small-size joins in the context of graph database management systems: (i) optimistic estimators that make uniformity and conditional independence assumptions; and (ii) the recent pessimistic estimators that use information theoretic linear programs (LPs). We begin by analyzing how optimistic estimators use pre-computed statistics to generate cardinality estimates. We show these estimators can be modeled as picking bottom-to-top paths in a cardinality estimation graph (CEG), which contains sub-queries as nodes and edges whose weights are average degree statistics. We show that existing optimistic estimators have either undefined or fixed choices for picking CEG paths as their estimates and ignore alternative choices. Instead, we outline a space of optimistic estimators to make an estimate on CEGs, which subsumes existing estimators. We show, using an extensive empirical analysis, that effective paths depend on the structure of the queries. While on acyclic queries and queries with small-size cycles, using the maximum-weight path is effective to address the well known underestimation problem, on queries with larger cycles these estimates tend to overestimate, which can be addressed by using minimum weight paths. We next show that optimistic estimators and seemingly disparate LP-based pessimistic estimators are in fact connected. Specifically, we show that CEGs can also model some recent pessimistic estimators. This connection allows us to adopt an optimization from pessimistic estimators to optimistic ones, and provide insights into the pessimistic estimators, such as showing that they have combinatorial solutions.

Fine tuning attribute weighted naive Bayes

Naive Bayes (NB) is one of the top 10 data mining algorithms due to its simplicity, efficiency and efficacy. However, both the unrealistic attribute conditional independence assumption and the unreliable conditional probability estimation limit its performance. Of numerous improved approaches, attribute weighting only focuses on alleviating the unrealistic attribute conditional independence assumption, while fine tuning devotes all the efforts to finding a more reliable conditional probability estimation. In this study, we argue that both of them are equally important to enhance the performance of NB and propose a novel model called fine tuned attribute weighted NB (FTAWNB) by combining fine tuning with attribute weighting into a uniform framework. In FTAWNB, we first exploit correlation-based attribute weighting to initialize the conditional probabilities, then for each misclassified training instance, the conditional probabilities are fine tuned iteratively to make them more reliable, and the fine tuning process will stop once the training classification accuracy no longer improves. Extensive experimental results show that FTAWNB significantly outperforms all the other existing state-of-the-art competitors.

Estimating survival parameters under conditionally independent left truncation.

Databases derived from electronic health records (EHRs) are commonly subject to left truncation, a type of selection bias that occurs when patients need to survive long enough to satisfy certain entry criteria. Standard methods to adjust for left truncation bias rely on an assumption of marginal independence between entry and survival times, which may not always be satisfied in practice. In this work, we examine how a weaker assumption of conditional independence can result in unbiased estimation of common statistical parameters. In particular, we show the estimability of conditional parameters in a truncated dataset, and of marginal parameters that leverage reference data containing non‐truncated data on confounders. The latter is complementary to observational causal inference methodology applied to real‐world external comparators, which is a common use case for real‐world databases. We implement our proposed methods in simulation studies, demonstrating unbiased estimation and valid statistical inference. We also illustrate estimation of a survival distribution under conditionally independent left truncation in a real‐world clinico‐genomic database.

Hierarchical sparse Cholesky decomposition with applications to high-dimensional spatio-temporal filtering

Spatial statistics often involves Cholesky decomposition of covariance matrices. To ensure scalability to high dimensions, several recent approximations have assumed a sparse Cholesky factor of the precision matrix. We propose a hierarchical Vecchia approximation, whose conditional-independence assumptions imply sparsity in the Cholesky factors of both the precision and the covariance matrix. This remarkable property is crucial for applications to high-dimensional spatiotemporal filtering. We present a fast and simple algorithm to compute our hierarchical Vecchia approximation, and we provide extensions to nonlinear data assimilation with non-Gaussian data based on the Laplace approximation. In several numerical comparisons, including a filtering analysis of satellite data, our methods strongly outperformed alternative approaches.

Multi-Modal Variational Graph Auto-Encoder for Recommendation Systems

Graph embedding based methods have been used in recommendation systems recently, owing to their advances in modeling nodes as embeddings in a low-dimensional space. By effective neighborhood aggregation, graph convolutional networks can exploit high-order connections of neighbors such that the learned embeddings could be more informative thus improve the recommendation performance. However, user and item representations learned by graph aggregation inherently contain uncertainty due to sparsity of user-item interactions and noise of item features. To address these challenges, we propose a multi-modal variational graph auto-encoder (MVGAE) method. Specifically, we design modality-specific variational encoders that learn a Gaussian variable for each node whereas the mean vector represents semantic information and the variance vector denotes the noise level of the corresponding modality. Moreover, with the conditional independence assumption, the modality-specific Gaussian node embeddings are fused according to the product-of-experts principle, where the semantic information in each modality is weighted based on the estimated uncertainty level. Extensive experiments on three public datasets, Amazon Movies, Amazon Electronics and AliShop-7 C, demonstrate that our proposed method achieves competitive performance when compared with the state-of-the-art algorithms.

Relaxing the Assumption of Conditional Independence in a Asymptotic Single Risk Factor Model

Relaxing the Assumption of Conditional Independence in a Asymptotic Single Risk Factor Model

Application of a newly developed naive Bayes algorithm in fire alarm

To address the problems of low recognition accuracy of traditional early fire warning systems in actual scenarios, a newly developed naive Bayes (NB) algorithm, namely, improved naive Bayes (INB), was proposed. An optimization method based on attribute weighting and an orthogonal matrix was used to improve the NB algorithm. Attribute weighting considers the influence of different values of each attribute on classification performance under every decision category; the orthogonal matrix weakens the linear relationship between the attributes reducing their correlations, which is more closely related to the conditional independence assumption. Data from the technology report of the National Institute of Standards and Technology (NIST) regarding fire research were used for the simulation, and eight datasets of different sizes were constructed for INB training and testing after filtering and normalization. A ten-fold cross-validation suggests that INB has been effectively trained and demonstrates the stable ability in fire alarms when the dataset contains 190 sets of samples; namely, the INB can be fully trained by using small datasets. A support vector machine (SVM), a back propagation (BP) neural network, and NB were selected for comparison. The results showed that the recognition accuracy, average precision, average recall, and average <inline-formula><tex-math id="M1">\begin{document}$\rm{F}_{1}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUST-2021-0258_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUST-2021-0258_M1.png"/></alternatives></inline-formula> measure of INB were 96.1%, 97.3%, 97.2%, and 97.3%, respectively, which is the highest among the four different algorithms. Additionally, INB has a better performance compared to NB, SVM, and BP neural networks when the training time is short . In conclusion, INB can be used as a core algorithm for fire alarm systems with excellent and stable fire alarm capabilities.

Cheapest-to-deliver collateral: a common factor approach

The collateral choice option gives the collateral posting party the opportunity to switch between different collateral currencies which is well-known to impact the asset price. Quantification of the option's value is of practical importance but remains challenging under the assumption of stochastic rates, as it is determined by an intractable distribution that requires involved approximations. Indeed, many practitioners still rely on deterministic spreads between the rates for valuation. We develop a scalable and stable stochastic model of the collateral spreads under the assumption of conditional independence. This allows for a common factor approximation that admits analytical results from which further estimators are obtained. We show that in modelling the spreads between collateral rates, a second-order model yields accurate results for the value of the collateral choice option. The model remains precise for a wide range of model parameters and is numerically efficient even for a large number of collateral currencies.

Re-visiting the Conditional Cash Transfer in India through the Partial Identification Approach

This study re-estimates the causal impacts of a conditional cash transfer (CCT) programme in India, namely the Janani Suraksha Yojana (JSY) scheme, on maternal and child healthcare use. The main goal is to provide new evidence and to assess the validity of the identification assumptions employed in previous studies on JSY. We achieve this by implementing a conservative partial identification approach. We find that the average treatment effects estimated under the conditional independence assumption are below the lower bound of the treatment effect estimated under weaker but more credible assumptions for institutional delivery, skilled birth attendance and postnatal care use. For antenatal care use and intakes of iron and folic acid supplements, and uptakes of tetanus toxoid injections, the average treatment effects under the conditional independence assumption are above the upper bound. These findings suggest that selection bias could not have been fully controlled for by the observable characteristics.

Conditional independence assumption and appropriate number of stages in dental developmental age estimation

When estimating the age of an individual it is critical that 1) age ranges are as narrow as possible while still capturing the true age of the individual with an acceptable frequency, and 2) this frequency is known. When multiple traits are used to produce a single age estimate, the simplest practice is to assume that the traits are conditionally independent from one another given age. Unfortunately, if the traits are correlated once the effect of age is accounted for, the resulting age intervals will be too narrow. The frequency at which the age interval captures the true age of the individual will be decreased below the expected value to some unknown degree. It is therefore critical that age estimation methods that include multiple traits incorporate the possible correlations between them. Moorrees et al. (1963) [1] scores of the permanent mandibular dentition from 2607 individuals between 2 and 23 years were used to produce and cross-validate a cumulative probit model for age estimation with an optimal number of stages for each tooth. Two correction methods for covariance of development between teeth were tested: the variance-covariance matrix for a multivariate normal, and the Boldsen et al. (2002) [2] ad-hoc method. Both correction methods successfully decreased age interval error rates from 21% to 23% in the uncorrected model to the expected value of 5%. These results demonstrate both the efficacy of these correction methods and the need to move away from assuming conditional independence in multi-trait age estimation.

A Novel Hybrid Approach: Instance Weighted Hidden Naive Bayes

Naive Bayes (NB) is easy to construct but surprisingly effective, and it is one of the top ten classification algorithms in data mining. The conditional independence assumption of NB ignores the dependency between attributes, so its probability estimates are often suboptimal. Hidden naive Bayes (HNB) adds a hidden parent to each attribute, which can reflect dependencies from all the other attributes. Compared with other Bayesian network algorithms, it offers significant improvements in classification performance and avoids structure learning. However, the assumption that HNB regards each instance equivalent in terms of probability estimation is not always true in real-world applications. In order to reflect different influences of different instances in HNB, the HNB model is modified into the improved HNB model. The novel hybrid approach called instance weighted hidden naive Bayes (IWHNB) is proposed in this paper. IWHNB combines instance weighting with the improved HNB model into one uniform framework. Instance weights are incorporated into the improved HNB model to calculate probability estimates in IWHNB. Extensive experimental results show that IWHNB obtains significant improvements in classification performance compared with NB, HNB and other state-of-the-art competitors. Meanwhile, IWHNB maintains the low time complexity that characterizes HNB.

Conditional independence test of failure and truncation times: Essential tool for method selection

Conditional independence assumption of truncation and failure times conditioning on covariates is a fundamental and common assumption in the regression analysis of left-truncated and right-censored data. Testing for this assumption is essential to ensure the correct inference on the failure time, but this has often been overlooked in the literature. With consideration of challenges caused by left truncation and right censoring, tests for this conditional independence assumption are developed in which the generalized odds ratio derived from a Cox proportional hazards model on the failure time and the concept of Kendall's tau are combined. Except for the Cox proportional hazards model, no additional model assumptions are imposed, and the distributions of the truncation time and conditioning variables are unspecified. The asymptotic properties of the test statistic are established and an easy implementation for obtaining its distribution is developed. The performance of the proposed test has been evaluated through simulation studies and two real studies.

Statistical file-matching of non-Gaussian data: A game theoretic approach

The statistical file-matching problem is a data integration problem with structured missing data. The general form involves the analysis of multiple datasets that only have a strict subset of variables jointly observed across all datasets. Missing-data imputation is complicated by the fact that the joint distribution of the variables is nonidentifiable as there are no completely observed cases. Nonparametric imputation methods typically involve an implicit conditional independence assumption that is forced by the missing-data pattern. Parametric imputation does not require conditional independence assumptions, but can be challenging due to identifiability issues and the difficulty of parameter estimation. The identification problem can be studied using game theory, and it is possible to establish a general characterization of the minimax optimal strategy under negative log likelihood loss. For non-Gaussian models, imputation using the minimax optimal strategy can lead to different results compared to generic methods. Computationally feasible procedures for parameter estimation can be implemented using data augmentation schemes and the EM algorithm. Comparisons of the minimax optimal imputation scheme to standard algorithms on real data from flow cytometry show that minimax strategies can better preserve the joint distribution of the variables.

The influence of personality traits on university performance: Evidence from Italian freshmen students.

Despite several attempts to provide a definite pattern regarding the effects of personality traits on performance in higher education, the debate over the nature of the relationship is far from being conclusive. The use of different subject pools and sample sizes, as well as the use of identification strategies that either do not adequately account for selection bias or are unable to establish causality between measures of academic performance and noncognitive skills, are possible sources of heterogeneity. This paper investigates the impact of the Big Five traits, as measured before the beginning of the academic year, on the grade point average achieved in the first year after the enrolment, taking advantage of a unique and large dataset from a cohort of Italian students in all undergraduate programs containing detailed information on student and parental characteristics. Relying on a robust strategy to credibly satisfy the conditional independence assumption, we find that higher levels of conscientiousness and openness to experience positively affect student score.

Conditional Independence Structures Over Four Discrete Random Variables Revisited: Conditional Ingleton Inequalities

The paper deals with conditional linear information inequalities valid for entropy functions induced by discrete random variables. Specifically, the so-called conditional Ingleton inequalities are in the center of interest: these are valid under conditional independence assumptions on the inducing random variables. We discuss five inequalities of this particular type, four of which has appeared earlier in the literature. Besides the proof of the new fifth inequality, simpler proofs of (some of) former inequalities are presented. These five information inequalities are used to characterize all conditional independence structures induced by four discrete random variables.