Language Learning From Positive Evidence,Reconsidered: A Simplicity‐Based Approach

Children learn their native language by exposure to their linguistic and communicative environment, but apparently without requiring that their mistakes be corrected. Such learning from “positive evidence” has been viewed as raising “logical” problems for language acquisition. In particular, without correction, how is the child to recover from conjecturing an over‐general grammar, which will be consistent with any sentence that the child hears? There have been many proposals concerning how this “logical problem” can be dissolved. In this study, we review recent formal results showing that the learner has sufficient data to learn successfully from positive evidence, if it favors the simplest encoding of the linguistic input. Results include the learnability of linguistic prediction, grammaticality judgments, language production, and form‐meaning mappings. The simplicity approach can also be “scaled down” to analyze the learnability of specific linguistic constructions, and it is amenable to empirical testing as a framework for describing human language acquisition.     

Development of a generic zebrafish embryo PBPK model and application to the developmental toxicity assessment of valproic acid analogs

In order to better explain, predict, or extrapolate to humans the developmental toxicity effects of chemicals to zebrafish (Danio rerio) embryos, we developed a physiologically-based pharmacokinetic (PBPK) model designed to predict organ concentrations of neutral or ionizable chemicals, up to 120 h post-fertilization. Chemicals’ distribution is modeled in the cells, lysosomes, and mitochondria of ten organs of the embryo. The model’s partition coefficients are calculated with sub-models using physicochemical properties of the chemicals of interest. The model accounts for organ growth and changes in metabolic clearance with time. We compared ab initio model predictions to data obtained on culture medium and embryo concentrations of valproic acid (VPA) and nine analogs during continuous dosing under the OECD test guideline 236. We further improved the predictions by estimating metabolic clearance and partition coefficients from the data by Bayesian calibration. We also assessed the performance of the model at reproducing data published by Brox et al. (2016) on VPA and 16 other chemicals. We finally compared dose-response relationships calculated for mortality and malformations on the basis of predicted whole embryo concentrations versus those based on nominal water concentrations. The use of target organ concentrations substantially shifted the magnitude of dose-response parameters and the relative toxicity ranking of chemicals studied.     

A Bayesian model of the disambiguation of gravitoinertial force by visual cues

The otoliths are stimulated in the same fashion by gravitational and inertial forces, so otolith signals are ambiguous indicators of self-orientation. The ambiguity can be resolved with added visual information indicating orientation and acceleration with respect to the earth. Here we present a Bayesian model of the statistically optimal combination of noisy vestibular and visual signals. Likelihoods associated with sensory measurements are represented in an orientation/acceleration space. The likelihood function associated with the otolith signal illustrates the ambiguity; there is no unique solution for self-orientation or acceleration. Likelihood functions associated with other sensory signals can resolve this ambiguity. In addition, we propose two priors, each acting on a dimension in the orientation/acceleration space: the idiotropic prior and the no-acceleration prior. We conducted experiments using a motion platform and attached visual display to examine the influence of visual signals on the interpretation of the otolith signal. Subjects made pitch and acceleration judgments as the vestibular and visual signals were manipulated independently. Predictions of the model were confirmed: (1) visual signals affected the interpretation of the otolith signal, (2) less variable signals had more influence on perceived orientation and acceleration than more variable ones, and (3) combined estimates were more precise than single-cue estimates. We also show that the model can explain some well-known phenomena including the perception of upright in zero gravity, the Aubert effect, and the somatogravic illusion.     

Gene expression profile class prediction using linear Bayesian classifiers

Due to recent advances in DNA microarray technology, using gene expression profiles, diagnostic category of tissue samples can be predicted with high accuracy. In this study, we discuss shortcomings of some existing gene expression profile classification methods and propose a new approach based on linear Bayesian classifiers. In our approach, we first construct gene-level linear classifiers to identify genes that provide high class-prediction accuracies, i.e., low error rates. After this screening phase, starting with the gene that offers the lowest error rate, we construct a multi-dimensional linear classifier by incorporating next best-performing genes, until the prediction error becomes minimum or 0, if possible. When we compared classification performance of our approach against prediction analysis of microarrays (PAM) and support vector machines (SVM) based approaches, we found that our method outperforms PAM and produces comparable results with SVM. In addition, we observed that the gene selection scheme of PAM could be misleading. Albeit SVM achieves relatively higher prediction performance, it has two major disadvantages: Complexity and lack of insight about important genes. Our intuitive approach offers competing performance and also an efficient means for finding important genes.     

Improving estimation and prediction in linear regression incorporating external information from an established reduced model

We consider a situation where there is rich historical data available for the coefficients and their standard errors in a linear regression model describing the association between a continuous outcome variable Y and a set of predicting factors X , from a large study. We would like to use this summary information for improving inference in an expanded model of interest, Y given X , B . The additional variable B is a new biomarker, measured on a small number of subjects in a new dataset. We formulate the problem in an inferential framework where the historical information is translated in terms of nonlinear constraints on the parameter space and propose both frequentist and Bayes solutions to this problem. We show that a Bayesian transformation approach proposed by Gunn and Dunson is a simple and effective computational method to conduct approximate Bayesian inference for this constrained parameter problem. The simulation results comparing these methods indicate that historical information on E( Y | X ) can improve the efficiency of estimation and enhance the predictive power in the regression model of interest E( Y | X , B ). We illustrate our methodology by enhancing a published prediction model for bone lead levels in terms of blood lead and other covariates, with a new biomarker defined through a genetic risk score.     

Bayesian inference for unidirectional misclassification of a binary response trait

When assessing association between a binary trait and some covariates, the binary response may be subject to unidirectional misclassification. Unidirectional misclassification can occur when revealing a particular level of the trait is associated with a type of cost, such as a social desirability or financial cost. The feasibility of addressing misclassification is commonly obscured by model identification issues. The current paper attempts to study the efficacy of inference when the binary response variable is subject to unidirectional misclassification. From a theoretical perspective, we demonstrate that the key model parameters possess identifiability, except for the case with a single binary covariate. From a practical standpoint, the logistic model with quantitative covariates can be weakly identified, in the sense that the Fisher information matrix may be near singular. This can make learning some parameters difficult under certain parameter settings, even with quite large samples. In other cases, the stronger identification enables the model to provide more effective adjustment for unidirectional misclassification. An extension to the Poisson approximation of the binomial model reveals the identifiability of the Poisson and zero‐inflated Poisson models. For fully identified models, the proposed method adjusts for misclassification based on learning from data. For binary models where there is difficulty in identification, the method is useful for sensitivity analyses on the potential impact from unidirectional misclassification.     

A Bayesian semiparametric latent variable approach to causal mediation

In assessing causal mediation effects in randomized studies, a challenge is that the direct and indirect effects can vary across participants due to different measured and unmeasured characteristics. In that case, the population effect estimated from standard approaches implicitly averages over and does not estimate the heterogeneous direct and indirect effects. We propose a Bayesian semiparametric method to estimate heterogeneous direct and indirect effects via clusters, where the clusters are formed by both individual covariate profiles and individual effects due to unmeasured characteristics. These cluster‐specific direct and indirect effects can be estimated through a set of regression models where specific coefficients are clustered by a stick‐breaking prior. To let clustering be appropriately informed by individual direct and indirect effects, we specify a data‐dependent prior. We conduct simulation studies to assess performance of the proposed method compared to other methods. We use this approach to estimate heterogeneous causal direct and indirect effects of an expressive writing intervention for patients with renal cell carcinoma.     

Multilevel moderated mediation model with ordinal outcome

Although increasingly complex models have been proposed in mediation literature, there is no model nor software that incorporates the multiple possible generalizations of the simple mediation model jointly. We propose a flexible moderated mediation model allowing for (1) a hierarchical structure of clustered data, (2) more and possibly correlated mediators, and (3) an ordinal outcome. The motivating data set is obtained from a European study in nursing research. Patients' willingness to recommend their treating hospital was recorded in an ordinal way. The research question is whether such recommendation directly depends on system‐level features in the organization of nursing care, or whether these associations are mediated by 2 measurements of nursing care left undone and possibly moderated by nurse education. We have developed a Bayesian approach and accompanying program that takes all the above generalizations into account.     

Estimation of discrete games with correlated types

In this paper, I focus on the identification and estimation of static games of incomplete information with correlated types. Instead of making the independence assumption on players' types in order to simplify the equilibrium set, I propose an approach that allows me to identify subsets of the space of covariates (i.e. publicly observed state variables in payoff functions), for which there exists a unique pure strategy Bayesian Nash equilibrium (BNE) and the equilibrium strategies are monotonic functions. Moreover, I characterize the monotonic pure strategy BNE in a simple manner and propose an estimation procedure that uses observations only from the subset of the covariate space where the game admits a unique monotonic pure strategy BNE. Furthermore, I show that the proposed estimator is ‐consistent and has a limiting normal distribution.